From 05be488b297ec9b8d6aa5a2d5dde17814a75876d Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Thu, 26 Nov 2020 15:04:30 +0100 Subject: [PATCH 01/70] Refactorings and cleanings- Used andb_and not to clash with ssrbool.andP- Move syntactic equality checking to a separate safechecker library- move monadic combinators to monad_utils --- checker/theories/Closed.v | 28 +-- checker/theories/Substitution.v | 12 +- checker/theories/Weakening.v | 10 +- pcuic/_CoqProject.in | 1 + pcuic/theories/PCUICArities.v | 4 +- pcuic/theories/PCUICCanonicity.v | 2 +- pcuic/theories/PCUICConversion.v | 16 +- pcuic/theories/PCUICCumulativity.v | 6 +- pcuic/theories/PCUICGlobalEnv.v | 77 +++++++ pcuic/theories/PCUICInductiveInversion.v | 64 +++--- pcuic/theories/PCUICNameless.v | 2 +- pcuic/theories/PCUICSR.v | 20 +- pcuic/theories/PCUICSigmaCalculus.v | 18 +- pcuic/theories/PCUICSubstitution.v | 14 +- pcuic/theories/PCUICUnivSubstitution.v | 2 +- pcuic/theories/PCUICWeakening.v | 8 +- pcuic/theories/PCUICWeakeningEnv.v | 4 +- pcuic/theories/PCUICWfUniverses.v | 32 +-- safechecker/_CoqProject.in | 1 + safechecker/theories/PCUICEqualityDec.v | 175 +++++++++++++++ safechecker/theories/PCUICSafeChecker.v | 94 ++------ safechecker/theories/PCUICSafeConversion.v | 240 +++------------------ template-coq/theories/BasicAst.v | 6 +- template-coq/theories/monad_utils.v | 25 +++ template-coq/theories/utils/All_Forall.v | 31 ++- template-coq/theories/utils/MCProd.v | 12 +- template-coq/theories/utils/MCSquash.v | 5 + template-coq/theories/utils/wGraph.v | 21 +- 28 files changed, 481 insertions(+), 449 deletions(-) create mode 100644 pcuic/theories/PCUICGlobalEnv.v create mode 100644 safechecker/theories/PCUICEqualityDec.v diff --git a/checker/theories/Closed.v b/checker/theories/Closed.v index 672c5ef80..98ec0fba9 100644 --- a/checker/theories/Closed.v +++ b/checker/theories/Closed.v @@ -18,7 +18,7 @@ Definition closedn_ctx n ctx := Lemma closed_decl_upwards k d : closed_decl k d -> forall k', k <= k' -> closed_decl k' d. Proof. case: d => na [body|] ty; rewrite /closed_decl /=. - move/andP => [cb cty] k' lek'. do 2 rewrite (@closed_upwards k) //. + move/andb_and => [cb cty] k' lek'. do 2 rewrite (@closed_upwards k) //. move=> cty k' lek'; rewrite (@closed_upwards k) //. Qed. @@ -197,7 +197,7 @@ Lemma closedn_ctx_cons n d Γ : closedn_ctx n (d :: Γ) -> closedn_ctx n Γ && c Proof. unfold closedn_ctx. simpl. rewrite mapi_app. rewrite forallb_app. - move/andP => [] -> /=. now rewrite Nat.add_0_r List.rev_length andb_true_r. + move/andb_and => [] -> /=. now rewrite Nat.add_0_r List.rev_length andb_true_r. Qed. Lemma closedn_ctx_app n Γ Γ' : @@ -216,8 +216,8 @@ Lemma closedn_mkProd_or_LetIn (Γ : context) d T : closedn (S #|Γ|) T -> closedn #|Γ| (mkProd_or_LetIn d T). Proof. destruct d as [na [b|] ty]; simpl in *. unfold closed_decl. - simpl. now move/andP => [] -> ->. - simpl. now move/andP => [] /= _ -> ->. + simpl. now move/andb_and => [] -> ->. + simpl. now move/andb_and => [] /= _ -> ->. Qed. Lemma closedn_mkLambda_or_LetIn (Γ : context) d T : @@ -225,8 +225,8 @@ Lemma closedn_mkLambda_or_LetIn (Γ : context) d T : closedn (S #|Γ|) T -> closedn #|Γ| (mkLambda_or_LetIn d T). Proof. destruct d as [na [b|] ty]; simpl in *. unfold closed_decl. - simpl. now move/andP => [] -> ->. - simpl. now move/andP => [] /= _ -> ->. + simpl. now move/andb_and => [] -> ->. + simpl. now move/andb_and => [] /= _ -> ->. Qed. Lemma closedn_it_mkProd_or_LetIn @@ -236,7 +236,7 @@ Lemma closedn_it_mkProd_or_LetIn Proof. induction ctx in Γ, T |- *. simpl. - now rewrite Nat.add_0_r. - - move/closedn_ctx_cons/andP => [] cctx ca cT. + - move/closedn_ctx_cons/andb_and => [] cctx ca cT. apply (IHctx Γ (mkProd_or_LetIn a T) cctx). simpl in cT. rewrite <- app_length. eapply closedn_mkProd_or_LetIn; @@ -250,7 +250,7 @@ Lemma closedn_it_mkLambda_or_LetIn Proof. induction ctx in Γ, T |- *. simpl. - now rewrite Nat.add_0_r. - - move/closedn_ctx_cons/andP => [] cctx ca cT. + - move/closedn_ctx_cons/andb_and => [] cctx ca cT. apply (IHctx Γ (mkLambda_or_LetIn a T) cctx). simpl in cT. rewrite <- app_length. eapply closedn_mkLambda_or_LetIn; @@ -338,7 +338,7 @@ Proof. rewrite /closed_decl /map_decl /= Nat.add_0_r List.rev_length subst_context_length. inv X'. unfold closed_decl in H0. simpl in H0. rewrite List.rev_length Nat.add_0_r in H0. - move/andP: H0 => [Hl Hr]. + move/andb_and: H0 => [Hl Hr]. rewrite !closedn_subst /= ?H //; eapply closed_upwards; eauto; try lia. - intros. eapply Alli_app in X as [X X']. rewrite subst_context_snoc. simpl. eapply Alli_app_inv. @@ -364,7 +364,7 @@ Proof. inv X'. unfold closed_decl in H. simpl in H. rewrite List.rev_length Nat.add_0_r in H. clear X1. eapply closed_subst_context; auto. - now move/andP: H => []. + now move/andb_and: H => []. - intros. eapply Alli_app in X as [X X']. eapply IHΔ; eauto. inv X'. unfold closed_decl in H. simpl in H. @@ -451,7 +451,7 @@ Proof. rewrite smash_context_length in X. simpl in X. eapply nth_error_Some_length in Heq'. rewrite smash_context_length in Heq'. simpl in Heq'. unfold closed_decl in X. - move/andP: X => [] _ cl. + move/andb_and: X => [] _ cl. eapply closed_upwards. eauto. rewrite arities_context_length. rewrite context_assumptions_app parslen. rewrite context_assumptions_app in Heq'. lia. @@ -569,7 +569,7 @@ Proof. simpl; intros ->. apply closedn_All_local_closed in Hwfi. rewrite closedn_ctx_app in Hwfi. - move/andP: Hwfi => [] clΓ clctx. + move/andb_and: Hwfi => [] clΓ clctx. apply closedn_it_mkProd_or_LetIn => //. + destruct s. rewrite andb_true_r in p. intuition auto. Qed. @@ -649,12 +649,12 @@ Proof. rewrite /closed_inductive_body. apply andb_and; split. apply andb_and. split. - apply onArity in oib. hnf in oib. - now move/andP: oib => []. + now move/andb_and: oib => []. - pose proof (onConstructors oib). red in X. eapply All_forallb. eapply All2_All_left; eauto. firstorder auto. eapply on_ctype in X0. - now move/andP: X0 => []. + now move/andb_and: X0 => []. - eapply All_forallb. pose proof (onProjections oib). destruct (eq_dec (ind_projs x) []) as [->|eq]; try constructor. diff --git a/checker/theories/Substitution.v b/checker/theories/Substitution.v index d8fa43330..8c5824a71 100644 --- a/checker/theories/Substitution.v +++ b/checker/theories/Substitution.v @@ -125,7 +125,7 @@ Qed. Lemma subst_decl_closed n k d : wf_decl d -> closed_decl k d -> subst_decl n k d = d. Proof. case: d => na [body|] ty; rewrite /closed_decl /subst_decl /map_decl /wf_decl /= => [[wfb wfty]]. - move/andP => [cb cty]. rewrite !subst_closedn //. + move/andb_and => [cb cty]. rewrite !subst_closedn //. move=> cty; now rewrite !subst_closedn //. Qed. @@ -362,7 +362,7 @@ Proof. move: H. rewrite /closed_inductive_decl /lift_mutual_inductive_body. destruct decl; simpl in *. - move/andP => [clpar clbodies]. f_equal. + move/andb_and => [clpar clbodies]. f_equal. rewrite [fold_context _ _]closed_ctx_subst; try easy. eapply Forall_All; eauto. eapply forallb_All in clbodies. apply Forall_All in wfbodies. @@ -372,7 +372,7 @@ Proof. 2:{ intros. eapply X0. } simpl. move: clb. rewrite /closed_inductive_body. - destruct oib; simpl. move=> /andP[/andP [ci ct] cp]. + destruct oib; simpl. move=> /andb_and[/andb_and [ci ct] cp]. destruct wfb; simpl in *. f_equal. rewrite subst_closedn; eauto. eapply closed_upwards; eauto; lia. @@ -581,7 +581,7 @@ Proof. induction ctx using rev_ind; try easy. move=> n0. rewrite /closedn_ctx !rev_app_distr /id /=. - intro Hwf. move /andP => [closedx Hctx]. + intro Hwf. move /andb_and => [closedx Hctx]. apply All_app in Hwf as [? X]; inv X. rewrite subst_decl_closed //. rewrite (closed_decl_upwards n0) //; lia. @@ -1759,7 +1759,7 @@ Proof. apply onArity in on_ind as [s' Hindty]. pose proof (typing_wf (Σ.1, ind_universes mdecl) wfΣ _ _ _ Hindty) as [clty _]. apply typecheck_closed in Hindty as [_ Hindty]; eauto. symmetry. - move/andP/proj1: Hindty. rewrite -(closedn_subst_instance_constr _ _ u) => Hty. + move/andb_and/proj1: Hindty. rewrite -(closedn_subst_instance_constr _ _ u) => Hty. apply: (subst_closedn s #|Δ|); auto with wf. eapply closed_upwards. eauto. simpl; lia. @@ -1784,7 +1784,7 @@ Proof. destruct isdecl as [_ oind]. clear -oind wfΣ. apply onArity in oind; destruct oind as [s HH]; cbn in *. apply typecheck_closed in HH; eauto. - apply snd in HH. apply andP in HH; apply HH. } + apply snd in HH. apply andb_and in HH; apply HH. } simpl. econstructor. all: eauto. -- eapply subst_build_case_predicate_type in H1; tea. simpl in *. subst params. rewrite firstn_map. diff --git a/checker/theories/Weakening.v b/checker/theories/Weakening.v index 5a6031bfb..7444ba862 100644 --- a/checker/theories/Weakening.v +++ b/checker/theories/Weakening.v @@ -134,14 +134,14 @@ Qed. Lemma lift_decl_closed n k d : closed_decl k d -> lift_decl n k d = d. Proof. case: d => na [body|] ty; rewrite /closed_decl /lift_decl /map_decl /=. - move/andP => [cb cty]. now rewrite !lift_closed //. + move/andb_and => [cb cty]. now rewrite !lift_closed //. move=> cty; now rewrite !lift_closed //. Qed. Lemma closed_decl_upwards k d : closed_decl k d -> forall k', k <= k' -> closed_decl k' d. Proof. case: d => na [body|] ty; rewrite /closed_decl /=. - move/andP => [cb cty] k' lek'. do 2 rewrite (@closed_upwards k) //. + move/andb_and => [cb cty] k' lek'. do 2 rewrite (@closed_upwards k) //. move=> cty k' lek'; rewrite (@closed_upwards k) //. Qed. @@ -305,7 +305,7 @@ Proof. move: Hdecl. rewrite /closed_inductive_decl /lift_mutual_inductive_body. destruct decl; simpl. - move/andP => [clpar clbodies]. f_equal. + move/andb_and => [clpar clbodies]. f_equal. now rewrite [fold_context _ _]closed_ctx_lift. eapply forallb_All in clbodies. eapply Alli_mapi_id. @@ -313,7 +313,7 @@ Proof. 2:{ intros. eapply X0. } simpl; intros. move: H0. rewrite /closed_inductive_body. - destruct x; simpl. move=> /andP[/andP [ci ct] cp]. + destruct x; simpl. move=> /andb_and[/andb_and [ci ct] cp]. f_equal. rewrite lift_closed; eauto. eapply closed_upwards; eauto; lia. eapply All_map_id. eapply forallb_All in ct. @@ -501,7 +501,7 @@ Proof. induction ctx using rev_ind. move=> //. move=> n0. rewrite /closedn_ctx !rev_app_distr /id /=. - move/andP => [closedx Hctx]. + move/andb_and => [closedx Hctx]. rewrite lift_decl_closed. rewrite (@closed_decl_upwards n0) //; try lia. f_equal. now rewrite IHctx. Qed. diff --git a/pcuic/_CoqProject.in b/pcuic/_CoqProject.in index 4ce3a6f5c..1a946ce6d 100644 --- a/pcuic/_CoqProject.in +++ b/pcuic/_CoqProject.in @@ -10,6 +10,7 @@ theories/PCUICReflect.v theories/PCUICLiftSubst.v theories/PCUICUnivSubst.v theories/PCUICTyping.v +theories/PCUICGlobalEnv.v theories/PCUICInversion.v theories/PCUICPosition.v theories/PCUICNormal.v diff --git a/pcuic/theories/PCUICArities.v b/pcuic/theories/PCUICArities.v index c6d27e8d6..8e5ac2e1b 100644 --- a/pcuic/theories/PCUICArities.v +++ b/pcuic/theories/PCUICArities.v @@ -319,13 +319,13 @@ Lemma subslet_app_closed {cf:checker_flags} Σ Γ s s' Δ Δ' : subslet Σ Γ (s ++ s') (Δ' ,,, Δ). Proof. induction 1 in s', Δ'; simpl; auto; move=> sub'; - rewrite closedn_ctx_snoc => /andP [clctx clt]; + rewrite closedn_ctx_snoc => /andb_and [clctx clt]; try constructor; auto. - pose proof (subslet_length X). rewrite Nat.add_0_r in clt. rewrite /closed_decl /= -H in clt. rewrite subst_app_simpl /= (subst_closedn s') //. - pose proof (subslet_length X). rewrite Nat.add_0_r in clt. - rewrite /closed_decl /= -H in clt. move/andP: clt => [clt clT]. + rewrite /closed_decl /= -H in clt. move/andb_and: clt => [clt clT]. replace (subst0 s t) with (subst0 (s ++ s') t). + constructor; auto. rewrite !subst_app_simpl /= !(subst_closedn s') //. diff --git a/pcuic/theories/PCUICCanonicity.v b/pcuic/theories/PCUICCanonicity.v index 96dffdc1b..02173dd00 100644 --- a/pcuic/theories/PCUICCanonicity.v +++ b/pcuic/theories/PCUICCanonicity.v @@ -18,7 +18,7 @@ Module P := PCUICWcbvEval. Local Existing Instance config.extraction_checker_flags. Require Import Equations.Prop.DepElim. -Require Import ssreflect. +Require Import ssreflect ssrbool. Lemma negb_False (p : bool) : negb p -> p -> False. Proof. diff --git a/pcuic/theories/PCUICConversion.v b/pcuic/theories/PCUICConversion.v index f1c1d56cf..41adb575b 100644 --- a/pcuic/theories/PCUICConversion.v +++ b/pcuic/theories/PCUICConversion.v @@ -2595,12 +2595,12 @@ Proof. induction Δ as [|d Δ] in cl, wf0 |- *. - constructor. - simpl. - rewrite closedn_ctx_cons in cl. apply andP in cl as [clctx cld]. + rewrite closedn_ctx_cons in cl. apply andb_and in cl as [clctx cld]. simpl in wf0. destruct d as [na [b|] ty] => /=. * depelim wf0; simpl in *. simpl in cld. unfold closed_decl in cld. simpl in cld. simpl. - apply andP in cld as [clb clty]. + apply andb_and in cld as [clb clty]. constructor; auto. constructor; [reflexivity|..]. ** apply weaken_conv; auto; autorewrite with len. 1:now rewrite closedn_subst_instance_context. @@ -3047,8 +3047,8 @@ Proof. - simpl. constructor. - rewrite /= closed_ctx_decl in wf. rewrite /= closed_ctx_decl in wf'. - move/andP: wf => [wfd wf]. - move/andP: wf' => [wfd' wf']. + move/andb_and: wf => [wfd wf]. + move/andb_and: wf' => [wfd' wf']. constructor; auto. + now eapply IHX. + depelim p. constructor; auto. @@ -3058,12 +3058,12 @@ Proof. now autorewrite with len in wfd'. - rewrite /= closed_ctx_decl in wf. rewrite /= closed_ctx_decl in wf'. - move/andP: wf => [wfd wf]. - move/andP: wf' => [wfd' wf']. + move/andb_and: wf => [wfd wf]. + move/andb_and: wf' => [wfd' wf']. constructor; auto. + now eapply IHX. - + move/andP: wfd => /= [wfb wft]. - move/andP: wfd' => /= [wfb' wft']. + + move/andb_and: wfd => /= [wfb wft]. + move/andb_and: wfd' => /= [wfb' wft']. autorewrite with len in *. rewrite <- (context_relation_length X) in *. depelim p; constructor; auto. diff --git a/pcuic/theories/PCUICCumulativity.v b/pcuic/theories/PCUICCumulativity.v index 30de075ac..0d55590d5 100644 --- a/pcuic/theories/PCUICCumulativity.v +++ b/pcuic/theories/PCUICCumulativity.v @@ -1,5 +1,5 @@ (* Distributed under the terms of the MIT license. *) -From MetaCoq.Template Require Import config utils. +From MetaCoq.Template Require Import config utils BasicAst. From MetaCoq.PCUIC Require Import PCUICRelations PCUICAst PCUICAstUtils PCUICLiftSubst PCUICEquality PCUICUnivSubst PCUICReduction. @@ -286,10 +286,6 @@ Proof. eapply red_conv_conv_inv; eauto. now constructor. Qed. -Inductive conv_pb := -| Conv -| Cumul. - Definition conv_cum {cf:checker_flags} leq Σ Γ u v := match leq with | Conv => ∥ Σ ;;; Γ |- u = v ∥ diff --git a/pcuic/theories/PCUICGlobalEnv.v b/pcuic/theories/PCUICGlobalEnv.v new file mode 100644 index 000000000..22fc41aa8 --- /dev/null +++ b/pcuic/theories/PCUICGlobalEnv.v @@ -0,0 +1,77 @@ +(* Distributed under the terms of the MIT license. *) +From Coq Require Import ProofIrrelevance. +From MetaCoq.Template Require Import config utils uGraph. +From MetaCoq.PCUIC Require Import PCUICAst PCUICAstUtils + PCUICReflect PCUICTyping. + +Definition wf_global_uctx_invariants {cf:checker_flags} Σ : + wf Σ -> + global_uctx_invariants (global_uctx Σ). +Proof. + intros HΣ. split. + - cbn. eapply LevelSet.mem_spec, global_levels_Set. + - unfold global_uctx. + simpl. intros [[l ct] l'] Hctr. simpl in *. + induction Σ in HΣ, l, ct, l', Hctr |- *. + + apply ConstraintSetFact.empty_iff in Hctr; contradiction. + + simpl in *. apply ConstraintSet.union_spec in Hctr. + destruct Hctr as [Hctr|Hctr]. + * split. + -- inversion HΣ; subst. + destruct H2 as [HH1 [HH HH3]]. + subst udecl. destruct d as [decl|decl]; simpl in *. + ++ destruct decl; simpl in *. + destruct cst_universes ; [ + eapply (HH (l, ct, l') Hctr) + | apply ConstraintSetFact.empty_iff in Hctr ; contradiction + ]. + ++ destruct decl. simpl in *. + destruct ind_universes ; [ + eapply (HH (l, ct, l') Hctr) + | apply ConstraintSetFact.empty_iff in Hctr; contradiction + ]. + -- inversion HΣ. subst. + destruct H2 as [HH1 [HH HH3]]. + subst udecl. destruct d as [decl|decl]. + all: simpl in *. + ++ destruct decl. simpl in *. + destruct cst_universes ; [ + eapply (HH (l, ct, l') Hctr) + | apply ConstraintSetFact.empty_iff in Hctr; contradiction + ]. + ++ destruct decl. simpl in *. + destruct ind_universes; [ + eapply (HH (l, ct, l') Hctr) + | apply ConstraintSetFact.empty_iff in Hctr; contradiction + ]. + * inversion HΣ. subst. + split. + all: apply LevelSet.union_spec. + all: right. + all: unshelve eapply (IHΣ _ _ _ _ Hctr). + all: try eassumption. +Qed. + +Definition wf_ext_global_uctx_invariants {cf:checker_flags} Σ : + wf_ext Σ -> + global_uctx_invariants (global_ext_uctx Σ). +Proof. + intros HΣ. split. + - apply LevelSet.union_spec. right. apply LevelSet.mem_spec, global_levels_Set. + - destruct Σ as [Σ φ]. destruct HΣ as [HΣ Hφ]. + destruct (wf_global_uctx_invariants _ HΣ) as [_ XX]. + unfold global_ext_uctx, global_ext_levels, global_ext_constraints. + simpl. intros [[l ct] l'] Hctr. simpl in *. apply ConstraintSet.union_spec in Hctr. + destruct Hctr as [Hctr|Hctr]. + + destruct Hφ as [_ [HH _]]. apply (HH _ Hctr). + + specialize (XX _ Hctr). + split; apply LevelSet.union_spec; right; apply XX. +Qed. + +Definition global_ext_uctx_consistent {cf:checker_flags} Σ + : wf_ext Σ -> consistent (global_ext_uctx Σ).2. +Proof. + intros HΣ. cbn. unfold global_ext_constraints. + unfold wf_ext, on_global_env_ext in HΣ. + destruct HΣ as [_ [_ [_ HH]]]. apply HH. +Qed. diff --git a/pcuic/theories/PCUICInductiveInversion.v b/pcuic/theories/PCUICInductiveInversion.v index 9cc4cb090..75b9b34ed 100644 --- a/pcuic/theories/PCUICInductiveInversion.v +++ b/pcuic/theories/PCUICInductiveInversion.v @@ -456,7 +456,7 @@ Proof. intros eqr. exists ind. destruct (map_option_out (map check_one_cofix mfix)) eqn:eqfixes. - move/andP: eqr => [eqinds rk]. + move/andb_and: eqr => [eqinds rk]. split; auto. constructor. - move: hcof. unfold check_one_cofix. @@ -482,7 +482,7 @@ Proof. noconf eqfixes. specialize (IHmfix _ eq_refl). simpl in eqinds. - move/andP: eqinds => [eqk eql0]. + move/andb_and: eqinds => [eqk eql0]. constructor; auto. clear IHmfix hcofs d. destruct a as [dname dbody dtype rarg] => /=. unfold check_one_cofix in hcof. @@ -716,8 +716,8 @@ Qed. Lemma test_decl_impl (f g : term -> bool) x : (forall x, f x -> g x) -> test_decl f x -> test_decl g x. Proof. intros Hf; rewrite /test_decl. - move/andP=> [Hd Hb]. - apply/andP; split; eauto. + move/andb_and=> [Hd Hb]. + apply/andb_and; split; eauto. eapply option_all_impl; eauto. Qed. @@ -733,7 +733,7 @@ Lemma closedn_ctx_upwards k k' Γ : closedn_ctx k' Γ. Proof. induction Γ; auto. rewrite !closed_ctx_decl /=. - move/andP => [cla clΓ] le. + move/andb_and => [cla clΓ] le. rewrite (IHΓ clΓ le). rewrite (closed_decl_upwards _ _ cla) //. lia. Qed. @@ -769,9 +769,9 @@ Proof. induction Γ as [|[na [b|] ty] Γ] using ctx_length_rev_ind; intros k k' t; rewrite ?closedn_ctx_app /= /id /=; simpl; auto. - now rewrite /expand_lets /expand_lets_k /= subst_empty lift0_id. - - rewrite andb_true_r /id; move/andP=> [cld clΓ]. len. + - rewrite andb_true_r /id; move/andb_and=> [cld clΓ]. len. rewrite !expand_lets_k_vdef. - simpl in cld |- *. move/andP: cld => /= [clb _]. + simpl in cld |- *. move/andb_and: cld => /= [clb _]. rewrite Nat.add_0_r in clb. specialize (H (subst_context [b] 0 Γ) ltac:(len; lia)). autorewrite with len in H. rewrite H /=. @@ -779,7 +779,7 @@ Proof. now rewrite Nat.add_0_r. now rewrite /= clb. rewrite -Nat.add_assoc -closedn_subst_eq. simpl. now rewrite clb. simpl; lia_f_equal. - - len. rewrite andb_true_r /=; move/andP => [clty clΓ]. + - len. rewrite andb_true_r /=; move/andb_and => [clty clΓ]. rewrite !expand_lets_k_vass. simpl. specialize (H Γ ltac:(len; lia) (S k)). rewrite Nat.add_assoc !Nat.add_succ_r !Nat.add_0_r. apply H. @@ -925,13 +925,13 @@ Proof. induction Γ in k |- *; intros cl; simpl; auto. destruct a as [na [b|] ty] => /=. len. - rewrite closed_ctx_decl in cl. move/andP: cl => [cld clΓ]. + rewrite closed_ctx_decl in cl. move/andb_and: cl => [cld clΓ]. simpl. f_equal. rewrite distr_subst. len. simpl in cld. rewrite IHΓ //. f_equal. rewrite simpl_subst_k. len. rewrite context_assumptions_smash_context /= //. - rewrite lift_closed //. now move/andP: cld => /= //. + rewrite lift_closed //. now move/andb_and: cld => /= //. rewrite IHΓ //. simpl map. @@ -950,7 +950,7 @@ Proof. rewrite lift_extended_subst. rewrite map_map_compose. rewrite map_subst_lift1. - rewrite closed_ctx_decl in cl. move/andP: cl => [cld clΓ]. + rewrite closed_ctx_decl in cl. move/andb_and: cl => [cld clΓ]. now rewrite IHΓ // Nat.add_1_r. Qed. @@ -1003,13 +1003,13 @@ Lemma subst_map_lift_lift_context (Γ : context) k s : Proof. induction Γ as [|[? [] ?] ?] in k |- *; intros cl; auto; rewrite lift_context_snoc !subst_context_snoc /= /subst_decl /map_decl /=; - rewrite closed_ctx_decl in cl; move/andP: cl => [cld clΓ]. + rewrite closed_ctx_decl in cl; move/andb_and: cl => [cld clΓ]. - rewrite IHΓ //. f_equal. f_equal. f_equal; len. - rewrite closed_subst_map_lift //. now move/andP: cld => /=. + rewrite closed_subst_map_lift //. now move/andb_and: cld => /=. lia_f_equal. len. - rewrite closed_subst_map_lift //. now move/andP: cld => /=. + rewrite closed_subst_map_lift //. now move/andb_and: cld => /=. lia_f_equal. - f_equal. apply IHΓ => //. f_equal; len. rewrite closed_subst_map_lift //. @@ -1076,7 +1076,7 @@ Proof. { unshelve epose proof (on_minductive_wf_params_indices _ _ _ _ wfΣ _ oib). pcuic. eapply closed_wf_local in X => //. rewrite closedn_ctx_app in X; simpl; eauto. - move/andP: X; intuition auto; + move/andb_and: X; intuition auto; now rewrite closedn_subst_instance_context. } assert (closedn_ctx (#|ind_params mdecl| + #|cshape_args cshape|) (subst_instance_context u (ind_indices oib))) as clinds'. @@ -2066,7 +2066,7 @@ Proof. autorewrite with len in IHpos. eapply IHpos; eauto. simpl; constructor; auto. simpl in isty. eapply isType_tProd in isty as [Hty Ht]; eauto. - rewrite closedn_ctx_cons /=. apply/andP; split; auto. simpl. + rewrite closedn_ctx_cons /=. apply/andb_and; split; auto. simpl. eapply closed_upwards; eauto; lia. simpl in isty. eapply isType_tProd in isty as [Hty Ht]; eauto. Qed. @@ -2144,7 +2144,7 @@ Proof. now rewrite subst_instance_context_app app_context_assoc. * eapply closed_wf_local in wf; eauto. rewrite closedn_subst_instance_context app_assoc in wf. - now rewrite closedn_ctx_app /= in wf; move/andP: wf => [wfars wf]. + now rewrite closedn_ctx_app /= in wf; move/andb_and: wf => [wfars wf]. * now rewrite subst_instance_context_app app_context_assoc. - elimtype False; now depelim ass. - elimtype False; now depelim ass. @@ -2523,14 +2523,14 @@ Proof. specialize (clcstra _ H0). simpl in *. destruct x as [[l c] r]; rewrite /subst_instance_cstr; simpl. - move/andP: clcstra => [cll clr]. + move/andb_and: clcstra => [cll clr]. rewrite !closedu_subst_instance_level_app //. subst c; exists x; split; auto. specialize (clcstra _ H0). simpl in *. destruct x as [[l c] r]; rewrite /subst_instance_cstr; simpl. - move/andP: clcstra => [cll clr]. + move/andb_and: clcstra => [cll clr]. rewrite !closedu_subst_instance_level_app //. Qed. @@ -2586,7 +2586,7 @@ Proof. specialize (clcstra _ inc'). simpl in *. destruct c' as [[l c] r]; rewrite /subst_instance_cstr; simpl. - move/andP: clcstra => [cll clr]. + move/andb_and: clcstra => [cll clr]. rewrite !closedu_subst_instance_level_lift //. - subst c. @@ -2596,7 +2596,7 @@ Proof. specialize (clcstra _ H0). simpl in *. destruct x as [[l c] r]; rewrite /subst_instance_cstr; simpl. - move/andP: clcstra => [cll clr]. + move/andb_and: clcstra => [cll clr]. rewrite !closedu_subst_instance_level_lift //. Qed. @@ -3046,13 +3046,13 @@ Proof. eapply (weaken_cumul_ctx _ Γ) in args => //. 4:eapply spu. 2:{ eapply closed_wf_local; eauto. } - 2:{ rewrite closedn_ctx_app; apply /andP. split => //. simpl. + 2:{ rewrite closedn_ctx_app; apply /andb_and. split => //. simpl. len. simpl. eapply closedn_smash_context => //. len; simpl. pose proof (on_minductive_wf_params_indices_inst _ _ _ _ _ wfΣ (proj1 decli) oib cu') as wf'. eapply closed_wf_local in wf'; eauto. rewrite subst_instance_context_app in wf'. - rewrite closedn_ctx_app in wf'. move/andP: wf'=> [_ clargs]. + rewrite closedn_ctx_app in wf'. move/andb_and: wf'=> [_ clargs]. simpl in clargs; autorewrite with len in clargs. eapply closedn_smash_context => //. rewrite closedn_subst_instance_context. @@ -3181,14 +3181,14 @@ Proof. eapply (weaken_cumul_ctx _ Γ) in args => //. 4:eapply spu. 2:{ eapply closed_wf_local; eauto. } - 2:{ rewrite closedn_ctx_app; apply /andP. split => //. simpl. + 2:{ rewrite closedn_ctx_app; apply /andb_and. split => //. simpl. len. simpl. eapply closedn_smash_context. rewrite -(Nat.add_0_l (context_assumptions _)). eapply closedn_ctx_subst. len; simpl. 2:{ eapply declared_minductive_closed_inds; eauto. } epose proof (on_constructor_wf_args _ _ _ _ _ _ wfΣ decli onind oib onc) as wf'; eauto. eapply closed_wf_local in wf'; eauto. - rewrite closedn_ctx_app in wf'. move/andP: wf'=> [_ clargs]. + rewrite closedn_ctx_app in wf'. move/andb_and: wf'=> [_ clargs]. simpl in clargs; autorewrite with len in clargs. rewrite closedn_subst_instance_context. rewrite Nat.add_comm. @@ -3290,7 +3290,7 @@ Proof. eapply closedn_ctx_subst; cbn. rewrite /ind_subst; len. epose proof (on_constructor_inst u wfΣ decli onind _ onc cu) as [wfarpars _]; auto. move/closed_wf_local: wfarpars. rewrite !subst_instance_context_app closedn_ctx_app. - now move/andP; len. + now move/andb_and; len. rewrite /ind_subst. eapply declared_minductive_closed_inds; eauto. } { len. simpl. rewrite expand_lets_app in clx. rewrite -(subst_instance_context_assumptions u' (ind_params _)). @@ -3309,7 +3309,7 @@ Proof. eapply closedn_ctx_subst; cbn. rewrite /ind_subst; len. epose proof (on_constructor_inst _ wfΣ decli onind _ onc cu') as [wfarpars _]; auto. move/closed_wf_local: wfarpars. rewrite !subst_instance_context_app closedn_ctx_app. - now move/andP; len. + now move/andb_and; len. rewrite /ind_subst. eapply declared_minductive_closed_inds; eauto. now rewrite /argctx /argctx'; len. } rewrite smash_context_app smash_context_acc in cxy. @@ -3876,7 +3876,7 @@ Proof. fold parsubst. move: (context_subst_length sppars); len => <-. epose proof (on_minductive_wf_params_indices_inst _ _ _ _ _ wfΣ (proj1 isdecl) oib cu). eapply PCUICClosed.closed_wf_local in X; auto. move: X. - now rewrite subst_instance_context_app PCUICClosed.closedn_ctx_app /=; len => /andP [_ H]. + now rewrite subst_instance_context_app PCUICClosed.closedn_ctx_app /=; len => /andb_and [_ H]. rewrite lift_context_subst_context //. + eapply isType_weakening; eauto. eapply spargs. @@ -3957,8 +3957,8 @@ Proof. { eapply validity in Hp; auto. eapply PCUICWfUniverses.isType_wf_universes in Hp. rewrite PCUICWfUniverses.wf_universes_it_mkProd_or_LetIn in Hp. - move/andP: Hp => [_ Hp]. - now apply (PCUICWfUniverses.reflect_bP (PCUICWfUniverses.wf_universe_reflect _ _)) in Hp. auto. } + move/andb_and: Hp => [_ Hp]. + now apply (ssrbool.elimT PCUICWfUniverses.wf_universe_reflect) in Hp. auto. } rewrite !subst_instance_context_app in wf. assert (sorts_local_ctx (lift_typing typing) Σ Γ (subst_context parsubst 0 @@ -4063,7 +4063,7 @@ Proof. fold parsubst. move: (context_subst_length sppars); len => <-. epose proof (on_minductive_wf_params_indices_inst _ _ _ _ _ wfΣ (proj1 decli) oib cu). eapply PCUICClosed.closed_wf_local in X0; auto. move: X0. - now rewrite subst_instance_context_app PCUICClosed.closedn_ctx_app /=; len => /andP [_ ?]. + now rewrite subst_instance_context_app PCUICClosed.closedn_ctx_app /=; len => /andb_and [_ ?]. rewrite lift_context_subst_context //. } split. { eapply isType_it_mkProd_or_LetIn; eauto. @@ -4137,7 +4137,7 @@ Proof. eapply (closedn_ctx_subst 0). len. simpl. 2:eapply declared_minductive_closed_inds; eauto. eapply closed_wf_local in wf; eauto. move: wf. - now rewrite !closedn_ctx_app /=; len => /andP [_ ?]. + now rewrite !closedn_ctx_app /=; len => /andb_and [_ ?]. now rewrite lift_context_subst_context. } len. rewrite (subst_cstr_concl_head ind u mdecl (cshape_args cs) _ _). diff --git a/pcuic/theories/PCUICNameless.v b/pcuic/theories/PCUICNameless.v index af703f73e..d2bde580c 100644 --- a/pcuic/theories/PCUICNameless.v +++ b/pcuic/theories/PCUICNameless.v @@ -122,7 +122,7 @@ Definition nlg (Σ : global_env_ext) : global_env_ext := Ltac destruct_one_andb := lazymatch goal with | h : is_true (_ && _) |- _ => - apply andP in h ; destruct h as [? ?] + apply andb_and in h ; destruct h as [? ?] end. Ltac destruct_andb := diff --git a/pcuic/theories/PCUICSR.v b/pcuic/theories/PCUICSR.v index a2d36c930..9c09090ad 100644 --- a/pcuic/theories/PCUICSR.v +++ b/pcuic/theories/PCUICSR.v @@ -354,8 +354,8 @@ Proof. assert (wfps : wf_universe Σ ps). { eapply validity in typep; auto. eapply PCUICWfUniverses.isType_wf_universes in typep. rewrite PCUICWfUniverses.wf_universes_it_mkProd_or_LetIn in typep. - move/andP: typep => /= [_ /andP[_ typep]]. - now apply (PCUICWfUniverses.reflect_bP (PCUICWfUniverses.wf_universe_reflect _ _)) in typep. auto. } + move/andb_and: typep => /= [_ /andb_and[_ typep]]. + now apply (ssrbool.elimT PCUICWfUniverses.wf_universe_reflect) in typep. auto. } eapply wf_arity_spine_typing_spine => //. split. { (* Predicate instantiation is well typed *) @@ -412,7 +412,7 @@ Proof. eapply closed_wf_local in wfcl; auto. rewrite !subst_instance_context_app in wfcl. rewrite closedn_ctx_app in wfcl. - move/andP: wfcl => []. autorewrite with len. now auto. } + move/andb_and: wfcl => []. autorewrite with len. now auto. } eapply arity_spine_it_mkProd_or_LetIn; eauto. { unfold to_extended_list, to_extended_list_k. rewrite /argctxu in X0. simpl. rewrite -H in X0. eapply X0. } @@ -467,7 +467,7 @@ Proof. epose proof (on_minductive_wf_params_indices_inst _ _ u _ _ _ (proj1 decli) oib cu). rewrite subst_instance_context_app in X1. eapply closed_wf_local in X1; eauto. rewrite closedn_ctx_app in X1. autorewrite with len in X1. - now move/andP: X1 => []. + now move/andb_and: X1 => []. } simpl. eapply conv_cumul; apply mkApps_conv_args; auto. @@ -700,8 +700,8 @@ Proof. assert (wfps : wf_universe Σ ps). { eapply validity in typep; auto. eapply PCUICWfUniverses.isType_wf_universes in typep. rewrite PCUICWfUniverses.wf_universes_it_mkProd_or_LetIn in typep. - move/andP: typep => /= [_ /andP[_ typep]]. - now apply (PCUICWfUniverses.reflect_bP (PCUICWfUniverses.wf_universe_reflect _ _)) in typep. auto. } + move/andb_and: typep => /= [_ /andb_and[_ typep]]. + now apply (ssrbool.elimT PCUICWfUniverses.wf_universe_reflect) in typep. auto. } pose proof (context_subst_fun cparsubst spars). subst parsubst'. clear cparsubst. eapply type_mkApps. eauto. eapply wf_arity_spine_typing_spine; eauto. @@ -725,14 +725,14 @@ Proof. unshelve eapply isType_mkApps_Ind in wat as [parsubst [argsubst wat]]; eauto. set (oib := on_declared_inductive wf isdecl) in *. clearbody oib. destruct oib as [onind oib]. - destruct wat as [[spars sargs] cu]. + destruct wat as [[spars sargs] cu]. unshelve eapply (build_case_predicate_type_spec (Σ.1, _)) in heq_build_case_predicate_type as [parsubst' [cparsubst Hpty]]; eauto. rewrite {}Hpty in typep. assert (wfps : wf_universe Σ ps). { eapply validity in typep; auto. eapply PCUICWfUniverses.isType_wf_universes in typep. rewrite PCUICWfUniverses.wf_universes_it_mkProd_or_LetIn in typep. - move/andP: typep => /= [_ /andP[_ typep]]. - now apply (PCUICWfUniverses.reflect_bP (PCUICWfUniverses.wf_universe_reflect _ _)) in typep. auto. } + move/andb_and: typep => /= [_ /andb_and[_ typep]]. + now apply (ssrbool.elimT PCUICWfUniverses.wf_universe_reflect) in typep. auto. } subst npar. pose proof (context_subst_fun cparsubst spars). subst parsubst'. clear cparsubst. eapply type_mkApps. eauto. @@ -1102,7 +1102,7 @@ Proof. clear projsubsl. eapply closed_wf_local in wfdecl. rewrite closedn_ctx_app in wfdecl. - move/andP: wfdecl => [_ wfdecl]. + move/andb_and: wfdecl => [_ wfdecl]. autorewrite with len in wfdecl. simpl in wfdecl. eapply closedn_ctx_decl in wfdecl; eauto. diff --git a/pcuic/theories/PCUICSigmaCalculus.v b/pcuic/theories/PCUICSigmaCalculus.v index 35810051a..b0cb70107 100644 --- a/pcuic/theories/PCUICSigmaCalculus.v +++ b/pcuic/theories/PCUICSigmaCalculus.v @@ -359,21 +359,21 @@ Proof. try (try rewrite H; try rewrite H0 ; try rewrite H1 ; easy); try solve [f_equal; solve_all]. - apply Hs. now eapply Nat.ltb_lt. - - move/andP: clt => []. intros. f_equal; eauto. + - move/andb_and: clt => []. intros. f_equal; eauto. eapply H0; eauto. intros. eapply up_ext_closed; eauto. - - move/andP: clt => []. intros. f_equal; eauto. now eapply H0, up_ext_closed. - - move/andP: clt => [] /andP[] ?. intros. f_equal; eauto. + - move/andb_and: clt => []. intros. f_equal; eauto. now eapply H0, up_ext_closed. + - move/andb_and: clt => [] /andb_and[] ?. intros. f_equal; eauto. now eapply H1, up_ext_closed. - - move/andP: clt => [] ? ?. f_equal; eauto. - - move/andP: clt => [] /andP[] ? ? b1. + - move/andb_and: clt => [] ? ?. f_equal; eauto. + - move/andb_and: clt => [] /andb_and[] ? ? b1. red in X. solve_all. f_equal; eauto. eapply All_map_eq. eapply (All_impl b1). firstorder. - f_equal; eauto. red in X. solve_all. - move/andP: b => []. eauto. intros. + move/andb_and: b => []. eauto. intros. apply map_def_eq_spec; eauto. eapply b0; eauto. now apply up_ext_closed. - f_equal; eauto. red in X. solve_all. - move/andP: b => []. eauto. intros. + move/andb_and: b => []. eauto. intros. apply map_def_eq_spec; eauto. eapply b0; eauto. now apply up_ext_closed. Qed. @@ -1151,7 +1151,7 @@ Lemma inst_decl_closed : Proof. intros σ k d. case: d => na [body|] ty. all: rewrite /closed_decl /inst_decl /map_decl /=. - - move /andP => [cb cty]. rewrite !inst_closed //. + - move /andb_and => [cb cty]. rewrite !inst_closed //. - move => cty. rewrite !inst_closed //. Qed. @@ -1166,7 +1166,7 @@ Proof. induction ctx using rev_ind; try easy. move => n. rewrite /closedn_ctx !rev_app_distr /id /=. - move /andP => [closedx Hctx]. + move /andb_and => [closedx Hctx]. rewrite inst_decl_closed //. f_equal. now rewrite IHctx. Qed. diff --git a/pcuic/theories/PCUICSubstitution.v b/pcuic/theories/PCUICSubstitution.v index 4ab91eead..1fd828974 100644 --- a/pcuic/theories/PCUICSubstitution.v +++ b/pcuic/theories/PCUICSubstitution.v @@ -100,7 +100,7 @@ Qed. Lemma subst_decl_closed n k d : closed_decl k d -> subst_decl n k d = d. Proof. case: d => na [body|] ty; rewrite /closed_decl /subst_decl /map_decl /=. - - move/andP => [cb cty]. rewrite !subst_closedn //. + - move/andb_and => [cb cty]. rewrite !subst_closedn //. - move=> cty; now rewrite !subst_closedn //. Qed. @@ -122,7 +122,7 @@ Proof. induction ctx using rev_ind; try easy. move=> n0. rewrite /closedn_ctx !rev_app_distr /id /=. - move/andP => [closedx Hctx]. + move/andb_and => [closedx Hctx]. rewrite subst_decl_closed //. - rewrite (closed_decl_upwards n0) //; lia. - f_equal. now rewrite IHctx. @@ -353,7 +353,7 @@ Proof. move: Hdecl. rewrite /closed_inductive_decl /lift_mutual_inductive_body. destruct decl; simpl. - move/andP => [clpar clbodies]. f_equal. + move/andb_and => [clpar clbodies]. f_equal. - now rewrite [fold_context _ _]closed_ctx_subst. - eapply forallb_All in clbodies. eapply Alli_mapi_id. @@ -361,7 +361,7 @@ Proof. intros. eapply H. * simpl; intros. move: H. rewrite /closed_inductive_body. - destruct x; simpl. move=> /andP[/andP [ci ct] cp]. + destruct x; simpl. move=> /andb_and[/andb_and [ci ct] cp]. f_equal. + rewrite subst_closedn; eauto. eapply closed_upwards; eauto; lia. @@ -2328,7 +2328,7 @@ Proof. eapply on_declared_inductive in isdecl as [on_mind on_ind]; auto. apply onArity in on_ind as [[s' Hindty] _]. apply typecheck_closed in Hindty as [_ Hindty]; eauto. symmetry. - move/andP/proj1: Hindty. rewrite -(closedn_subst_instance_constr _ _ u) => Hty. + move/andb_and/proj1: Hindty. rewrite -(closedn_subst_instance_constr _ _ u) => Hty. apply: (subst_closedn s #|Δ|); auto with wf. eapply closed_upwards. eauto. simpl; lia. @@ -2578,7 +2578,7 @@ Proof. eapply on_declared_inductive in isdecl as [on_mind on_ind]; auto. apply onArity in on_ind as [s' Hindty]. apply typecheck_closed in Hindty as [_ Hindty]; eauto. symmetry. - move/andP/proj1: Hindty. rewrite -(closedn_subst_instance_constr _ _ u) => Hty. + move/andb_and/proj1: Hindty. rewrite -(closedn_subst_instance_constr _ _ u) => Hty. apply: (subst_closedn s #|Δ|); auto with wf. eapply closed_upwards. 1: eauto. simpl; lia. @@ -2602,7 +2602,7 @@ Proof. destruct isdecl as [_ oind]. clear -oind wfΣ. apply onArity in oind; destruct oind as [s HH]; cbn in *. apply typecheck_closed in HH; eauto. - apply snd in HH. apply andP in HH; apply HH. } + apply snd in HH. apply andb_and in HH; apply HH. } simpl. econstructor. all: eauto. + eapply subst_build_case_predicate_type in H0; tea. * simpl in *. subst params. rewrite firstn_map. diff --git a/pcuic/theories/PCUICUnivSubstitution.v b/pcuic/theories/PCUICUnivSubstitution.v index 85b7082c4..370f5e8ab 100644 --- a/pcuic/theories/PCUICUnivSubstitution.v +++ b/pcuic/theories/PCUICUnivSubstitution.v @@ -2128,7 +2128,7 @@ Section SubstIdentity. - destruct cu as [decl' [sizeu vc]]. clear sizeu vc. induction u; simpl; auto. - move/andP: decl' => [ina au]. specialize (IHu au). + move/andb_and: decl' => [ina au]. specialize (IHu au). rewrite [map _ u]IHu. f_equal. clear au. destruct a; simpl; auto. eapply LevelSet.mem_spec in ina. diff --git a/pcuic/theories/PCUICWeakening.v b/pcuic/theories/PCUICWeakening.v index c7c0021f8..80b9b220f 100644 --- a/pcuic/theories/PCUICWeakening.v +++ b/pcuic/theories/PCUICWeakening.v @@ -274,7 +274,7 @@ Proof. move: Hdecl. rewrite /closed_inductive_decl /lift_mutual_inductive_body. destruct decl; simpl. - move/andP => [clpar clbodies]. f_equal. + move/andb_and => [clpar clbodies]. f_equal. - now rewrite [fold_context _ _]closed_ctx_lift. - eapply forallb_All in clbodies. eapply Alli_mapi_id. @@ -282,7 +282,7 @@ Proof. intros. eapply H0. * simpl; intros. move: H0. rewrite /closed_inductive_body. - destruct x; simpl. move=> /andP[/andP [ci ct] cp]. + destruct x; simpl. move=> /andb_and[/andb_and [ci ct] cp]. f_equal. + rewrite lift_closed; eauto. eapply closed_upwards; eauto; lia. @@ -475,7 +475,7 @@ Proof. 1: move=> //. move=> n0. rewrite /closedn_ctx !rev_app_distr /id /=. - move/andP => [closedx Hctx]. + move/andb_and => [closedx Hctx]. rewrite lift_decl_closed. - rewrite (@closed_decl_upwards n0) //; try lia. - f_equal. now rewrite IHctx. @@ -1187,7 +1187,7 @@ Proof. pose proof (closed_wf_local wfΣ (typing_wf_local ty)). specialize (X _ ty). eapply PCUICClosed.typecheck_closed in ty as [_ closed]; auto. - move/andP: closed => [ct cT]. + move/andb_and: closed => [ct cT]. rewrite !lift_closed // in X. now rewrite closed_ctx_lift in X. Qed. diff --git a/pcuic/theories/PCUICWeakeningEnv.v b/pcuic/theories/PCUICWeakeningEnv.v index aa29c3b49..56da09a65 100644 --- a/pcuic/theories/PCUICWeakeningEnv.v +++ b/pcuic/theories/PCUICWeakeningEnv.v @@ -417,7 +417,7 @@ Proof. intros ext wfΣ'. unfold wf_fixpoint. destruct map_option_out as [[|ind inds]|]; auto. - move/andP => [->] /=. + move/andb_and => [->] /=. now apply extends_check_recursivity_kind. Qed. @@ -427,7 +427,7 @@ Proof. intros ext wfΣ'. unfold wf_cofixpoint. destruct map_option_out as [[|ind inds]|]; auto. - move/andP => [->] /=. + move/andb_and => [->] /=. now apply extends_check_recursivity_kind. Qed. diff --git a/pcuic/theories/PCUICWfUniverses.v b/pcuic/theories/PCUICWfUniverses.v index d052f5bcd..e5bfaa299 100644 --- a/pcuic/theories/PCUICWfUniverses.v +++ b/pcuic/theories/PCUICWfUniverses.v @@ -13,16 +13,6 @@ Require Import ssreflect ssrbool. From MetaCoq.PCUIC Require Import PCUICInduction. -Lemma forallbP {A} (P : A -> Prop) (p : A -> bool) l : (forall x, reflect (P x) (p x)) -> reflect (Forall P l) (forallb p l). -Proof. - intros Hp. - apply: (iffP idP). - - induction l; rewrite /= //. move/andP => [pa pl]. - constructor; auto. now apply/(Hp _). - - induction 1; rewrite /= // IHForall // andb_true_r. - now apply/(Hp _). -Qed. - Section CheckerFlags. Context {cf:checker_flags}. @@ -284,7 +274,7 @@ Section CheckerFlags. | _ => true end. - Lemma wf_universe_reflect (u : Universe.t) : + Lemma wf_universe_reflect {u : Universe.t} : reflect (wf_universe Σ u) (wf_universeb u). Proof. destruct u; simpl; try now constructor. @@ -297,12 +287,6 @@ Section CheckerFlags. now eapply LS.mem_spec in H. Qed. - Lemma reflect_bP {P b} (r : reflect P b) : b -> P. - Proof. destruct r; auto. discriminate. Qed. - - Lemma reflect_Pb {P b} (r : reflect P b) : P -> b. - Proof. destruct r; auto. Qed. - Fixpoint wf_universes t := match t with | tSort s => wf_universeb s @@ -366,6 +350,7 @@ Section CheckerFlags. Qed. End WfUniverses. + Arguments wf_universe_reflect {Σ u}. Ltac to_prop := repeat match goal with @@ -375,8 +360,8 @@ Section CheckerFlags. Ltac to_wfu := repeat match goal with - | [ H: is_true (wf_universeb _ ?x) |- _ ] => apply (reflect_bP (wf_universe_reflect _ x)) in H - | [ |- is_true (wf_universeb _ ?x) ] => apply (reflect_Pb (wf_universe_reflect _ x)) + | [ H: is_true (wf_universeb _ ?x) |- _ ] => apply (elimT (@wf_universe_reflect _ x)) in H + | [ |- is_true (wf_universeb _ ?x) ] => apply (introT (@wf_universe_reflect _ x)) end. Lemma wf_universes_inst {Σ : global_env_ext} univs t u : @@ -580,7 +565,7 @@ Section CheckerFlags. rewrite wf_universes_subst. clear -s. generalize 0. induction args as [|[na [b|] ty] args] in sorts, s |- *; simpl in *; auto. - - destruct s as [? [[s' wf] [? ?]%MCProd.andP]]. + - destruct s as [? [[s' wf] [? ?]%andb_and]]. constructor; eauto. rewrite wf_universes_subst. eapply IHargs; eauto. now rewrite wf_universes_lift. @@ -803,7 +788,7 @@ Section CheckerFlags. eapply wf_sorts_local_ctx_smash in s. eapply wf_sorts_local_ctx_nth_error in s as [? [? H]]; eauto. red in H. destruct x0. now move/andP: H => []. - now destruct H as [s [Hs _]%MCProd.andP]. + now destruct H as [s [Hs _]%andb_and]. - apply/andP; split; auto. solve_all. move:a => [s [Hty /andP[wfty wfs]]]. @@ -831,17 +816,18 @@ Section CheckerFlags. Σ ;;; Γ |- t : tSort s -> wf_universe Σ s. Proof. intros wfΣ Hty. - apply typing_wf_universes in Hty as [_ wfs]%MCProd.andP; auto. + apply typing_wf_universes in Hty as [_ wfs]%andb_and; auto. simpl in wfs. now to_wfu. Qed. Lemma isType_wf_universes {Σ Γ T} : wf Σ.1 -> isType Σ Γ T -> wf_universes Σ T. Proof. - intros wfΣ [s Hs]. now eapply typing_wf_universes in Hs as [HT _]%MCProd.andP. + intros wfΣ [s Hs]. now eapply typing_wf_universes in Hs as [HT _]%andb_and. Qed. End CheckerFlags. +Arguments wf_universe_reflect {Σ u}. Hint Resolve @wf_universe_type1 @wf_universe_super @wf_universe_sup @wf_universe_product : pcuic. Hint Extern 4 (wf_universe _ ?u) => diff --git a/safechecker/_CoqProject.in b/safechecker/_CoqProject.in index b9041b4c1..08d8cbe7d 100644 --- a/safechecker/_CoqProject.in +++ b/safechecker/_CoqProject.in @@ -1,6 +1,7 @@ -R theories MetaCoq.SafeChecker theories/PCUICSafeReduce.v +theories/PCUICEqualityDec.v theories/PCUICSafeConversion.v theories/PCUICWfReduction.v theories/PCUICSafeChecker.v diff --git a/safechecker/theories/PCUICEqualityDec.v b/safechecker/theories/PCUICEqualityDec.v new file mode 100644 index 000000000..0c12c3d60 --- /dev/null +++ b/safechecker/theories/PCUICEqualityDec.v @@ -0,0 +1,175 @@ +(* Distributed under the terms of the MIT license. *) +From Coq Require Import ProofIrrelevance ssreflect ssrbool. +From MetaCoq.Template Require Import config utils uGraph. +From MetaCoq.PCUIC Require Import PCUICAst PCUICAstUtils + PCUICReflect PCUICLiftSubst PCUICUnivSubst PCUICTyping PCUICGlobalEnv + PCUICCumulativity PCUICEquality. + +Require Import Equations.Prop.DepElim. +From Equations Require Import Equations. + +Local Set Keyed Unification. + +Set Default Goal Selector "!". + +(** Checking equality *) + +Section EqualityDec. + Context {cf : checker_flags}. + Context (Σ : global_env_ext). + Context (hΣ : ∥ wf Σ ∥) (Hφ : ∥ on_udecl Σ.1 Σ.2 ∥). + Context (G : universes_graph) (HG : is_graph_of_uctx G (global_ext_uctx Σ)). + + Local Definition hΣ' : ∥ wf_ext Σ ∥. + Proof. + destruct hΣ, Hφ; now constructor. + Defined. + + Definition conv_pb_relb pb := + match pb with + | Conv => check_eqb_universe G + | Cumul => check_leqb_universe G + end. + + Definition eqb_termp_napp pb napp := + eqb_term_upto_univ_napp Σ (check_eqb_universe G) (conv_pb_relb pb) napp. + + Lemma eqb_termp_napp_spec pb napp t u : + eqb_termp_napp pb napp t u -> + eq_termp_napp pb Σ napp t u. + Proof. + pose proof hΣ'. + apply eqb_term_upto_univ_impl. + - intros u1 u2. + eapply (check_eqb_universe_spec' G (global_ext_uctx Σ)). + + sq. now eapply wf_ext_global_uctx_invariants. + + sq; now eapply global_ext_uctx_consistent. + + assumption. + - intros u1 u2. + destruct pb. + + eapply (check_eqb_universe_spec' G (global_ext_uctx Σ)). + * sq; now eapply wf_ext_global_uctx_invariants. + * sq; now eapply global_ext_uctx_consistent. + * assumption. + + eapply (check_leqb_universe_spec' G (global_ext_uctx Σ)). + * sq; now eapply wf_ext_global_uctx_invariants. + * sq; now eapply global_ext_uctx_consistent. + * assumption. + Qed. + + Definition eqb_termp pb := (eqb_termp_napp pb 0). + Definition eqb_term := (eqb_termp Conv). + Definition leqb_term := (eqb_termp Cumul). + + Lemma leqb_term_spec t u : + leqb_term t u -> + leq_term Σ (global_ext_constraints Σ) t u. + Proof. + intros. + now apply eqb_termp_napp_spec in H. + Qed. + + Notation eq_term Σ t u := (eq_term Σ Σ t u). + + Lemma eqb_term_spec t u : + eqb_term t u -> + eq_term Σ t u. + Proof. + intros. + now apply eqb_termp_napp_spec in H. + Qed. + + Lemma eqb_term_refl : + forall t, eqb_term t t. + Proof. + intro t. eapply eqb_term_upto_univ_refl. + all: apply check_eqb_universe_refl. + Qed. + + Definition eqb_binder_annot {A} (b b' : binder_annot A) : bool := + eqb b.(binder_relevance) b'.(binder_relevance). + + Lemma eq_binder_annot_reflect {A} na na' : reflect (eq_binder_annot (A:=A) na na') (eqb_binder_annot na na'). + Proof. + unfold eq_binder_annot, eqb_binder_annot. + destruct (eqb_spec na.(binder_relevance) na'.(binder_relevance)); constructor; auto. + Qed. + + Fixpoint eqb_ctx (Γ Δ : context) : bool := + match Γ, Δ with + | [], [] => true + | {| decl_name := na1 ; decl_body := None ; decl_type := t1 |} :: Γ, + {| decl_name := na2 ; decl_body := None ; decl_type := t2 |} :: Δ => + eqb_binder_annot na1 na2 && eqb_term t1 t2 && eqb_ctx Γ Δ + | {| decl_name := na1 ; decl_body := Some b1 ; decl_type := t1 |} :: Γ, + {| decl_name := na2 ; decl_body := Some b2 ; decl_type := t2 |} :: Δ => + eqb_binder_annot na1 na2 && eqb_term b1 b2 && eqb_term t1 t2 && eqb_ctx Γ Δ + | _, _ => false + end. + + Lemma eqb_binder_annot_spec {A} na na' : eqb_binder_annot (A:=A) na na' -> eq_binder_annot (A:=A) na na'. + Proof. apply (elimT (eq_binder_annot_reflect _ _)). Qed. + + Lemma eqb_ctx_spec : + forall Γ Δ, + eqb_ctx Γ Δ -> + eq_context_upto Σ (eq_universe Σ) (eq_universe Σ) Γ Δ. + Proof. + intros Γ Δ h. + induction Γ as [| [na [b|] A] Γ ih ] in Δ, h |- *. + all: destruct Δ as [| [na' [b'|] A'] Δ]. + all: try discriminate. + - constructor. + - simpl in h. apply andb_andI in h as [[[h1 h2]%andb_and h3]%andb_and h4]. + constructor. + + now apply eqb_binder_annot_spec in h1. + + eapply eqb_term_spec. assumption. + + eapply eqb_term_spec. assumption. + + eapply ih. assumption. + - simpl in h. apply andb_and in h as [[h1 h2]%andb_and h3]. + constructor. + + now apply eqb_binder_annot_spec. + + eapply eqb_term_spec. assumption. + + eapply ih. assumption. + Qed. + + Definition eqb_opt_term (t u : option term) := + match t, u with + | Some t, Some u => eqb_term t u + | None, None => true + | _, _ => false + end. + + Lemma eqb_opt_term_spec t u + : eqb_opt_term t u -> eq_opt_term false Σ (global_ext_constraints Σ) t u. + Proof. + destruct t, u; try discriminate; cbn => //. + apply eqb_term_spec; tea. + Qed. + + Definition eqb_decl (d d' : context_decl) := + eqb_binder_annot d.(decl_name) d'.(decl_name) && + eqb_opt_term d.(decl_body) d'.(decl_body) && eqb_term d.(decl_type) d'.(decl_type). + + Lemma eqb_decl_spec d d' + : eqb_decl d d' -> eq_decl false Σ (global_ext_constraints Σ) d d'. + Proof. + unfold eqb_decl, eq_decl. + intro H. rtoProp. apply eqb_opt_term_spec in H1. + eapply eqb_term_spec in H0; tea. + eapply eqb_binder_annot_spec in H. + repeat split; eauto. + Qed. + + Definition eqb_context (Γ Δ : context) := forallb2 eqb_decl Γ Δ. + + Lemma eqb_context_spec Γ Δ + : eqb_context Γ Δ -> eq_context false Σ (global_ext_constraints Σ) Γ Δ. + Proof. + unfold eqb_context, eq_context. + intro HH. apply forallb2_All2 in HH. + eapply All2_impl; try eassumption. + cbn. apply eqb_decl_spec. + Qed. + +End EqualityDec. \ No newline at end of file diff --git a/safechecker/theories/PCUICSafeChecker.v b/safechecker/theories/PCUICSafeChecker.v index f34e8c8ff..ef1d6f437 100644 --- a/safechecker/theories/PCUICSafeChecker.v +++ b/safechecker/theories/PCUICSafeChecker.v @@ -6,12 +6,13 @@ From MetaCoq.PCUIC Require Import PCUICAst PCUICAstUtils PCUICWeakening PCUICPosition PCUICCumulativity PCUICSafeLemmata PCUICSN PCUICPretty PCUICArities PCUICConfluence PCUICSize PCUICContextConversion PCUICConversion PCUICWfUniverses + PCUICGlobalEnv (* Used for support lemmas *) PCUICInductives PCUICWfUniverses PCUICContexts PCUICSubstitution PCUICSpine PCUICInductiveInversion PCUICClosed PCUICUnivSubstitution PCUICWeakeningEnv. -From MetaCoq.SafeChecker Require Import PCUICSafeReduce PCUICSafeConversion PCUICWfReduction. +From MetaCoq.SafeChecker Require Import PCUICSafeReduce PCUICEqualityDec PCUICSafeConversion PCUICWfReduction. From Equations Require Import Equations. Require Import ssreflect ssrbool. @@ -57,29 +58,6 @@ Proof. intros; sq; now eapply wf_local_rel_app_inv. Qed. -Fixpoint monad_All {T} {M : Monad T} {A} {P} (f : forall x, T (P x)) l : T (@All A P l) - := match l with - | [] => ret All_nil - | a :: l => X <- f a ;; - Y <- monad_All f l ;; - ret (All_cons X Y) - end. - -Fixpoint monad_All2 {T E} {M : Monad T} {M' : MonadExc E T} wrong_sizes - {A B R} (f : forall x y, T (R x y)) l1 l2 - : T (@All2 A B R l1 l2) - := match l1, l2 with - | [], [] => ret All2_nil - | a :: l1, b :: l2 => X <- f a b ;; - Y <- monad_All2 wrong_sizes f l1 l2 ;; - ret (All2_cons X Y) - | _, _ => raise wrong_sizes - end. - - -Definition monad_prod {T} {M : Monad T} {A B} (x : T A) (y : T B): T (A * B) - := X <- x ;; Y <- y ;; ret (X, Y). - Definition check_dec {T E} {M : Monad T} {M' : MonadExc E T} (e : E) {P} (H : {P} + {~ P}) : T P @@ -363,7 +341,8 @@ Qed. Lemma wf_ext_gc_of_uctx {cf:checker_flags} {Σ : global_env_ext} (HΣ : ∥ wf_ext Σ ∥) : ∑ uctx', gc_of_uctx (global_ext_uctx Σ) = Some uctx'. Proof. - pose proof (global_ext_uctx_consistent _ HΣ) as HC. + assert (consistent (global_ext_uctx Σ).2) as HC. + { sq; apply (global_ext_uctx_consistent _ HΣ). } destruct Σ as [Σ φ]. simpl in HC. unfold gc_of_uctx; simpl in *. @@ -380,11 +359,6 @@ Proof. exists (make_graph uctx). unfold is_graph_of_uctx. now rewrite Huctx. Defined. -Lemma map_squash {A B} (f : A -> B) : ∥ A ∥ -> ∥ B ∥. -Proof. - intros []; constructor; auto. -Qed. - Lemma destArity_mkApps_None ctx t l : destArity ctx t = None -> destArity ctx (mkApps t l) = None. Proof. @@ -713,8 +687,8 @@ Section Typecheck. pose proof HΣ'. intros HH. refine (check_constraints_spec G (global_ext_uctx Σ) _ _ HG _ HH). - now apply wf_ext_global_uctx_invariants. - now apply global_ext_uctx_consistent. + sq; now eapply wf_ext_global_uctx_invariants. + sq; now apply global_ext_uctx_consistent. Qed. Lemma is_graph_of_uctx_levels (l : Level.t) : @@ -759,45 +733,6 @@ Section Typecheck. - eapply check_constraints_spec; eauto. Qed. - Definition eqb_opt_term (t u : option term) := - match t, u with - | Some t, Some u => eqb_term Σ G t u - | None, None => true - | _, _ => false - end. - - Lemma eqb_opt_term_spec t u - : eqb_opt_term t u -> eq_opt_term false Σ (global_ext_constraints Σ) t u. - Proof. - destruct t, u; try discriminate; cbn. - apply eqb_term_spec; tea. trivial. - Qed. - - Definition eqb_decl (d d' : context_decl) := - eqb_binder_annot d.(decl_name) d'.(decl_name) && - eqb_opt_term d.(decl_body) d'.(decl_body) && eqb_term Σ G d.(decl_type) d'.(decl_type). - - Lemma eqb_decl_spec d d' - : eqb_decl d d' -> eq_decl false Σ (global_ext_constraints Σ) d d'. - Proof. - unfold eqb_decl, eq_decl. - intro H. rtoProp. apply eqb_opt_term_spec in H1. - eapply eqb_term_spec in H0; tea. - eapply eqb_binder_annot_spec in H. - repeat split; eauto. - Qed. - - Definition eqb_context (Γ Δ : context) := forallb2 eqb_decl Γ Δ. - - Lemma eqb_context_spec Γ Δ - : eqb_context Γ Δ -> eq_context false Σ (global_ext_constraints Σ) Γ Δ. - Proof. - unfold eqb_context, eq_context. - intro HH. apply forallb2_All2 in HH. - eapply All2_impl; try eassumption. - cbn. apply eqb_decl_spec. - Qed. - Obligation Tactic := Program.Tactics.program_simplify ; eauto 2. Program Definition check_is_allowed_elimination (u : Universe.t) (al : allowed_eliminations) : @@ -1075,7 +1010,7 @@ Section Typecheck. Next Obligation. intros; sq; now econstructor. Defined. (* tSort *) Next Obligation. - eapply (reflect_bP (wf_universe_reflect _ _)) in H. + eapply (elimT wf_universe_reflect) in H. sq; econstructor; tas. Defined. (* tProd *) @@ -1163,7 +1098,7 @@ Section Typecheck. rewrite -Heq_anonymous0 /=. intros ->. eapply PCUICInductives.isType_it_mkProd_or_LetIn_inv in t; eauto. eapply isType_wf_universes in t. simpl in t. - now exact (PCUICWfUniverses.reflect_bP (wf_universe_reflect _ _) t). auto. + now exact (elimT wf_universe_reflect t). auto. Qed. Next Obligation. @@ -1189,7 +1124,7 @@ Section Typecheck. rewrite -Heq_anonymous0 /=. intros ->. eapply PCUICInductives.isType_it_mkProd_or_LetIn_inv in X; eauto. eapply isType_wf_universes in X. simpl in X. - now exact (PCUICWfUniverses.reflect_bP (wf_universe_reflect _ _) X). auto. } + now exact (elimT wf_universe_reflect X). auto. } have [pctx' da] : (∑ pctx', destArity [] pty' = Some (pctx', ps)). { symmetry in Heq_anonymous1. unshelve eapply (PCUICInductives.build_case_predicate_type_spec (Σ.1, ind_universes d)) in Heq_anonymous1 as [parsubst [_ ->]]. @@ -1198,6 +1133,8 @@ Section Typecheck. eapply PCUICInductiveInversion.build_branches_type_wt. 6:eapply X. all:eauto. Defined. + Obligation Tactic := simpl; intros. + Next Obligation. rename Heq_anonymous2 into XX2. symmetry in XX2. simpl in *. eapply isconv_sound in XX2. @@ -1206,7 +1143,7 @@ Section Typecheck. change (eqb (ind_npars decl) par = true) in H1. destruct (eqb_spec (ind_npars decl) par) as [e|e]; [|discriminate]; subst. depelim HH. - sq. auto. now depelim X10. + sq. auto. now depelim X. Defined. Next Obligation. sq. now depelim HH. @@ -1240,7 +1177,7 @@ Section Typecheck. rewrite -Heq_anonymous0 /=. intros ->. eapply PCUICInductives.isType_it_mkProd_or_LetIn_inv in X; eauto. eapply isType_wf_universes in X. simpl in X. - now exact (PCUICWfUniverses.reflect_bP (wf_universe_reflect _ _) X). auto. } + now exact (elimT wf_universe_reflect X). auto. } have [pctx' da] : (∑ pctx', destArity [] pty' = Some (pctx', ps)). { symmetry in Heq_anonymous1. unshelve eapply (PCUICInductives.build_case_predicate_type_spec (Σ.1, ind_universes d)) in Heq_anonymous1 as [parsubst [_ ->]]. @@ -1643,7 +1580,7 @@ Section CheckEnv. [|intro XX; rewrite XX in Huctx; discriminate Huctx]. intros ctrs Hctrs. rewrite Hctrs in Huctx. simpl in *. eapply (is_consistent_spec (global_ext_uctx (Σ, udecl))). - { apply wf_global_uctx_invariants in HΣ. + { sq. apply wf_global_uctx_invariants in HΣ. split. + clear -HΣ. cbn. apply LevelSet.union_spec; right. apply HΣ. @@ -3357,7 +3294,7 @@ Section CheckEnv. eapply forallbP_cond; eauto. clear wfcs. simpl; intros c wfc. pose proof (check_leqb_universe_spec' G (global_ext_uctx Σ)). - forward H. apply wf_ext_global_uctx_invariants; auto. now sq. + forward H. apply wf_ext_global_uctx_invariants; auto. forward H. apply wfΣ. eapply forallbP_cond; eauto. simpl. intros x wfx. specialize (H wfG x ind_sort). simpl. @@ -3403,6 +3340,7 @@ Section CheckEnv. | false => ret _ end end. + Next Obligation. unfold check_ind_sorts. simpl. now rewrite H. diff --git a/safechecker/theories/PCUICSafeConversion.v b/safechecker/theories/PCUICSafeConversion.v index 668a22d77..d0178386a 100644 --- a/safechecker/theories/PCUICSafeConversion.v +++ b/safechecker/theories/PCUICSafeConversion.v @@ -2,12 +2,12 @@ From Coq Require Import ProofIrrelevance. From MetaCoq.Template Require Import config utils uGraph. From MetaCoq.PCUIC Require Import PCUICAst PCUICAstUtils - PCUICReflect PCUICLiftSubst PCUICUnivSubst PCUICTyping + PCUICReflect PCUICLiftSubst PCUICUnivSubst PCUICTyping PCUICGlobalEnv PCUICCumulativity PCUICEquality PCUICConversion PCUICSafeLemmata PCUICNormal PCUICInversion PCUICReduction PCUICPosition PCUICPrincipality PCUICContextConversion PCUICSN PCUICUtils PCUICWeakening PCUICConvCumInversion. -From MetaCoq.SafeChecker Require Import PCUICSafeReduce. +From MetaCoq.SafeChecker Require Import PCUICEqualityDec PCUICSafeReduce. Require Import Equations.Prop.DepElim. From Equations Require Import Equations. @@ -25,79 +25,6 @@ Module PSR := PCUICSafeReduce. *) - -Definition wf_global_uctx_invariants {cf:checker_flags} Σ : - ∥ wf Σ ∥ -> - global_uctx_invariants (global_uctx Σ). -Proof. - intros [HΣ]. split. - - cbn. eapply LevelSet.mem_spec, global_levels_Set. - - unfold global_uctx. - simpl. intros [[l ct] l'] Hctr. simpl in *. - induction Σ in HΣ, l, ct, l', Hctr |- *. - + apply ConstraintSetFact.empty_iff in Hctr; contradiction. - + simpl in *. apply ConstraintSet.union_spec in Hctr. - destruct Hctr as [Hctr|Hctr]. - * split. - -- inversion HΣ; subst. - destruct H2 as [HH1 [HH HH3]]. - subst udecl. destruct d as [decl|decl]; simpl in *. - ++ destruct decl; simpl in *. - destruct cst_universes ; [ - eapply (HH (l, ct, l') Hctr) - | apply ConstraintSetFact.empty_iff in Hctr ; contradiction - ]. - ++ destruct decl. simpl in *. - destruct ind_universes ; [ - eapply (HH (l, ct, l') Hctr) - | apply ConstraintSetFact.empty_iff in Hctr; contradiction - ]. - -- inversion HΣ. subst. - destruct H2 as [HH1 [HH HH3]]. - subst udecl. destruct d as [decl|decl]. - all: simpl in *. - ++ destruct decl. simpl in *. - destruct cst_universes ; [ - eapply (HH (l, ct, l') Hctr) - | apply ConstraintSetFact.empty_iff in Hctr; contradiction - ]. - ++ destruct decl. simpl in *. - destruct ind_universes; [ - eapply (HH (l, ct, l') Hctr) - | apply ConstraintSetFact.empty_iff in Hctr; contradiction - ]. - * inversion HΣ. subst. - split. - all: apply LevelSet.union_spec. - all: right. - all: unshelve eapply (IHΣ _ _ _ _ Hctr). - all: try eassumption. -Qed. - -Definition wf_ext_global_uctx_invariants {cf:checker_flags} Σ : - ∥ wf_ext Σ ∥ -> - global_uctx_invariants (global_ext_uctx Σ). -Proof. - intros [HΣ]. split. - - apply LevelSet.union_spec. right. apply LevelSet.mem_spec, global_levels_Set. - - destruct Σ as [Σ φ]. destruct HΣ as [HΣ Hφ]. - destruct (wf_global_uctx_invariants _ (sq HΣ)) as [_ XX]. - unfold global_ext_uctx, global_ext_levels, global_ext_constraints. - simpl. intros [[l ct] l'] Hctr. simpl in *. apply ConstraintSet.union_spec in Hctr. - destruct Hctr as [Hctr|Hctr]. - + destruct Hφ as [_ [HH _]]. apply (HH _ Hctr). - + specialize (XX _ Hctr). - split; apply LevelSet.union_spec; right; apply XX. -Qed. - -Definition global_ext_uctx_consistent {cf:checker_flags} Σ - : ∥ wf_ext Σ ∥ -> consistent (global_ext_uctx Σ).2. - intros [HΣ]. cbn. unfold global_ext_constraints. - unfold wf_ext, on_global_env_ext in HΣ. - destruct HΣ as [_ [_ [_ HH]]]. apply HH. -Qed. - - Section Conversion. Context {cf : checker_flags}. @@ -492,112 +419,10 @@ Section Conversion. simpl in *. eapply R_aux_stateR. all: simpl. all: auto. Qed. - - Definition conv_pb_relb pb := - match pb with - | Conv => check_eqb_universe G - | Cumul => check_leqb_universe G - end. - - Definition eqb_termp_napp pb napp := - eqb_term_upto_univ_napp Σ (check_eqb_universe G) (conv_pb_relb pb) napp. - - Lemma eqb_termp_napp_spec pb napp t u : - eqb_termp_napp pb napp t u -> - eq_termp_napp pb Σ napp t u. - Proof. - pose proof hΣ'. - apply eqb_term_upto_univ_impl. - - intros u1 u2. - eapply (check_eqb_universe_spec' G (global_ext_uctx Σ)). - + now eapply wf_ext_global_uctx_invariants. - + now eapply global_ext_uctx_consistent. - + assumption. - - intros u1 u2. - destruct pb. - + eapply (check_eqb_universe_spec' G (global_ext_uctx Σ)). - * now eapply wf_ext_global_uctx_invariants. - * now eapply global_ext_uctx_consistent. - * assumption. - + eapply (check_leqb_universe_spec' G (global_ext_uctx Σ)). - * now eapply wf_ext_global_uctx_invariants. - * now eapply global_ext_uctx_consistent. - * assumption. - Qed. - - Definition eqb_termp pb := (eqb_termp_napp pb 0). - Definition eqb_term := (eqb_termp Conv). - Definition leqb_term := (eqb_termp Cumul). - - Lemma leqb_term_spec t u : - leqb_term t u -> - leq_term Σ (global_ext_constraints Σ) t u. - Proof. - intros. - now apply eqb_termp_napp_spec in H. - Qed. - - Lemma eqb_term_spec t u : - eqb_term t u -> - eq_term Σ t u. - Proof. - intros. - now apply eqb_termp_napp_spec in H. - Qed. - - Lemma eqb_term_refl : - forall t, eqb_term t t. - Proof. - intro t. eapply eqb_term_upto_univ_refl. - all: apply check_eqb_universe_refl. - Qed. - - Definition eqb_binder_annot {A} (b b' : binder_annot A) : bool := - eqb b.(binder_relevance) b'.(binder_relevance). - - Lemma eq_binder_annot_reflect {A} na na' : reflect (eq_binder_annot (A:=A) na na') (eqb_binder_annot na na'). - Proof. - unfold eq_binder_annot, eqb_binder_annot. - destruct (eqb_spec na.(binder_relevance) na'.(binder_relevance)); constructor; auto. - Qed. - - Fixpoint eqb_ctx (Γ Δ : context) : bool := - match Γ, Δ with - | [], [] => true - | {| decl_name := na1 ; decl_body := None ; decl_type := t1 |} :: Γ, - {| decl_name := na2 ; decl_body := None ; decl_type := t2 |} :: Δ => - eqb_binder_annot na1 na2 && eqb_term t1 t2 && eqb_ctx Γ Δ - | {| decl_name := na1 ; decl_body := Some b1 ; decl_type := t1 |} :: Γ, - {| decl_name := na2 ; decl_body := Some b2 ; decl_type := t2 |} :: Δ => - eqb_binder_annot na1 na2 && eqb_term b1 b2 && eqb_term t1 t2 && eqb_ctx Γ Δ - | _, _ => false - end. - Lemma eqb_binder_annot_spec {A} na na' : eqb_binder_annot (A:=A) na na' -> eq_binder_annot (A:=A) na na'. - Proof. apply (PCUICWfUniverses.reflect_bP (eq_binder_annot_reflect _ _)). Qed. - - Lemma eqb_ctx_spec : - forall Γ Δ, - eqb_ctx Γ Δ -> - eq_context_upto Σ (eq_universe Σ) (eq_universe Σ) Γ Δ. - Proof. - intros Γ Δ h. - induction Γ as [| [na [b|] A] Γ ih ] in Δ, h |- *. - all: destruct Δ as [| [na' [b'|] A'] Δ]. - all: try discriminate. - - constructor. - - simpl in h. apply andP in h as [[[h1 h2]%andP h3]%andP h4]. - constructor. - + now apply eqb_binder_annot_spec in h1. - + eapply eqb_term_spec. assumption. - + eapply eqb_term_spec. assumption. - + eapply ih. assumption. - - simpl in h. apply andP in h as [[h1 h2]%andP h3]. - constructor. - + now apply eqb_binder_annot_spec. - + eapply eqb_term_spec. assumption. - + eapply ih. assumption. - Qed. + Notation eqb_ctx := (eqb_ctx Σ G). + Notation eqb_term := (eqb_term Σ G). + Notation leqb_term := (leqb_term Σ G). Definition eqb_term_stack t1 π1 t2 π2 := eqb_ctx (stack_context π1) (stack_context π2) && @@ -612,12 +437,12 @@ Section Conversion. eq_term Σ (zipp t1 π1) (zipp t2 π2). Proof. intros Γ t1 π1 t2 π2 h. - apply andP in h as [h1 h2]. + apply andb_and in h as [h1 h2]. split. - eapply eq_context_upto_cat. + eapply eq_context_upto_refl; tc. - + eapply eqb_ctx_spec. assumption. - - eapply eqb_term_spec. assumption. + + eapply eqb_ctx_spec; eassumption. + - eapply eqb_term_spec; eassumption. Qed. Definition leqb_term_stack t1 π1 t2 π2 := @@ -633,12 +458,12 @@ Section Conversion. leq_term Σ Σ (zipp t1 π1) (zipp t2 π2). Proof. intros Γ t1 π1 t2 π2 h. - apply andP in h as [h1 h2]. + apply andb_and in h as [h1 h2]. split. - eapply eq_context_upto_cat. + eapply eq_context_upto_refl; tc. - + eapply eqb_ctx_spec. assumption. - - eapply leqb_term_spec. assumption. + + eapply eqb_ctx_spec; eassumption. + - eapply leqb_term_spec; eassumption. Qed. Notation conv_stack_ctx Γ π1 π2 := @@ -1508,14 +1333,15 @@ Section Conversion. eapply Forall2_impl. 1: eassumption. intros. eapply (check_eqb_universe_spec' G (global_ext_uctx Σ)). all: auto. - + eapply wf_ext_global_uctx_invariants. - eapply hΣ'. - + eapply global_ext_uctx_consistent. - eapply hΣ'. + + destruct hΣ'. sq. eapply wf_ext_global_uctx_invariants. + eapply X. + + destruct hΣ'. sq; eapply global_ext_uctx_consistent; assumption. Qed. Arguments LevelSet.mem : simpl never. + Notation conv_pb_relb := (conv_pb_relb G). + Lemma conv_pb_relb_complete leq u u' : wf_universe Σ u -> wf_universe Σ u' -> @@ -1525,11 +1351,11 @@ Section Conversion. intros all1 all2 conv. destruct leq; cbn. - eapply check_eqb_universe_complete; eauto. - + apply wf_ext_global_uctx_invariants, hΣ'. - + apply global_ext_uctx_consistent, hΣ'. + + destruct hΣ' as [hΣ']; apply wf_ext_global_uctx_invariants, hΣ'. + + destruct hΣ' as [hΣ']; apply global_ext_uctx_consistent, hΣ'. - eapply check_leqb_universe_complete; eauto. - + apply wf_ext_global_uctx_invariants, hΣ'. - + apply global_ext_uctx_consistent, hΣ'. + + destruct hΣ' as [hΣ']; apply wf_ext_global_uctx_invariants, hΣ'. + + destruct hΣ' as [hΣ']; apply global_ext_uctx_consistent, hΣ'. Qed. Lemma get_level_make l : @@ -2107,7 +1933,7 @@ Section Conversion. change (true = eqb u.(rarg) v.(rarg)) in eq1. destruct (eqb_spec u.(rarg) v.(rarg)). 2: discriminate. symmetry in eqann. - apply (PCUICWfUniverses.reflect_bP (eq_binder_annot_reflect _ _)) in eqann. + apply (ssrbool.elimT (eq_binder_annot_reflect _ _)) in eqann. split; auto. destruct fk; simpl in *. all: intuition eauto. @@ -2141,7 +1967,7 @@ Section Conversion. change (true = eqb u.(rarg) v.(rarg)) in eq1. destruct (eqb_spec u.(rarg) v.(rarg)). 2: discriminate. symmetry in eqann. - apply (PCUICWfUniverses.reflect_bP (eq_binder_annot_reflect _ _)) in eqann. + apply (ssrbool.elimT (eq_binder_annot_reflect _ _)) in eqann. clear eq1. destruct fk. all: intuition eauto. @@ -2160,8 +1986,9 @@ Section Conversion. Next Obligation. destruct H as [H]; inversion H; destruct X as [_ [eq_uv eqann]]. change (?ru =? ?rv) with (eqb ru rv) in eq1. - pose proof (PCUICWfUniverses.reflect_Pb (eq_binder_annot_reflect (dname u) (dname v))). - rewrite <- neqann in H0. specialize (H0 eqann). discriminate. + symmetry in neqann. + pose proof (eq_binder_annot_reflect (dname u) (dname v)) as r. + now apply (ssrbool.elimF r neqann). Qed. Next Obligation. destruct H as [H]; inversion H; destruct X as [_ [eq_uv eqann]]. @@ -2521,7 +2348,7 @@ Section Conversion. Proof. intros eq ir. destruct ir as (_&[wh]). - apply eqb_term_spec in eq. + apply eqb_term_spec in eq; tea. epose proof (reduce_term_complete _ _ _ _ _ _) as [wh']. eapply whnf_eq_term in eq; [|exact wh']. rewrite zipp_as_mkApps in wh. @@ -2573,7 +2400,7 @@ Section Conversion. Proof. intros eq%eq_sym ir. destruct ir as (_&[wh]). - apply eqb_term_spec in eq. + apply eqb_term_spec in eq; tea. epose proof (reduce_term_complete _ _ _ _ _ _) as [wh']. eapply whnf_eq_term in eq; [|exact wh']. rewrite zipp_as_mkApps in wh. @@ -3009,9 +2836,7 @@ Section Conversion. simpl_stacks. destruct hΣ. apply Lambda_conv_cum_inv in H as (?&?&?); auto. - apply (PCUICWfUniverses.reflect_Pb (eq_binder_annot_reflect _ _)) in H. - unfold eq_binder_annot in H. unfold eqb_binder_annot in H; simpl in H. - congruence. + eapply (ssrbool.elimF (eq_binder_annot_reflect _ _)); tea. Qed. Next Obligation. (* Contrapositive of previous obligation *) @@ -3087,9 +2912,8 @@ Section Conversion. apply mkApps_Prod_nil in h2; auto. rewrite h1, h2 in H. apply Prod_conv_cum_inv in H as (?&?&?); auto. - apply (PCUICWfUniverses.reflect_Pb (eq_binder_annot_reflect _ _)) in H. - unfold eq_binder_annot in H. unfold eqb_binder_annot in H; simpl in H. - congruence. + eapply (ssrbool.elimF (eq_binder_annot_reflect _ _)); tea. + now unfold eqb_binder_annot. Qed. Next Obligation. (* Domains are not convertible *) @@ -4440,7 +4264,7 @@ Section Conversion. isconv_prog leq t1 π1 rt2' (θ2' +++ θ2) aux } } ; - | @exist None nored2 with inspect (eqb_termp_napp leq #|(decompose_stack π1).1| t1 t2) := { + | @exist None nored2 with inspect (eqb_termp_napp Σ G leq #|(decompose_stack π1).1| t1 t2) := { | @exist true eq1 := isconv_args leq t1 π1 t2 π2 aux; | @exist false noteq := no ( @@ -4651,7 +4475,7 @@ Section Conversion. rewrite Nat.add_0_r. apply All2_length in a. rewrite a in eq1. - apply eqb_termp_napp_spec; eauto. + eapply eqb_termp_napp_spec; eauto. Qed. Next Obligation. apply h; clear h. diff --git a/template-coq/theories/BasicAst.v b/template-coq/theories/BasicAst.v index e4993b2d6..355443d70 100644 --- a/template-coq/theories/BasicAst.v +++ b/template-coq/theories/BasicAst.v @@ -208,7 +208,11 @@ Inductive recursivity_kind := | CoFinite (* = coinductive *) | BiFinite (* = non-recursive, like in "Record" definitions *). - +(* The kind of a conversion problem *) +Inductive conv_pb := + | Conv + | Cumul. + (* Parametrized by term because term is not yet defined *) Record def term := mkdef { diff --git a/template-coq/theories/monad_utils.v b/template-coq/theories/monad_utils.v index c7bed7d9c..b7befc6fb 100644 --- a/template-coq/theories/monad_utils.v +++ b/template-coq/theories/monad_utils.v @@ -2,6 +2,9 @@ * monad library. *) Require Import List. +From MetaCoq.Template Require Import All_Forall. + +Import ListNotations. Set Universe Polymorphism. @@ -106,3 +109,25 @@ End MonadOperations. Definition monad_iter {T : Type -> Type} {M A} (f : A -> T unit) (l : list A) : T unit := @monad_fold_left T M _ _ (fun _ => f) l tt. + +Fixpoint monad_All {T} {M : Monad T} {A} {P} (f : forall x, T (P x)) l : T (@All A P l) := match l with + | [] => ret All_nil + | a :: l => X <- f a ;; + Y <- monad_All f l ;; + ret (All_cons X Y) + end. + +Fixpoint monad_All2 {T E} {M : Monad T} {M' : MonadExc E T} wrong_sizes + {A B R} (f : forall x y, T (R x y)) l1 l2 : T (@All2 A B R l1 l2) := + match l1, l2 with + | [], [] => ret All2_nil + | a :: l1, b :: l2 => X <- f a b ;; + Y <- monad_All2 wrong_sizes f l1 l2 ;; + ret (All2_cons X Y) + | _, _ => raise wrong_sizes + end. + +Definition monad_prod {T} {M : Monad T} {A B} (x : T A) (y : T B): T (A * B)%type + := X <- x ;; Y <- y ;; ret (X, Y). + + diff --git a/template-coq/theories/utils/All_Forall.v b/template-coq/theories/utils/All_Forall.v index 35add2c54..97b302cfe 100644 --- a/template-coq/theories/utils/All_Forall.v +++ b/template-coq/theories/utils/All_Forall.v @@ -6,7 +6,7 @@ Import ListNotations. Local Ltac inv H := inversion_clear H. Local Coercion is_true : bool >-> Sortclass. -Derive Signature for Forall. +Derive Signature for Forall Forall2. (** Combinators *) @@ -99,10 +99,23 @@ Lemma forallb_Forall {A} (p : A -> bool) l Proof. split. induction 1; rewrite /= // H IHForall //. - induction l; rewrite /= //. move/andP => [pa pl]. + induction l; rewrite /= //. rewrite andb_and. + intros [pa pl]. constructor; auto. Qed. +Lemma forallbP {A} (P : A -> Prop) (p : A -> bool) l : + (forall x, reflect (P x) (p x)) -> + reflect (Forall P l) (forallb p l). +Proof. + intros Hp. + apply iff_reflect; change (forallb p l = true) with (forallb p l : Prop); split. + - induction 1; rewrite /= // IHForall // andb_true_r. + now destruct (Hp x). + - induction l; rewrite /= //. rewrite andb_and. + intros [pa pl]. + constructor; auto. now destruct (Hp a). +Qed. Lemma map_eq_inj {A B} (f g : A -> B) l: map f l = map g l -> All (fun x => f x = g x) l. @@ -162,7 +175,7 @@ Lemma forallb2_app {A} (p : A -> A -> bool) l l' q q' : -> is_true (forallb2 p (l ++ q) (l' ++ q')). Proof. induction l in l' |- *; destruct l'; simpl; try congruence. - move=> /andP[/andP[pa pl] pq]. now rewrite pa IHl // pl pq. + move=> /andb_and[/andb_and[pa pl] pq]. now rewrite pa IHl // pl pq. Qed. Lemma All2_map {A B C D} (R : C -> D -> Type) (f : A -> C) (g : B -> D) l l' : @@ -440,18 +453,18 @@ Qed. Lemma Alli_rev {A} {P : nat -> A -> Type} k l : Alli P k l -> - Alli (fun k' => P (pred #|l| - k' + k)) 0 (List.rev l). + Alli (fun k' => P (Nat.pred #|l| - k' + k)) 0 (List.rev l). Proof. revert k. induction l using rev_ind; simpl; intros; try constructor. eapply Alli_app in X. intuition. rewrite rev_app_distr. rewrite app_length. simpl. constructor. - replace (pred (#|l| + 1) - 0) with #|l| by lia. + replace (Nat.pred (#|l| + 1) - 0) with #|l| by lia. inversion b. eauto. specialize (IHl _ a). eapply Alli_shift. eapply Alli_impl. eauto. simpl; intros. - now replace (pred (#|l| + 1) - S n) with (pred #|l| - n) by lia. + now replace (Nat.pred (#|l| + 1) - S n) with (Nat.pred #|l| - n) by lia. Qed. @@ -1654,8 +1667,8 @@ Lemma forallb_nth {A} (l : list A) (n : nat) P d : forallb P l -> n < #|l| -> exists x, (nth n l d = x) /\ P x. Proof. induction l in n |- *; destruct n; simpl; auto; try easy. - move/andP => [pa pl] pn. exists a; easy. - move/andP => [pa pl] pn. specialize (IHl n pl). + move/andb_and => [pa pl] pn. exists a; easy. + move/andb_and => [pa pl] pn. specialize (IHl n pl). apply IHl; lia. Qed. @@ -1888,7 +1901,7 @@ Proof. - destruct l'. 2: discriminate. constructor. - destruct l'. 1: discriminate. - simpl in h. apply andP in h as [? ?]. + simpl in h. move/andb_and: h => [? ?]. constructor. all: auto. Qed. diff --git a/template-coq/theories/utils/MCProd.v b/template-coq/theories/utils/MCProd.v index 2e32a2f2c..5631a042c 100644 --- a/template-coq/theories/utils/MCProd.v +++ b/template-coq/theories/utils/MCProd.v @@ -1,4 +1,7 @@ -From Coq Require Import Bool. +From Coq Require Import Bool RelationClasses. +Require Import ssreflect. + +Local Coercion is_true : bool >-> Sortclass. Declare Scope pair_scope. @@ -46,11 +49,12 @@ Qed. Definition on_pi2 {A B C} (f : B -> B) (p : A * B * C) : A * B * C := (fst (fst p), f (snd (fst p)), snd p). - -Lemma andb_and b b' : is_true (b && b') <-> is_true b /\ is_true b'. +(** It would be tempting to import ssrbool here, however + https://github.com/coq/coq/issues/13486 prevents this. *) +Lemma andb_and b b' : b && b' <-> b /\ b'. Proof. apply andb_true_iff. Qed. -Lemma andP {b b'} : is_true (b && b') -> is_true b /\ is_true b'. +Lemma andb_andI {b b'} : b && b' -> b /\ b'. Proof. apply andb_and. Qed. Definition fst_eq {A B} {x x' : A} {y y' : B} diff --git a/template-coq/theories/utils/MCSquash.v b/template-coq/theories/utils/MCSquash.v index 3169de128..20749333e 100644 --- a/template-coq/theories/utils/MCSquash.v +++ b/template-coq/theories/utils/MCSquash.v @@ -4,6 +4,11 @@ Record squash (A : Type) : Prop := sq { _ : A }. Notation "∥ T ∥" := (squash T) (at level 10). Arguments sq {_} _. +Lemma map_squash {A B} (f : A -> B) : ∥ A ∥ -> ∥ B ∥. +Proof. + intros []; constructor; auto. +Qed. + Ltac sq := repeat match goal with | H : ∥ _ ∥ |- _ => case H; clear H; intro H diff --git a/template-coq/theories/utils/wGraph.v b/template-coq/theories/utils/wGraph.v index 0bd96a0dc..4a4220d42 100644 --- a/template-coq/theories/utils/wGraph.v +++ b/template-coq/theories/utils/wGraph.v @@ -491,12 +491,12 @@ Module WeightedGraph (V : UsualOrderedTypeWithLeibniz) (VSet : MSetList.SWithLei Next Obligation. split. - eapply VSetProp.Add_add. - - apply andP in Hp0 as [h1 h2]. + - apply andb_andI in Hp0 as [h1 h2]. apply negb_true_iff in h1. apply VSetFact.not_mem_iff in h1. assumption. Defined. Next Obligation. - apply andP in Hp0 as [? ?]. auto. + apply andb_andI in Hp0 as [? ?]. auto. Defined. @@ -507,23 +507,6 @@ Module WeightedGraph (V : UsualOrderedTypeWithLeibniz) (VSet : MSetList.SWithLei reflexivity. specialize (IHp q); intuition. Qed. - - (* Lemma DisjointAdd_add {s s' x y} (H : DisjointAdd x s s') (H' : x <> y) *) - (* : DisjointAdd x (VSet.add y s) (VSet.add y s'). *) - (* Proof. *) - (* repeat split. 2: intros [H0|H0]. *) - (* - intro H0. apply VSet.add_spec in H0. *) - (* destruct H0 as [H0|H0]. *) - (* right; subst; apply VSet.add_spec; left; reflexivity. *) - (* apply H in H0. destruct H0 as [H0|H0]; [left; assumption |right]. *) - (* apply VSet.add_spec; right; assumption. *) - (* - subst. apply VSet.add_spec; right. apply H; left; reflexivity. *) - (* - apply VSet.add_spec in H0; apply VSet.add_spec; destruct H0 as [H0|H0]. *) - (* left; assumption. right. apply H. right; assumption. *) - (* - intro H0. apply VSet.add_spec in H0; destruct H0 as [H0|H0]. *) - (* contradiction. now apply H. *) - (* Qed. *) - Lemma DisjointAdd_add1 {s0 s1 s2 x y} (H1 : DisjointAdd x s0 s1) (H2 : DisjointAdd y s1 s2) : DisjointAdd x (VSet.add y s0) s2. From 96778d19d7ca42677c61f2ba5533ac3fbc4df0f5 Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Thu, 26 Nov 2020 18:03:53 +0100 Subject: [PATCH 02/70] Remove distracting notation overriden warning --- pcuic/theories/PCUICToTemplateCorrectness.v | 2 ++ 1 file changed, 2 insertions(+) diff --git a/pcuic/theories/PCUICToTemplateCorrectness.v b/pcuic/theories/PCUICToTemplateCorrectness.v index c3889746a..76d8e9fa4 100644 --- a/pcuic/theories/PCUICToTemplateCorrectness.v +++ b/pcuic/theories/PCUICToTemplateCorrectness.v @@ -2,8 +2,10 @@ From MetaCoq.PCUIC Require Import PCUICAst PCUICAstUtils PCUICInduction PCUICLiftSubst PCUICEquality PCUICUnivSubst PCUICTyping PCUICGeneration. +Set Warnings "-notation-overridden". From MetaCoq.Template Require Import config utils Ast TypingWf WfInv UnivSubst LiftSubst. +Set Warnings "+notation_overridden". Require Import PCUICToTemplate. From 0516e48b868011a81772ee3f9448616c7774ffd5 Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Thu, 26 Nov 2020 18:28:35 +0100 Subject: [PATCH 03/70] Adapt depgraph to Mac OS poor unix support --- dependency-graph/generate-depgraph.sh | 20 +++++++++++++------- 1 file changed, 13 insertions(+), 7 deletions(-) diff --git a/dependency-graph/generate-depgraph.sh b/dependency-graph/generate-depgraph.sh index 92c666d4b..ccb7497db 100755 --- a/dependency-graph/generate-depgraph.sh +++ b/dependency-graph/generate-depgraph.sh @@ -1,4 +1,8 @@ -#!/bin/bash +#!/usr/local/bin/bash + +SED=`which gsed || which sed` + +echo "sed is " $SED ############################################################### # @@ -10,6 +14,8 @@ # cd dependency-graph # ./generate-depgraph.sh depgraph-2020-09-24 # +# Requires: graphviz for .dot to .png/.svg generation, +# a recent bash (not the one shipped with OS X Catalina for example) ############################################################### @@ -27,23 +33,23 @@ folders[erasure]=tan # Two first lines echo "digraph dependencies {" > $dot_file echo "node[style=filled]" >> $dot_file - for folder in "${!folders[@]}" do cd ../$folder + echo `pwd` coqdep -f _CoqProject -dumpgraph ../dependency-graph/$folder.dot > /dev/null cd ../dependency-graph # remove the first and last lines - sed -i '1d' $folder.dot - sed -i '$d' $folder.dot + $SED -i '1d' $folder.dot + $SED -i '$d' $folder.dot # change a bit the names of the nodes for otherfolder in "${!folders[@]}" do - sed -i "s@../$otherfolder/theories@$otherfolder@g" $folder.dot + $SED -i "s@../$otherfolder/theories@$otherfolder@g" $folder.dot done - sed -i "s/theories/$folder/g" $folder.dot + $SED -i "s/theories/$folder/g" $folder.dot # change the color of the nodes - sed -i "s/]/, color=${folders[$folder]}]/g" $folder.dot + $SED -i "s/]/, color=${folders[$folder]}]/g" $folder.dot # concatenate cat $folder.dot >> $dot_file rm -f $folder.dot From 5fcbe237ff806c40c103953518af0bfcc804774b Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Thu, 26 Nov 2020 18:29:05 +0100 Subject: [PATCH 04/70] Ignore notation-overridden warning temporarily --- pcuic/theories/TemplateToPCUICCorrectness.v | 2 ++ 1 file changed, 2 insertions(+) diff --git a/pcuic/theories/TemplateToPCUICCorrectness.v b/pcuic/theories/TemplateToPCUICCorrectness.v index 3015ed9ed..17f3312af 100644 --- a/pcuic/theories/TemplateToPCUICCorrectness.v +++ b/pcuic/theories/TemplateToPCUICCorrectness.v @@ -1,8 +1,10 @@ (* Distributed under the terms of the MIT license. *) From MetaCoq.Template Require Import config utils Ast TypingWf WfInv. +Set Warnings "-notation-overridden". From MetaCoq.PCUIC Require Import PCUICAst PCUICAstUtils PCUICCumulativity PCUICLiftSubst PCUICEquality PCUICUnivSubst PCUICTyping TemplateToPCUIC PCUICSubstitution PCUICGeneration. +Set Warnings "+notation-overridden". From Equations.Prop Require Import DepElim. From 6a0d02900c4af35109e2e089294a6c4a855fcd4b Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Thu, 26 Nov 2020 18:29:32 +0100 Subject: [PATCH 05/70] Dependency graph as of 2020-11-26 --- dependency-graph/depgraph-2020-11-26.dot | 339 ++++ dependency-graph/depgraph-2020-11-26.png | Bin 0 -> 1158736 bytes dependency-graph/depgraph-2020-11-26.svg | 2041 ++++++++++++++++++++++ 3 files changed, 2380 insertions(+) create mode 100644 dependency-graph/depgraph-2020-11-26.dot create mode 100644 dependency-graph/depgraph-2020-11-26.png create mode 100644 dependency-graph/depgraph-2020-11-26.svg diff --git a/dependency-graph/depgraph-2020-11-26.dot b/dependency-graph/depgraph-2020-11-26.dot new file mode 100644 index 000000000..4a2d876ba --- /dev/null +++ b/dependency-graph/depgraph-2020-11-26.dot @@ -0,0 +1,339 @@ +digraph dependencies { +node[style=filled] +"safechecker/Extraction"[label="Extraction", color=paleturquoise1] +"safechecker/PCUICSafeRetyping"[label="PCUICSafeRetyping", color=paleturquoise1] +"safechecker/SafeTemplateChecker"[label="SafeTemplateChecker", color=paleturquoise1] +"safechecker/PCUICSafeChecker"[label="PCUICSafeChecker", color=paleturquoise1] +"safechecker/PCUICWfReduction"[label="PCUICWfReduction", color=paleturquoise1] +"safechecker/PCUICSafeConversion"[label="PCUICSafeConversion", color=paleturquoise1] +"safechecker/PCUICEqualityDec"[label="PCUICEqualityDec", color=paleturquoise1] +"safechecker/PCUICSafeReduce"[label="PCUICSafeReduce", color=paleturquoise1] +"pcuic/PCUICValidity" -> "pcuic/PCUICAlpha" +"pcuic/PCUICWfUniverses" -> "pcuic/PCUICArities" +"template-coq/EnvironmentTyping" -> "pcuic/PCUICAst" +"pcuic/PCUICSize" -> "pcuic/PCUICAstUtils" +"template-coq/Reflect" -> "pcuic/PCUICAstUtils" +"template-coq/common/uGraph" -> "pcuic/PCUICAstUtils" +"pcuic/PCUICClosed" -> "pcuic/PCUICCSubst" +"pcuic/PCUICElimination" -> "pcuic/PCUICCanonicity" +"pcuic/PCUICSN" -> "pcuic/PCUICCanonicity" +"pcuic/PCUICWcbvEval" -> "pcuic/PCUICCanonicity" +"pcuic/PCUICWeakeningEnv" -> "pcuic/PCUICClosed" +"pcuic/PCUICParallelReductionConfluence" -> "pcuic/PCUICConfluence" +"pcuic/PCUICConfluence" -> "pcuic/PCUICContextConversion" +"pcuic/PCUICContextRelation" -> "pcuic/PCUICContextConversion" +"pcuic/PCUICTyping" -> "pcuic/PCUICContextRelation" +"pcuic/PCUICCtxShape" -> "pcuic/PCUICContexts" +"pcuic/PCUICCumulProp" -> "pcuic/PCUICConvCumInversion" +"pcuic/PCUICContextConversion" -> "pcuic/PCUICConversion" +"pcuic/PCUICInversion" -> "pcuic/PCUICCtxShape" +"pcuic/PCUICNameless" -> "pcuic/PCUICCtxShape" +"template-coq/UnivSubst" -> "pcuic/PCUICCtxShape" +"pcuic/PCUICSafeLemmata" -> "pcuic/PCUICCumulProp" +"pcuic/PCUICReduction" -> "pcuic/PCUICCumulativity" +"pcuic/PCUICCumulProp" -> "pcuic/PCUICElimination" +"pcuic/PCUICLiftSubst" -> "pcuic/PCUICEquality" +"pcuic/PCUICReflect" -> "pcuic/PCUICEquality" +"pcuic/PCUICTyping" -> "pcuic/PCUICGeneration" +"pcuic/PCUICTyping" -> "pcuic/PCUICGlobalEnv" +"pcuic/PCUICAstUtils" -> "pcuic/PCUICInduction" +"pcuic/PCUICValidity" -> "pcuic/PCUICInductiveInversion" +"pcuic/PCUICSpine" -> "pcuic/PCUICInductives" +"pcuic/PCUICConversion" -> "pcuic/PCUICInversion" +"pcuic/PCUICInduction" -> "pcuic/PCUICLiftSubst" +"pcuic/PCUICTyping" -> "pcuic/PCUICNameless" +"pcuic/PCUICContextRelation" -> "pcuic/PCUICNormal" +"template-coq/UnivSubst" -> "pcuic/PCUICNormal" +"pcuic/PCUICSubstitution" -> "pcuic/PCUICParallelReduction" +"pcuic/PCUICParallelReduction" -> "pcuic/PCUICParallelReductionConfluence" +"pcuic/PCUICEquality" -> "pcuic/PCUICPosition" +"pcuic/PCUICLiftSubst" -> "pcuic/PCUICPretty" +"pcuic/PCUICCumulProp" -> "pcuic/PCUICPrincipality" +"pcuic/PCUICPosition" -> "pcuic/PCUICReduction" +"pcuic/PCUICRelations" -> "pcuic/PCUICReduction" +"pcuic/PCUICUnivSubst" -> "pcuic/PCUICReduction" +"pcuic/PCUICInduction" -> "pcuic/PCUICReflect" +"pcuic/PCUICSafeLemmata" -> "pcuic/PCUICSN" +"pcuic/PCUICAlpha" -> "pcuic/PCUICSR" +"pcuic/PCUICInductiveInversion" -> "pcuic/PCUICSR" +"pcuic/PCUICNormal" -> "pcuic/PCUICSafeLemmata" +"pcuic/PCUICSR" -> "pcuic/PCUICSafeLemmata" +"pcuic/PCUICWeakening" -> "pcuic/PCUICSigmaCalculus" +"pcuic/PCUICAst" -> "pcuic/PCUICSize" +"pcuic/PCUICArities" -> "pcuic/PCUICSpine" +"pcuic/PCUICSigmaCalculus" -> "pcuic/PCUICSubstitution" +"pcuic/PCUICUnivSubstitution" -> "pcuic/PCUICSubstitution" +"pcuic/PCUICCumulativity" -> "pcuic/PCUICTyping" +"pcuic/PCUICUtils" -> "pcuic/PCUICTyping" +"template-coq/utils/LibHypsNaming" -> "pcuic/PCUICTyping" +"pcuic/PCUICLiftSubst" -> "pcuic/PCUICUnivSubst" +"pcuic/PCUICWeakening" -> "pcuic/PCUICUnivSubstitution" +"pcuic/PCUICAstUtils" -> "pcuic/PCUICUtils" +"pcuic/PCUICInductives" -> "pcuic/PCUICValidity" +"pcuic/PCUICCSubst" -> "pcuic/PCUICWcbvEval" +"pcuic/PCUICSR" -> "pcuic/PCUICWcbvEval" +"pcuic/PCUICClosed" -> "pcuic/PCUICWeakening" +"pcuic/PCUICGeneration" -> "pcuic/PCUICWeakening" +"pcuic/PCUICTyping" -> "pcuic/PCUICWeakeningEnv" +"pcuic/PCUICContexts" -> "pcuic/PCUICWfUniverses" +"pcuic/PCUICAst" -> "pcuic/TemplateToPCUIC" +"template-coq/Environment" -> "template-coq/Ast" +"template-coq/Ast" -> "template-coq/AstUtils" +"template-coq/utils" -> "template-coq/BasicAst" +"template-coq/Universes" -> "template-coq/Environment" +"template-coq/AstUtils" -> "template-coq/EnvironmentTyping" +"template-coq/AstUtils" -> "template-coq/Induction" +"template-coq/Induction" -> "template-coq/LiftSubst" +"template-coq/Induction" -> "template-coq/Reflect" +"template-coq/EnvironmentTyping" -> "template-coq/Typing" +"template-coq/UnivSubst" -> "template-coq/Typing" +"template-coq/LiftSubst" -> "template-coq/UnivSubst" +"template-coq/BasicAst" -> "template-coq/Universes" +"template-coq/config" -> "template-coq/Universes" +"template-coq/Universes" -> "template-coq/common/uGraph" +"template-coq/utils/wGraph" -> "template-coq/common/uGraph" +"template-coq/utils/All_Forall" -> "template-coq/monad_utils" +"template-coq/monad_utils" -> "template-coq/utils" +"template-coq/utils/MCUtils" -> "template-coq/utils" +"template-coq/utils/MCOption" -> "template-coq/utils/All_Forall" +"template-coq/utils/MCSquash" -> "template-coq/utils/All_Forall" +"template-coq/utils/MCPrelude" -> "template-coq/utils/MCList" +"template-coq/utils/MCRelations" -> "template-coq/utils/MCList" +"template-coq/utils/MCList" -> "template-coq/utils/MCOption" +"template-coq/utils/MCProd" -> "template-coq/utils/MCOption" +"template-coq/utils/MCCompare" -> "template-coq/utils/MCString" +"template-coq/utils/All_Forall" -> "template-coq/utils/MCUtils" +"template-coq/utils/MCArith" -> "template-coq/utils/MCUtils" +"template-coq/utils/MCEquality" -> "template-coq/utils/MCUtils" +"template-coq/utils/MCString" -> "template-coq/utils/MCUtils" +"template-coq/utils/MCUtils" -> "template-coq/utils/wGraph" +"safechecker/SafeTemplateChecker" -> "safechecker/Extraction" +"pcuic/PCUICGlobalEnv" -> "safechecker/PCUICEqualityDec" +"safechecker/PCUICWfReduction" -> "safechecker/PCUICSafeChecker" +"pcuic/PCUICConvCumInversion" -> "safechecker/PCUICSafeConversion" +"pcuic/PCUICPrincipality" -> "safechecker/PCUICSafeConversion" +"safechecker/PCUICEqualityDec" -> "safechecker/PCUICSafeConversion" +"safechecker/PCUICSafeReduce" -> "safechecker/PCUICSafeConversion" +"pcuic/PCUICCanonicity" -> "safechecker/PCUICSafeReduce" +"safechecker/PCUICSafeChecker" -> "safechecker/PCUICSafeRetyping" +"pcuic/PCUICPretty" -> "safechecker/PCUICWfReduction" +"safechecker/PCUICSafeConversion" -> "safechecker/PCUICWfReduction" +"pcuic/TemplateToPCUIC" -> "safechecker/SafeTemplateChecker" +"template-coq/Typing" -> "safechecker/SafeTemplateChecker" +"safechecker/PCUICSafeChecker" -> "safechecker/SafeTemplateChecker" +"template-coq/Extraction"[label="Extraction", color=aquamarine] +"template-coq/Constants"[label="Constants", color=aquamarine] +"template-coq/monad_utils"[label="monad_utils", color=aquamarine] +"template-coq/TemplateMonad/Extractable"[label="Extractable", color=aquamarine] 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+"template-coq/utils/MCCompare"[label="MCCompare", color=aquamarine] +"template-coq/utils/MCArith"[label="MCArith", color=aquamarine] +"template-coq/utils/All_Forall"[label="All_Forall", color=aquamarine] +"template-coq/utils/MCPrelude"[label="MCPrelude", color=aquamarine] +"template-coq/TemplateMonad" -> "template-coq/Constants" +"template-coq/TemplateMonad/Extractable" -> "template-coq/Constants" +"template-coq/common/uGraph" -> "template-coq/Constants" +"template-coq/Pretty" -> "template-coq/Extraction" +"template-coq/Reflect" -> "template-coq/Extraction" +"template-coq/TemplateMonad/Extractable" -> "template-coq/Extraction" +"template-coq/UnivSubst" -> "template-coq/Extraction" +"template-coq/AstUtils" -> "template-coq/Kernames" +"template-coq/LiftSubst" -> "template-coq/Pretty" +"template-coq/TemplateMonad/Core" -> "template-coq/TemplateMonad" +"template-coq/Ast" -> "template-coq/TemplateMonad/Common" +"template-coq/AstUtils" -> "template-coq/TemplateMonad/Core" +"template-coq/TemplateMonad/Common" -> "template-coq/TemplateMonad/Core" +"template-coq/AstUtils" -> "template-coq/TemplateMonad/Extractable" +"template-coq/TemplateMonad/Common" -> "template-coq/TemplateMonad/Extractable" +"template-coq/Typing" -> "template-coq/TypingWf" +"template-coq/AstUtils" -> "template-coq/WfInv" +"checker/All"[label="All", color=seagreen3] +"checker/Normal"[label="Normal", color=seagreen3] +"checker/Retyping"[label="Retyping", color=seagreen3] +"checker/WcbvEval"[label="WcbvEval", color=seagreen3] +"checker/Checker"[label="Checker", color=seagreen3] +"checker/Substitution"[label="Substitution", color=seagreen3] +"checker/Weakening"[label="Weakening", color=seagreen3] +"checker/Closed"[label="Closed", color=seagreen3] +"checker/WeakeningEnv"[label="WeakeningEnv", color=seagreen3] +"checker/Generation"[label="Generation", color=seagreen3] +"template-coq/Loader" -> "template-coq/All" +"template-coq/Typing" -> "template-coq/All" +"template-coq/Constants" -> "template-coq/Loader" +"template-coq/All" -> "checker/All" +"checker/Retyping" -> "checker/All" +"checker/Substitution" -> "checker/All" +"template-coq/Typing" -> "checker/Checker" +"template-coq/common/uGraph" -> "checker/Checker" +"template-coq/Reflect" -> "checker/Closed" +"template-coq/TypingWf" -> "checker/Closed" +"checker/WeakeningEnv" -> "checker/Closed" +"template-coq/Reflect" -> "checker/Generation" +"template-coq/Typing" -> "checker/Generation" +"template-coq/Typing" -> "checker/Normal" +"checker/Checker" -> "checker/Retyping" +"checker/Generation" -> "checker/Substitution" +"checker/Weakening" -> "checker/Substitution" +"template-coq/Reflect" -> "checker/WcbvEval" +"template-coq/Typing" -> "checker/WcbvEval" +"template-coq/WfInv" -> "checker/WcbvEval" +"checker/Closed" -> "checker/Weakening" +"template-coq/Typing" -> "checker/WeakeningEnv" +"template-coq/utils/LibHypsNaming" -> "checker/WeakeningEnv" +"erasure/Erasure"[label="Erasure", color=tan] +"erasure/EOptimizePropDiscr"[label="EOptimizePropDiscr", color=tan] +"erasure/ErasureFunction"[label="ErasureFunction", color=tan] +"erasure/ErasureCorrectness"[label="ErasureCorrectness", color=tan] +"erasure/EArities"[label="EArities", color=tan] +"erasure/EInversion"[label="EInversion", color=tan] +"erasure/ESubstitution"[label="ESubstitution", color=tan] +"erasure/Prelim"[label="Prelim", color=tan] +"erasure/Extraction"[label="Extraction", color=tan] +"erasure/EAll"[label="EAll", color=tan] +"erasure/EDeps"[label="EDeps", color=tan] +"erasure/Extract"[label="Extract", color=tan] +"erasure/ETyping"[label="ETyping", color=tan] +"erasure/EWndEval"[label="EWndEval", color=tan] +"erasure/EWcbvEval"[label="EWcbvEval", color=tan] +"erasure/ECSubst"[label="ECSubst", color=tan] +"erasure/EPretty"[label="EPretty", color=tan] +"erasure/EReflect"[label="EReflect", color=tan] +"erasure/ELiftSubst"[label="ELiftSubst", color=tan] +"erasure/EInduction"[label="EInduction", color=tan] +"erasure/EAstUtils"[label="EAstUtils", color=tan] +"erasure/EAst"[label="EAst", color=tan] +"erasure/EWcbvEval" -> "erasure/EAll" +"erasure/EWndEval" -> "erasure/EAll" +"erasure/Extract" -> "erasure/EAll" +"pcuic/PCUICCanonicity" -> "erasure/EArities" +"pcuic/PCUICPrincipality" -> "erasure/EArities" +"erasure/Extract" -> "erasure/EArities" +"template-coq/Universes" -> "erasure/EAst" +"template-coq/Kernames" -> "erasure/EAstUtils" +"erasure/EAst" -> "erasure/EAstUtils" +"erasure/ELiftSubst" -> "erasure/ECSubst" +"erasure/ESubstitution" -> "erasure/EDeps" +"erasure/EAst" -> "erasure/EInduction" +"erasure/Prelim" -> "erasure/EInversion" +"erasure/EInduction" -> "erasure/ELiftSubst" +"erasure/ErasureFunction" -> "erasure/EOptimizePropDiscr" +"erasure/ETyping" -> "erasure/EPretty" +"pcuic/PCUICReflect" -> "erasure/EReflect" +"erasure/EInduction" -> "erasure/EReflect" +"erasure/Prelim" -> "erasure/ESubstitution" +"erasure/EAstUtils" -> "erasure/ETyping" +"erasure/ELiftSubst" -> "erasure/ETyping" +"erasure/EReflect" -> "erasure/ETyping" +"pcuic/PCUICWcbvEval" -> "erasure/EWcbvEval" +"erasure/ECSubst" -> "erasure/EWcbvEval" +"erasure/ETyping" -> "erasure/EWcbvEval" +"erasure/ETyping" -> "erasure/EWndEval" +"safechecker/SafeTemplateChecker" -> "erasure/Erasure" +"template-coq/Pretty" -> "erasure/Erasure" +"erasure/EOptimizePropDiscr" -> "erasure/Erasure" +"erasure/EPretty" -> "erasure/Erasure" +"erasure/EDeps" -> "erasure/ErasureCorrectness" +"erasure/EInversion" -> "erasure/ErasureCorrectness" +"safechecker/PCUICSafeRetyping" -> "erasure/ErasureFunction" +"erasure/ErasureCorrectness" -> "erasure/ErasureFunction" +"pcuic/PCUICElimination" -> "erasure/Extract" +"erasure/ETyping" -> "erasure/Extract" +"erasure/Erasure" -> "erasure/Extraction" +"safechecker/PCUICSafeChecker" -> "erasure/Prelim" +"erasure/EArities" -> "erasure/Prelim" +"erasure/EWcbvEval" -> "erasure/Prelim" +"pcuic/PCUICToTemplateCorrectness"[label="PCUICToTemplateCorrectness", color=lemonchiffon1] +"pcuic/PCUICToTemplate"[label="PCUICToTemplate", color=lemonchiffon1] +"pcuic/TemplateToPCUICCorrectness"[label="TemplateToPCUICCorrectness", color=lemonchiffon1] +"pcuic/TemplateToPCUIC"[label="TemplateToPCUIC", color=lemonchiffon1] +"pcuic/PCUICSafeLemmata"[label="PCUICSafeLemmata", color=lemonchiffon1] +"pcuic/PCUICSigmaCalculus"[label="PCUICSigmaCalculus", color=lemonchiffon1] +"pcuic/PCUICPrincipality"[label="PCUICPrincipality", color=lemonchiffon1] +"pcuic/PCUICSN"[label="PCUICSN", color=lemonchiffon1] +"pcuic/PCUICElimination"[label="PCUICElimination", color=lemonchiffon1] +"pcuic/PCUICCumulProp"[label="PCUICCumulProp", color=lemonchiffon1] +"pcuic/PCUICPretty"[label="PCUICPretty", color=lemonchiffon1] +"pcuic/PCUICWcbvEval"[label="PCUICWcbvEval", color=lemonchiffon1] +"pcuic/PCUICCSubst"[label="PCUICCSubst", color=lemonchiffon1] +"pcuic/PCUICCanonicity"[label="PCUICCanonicity", color=lemonchiffon1] +"pcuic/PCUICSR"[label="PCUICSR", color=lemonchiffon1] +"pcuic/PCUICInductiveInversion"[label="PCUICInductiveInversion", color=lemonchiffon1] +"pcuic/PCUICValidity"[label="PCUICValidity", color=lemonchiffon1] +"pcuic/PCUICInductives"[label="PCUICInductives", color=lemonchiffon1] +"pcuic/PCUICSpine"[label="PCUICSpine", color=lemonchiffon1] +"pcuic/PCUICWfUniverses"[label="PCUICWfUniverses", color=lemonchiffon1] +"pcuic/PCUICArities"[label="PCUICArities", color=lemonchiffon1] +"pcuic/PCUICContexts"[label="PCUICContexts", color=lemonchiffon1] +"pcuic/PCUICCtxShape"[label="PCUICCtxShape", color=lemonchiffon1] +"pcuic/PCUICAlpha"[label="PCUICAlpha", color=lemonchiffon1] +"pcuic/PCUICGeneration"[label="PCUICGeneration", color=lemonchiffon1] +"pcuic/PCUICConvCumInversion"[label="PCUICConvCumInversion", color=lemonchiffon1] +"pcuic/PCUICConversion"[label="PCUICConversion", color=lemonchiffon1] +"pcuic/PCUICContextConversion"[label="PCUICContextConversion", color=lemonchiffon1] +"pcuic/PCUICContextRelation"[label="PCUICContextRelation", color=lemonchiffon1] +"pcuic/PCUICConfluence"[label="PCUICConfluence", color=lemonchiffon1] +"pcuic/PCUICParallelReductionConfluence"[label="PCUICParallelReductionConfluence", color=lemonchiffon1] +"pcuic/PCUICParallelReduction"[label="PCUICParallelReduction", color=lemonchiffon1] +"pcuic/PCUICReduction"[label="PCUICReduction", color=lemonchiffon1] +"pcuic/PCUICCumulativity"[label="PCUICCumulativity", color=lemonchiffon1] +"pcuic/PCUICSubstitution"[label="PCUICSubstitution", color=lemonchiffon1] +"pcuic/PCUICUnivSubstitution"[label="PCUICUnivSubstitution", color=lemonchiffon1] +"pcuic/PCUICWeakening"[label="PCUICWeakening", color=lemonchiffon1] +"pcuic/PCUICClosed"[label="PCUICClosed", color=lemonchiffon1] +"pcuic/PCUICWeakeningEnv"[label="PCUICWeakeningEnv", color=lemonchiffon1] +"pcuic/PCUICEquality"[label="PCUICEquality", color=lemonchiffon1] +"pcuic/PCUICNameless"[label="PCUICNameless", color=lemonchiffon1] +"pcuic/PCUICNormal"[label="PCUICNormal", color=lemonchiffon1] +"pcuic/PCUICPosition"[label="PCUICPosition", color=lemonchiffon1] +"pcuic/PCUICInversion"[label="PCUICInversion", color=lemonchiffon1] +"pcuic/PCUICGlobalEnv"[label="PCUICGlobalEnv", color=lemonchiffon1] +"pcuic/PCUICTyping"[label="PCUICTyping", color=lemonchiffon1] +"pcuic/PCUICUnivSubst"[label="PCUICUnivSubst", color=lemonchiffon1] +"pcuic/PCUICLiftSubst"[label="PCUICLiftSubst", color=lemonchiffon1] +"pcuic/PCUICReflect"[label="PCUICReflect", color=lemonchiffon1] +"pcuic/PCUICInduction"[label="PCUICInduction", color=lemonchiffon1] +"pcuic/PCUICAstUtils"[label="PCUICAstUtils", color=lemonchiffon1] +"pcuic/PCUICSize"[label="PCUICSize", color=lemonchiffon1] +"pcuic/PCUICAst"[label="PCUICAst", color=lemonchiffon1] +"pcuic/PCUICRelations"[label="PCUICRelations", color=lemonchiffon1] +"pcuic/PCUICUtils"[label="PCUICUtils", color=lemonchiffon1] +"pcuic/PCUICAstUtils" -> "pcuic/PCUICToTemplate" +"template-coq/TypingWf" -> "pcuic/PCUICToTemplateCorrectness" +"template-coq/WfInv" -> "pcuic/PCUICToTemplateCorrectness" +"pcuic/PCUICGeneration" -> "pcuic/PCUICToTemplateCorrectness" +"pcuic/PCUICToTemplate" -> "pcuic/PCUICToTemplateCorrectness" +"template-coq/TypingWf" -> "pcuic/TemplateToPCUICCorrectness" +"template-coq/WfInv" -> "pcuic/TemplateToPCUICCorrectness" +"pcuic/PCUICSubstitution" -> "pcuic/TemplateToPCUICCorrectness" +"pcuic/TemplateToPCUIC" -> "pcuic/TemplateToPCUICCorrectness" +} diff --git a/dependency-graph/depgraph-2020-11-26.png b/dependency-graph/depgraph-2020-11-26.png new file mode 100644 index 0000000000000000000000000000000000000000..3dfdcae3699d5ba5a470c03ce53be00cc13188d2 GIT binary patch literal 1158736 zcmZsD1z43?v^F48f+CG{gLHT2q068_N?N)@L?k7pn?obrsq~>6C8fK&|L@?;z`g%{ z=FI5BGvEH!UVE)~t-ap&5U8vujfV091qKEN4J0F>3Il^e0|SGdh=c(AgloZU9QXs_ zot(4;%q{evw8oq$7#LC*kc6nZOVZYibM)wO7jS=BZmT^+epejO=juVycaSqPNP?X-G(czB)ew(vF^L{o-QhKfJy!m3%Ei zSI__C(j%#yiGA+C)!TX2<*BLO>NRo;3u*)hCuiZf!TS>W)pCh!k8|oif;LVf9j}7puuA1Bab(m^m`A5xhbW=22Ss7(9Uq?z>iXqAmc(CLW 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90669b338aae599a37f9f96fc52742d12216c2c2 Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Thu, 26 Nov 2020 18:35:35 +0100 Subject: [PATCH 06/70] Fix due to move of conv_pb definition --- erasure/theories/EDeps.v | 2 ++ erasure/theories/ErasureCorrectness.v | 2 +- erasure/theories/Prelim.v | 2 +- safechecker/_PluginProject.in | 2 ++ safechecker/src/metacoq_safechecker_plugin.mlpack | 1 + template-coq/theories/Extraction.v | 1 + 6 files changed, 8 insertions(+), 2 deletions(-) diff --git a/erasure/theories/EDeps.v b/erasure/theories/EDeps.v index 4854d38b4..5dda4f59d 100644 --- a/erasure/theories/EDeps.v +++ b/erasure/theories/EDeps.v @@ -3,10 +3,12 @@ From Equations Require Import Equations. From MetaCoq.PCUIC Require Import PCUICAst PCUICAstUtils PCUICTyping PCUICInversion PCUICWeakeningEnv. +Set Warnings "-notation-overridden". From MetaCoq.Erasure Require Import EAst EAstUtils ECSubst EInduction ELiftSubst ESubstitution ETyping Extract EWcbvEval Prelim. +Set Warnings "+notation-overridden". From MetaCoq.Template Require Import config utils monad_utils. Derive NoConfusion for term. diff --git a/erasure/theories/ErasureCorrectness.v b/erasure/theories/ErasureCorrectness.v index 3f25e1cd0..cad838654 100644 --- a/erasure/theories/ErasureCorrectness.v +++ b/erasure/theories/ErasureCorrectness.v @@ -1186,7 +1186,7 @@ Proof. simpl in b. rewrite fix_context_length in b. now rewrite Nat.add_0_r. - unfold test_def in a. apply andP in a as [_ Hbod]. + unfold test_def in a. apply andb_and in a as [_ Hbod]. rewrite fix_context_length. now rewrite Nat.add_0_r in Hbod. eauto with pcuic. diff --git a/erasure/theories/Prelim.v b/erasure/theories/Prelim.v index 75dc978cb..f8fa1ba89 100644 --- a/erasure/theories/Prelim.v +++ b/erasure/theories/Prelim.v @@ -267,7 +267,7 @@ Proof. rewrite emkApps_snoc in i. inv i. - destruct (EAstUtils.mkApps_elim t l). EAstUtils.solve_discr. rewrite Ee.value_head_spec in i. - move/andP: i => [H H']. + move/andb_and: i => [H H']. eapply Ee.atom_mkApps in H' as [H1 _]. destruct n, L; discriminate. - unfold Ee.isStuckFix in i. destruct f; try now inversion i. diff --git a/safechecker/_PluginProject.in b/safechecker/_PluginProject.in index 1e90c5714..cfeeda7dd 100644 --- a/safechecker/_PluginProject.in +++ b/safechecker/_PluginProject.in @@ -85,6 +85,8 @@ src/pCUICPretty.ml # From SafeChecker src/pCUICSafeReduce.mli src/pCUICSafeReduce.ml +src/pCUICEqualityDec.mli +src/pCUICEqualityDec.ml src/pCUICSafeConversion.mli src/pCUICSafeConversion.ml src/pCUICSafeChecker.mli diff --git a/safechecker/src/metacoq_safechecker_plugin.mlpack b/safechecker/src/metacoq_safechecker_plugin.mlpack index e4e3f623a..4d1b6a859 100644 --- a/safechecker/src/metacoq_safechecker_plugin.mlpack +++ b/safechecker/src/metacoq_safechecker_plugin.mlpack @@ -33,6 +33,7 @@ PCUICCumulativity PCUICUnivSubst PCUICSafeReduce +PCUICEqualityDec PCUICSafeConversion PCUICSafeChecker SafeTemplateChecker diff --git a/template-coq/theories/Extraction.v b/template-coq/theories/Extraction.v index 69509d490..ecaf3f522 100644 --- a/template-coq/theories/Extraction.v +++ b/template-coq/theories/Extraction.v @@ -38,6 +38,7 @@ Extraction Library EqDecInstances. Extraction Library Induction. Extraction Library LiftSubst. Extraction Library UnivSubst. +Extraction Library BasicAst. Extraction Library Reflect. Extraction Library Pretty. Extraction Library config. From 369e6004adcfd2485d1006e49bffcf69e5a465d2 Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Thu, 26 Nov 2020 20:19:48 +0100 Subject: [PATCH 07/70] WIP cleaning up --- pcuic/theories/PCUICAstUtils.v | 13 +++ pcuic/theories/PCUICSR.v | 133 ++++++++++-------------- pcuic/theories/PCUICTyping.v | 4 +- safechecker/theories/PCUICSafeChecker.v | 44 -------- template-coq/theories/BasicAst.v | 43 ++++---- template-coq/theories/Universes.v | 61 +++++++++-- template-coq/theories/monad_utils.v | 18 +++- template-coq/theories/utils/MCPrelude.v | 5 +- 8 files changed, 167 insertions(+), 154 deletions(-) diff --git a/pcuic/theories/PCUICAstUtils.v b/pcuic/theories/PCUICAstUtils.v index c8744d6ba..07375fdfe 100644 --- a/pcuic/theories/PCUICAstUtils.v +++ b/pcuic/theories/PCUICAstUtils.v @@ -68,6 +68,19 @@ Fixpoint decompose_app_rec (t : term) l := Definition decompose_app t := decompose_app_rec t []. +Definition mkApps_decompose_app_rec t l : + mkApps t l = mkApps (fst (decompose_app_rec t l)) (snd (decompose_app_rec t l)). +Proof. + revert l; induction t; try reflexivity. + intro l; cbn in *. + transitivity (mkApps t1 ((t2 ::l))). reflexivity. + now rewrite IHt1. +Qed. + +Definition mkApps_decompose_app t : + t = mkApps (fst (decompose_app t)) (snd (decompose_app t)) + := mkApps_decompose_app_rec t []. + Lemma decompose_app_rec_mkApps f l l' : decompose_app_rec (mkApps f l) l' = decompose_app_rec f (l ++ l'). Proof. diff --git a/pcuic/theories/PCUICSR.v b/pcuic/theories/PCUICSR.v index 9c09090ad..82ffc4429 100644 --- a/pcuic/theories/PCUICSR.v +++ b/pcuic/theories/PCUICSR.v @@ -12,10 +12,10 @@ From MetaCoq.PCUIC Require Import PCUICAst PCUICAstUtils PCUICUtils Require Import ssreflect. From Equations Require Import Equations. Require Import Equations.Prop.DepElim. - - Local Set SimplIsCbn. +Implicit Types (cf : checker_flags) (Σ : global_env_ext). + Derive Signature for OnOne2_local_env. Ltac rename_hyp h ht ::= my_rename_hyp h ht. @@ -29,21 +29,20 @@ Hint Rewrite projs_length : len. (** The subject reduction property of the system: *) -Definition SR_red1 {cf:checker_flags} (Σ : global_env_ext) Γ t T := +Definition SR_red1 {cf} Σ Γ t T := forall u (Hu : red1 Σ Γ t u), Σ ;;; Γ |- u : T. (* Preservation of wf_*fixpoint *) -Lemma wf_fixpoint_red1_type {cf:checker_flags} (Σ : global_env_ext) Γ mfix mfix1 : - wf Σ.1 -> - wf_fixpoint Σ.1 mfix -> +Lemma wf_fixpoint_red1_type {cf Σ} {wfΣ : wf Σ} Γ mfix mfix1 : + wf_fixpoint Σ mfix -> OnOne2 (fun x y : def term => red1 Σ Γ (dtype x) (dtype y) × (dname x, dbody x, rarg x) = (dname y, dbody y, rarg y)) mfix mfix1 -> - wf_fixpoint Σ.1 mfix1. + wf_fixpoint Σ mfix1. Proof. - intros wfΣ wffix o. + intros wffix o. move: wffix; unfold wf_fixpoint. enough (forall inds, map_option_out (map check_one_fix mfix) = Some inds -> map_option_out (map check_one_fix mfix1) = Some inds) => //. @@ -75,16 +74,15 @@ Proof. discriminate. Qed. -Lemma wf_fixpoint_red1_body {cf:checker_flags} (Σ : global_env_ext) Γ mfix mfix1 : - wf Σ.1 -> - wf_fixpoint Σ.1 mfix -> +Lemma wf_fixpoint_red1_body {cf Σ} {wfΣ : wf Σ} Γ mfix mfix1 : + wf_fixpoint Σ mfix -> OnOne2 (fun x y : def term => red1 Σ Γ (dbody x) (dbody y) × (dname x, dtype x, rarg x) = (dname y, dtype y, rarg y)) mfix mfix1 -> - wf_fixpoint Σ.1 mfix1. + wf_fixpoint Σ mfix1. Proof. - intros wfΣ wffix o. + intros wffix o. move: wffix; unfold wf_fixpoint. enough (map check_one_fix mfix = map check_one_fix mfix1) as -> => //. induction o. @@ -1313,8 +1311,6 @@ Proof. eapply type_Cumul; eauto. Qed. -Print Assumptions sr_red1. - Definition sr_stmt {cf:checker_flags} (Σ : global_env_ext) Γ t T := forall u, red Σ Γ t u -> Σ ;;; Γ |- u : T. @@ -1326,8 +1322,8 @@ Proof. eapply sr_red1 in Hty; eauto with wf. Qed. -Lemma subject_reduction1 {cf:checker_flags} {Σ Γ t u T} - : wf Σ.1 -> Σ ;;; Γ |- t : T -> red1 Σ.1 Γ t u -> Σ ;;; Γ |- u : T. +Lemma subject_reduction1 {cf Σ} {wfΣ : wf Σ} {Γ t u T} + : Σ ;;; Γ |- t : T -> red1 Σ Γ t u -> Σ ;;; Γ |- u : T. Proof. intros. eapply subject_reduction; try eassumption. now apply red1_red. @@ -1336,24 +1332,11 @@ Defined. Section SRContext. Context {cf:checker_flags}. - (* todo: rename wf_local_app *) - Definition wf_local_app' {Σ Γ1 Γ2} : - wf_local Σ Γ1 -> wf_local_rel Σ Γ1 Γ2 - -> wf_local Σ (Γ1 ,,, Γ2). - Proof. - intros H1 H2. apply wf_local_local_rel. - apply wf_local_rel_local in H1. - apply wf_local_rel_app_inv; tas. - now rewrite app_context_nil_l. - Qed. - - Definition cumul_red_l' `{checker_flags} : - forall Σ Γ t u, - wf Σ.1 -> - red (fst Σ) Γ t u -> + Definition cumul_red_l' {Σ} {wfΣ : wf Σ} Γ t u : + red Σ Γ t u -> Σ ;;; Γ |- t <= u. Proof. - intros Σ Γ t u hΣ h. + intros h. induction h using red_rect'. - eapply cumul_refl'. - eapply PCUICConversion.cumul_trans ; try eassumption. @@ -1365,8 +1348,7 @@ Section SRContext. Hint Constructors OnOne2_local_env : aa. Hint Unfold red1_ctx : aa. - - Lemma red1_ctx_app Σ Γ Γ' Δ : + Lemma red1_ctx_app (Σ : global_env) Γ Γ' Δ : red1_ctx Σ Γ Γ' -> red1_ctx Σ (Γ ,,, Δ) (Γ' ,,, Δ). Proof. @@ -1374,7 +1356,7 @@ Section SRContext. intro H. simpl. constructor. now apply IHΔ. Qed. - Lemma red1_red_ctx Σ Γ Γ' : + Lemma red1_red_ctx (Σ : global_env) Γ Γ' : red1_ctx Σ Γ Γ' -> red_ctx Σ Γ Γ'. Proof. @@ -1387,7 +1369,7 @@ Section SRContext. apply refl_red. Qed. - Lemma nth_error_red1_ctx Σ Γ Γ' n decl : + Lemma nth_error_red1_ctx (Σ : global_env) Γ Γ' n decl : wf Σ -> nth_error Γ n = Some decl -> red1_ctx Σ Γ Γ' -> @@ -1421,13 +1403,12 @@ Section SRContext. eapply (weakening_red_0 wfΣ _ [_]); tas; cbnr. Qed. - Lemma wf_local_isType_nth Σ Γ n decl : - wf Σ.1 -> + Lemma wf_local_isType_nth {Σ} {wfΣ : wf Σ} Γ n decl : wf_local Σ Γ -> nth_error Γ n = Some decl -> ∑ s, Σ ;;; Γ |- lift0 (S n) (decl_type decl) : tSort s. Proof. - induction n in Γ, decl |- *; intros hΣ hΓ e; destruct Γ; + induction n in Γ, decl |- *; intros hΓ e; destruct Γ; cbn; inversion e; inversion hΓ; subst. all: try (destruct X0 as [s Ht]; exists s; eapply (weakening _ _ [_] _ (tSort s)); tas). @@ -1442,9 +1423,8 @@ Section SRContext. Ltac invs H := inversion H; subst. Ltac invc H := inversion H; subst; clear H. - Lemma subject_reduction_ctx Σ Γ Γ' t T : - wf Σ.1 -> - red1_ctx Σ.1 Γ Γ' -> + Lemma subject_reduction_ctx {Σ} {wfΣ : wf Σ} Γ Γ' t T : + red1_ctx Σ Γ Γ' -> Σ ;;; Γ |- t : T -> Σ ;;; Γ' |- t : T. Proof. assert(OnOne2_local_env @@ -1462,7 +1442,7 @@ Section SRContext. constructor. pcuic. constructor; pcuics. now apply red_conv, red1_red. - destruct d as [na [b|] ?]; constructor; auto; constructor; auto. all:pcuic. } - intros wfΣ r H. + intros r H. specialize (X r). assert(wf_local Σ Γ'). apply typing_wf_local in H. @@ -1494,11 +1474,10 @@ Section SRContext. - eapply context_conversion; eauto. Qed. - Lemma wf_local_red1 {Σ Γ Γ'} : - wf Σ.1 -> - red1_ctx Σ.1 Γ Γ' -> wf_local Σ Γ -> wf_local Σ Γ'. + Lemma wf_local_red1 {Σ} {wfΣ : wf Σ} {Γ Γ'} : + red1_ctx Σ Γ Γ' -> wf_local Σ Γ -> wf_local Σ Γ'. Proof. - intro hΣ. induction 1; cbn in *. + induction 1; cbn in *. - intro e. inversion e; subst; cbn in *. constructor; tas. destruct X0 as [s Ht]. exists s. eapply subject_reduction1; tea. @@ -1525,17 +1504,16 @@ Section SRContext. all:constructor; cbnr; eauto. Qed. - Lemma wf_local_red {Σ Γ Γ'} : - wf Σ.1 -> - red_ctx Σ.1 Γ Γ' -> wf_local Σ Γ -> wf_local Σ Γ'. + Lemma wf_local_red {Σ} {wfΣ : wf Σ} {Γ Γ'} : + red_ctx Σ Γ Γ' -> wf_local Σ Γ -> wf_local Σ Γ'. Proof. - intros hΣ h. apply red_ctx_clos_rt_red1_ctx in h. + intros h. apply red_ctx_clos_rt_red1_ctx in h. induction h; eauto using wf_local_red1. apply eq_context_upto_names_upto_names in e. eauto using wf_local_alpha. Qed. - Lemma wf_local_subst1 Σ (wfΣ : wf Σ.1) Γ na b t Γ' : + Lemma wf_local_subst1 {Σ} {wfΣ : wf Σ} Γ na b t Γ' : wf_local Σ (Γ ,,, [],, vdef na b t ,,, Γ') -> wf_local Σ (Γ ,,, subst_context [b] 0 Γ'). Proof. @@ -1575,23 +1553,21 @@ Section SRContext. intro H; simpl; constructor; cbn; eauto; now apply IHΔ. Qed. - Lemma isType_red1 {Σ Γ A B} : - wf Σ.1 -> - red1 (fst Σ) Γ A B -> + Lemma isType_red1 {Σ : global_env_ext} {wfΣ : wf Σ} {Γ A B} : isType Σ Γ A -> + red1 Σ Γ A B -> isType Σ Γ B. Proof. - intros wf red [s Hs]. + intros [s Hs] red. exists s. eapply subject_reduction1; eauto. Qed. - Lemma isWfArity_red1 {Σ Γ A B} : - wf Σ.1 -> - red1 (fst Σ) Γ A B -> + Lemma isWfArity_red1 {Σ} {wfΣ : wf Σ} {Γ A B} : isWfArity Σ Γ A -> + red1 Σ Γ A B -> isWfArity Σ Γ B. Proof. - intros wfΣ re [isty H]. + intros [isty H] re. split. eapply isType_red1; eauto. clear isty; revert H. induction re using red1_ind_all. @@ -1628,44 +1604,38 @@ Section SRContext. eexists _, s''. cbn. rewrite destArity_app ee'. reflexivity. Qed. - Lemma isWfArity_red {Σ Γ A B} : - wf Σ.1 -> - red (fst Σ) Γ A B -> + Lemma isWfArity_red {Σ} {wfΣ : wf Σ} {Γ A B} : isWfArity Σ Γ A -> + red Σ Γ A B -> isWfArity Σ Γ B. Proof. induction 2 using red_rect'. - easy. - - intro. now eapply isWfArity_red1. + - now eapply isWfArity_red1. Qed. - Lemma isType_red {Σ Γ A B} : - wf Σ.1 -> - red (fst Σ) Γ A B -> - isType Σ Γ A -> - isType Σ Γ B. + Lemma isType_red {Σ} {wfΣ : wf Σ} {Γ T U} : + isType Σ Γ T -> red Σ Γ T U -> isType Σ Γ U. Proof. - intros ? ? [? ?]. - eexists. eapply subject_reduction; tea. + intros [s Hs] red; exists s. + eapply subject_reduction; eauto. Qed. - Lemma type_reduction {Σ Γ t A B} - : wf Σ.1 -> Σ ;;; Γ |- t : A -> red (fst Σ) Γ A B -> Σ ;;; Γ |- t : B. + Lemma type_reduction {Σ} {wfΣ : wf Σ} {Γ t A B} : + Σ ;;; Γ |- t : A -> red Σ Γ A B -> Σ ;;; Γ |- t : B. Proof. - intros HΣ' Ht Hr. + intros Ht Hr. eapply type_Cumul'. eassumption. 2: now eapply cumul_red_l'. - destruct (validity_term HΣ' Ht) as [s HA]. + destruct (validity_term wfΣ Ht) as [s HA]. exists s; eapply subject_reduction; eassumption. Defined. End SRContext. -Lemma isWAT_tLetIn {cf:checker_flags} {Σ : global_env_ext} (HΣ' : wf Σ) - {Γ} (HΓ : wf_local Σ Γ) {na t A B} +Lemma isType_tLetIn {cf} {Σ} {HΣ' : wf Σ} {Γ} {na t A B} : isType Σ Γ (tLetIn na t A B) - <~> (isType Σ Γ A × (Σ ;;; Γ |- t : A) - × isType Σ (Γ,, vdef na t A) B). + <~> (isType Σ Γ A × (Σ ;;; Γ |- t : A) × isType Σ (Γ,, vdef na t A) B). Proof. split; intro HH. - destruct HH as [s H]. @@ -1689,3 +1659,6 @@ Proof. * apply red1_red. apply red_zeta with (b':=tSort sB). Defined. + +(** Keep at the end to not disturb asynchronous proof processing *) +Print Assumptions sr_red1. diff --git a/pcuic/theories/PCUICTyping.v b/pcuic/theories/PCUICTyping.v index dd7fa91cb..0c7d77873 100644 --- a/pcuic/theories/PCUICTyping.v +++ b/pcuic/theories/PCUICTyping.v @@ -13,6 +13,8 @@ Require Import Equations.Type.Relation. From Equations Require Import Equations. Set Equations With UIP. +Implicit Types (cf : checker_flags) (Σ : global_env_ext). + (** * Typing derivations Inductive relations for reduction, conversion and typing of PCUIC terms. @@ -267,7 +269,7 @@ Definition isCoFinite (r : recursivity_kind) := | _ => false end. -Definition check_recursivity_kind Σ ind r := +Definition check_recursivity_kind (Σ : global_env) ind r := match lookup_env Σ ind with | Some (InductiveDecl mib) => Reflect.eqb mib.(ind_finite) r | _ => false diff --git a/safechecker/theories/PCUICSafeChecker.v b/safechecker/theories/PCUICSafeChecker.v index ef1d6f437..bf074c0b8 100644 --- a/safechecker/theories/PCUICSafeChecker.v +++ b/safechecker/theories/PCUICSafeChecker.v @@ -58,50 +58,6 @@ Proof. intros; sq; now eapply wf_local_rel_app_inv. Qed. -Definition check_dec {T E} {M : Monad T} {M' : MonadExc E T} (e : E) {P} - (H : {P} + {~ P}) - : T P - := match H with - | left x => ret x - | right _ => raise e - end. - -Definition check_eq_true {T E} {M : Monad T} {M' : MonadExc E T} b (e : E) - : T (b = true) - := if b return T (b = true) then ret eq_refl else raise e. - -Program Definition check_eq_nat {T E} {M : Monad T} {M' : MonadExc E T} n m (e : E) - : T (n = m) - := match Nat.eq_dec n m with - | left p => ret p - | right p => raise e - end. - -Definition mkApps_decompose_app_rec t l : - mkApps t l = mkApps (fst (decompose_app_rec t l)) (snd (decompose_app_rec t l)). -Proof. - revert l; induction t; try reflexivity. - intro l; cbn in *. - transitivity (mkApps t1 ((t2 ::l))). reflexivity. - now rewrite IHt1. -Qed. - -Definition mkApps_decompose_app t : - t = mkApps (fst (decompose_app t)) (snd (decompose_app t)) - := mkApps_decompose_app_rec t []. - -Lemma isType_red {cf:checker_flags} {Σ : global_env_ext} {wfΣ : wf Σ} {Γ T U} : - isType Σ Γ T -> red Σ Γ T U -> isType Σ Γ U. -Proof. - intros [s Hs] red; exists s. - eapply subject_reduction; eauto. -Qed. - - - - -Derive NoConfusion EqDec for allowed_eliminations. - Inductive type_error := | UnboundRel (n : nat) | UnboundVar (id : string) diff --git a/template-coq/theories/BasicAst.v b/template-coq/theories/BasicAst.v index 355443d70..6fc49a384 100644 --- a/template-coq/theories/BasicAst.v +++ b/template-coq/theories/BasicAst.v @@ -1,7 +1,6 @@ (* Distributed under the terms of the MIT license. *) From MetaCoq.Template Require Import utils. - (** ** Reification of names ** *) (** [Comment taken from Coq's code] @@ -37,6 +36,8 @@ Definition qualid := string. (* e.g. Datatypes.nat *) order is reversed to improve sharing. E.g. A.B.C is ["C";"B";"A"] *) Definition dirpath := list ident. +Instance dirpath_eqdec : Classes.EqDec dirpath := _. + Definition string_of_dirpath : dirpath -> string := String.concat "." ∘ rev. @@ -49,6 +50,7 @@ Inductive modpath := | MPfile (dp : dirpath) | MPbound (dp : dirpath) (id : ident) (i : nat) | MPdot (mp : modpath) (id : ident). +Derive NoConfusion EqDec for modpath. Fixpoint string_of_modpath (mp : modpath) : string := match mp with @@ -59,17 +61,19 @@ Fixpoint string_of_modpath (mp : modpath) : string := (** The absolute names of objects seen by kernel *) Definition kername := modpath × ident. +Instance kername_eqdec : Classes.EqDec kername := _. Definition string_of_kername (kn : kername) := string_of_modpath kn.1 ^ "." ^ kn.2. - (** Identifiers that are allowed to be anonymous (i.e. "_" in concrete syntax). *) Inductive name : Set := | nAnon | nNamed (_ : ident). +Derive NoConfusion EqDec for name. Inductive relevance : Set := Relevant | Irrelevant. +Derive NoConfusion EqDec for relevance. (** Binders annotated with relevance *) Record binder_annot (A : Type) := mkBindAnn { binder_name : A; binder_relevance : relevance }. @@ -78,6 +82,11 @@ Arguments mkBindAnn {_}. Arguments binder_name {_}. Arguments binder_relevance {_}. +Derive NoConfusion for binder_annot. + +Instance eqdec_binder_annot (A : Type) (e : Classes.EqDec A) : Classes.EqDec (binder_annot A). +Proof. ltac:(Equations.Prop.Tactics.eqdec_proof). Qed. + Definition map_binder_annot {A B} (f : A -> B) (b : binder_annot A) : binder_annot B := {| binder_name := f b.(binder_name); binder_relevance := b.(binder_relevance) |}. @@ -86,6 +95,7 @@ Definition eq_binder_annot {A} (b b' : binder_annot A) : Prop := (** Type of annotated names *) Definition aname := binder_annot name. +Instance anqme_eqdec : Classes.EqDec aname := _. Definition string_of_name (na : name) := match na with @@ -104,6 +114,8 @@ Record inductive : Set := mkInd { inductive_mind : kername ; inductive_ind : nat }. Arguments mkInd _%string _%nat. +Derive NoConfusion EqDec for inductive. + Definition string_of_inductive (i : inductive) := string_of_kername (inductive_mind i) ^ "," ^ string_of_nat (inductive_ind i). @@ -116,6 +128,8 @@ Inductive global_reference := | IndRef : inductive -> global_reference | ConstructRef : inductive -> nat -> global_reference. +Derive NoConfusion EqDec for global_reference. + Definition string_of_gref gr : string := match gr with @@ -127,20 +141,10 @@ Definition string_of_gref gr : string := "Constructor " ^ string_of_kername s ^ " " ^ (string_of_nat n) ^ " " ^ (string_of_nat k) end. -Definition kername_eq_dec (k k0 : kername) : {k = k0} + {k <> k0}. -Proof. - repeat (decide equality; eauto with eq_dec). -Defined. +Definition kername_eq_dec (k k0 : kername) : {k = k0} + {k <> k0} := Classes.eq_dec k k0. Hint Resolve kername_eq_dec : eq_dec. -Definition gref_eq_dec (gr gr' : global_reference) : {gr = gr'} + {~ gr = gr'}. -Proof. - decide equality; eauto with eq_dec. - destruct i, i0. - decide equality; eauto with eq_dec. - destruct i, i0. - decide equality; eauto with eq_dec. -Defined. +Definition gref_eq_dec (gr gr' : global_reference) : {gr = gr'} + {~ gr = gr'} := Classes.eq_dec gr gr'. Definition ident_eq (x y : ident) := match string_compare x y with @@ -194,25 +198,25 @@ Proof. now rewrite eq_inductive_refl, !PeanoNat.Nat.eqb_refl. Qed. - - (** The kind of a cast *) Inductive cast_kind : Set := | VmCast | NativeCast | Cast | RevertCast. +Derive NoConfusion EqDec for cast_kind. Inductive recursivity_kind := | Finite (* = inductive *) | CoFinite (* = coinductive *) | BiFinite (* = non-recursive, like in "Record" definitions *). +Derive NoConfusion EqDec for recursivity_kind. (* The kind of a conversion problem *) Inductive conv_pb := | Conv | Cumul. - +Derive NoConfusion EqDec for conv_pb. (* Parametrized by term because term is not yet defined *) Record def term := mkdef { @@ -226,6 +230,10 @@ Arguments dtype {term} _. Arguments dbody {term} _. Arguments rarg {term} _. +Derive NoConfusion for def. +Instance def_eq_dec {A} : Classes.EqDec A -> Classes.EqDec (def A). +Proof. ltac:(Equations.Prop.Tactics.eqdec_proof). Qed. + Definition string_of_def {A} (f : A -> string) (def : def A) := "(" ^ string_of_name (binder_name (dname def)) ^ "," ^ string_of_relevance (binder_relevance (dname def)) @@ -251,7 +259,6 @@ Proof. destruct d; reflexivity. Qed. Definition mfixpoint term := list (def term). - Definition test_def {A} (tyf bodyf : A -> bool) (d : def A) := tyf d.(dtype) && bodyf d.(dbody). diff --git a/template-coq/theories/Universes.v b/template-coq/theories/Universes.v index 2c6b89001..2e759517d 100644 --- a/template-coq/theories/Universes.v +++ b/template-coq/theories/Universes.v @@ -1,5 +1,6 @@ From Coq Require Import MSetList MSetFacts MSetProperties MSetDecide. From MetaCoq.Template Require Import utils BasicAst config. +From Equations Require Import Equations. Local Open Scope nat_scope. Local Open Scope string_scope2. @@ -23,15 +24,26 @@ Inductive universes := | UProp | USProp | UType (i : nat). +Derive NoConfusion EqDec for universes. Class Evaluable (A : Type) := val : valuation -> A -> nat. +(** This inductive classifies which eliminations are allowed for inductive types + in various sorts. *) +Inductive allowed_eliminations : Set := +| IntoSProp +| IntoPropSProp +| IntoSetPropSProp +| IntoAny. +Derive NoConfusion EqDec for allowed_eliminations. + (** Levels are Set or Level or Var *) Module Level. Inductive t_ : Set := | lSet | Level (_ : string) | Var (_ : nat) (* these are debruijn indices *). + Derive NoConfusion EqDec for t_. Definition t := t_. @@ -171,7 +183,7 @@ Qed. Module PropLevel. Inductive t := lSProp | lProp. - + Derive NoConfusion EqDec for t. (* Global Instance PropLevel_Evaluable : Evaluable t := fun v l => match l with lSProp => -1 @@ -299,6 +311,16 @@ Module UnivExprSet := MSetList.MakeWithLeibniz UnivExpr. Module UnivExprSetFact := WFactsOn UnivExpr UnivExprSet. Module UnivExprSetProp := WPropertiesOn UnivExpr UnivExprSet. +(* We have decidable equality w.r.t leibniz equality for sets of levels. + This means universes also have a decidable equality. *) +Instance univexprset_eq_dec : Classes.EqDec UnivExprSet.t. +Proof. + intros p p'. + destruct (UnivExprSet.eq_dec p p'). + - now left; eapply UnivExprSet.eq_leibniz in e. + - right. intros ->. apply n. reflexivity. +Qed. + Module Universe. (** A universe is a list of universe expressions which is: - sorted @@ -307,9 +329,20 @@ Module Universe. Record t0 := { t_set : UnivExprSet.t ; t_ne : UnivExprSet.is_empty t_set = false }. + Derive NoConfusion for t0. + + (** This needs a propositional UIP proof to show that [is_empty = false] is a set *) + Set Equations With UIP. + Instance t0_eqdec : EqDec t0. + Proof. eqdec_proof. Qed. + Inductive t_ := lProp | lSProp | lType (_ : t0). + Derive NoConfusion for t_. + Instance t_eqdec : EqDec t_. + Proof. eqdec_proof. Qed. + Definition t := t_. Coercion t_set : t0 >-> UnivExprSet.t. @@ -1011,10 +1044,12 @@ Qed. Module ConstraintType. Inductive t_ : Set := Le (z : Z) | Eq. + Derive NoConfusion EqDec for t_. + Definition t := t_. Definition eq : t -> t -> Prop := eq. Definition eq_equiv : Equivalence eq := _. - + Definition Le0 := Le 0. Definition Lt := Le 1. @@ -1059,6 +1094,7 @@ End ConstraintType. Module UnivConstraint. Definition t : Set := Level.t * ConstraintType.t * Level.t. + Definition eq : t -> t -> Prop := eq. Definition eq_equiv : Equivalence eq := _. @@ -1117,6 +1153,16 @@ Module ConstraintSet := MSetList.MakeWithLeibniz UnivConstraint. Module ConstraintSetFact := WFactsOn UnivConstraint ConstraintSet. Module ConstraintSetProp := WPropertiesOn UnivConstraint ConstraintSet. +(* Being built up from sorted lists without duplicates, constraint sets have + decidable equality. This is however not used in the development. *) +Set Equations With UIP. +Remark ConstraintSet_EqDec : EqDec ConstraintSet.t. +Proof. + intros p p'. + destruct (ConstraintSet.eq_dec p p'). + - now left; eapply ConstraintSet.eq_leibniz in e. + - right. intros ->. apply n. reflexivity. +Qed. (** {6 Universe instances} *) @@ -1187,6 +1233,7 @@ Module Variance. | Irrelevant : t | Covariant : t | Invariant : t. + Derive NoConfusion EqDec for t. (* val check_subtype : t -> t -> bool *) (* val sup : t -> t -> t *) @@ -1196,6 +1243,8 @@ Inductive universes_decl : Type := | Monomorphic_ctx (ctx : ContextSet.t) | Polymorphic_ctx (cst : AUContext.t). +Derive NoConfusion for universes_decl. + Definition monomorphic_udecl u := match u with | Monomorphic_ctx ctx => ctx @@ -1530,12 +1579,6 @@ Section Univ. (** Elimination restriction *) - Inductive allowed_eliminations : Set := - | IntoSProp - | IntoPropSProp - | IntoSetPropSProp - | IntoAny. - Definition is_allowed_elimination0 φ (into : Universe.t) (allowed : allowed_eliminations) : Prop := forall v, @@ -1563,7 +1606,6 @@ Section Univ. End Univ. - (* This universe is a hack used in plugings to generate fresh universes *) Definition fresh_universe : Universe.t. exact Universe.type0. Qed. (* This level is a hack used in plugings to generate fresh levels *) @@ -1765,6 +1807,7 @@ Definition string_of_universe_instance u := Inductive universes_entry := | Monomorphic_entry (ctx : ContextSet.t) | Polymorphic_entry (names : list name) (ctx : UContext.t). +Derive NoConfusion for universes_entry. Definition universes_entry_of_decl (u : universes_decl) : universes_entry := match u with diff --git a/template-coq/theories/monad_utils.v b/template-coq/theories/monad_utils.v index b7befc6fb..aa7e8fd45 100644 --- a/template-coq/theories/monad_utils.v +++ b/template-coq/theories/monad_utils.v @@ -3,6 +3,7 @@ *) Require Import List. From MetaCoq.Template Require Import All_Forall. +Coercion is_true : bool >-> Sortclass. Import ListNotations. @@ -130,4 +131,19 @@ Fixpoint monad_All2 {T E} {M : Monad T} {M' : MonadExc E T} wrong_sizes Definition monad_prod {T} {M : Monad T} {A B} (x : T A) (y : T B): T (A * B)%type := X <- x ;; Y <- y ;; ret (X, Y). - +(** monadic checks *) +Definition check_dec {T E} {M : Monad T} {M' : MonadExc E T} (e : E) {P} + (H : {P} + {~ P}) : T P + := match H with + | left x => ret x + | right _ => raise e + end. + +Definition check_eq_true {T E} {M : Monad T} {M' : MonadExc E T} (b : bool) (e : E) : T b := + if b return T b then ret eq_refl else raise e. + +Definition check_eq_nat {T E} {M : Monad T} {M' : MonadExc E T} n m (e : E) : T (n = m) := + match PeanoNat.Nat.eq_dec n m with + | left p => ret p + | right p => raise e + end. diff --git a/template-coq/theories/utils/MCPrelude.v b/template-coq/theories/utils/MCPrelude.v index 4760a85b8..b53d98f86 100644 --- a/template-coq/theories/utils/MCPrelude.v +++ b/template-coq/theories/utils/MCPrelude.v @@ -1,4 +1,7 @@ -Require Import Lia. +Require Import String ZArith Lia. +From Equations Require Import Equations. + +Derive NoConfusion EqDec for Strings.Ascii.ascii string positive Z. Declare Scope metacoq_scope. From 2c0b4f0f4b4d05e8ffb69e5a559a94e6fd5528e8 Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Thu, 26 Nov 2020 20:24:52 +0100 Subject: [PATCH 08/70] Rename wf_local_app -> wf_local_app_l --- checker/theories/Weakening.v | 2 +- pcuic/theories/PCUICElimination.v | 2 +- pcuic/theories/PCUICSR.v | 4 ++-- pcuic/theories/PCUICSpine.v | 10 +++++----- pcuic/theories/PCUICTyping.v | 8 ++++---- template-coq/theories/Typing.v | 6 +++--- 6 files changed, 16 insertions(+), 16 deletions(-) diff --git a/checker/theories/Weakening.v b/checker/theories/Weakening.v index 7444ba862..38e81d873 100644 --- a/checker/theories/Weakening.v +++ b/checker/theories/Weakening.v @@ -1112,7 +1112,7 @@ Proof. intros HΣ HΓΓ' * H. pose (weakening_typing Σ Γ [] Γ' t). forward t0; eauto. - forward t0; eauto. now eapply wf_local_app in HΓΓ'. + forward t0; eauto. now eapply wf_local_app_l in HΓΓ'. Qed. Definition fix_context_gen k mfix := diff --git a/pcuic/theories/PCUICElimination.v b/pcuic/theories/PCUICElimination.v index f6a858e40..3f210c7af 100644 --- a/pcuic/theories/PCUICElimination.v +++ b/pcuic/theories/PCUICElimination.v @@ -477,7 +477,7 @@ Proof. unshelve eapply PCUICInductiveInversion.on_constructor_inst in oi; eauto. destruct oi as [oi _]. rewrite !subst_instance_context_app in oi. - now eapply wf_local_app in oi. } + now eapply wf_local_app_l in oi. } apply s. rewrite subst_app_context in X0. diff --git a/pcuic/theories/PCUICSR.v b/pcuic/theories/PCUICSR.v index 82ffc4429..c9d8fcc80 100644 --- a/pcuic/theories/PCUICSR.v +++ b/pcuic/theories/PCUICSR.v @@ -1526,7 +1526,7 @@ Section SRContext. assert (subslet Σ Γ [b] [vdef na b t]). { pose proof (cons_let_def Σ Γ [] [] na b t) as XX. rewrite !subst_empty in XX. apply XX. constructor. - apply wf_local_app in X. inversion X; subst; cbn in *; assumption. + apply wf_local_app_l in X. inversion X; subst; cbn in *; assumption. } constructor; cbn; auto. 1: exists s. 1: unfold PCUICTerm.tSort. @@ -1538,7 +1538,7 @@ Section SRContext. assert (subslet Σ Γ [b] [vdef na b t]). { pose proof (cons_let_def Σ Γ [] [] na b t) as XX. rewrite !subst_empty in XX. apply XX. constructor. - apply wf_local_app in X. inversion X; subst; cbn in *; assumption. } + apply wf_local_app_l in X. inversion X; subst; cbn in *; assumption. } constructor; cbn; auto. exists s. unfold PCUICTerm.tSort. change (tSort s) with (subst [b] #|Γ'| (tSort s)). diff --git a/pcuic/theories/PCUICSpine.v b/pcuic/theories/PCUICSpine.v index 3bdb05f71..314ab52ff 100644 --- a/pcuic/theories/PCUICSpine.v +++ b/pcuic/theories/PCUICSpine.v @@ -298,7 +298,7 @@ Lemma arity_typing_spine {cf:checker_flags} Σ Γ Γ' s inst s' : ∑ instsubst, spine_subst Σ Γ inst instsubst Γ'. Proof. intros wfΣ wfΓ'; revert s inst s'. - assert (wf_local Σ Γ). now apply wf_local_app in wfΓ'. move X after wfΓ'. + assert (wf_local Σ Γ). now apply wf_local_app_l in wfΓ'. move X after wfΓ'. rename X into wfΓ. generalize (le_n #|Γ'|). generalize (#|Γ'|) at 2. @@ -349,7 +349,7 @@ Proof. * apply subslet_app. now rewrite subst_empty. repeat constructor. rewrite app_context_assoc in wfΓ'. simpl in wfΓ'. - apply wf_local_app in wfΓ'. depelim wfΓ'; now rewrite !subst_empty. + apply wf_local_app_l in wfΓ'. depelim wfΓ'; now rewrite !subst_empty. + rewrite PCUICCtxShape.context_assumptions_app /=. depelim Hsp. now eapply cumul_Prod_Sort_inv in c. @@ -388,7 +388,7 @@ Proof. * apply subslet_app => //. repeat constructor. rewrite app_context_assoc in wfΓ'. simpl in wfΓ'. - apply wf_local_app in wfΓ'. depelim wfΓ'. + apply wf_local_app_l in wfΓ'. depelim wfΓ'. rewrite !subst_empty. red in l0. eapply type_Cumul'; eauto. eapply conv_cumul. now symmetry. Qed. @@ -1430,7 +1430,7 @@ Proof. pose proof wf as wf'. rewrite -eql in wf'. rewrite app_context_assoc in wf'. - apply wf_local_app in wf'. depelim wf'. + apply wf_local_app_l in wf'. depelim wf'. eapply (weakening_typing); auto. * rewrite app_length /= Nat.add_1_r in IHc. constructor; auto. @@ -1438,7 +1438,7 @@ Proof. pose proof wf as wf'. rewrite -eql in wf'. rewrite app_context_assoc in wf'. - apply wf_local_app in wf'. depelim wf'. + apply wf_local_app_l in wf'. depelim wf'. rewrite Nat.add_0_r. eapply type_Cumul'. diff --git a/pcuic/theories/PCUICTyping.v b/pcuic/theories/PCUICTyping.v index 0c7d77873..39dcf3aa0 100644 --- a/pcuic/theories/PCUICTyping.v +++ b/pcuic/theories/PCUICTyping.v @@ -555,17 +555,17 @@ Lemma wf_ext_consistent {cf:checker_flags} Σ : Proof. intros [? [? [? [? ?]]]]; assumption. Qed. Hint Resolve wf_ext_consistent : core. -Lemma wf_local_app `{checker_flags} Σ (Γ Γ' : context) : wf_local Σ (Γ ,,, Γ') -> wf_local Σ Γ. +Lemma wf_local_app_l `{checker_flags} Σ (Γ Γ' : context) : wf_local Σ (Γ ,,, Γ') -> wf_local Σ Γ. Proof. induction Γ'. auto. simpl. intros H'; inv H'; eauto. Defined. -Hint Resolve wf_local_app : wf. +Hint Resolve wf_local_app_l : wf. Lemma typing_wf_local `{checker_flags} {Σ} {Γ t T} : Σ ;;; Γ |- t : T -> wf_local Σ Γ. Proof. - induction 1; eauto using wf_local_app. + induction 1; eauto using wf_local_app_l. Defined. Hint Extern 4 (wf_local _ ?Γ) => @@ -1249,7 +1249,7 @@ Section All_local_env. rewrite -skipn_app. now apply All_local_env_skipn. replace (n - #|Γ'|) with 0 by lia. now rewrite skipn_0. rewrite List.skipn_all2. lia. - now eapply wf_local_app in wf. + now eapply wf_local_app_l in wf. Qed. Definition on_local_decl_glob (P : term -> option term -> Type) d := diff --git a/template-coq/theories/Typing.v b/template-coq/theories/Typing.v index 456768237..07d592615 100644 --- a/template-coq/theories/Typing.v +++ b/template-coq/theories/Typing.v @@ -1019,17 +1019,17 @@ Proof. Defined. -Lemma wf_local_app `{checker_flags} Σ (Γ Γ' : context) : wf_local Σ (Γ ,,, Γ') -> wf_local Σ Γ. +Lemma wf_local_app_l `{checker_flags} Σ (Γ Γ' : context) : wf_local Σ (Γ ,,, Γ') -> wf_local Σ Γ. Proof. induction Γ'. auto. simpl. intros H'; inv H'; eauto. Defined. -Hint Resolve wf_local_app : wf. +Hint Resolve wf_local_app_l : wf. Lemma typing_wf_local `{checker_flags} {Σ} {Γ t T} : Σ ;;; Γ |- t : T -> wf_local Σ Γ. Proof. - induction 1; eauto using wf_local_app. + induction 1; eauto using wf_local_app_l. Defined. Hint Resolve typing_wf_local : wf. From 1aee3df5121b3926f3775062f3aa76d4d86bfeb9 Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Thu, 26 Nov 2020 20:30:26 +0100 Subject: [PATCH 09/70] Flip app/app_inv naming for wf_local_rel/All_local_env/wf_local --- checker/theories/Substitution.v | 4 +- checker/theories/Weakening.v | 6 +- erasure/theories/ESubstitution.v | 14 ++--- erasure/theories/ErasureCorrectness.v | 16 +++--- pcuic/theories/PCUICArities.v | 14 ++--- pcuic/theories/PCUICCanonicity.v | 14 +++-- pcuic/theories/PCUICContexts.v | 6 +- pcuic/theories/PCUICElimination.v | 6 +- pcuic/theories/PCUICInductiveInversion.v | 10 ++-- pcuic/theories/PCUICInductives.v | 10 ++-- pcuic/theories/PCUICPrincipality.v | 8 +-- pcuic/theories/PCUICSpine.v | 18 +++--- pcuic/theories/PCUICSubstitution.v | 24 ++++---- pcuic/theories/PCUICTyping.v | 56 +++++++++++++------ pcuic/theories/PCUICWeakening.v | 4 +- safechecker/theories/PCUICSafeChecker.v | 20 +++---- template-coq/_PluginProject | 4 ++ .../gen-src/metacoq_template_plugin.mlpack | 6 +- template-coq/theories/Extraction.v | 1 + template-coq/theories/Typing.v | 5 +- 20 files changed, 137 insertions(+), 109 deletions(-) diff --git a/checker/theories/Substitution.v b/checker/theories/Substitution.v index 8c5824a71..7b6ae4a7b 100644 --- a/checker/theories/Substitution.v +++ b/checker/theories/Substitution.v @@ -1644,7 +1644,7 @@ Lemma substitution_All_local_env_over `{cf : checker_flags} {Σ Γ Γ' Δ s} : Proof. intros wfΣ wfΓ. induction Δ; simpl; intros Hwf. - intros _. clear Hwf. simpl in wfΓ. now eapply All_local_env_app in wfΓ. + intros _. clear Hwf. simpl in wfΓ. now eapply All_local_env_app_inv in wfΓ. depelim Hwf; rewrite subst_context_snoc; simpl; constructor. eapply IHΔ; eauto. red. exists (tu.π1). simpl. @@ -1880,7 +1880,7 @@ Proof. pose proof (subst_destArity [] B s #|Δ|). rewrite Hd in H0. rewrite {}H0; auto. split; auto. - apply All_local_env_app_inv; intuition auto. + apply All_local_env_app; intuition auto. clear -sub a. induction ctx; try constructor; depelim a. -- rewrite subst_context_snoc. diff --git a/checker/theories/Weakening.v b/checker/theories/Weakening.v index 38e81d873..fa2447cfa 100644 --- a/checker/theories/Weakening.v +++ b/checker/theories/Weakening.v @@ -1074,7 +1074,7 @@ Proof. eapply typing_wf in t1. intuition. auto. eapply typing_wf in t1. intuition. auto. constructor. } split; auto. - apply All_local_env_app_inv; intuition auto. + apply All_local_env_app; intuition auto. clear -wf a. induction ctx; try constructor; depelim a. -- rewrite lift_context_snoc. @@ -1132,10 +1132,10 @@ Proof. generalize (@nil context_decl) as Δ. rewrite /fix_context_gen. intros Δ wfΔ. - eapply All_local_env_app_inv. split; auto. + eapply All_local_env_app. split; auto. induction a in Δ, wfΔ |- *; simpl; auto. constructor. simpl. - eapply All_local_env_app_inv. split; auto. + eapply All_local_env_app. split; auto. constructor. constructor. simpl. destruct p as [s Hs]. exists s. eapply (weakening Σ Γ Δ _ (tSort s)); auto. diff --git a/erasure/theories/ESubstitution.v b/erasure/theories/ESubstitution.v index b3c8f6801..fac131d22 100644 --- a/erasure/theories/ESubstitution.v +++ b/erasure/theories/ESubstitution.v @@ -129,7 +129,7 @@ Lemma Is_type_weakening: Proof. intros. destruct X2 as (T & ? & ?). eexists. split. eapply weakening_typing; eauto. - now apply All_local_env_app in X1. + now apply All_local_env_app_inv in X1. destruct s as [? | [u []]]. - left. clear - i. generalize (#|Γ''|), (#|Γ'|). induction T; cbn in *; intros; try now inv i. @@ -137,7 +137,7 @@ Proof. + now eapply IHT3. - right. exists u. split; eauto. eapply weakening_typing in t1; eauto. - now apply All_local_env_app in X1. + now apply All_local_env_app_inv in X1. Qed. Require Import MetaCoq.PCUIC.PCUICInversion. @@ -183,7 +183,7 @@ Proof. rewrite lift_context_snoc0, <- plus_n_O in *. eapply H1; eauto. cbn. econstructor. eauto. cbn. exists s1. eapply weakening_typing with (T := tSort s1); eauto. - now apply All_local_env_app in X2. + now apply All_local_env_app_inv in X2. - econstructor. + eapply H0; eauto. + pose proof (H1 Γ (PCUICAst.vdef n b b_ty :: Γ') Γ''). @@ -191,8 +191,8 @@ Proof. eapply H2; eauto. cbn. econstructor. eauto. cbn. 2: cbn; eapply weakening_typing; eauto. eapply weakening_typing in X0; eauto. - now apply All_local_env_app in X3. - now apply All_local_env_app in X3. + now apply All_local_env_app_inv in X3. + now apply All_local_env_app_inv in X3. - econstructor. + eauto. + eapply H4; eauto. @@ -210,7 +210,7 @@ Proof. eapply (All_impl X1). firstorder. eapply weakening_typing in HT; auto. - 2:{ apply All_local_env_app in X2 as [X2 _]. eapply X2. } + 2:{ apply All_local_env_app_inv in X2 as [X2 _]. eapply X2. } cbn in HT. eapply inversion_Fix in HT as (? & ? & ? & ? & ? & ? & ?) ; auto. clear a0 c. @@ -242,7 +242,7 @@ Proof. eapply (All_impl X1). firstorder. eapply weakening_typing in HT; auto. - 2:{ apply All_local_env_app in X2 as [X2 _]. eapply X2. } + 2:{ apply All_local_env_app_inv in X2 as [X2 _]. eapply X2. } cbn in HT. eapply inversion_CoFix in HT as (? & ? & ? & ? & ? & ? & ?) ; auto. clear a0 c. diff --git a/erasure/theories/ErasureCorrectness.v b/erasure/theories/ErasureCorrectness.v index cad838654..e490a3f9a 100644 --- a/erasure/theories/ErasureCorrectness.v +++ b/erasure/theories/ErasureCorrectness.v @@ -143,8 +143,8 @@ Proof. eapply typing_wf_local in a1. subst types. 2:eauto. - eapply All_local_env_app_inv. - eapply All_local_env_app in a1. intuition auto. + eapply All_local_env_app. + eapply All_local_env_app_inv in a1. intuition auto. (* clear -wfΣ X2 a2 b4 X1. *) eapply All_local_env_impl; eauto. simpl; intros. @@ -154,7 +154,7 @@ Proof. eapply typing_wf_local in X3. eapply PCUICSafeChecker.wf_local_app_inv. eauto. eapply wf_local_rel_local in X3. - eapply wf_local_rel_app in X3 as []. rewrite app_context_nil_l in w0. + eapply wf_local_rel_app_inv in X3 as []. rewrite app_context_nil_l in w0. eapply wf_local_rel_conv; eauto. destruct X3. exists x0. eapply PCUICContextConversion.context_conversion with (Γ ,,, Γ0); eauto. @@ -163,7 +163,7 @@ Proof. eapply typing_wf_local in t0. eapply PCUICSafeChecker.wf_local_app_inv. eauto. eapply wf_local_rel_local in t0. - eapply wf_local_rel_app in t0 as []. rewrite app_context_nil_l in w0. + eapply wf_local_rel_app_inv in t0 as []. rewrite app_context_nil_l in w0. eapply wf_local_rel_conv; eauto. - econstructor. @@ -176,8 +176,8 @@ Proof. eapply typing_wf_local in a0. subst types. 2:eauto. - eapply All_local_env_app_inv. - eapply All_local_env_app in a0. intuition auto. + eapply All_local_env_app. + eapply All_local_env_app_inv in a0. intuition auto. (* clear -wfΣ X2 a2 b4 X1. *) eapply All_local_env_impl; eauto. simpl; intros. @@ -187,7 +187,7 @@ Proof. eapply typing_wf_local in X3. eapply PCUICSafeChecker.wf_local_app_inv. eauto. eapply wf_local_rel_local in X3. - eapply wf_local_rel_app in X3 as []. rewrite app_context_nil_l in w0. + eapply wf_local_rel_app_inv in X3 as []. rewrite app_context_nil_l in w0. eapply wf_local_rel_conv; eauto. @@ -198,7 +198,7 @@ Proof. eapply typing_wf_local in t0. eapply PCUICSafeChecker.wf_local_app_inv. eauto. eapply wf_local_rel_local in t0. - eapply wf_local_rel_app in t0 as []. rewrite app_context_nil_l in w0. + eapply wf_local_rel_app_inv in t0 as []. rewrite app_context_nil_l in w0. eapply wf_local_rel_conv; eauto. Qed. diff --git a/pcuic/theories/PCUICArities.v b/pcuic/theories/PCUICArities.v index 8e5ac2e1b..3f006f21a 100644 --- a/pcuic/theories/PCUICArities.v +++ b/pcuic/theories/PCUICArities.v @@ -267,7 +267,7 @@ Proof. eapply (type_mkProd_or_LetIn _ _ {| decl_body := None |}) => /=; eauto. econstructor; eauto with pcuic. eapply typing_wf_local in Ht. - depelim Ht; eapply All_local_env_app in Ht; intuition auto. + depelim Ht; eapply All_local_env_app_inv in Ht; intuition auto. now rewrite sort_of_product_twice. Qed. @@ -594,17 +594,17 @@ Proof. + rewrite it_mkProd_or_LetIn_app. destruct x as [na [b|] ty]; cbn; move=> H. * apply inversion_LetIn in H as (s1 & A & H0 & H1 & H2 & H3); auto. - eapply All_local_env_app_inv; split; pcuic. - eapply All_local_env_app_inv. split. repeat constructor. now exists s1. + eapply All_local_env_app; split; pcuic. + eapply All_local_env_app. split. repeat constructor. now exists s1. auto. apply IHΔ in H2. - eapply All_local_env_app in H2. intuition auto. + eapply All_local_env_app_inv in H2. intuition auto. eapply All_local_env_impl; eauto. simpl. intros. now rewrite app_context_assoc. * apply inversion_Prod in H as (s1 & A & H0 & H1 & H2); auto. - eapply All_local_env_app_inv; split; pcuic. - eapply All_local_env_app_inv. split. repeat constructor. now exists s1. + eapply All_local_env_app; split; pcuic. + eapply All_local_env_app. split. repeat constructor. now exists s1. apply IHΔ in H1. - eapply All_local_env_app in H1. intuition auto. + eapply All_local_env_app_inv in H1. intuition auto. eapply All_local_env_impl; eauto. simpl. intros. now rewrite app_context_assoc. Qed. diff --git a/pcuic/theories/PCUICCanonicity.v b/pcuic/theories/PCUICCanonicity.v index 02173dd00..d0db7188f 100644 --- a/pcuic/theories/PCUICCanonicity.v +++ b/pcuic/theories/PCUICCanonicity.v @@ -285,8 +285,8 @@ Section Spines. * elimtype False; depelim ass. * simpl. rewrite !it_mkProd_or_LetIn_app /= /mkProd_or_LetIn /= //. intros wf sp; depelim sp. rewrite nth_error_nil //. - pose proof (All_local_env_app _ _ _ wf) as [_ wfty]. - eapply All_local_env_app in wfty as [wfty _]. depelim wfty. + pose proof (wf_local_app_inv wf) as [_ wfty]. + eapply wf_local_rel_app_inv in wfty as [wfty _]. depelim wfty. eapply cumul_Prod_inv in c as [dom codom]. 2-3:pcuic. assert (Σ ;;; Γ |- hd : ty). { eapply type_Cumul'; pcuic. eapply conv_cumul. now symmetry. } @@ -410,8 +410,8 @@ Section Spines. * elimtype False; depelim ass. * simpl. rewrite !it_mkProd_or_LetIn_app /= /mkProd_or_LetIn /= //. intros wf sp. - pose proof (All_local_env_app _ _ _ wf) as [_ wfty]. - eapply All_local_env_app in wfty as [wfty _]. depelim wfty. + pose proof (wf_local_app_inv wf) as [_ wfty]. + eapply All_local_env_app_inv in wfty as [wfty _]. depelim wfty. intros Hargs. eapply nth_error_None in Hargs. len in Hargs. len; simpl. depelim sp. @@ -1044,8 +1044,10 @@ Section WeakNormalization. clear wh_normal_empty_gen. now specialize (wh_neutral_empty_gen _ tyarg eq_refl). - move/andP: cl => [/andP[_ clc] _]. - eapply inversion_Case in typed; firstorder eauto. - - eapply inversion_Proj in typed; firstorder auto. + eapply inversion_Case in typed as (? & ? & ? & ? & ? & ? & ? & ? & ? & ? & ? & ? & ? & ? & ? & ? & ?); auto. + eapply wh_neutral_empty_gen; eauto. + - eapply inversion_Proj in typed as (? & ? & ? & ? & ? & ? & ? & ? & ?); auto. + eapply wh_neutral_empty_gen; eauto. - eapply wh_neutral_empty_gen in w; eauto. - eapply inversion_Sort in typed as (? & ? & ?); auto. eapply invert_cumul_sort_l in c as (? & ? & ?); auto. diff --git a/pcuic/theories/PCUICContexts.v b/pcuic/theories/PCUICContexts.v index 39b491063..97fa3f68b 100644 --- a/pcuic/theories/PCUICContexts.v +++ b/pcuic/theories/PCUICContexts.v @@ -514,7 +514,7 @@ Proof. intros wfΣ. induction Γ in Δ |- *; simpl; auto. intros wfΓ wfΔ. depelim wfΓ; simpl. - - apply IHΓ; auto. eapply All_local_env_app_inv. split; auto. + - apply IHΓ; auto. eapply All_local_env_app. split; auto. repeat constructor; auto. eapply All_local_env_impl; eauto. simpl; intros. unfold lift_typing in X |- *. @@ -543,8 +543,8 @@ Lemma wf_local_smash_end {cf:checker_flags} Σ Γ Δ : wf_local Σ (Γ ,,, Δ) -> wf_local Σ (Γ ,,, smash_context [] Δ). Proof. intros wfΣ wf. - apply All_local_env_app_inv. split. - now apply All_local_env_app in wf. + apply All_local_env_app. split. + now apply All_local_env_app_inv in wf. eapply wf_local_rel_smash_context; auto. Qed. diff --git a/pcuic/theories/PCUICElimination.v b/pcuic/theories/PCUICElimination.v index 3f210c7af..723d6039b 100644 --- a/pcuic/theories/PCUICElimination.v +++ b/pcuic/theories/PCUICElimination.v @@ -297,7 +297,7 @@ Proof. rewrite -{1}(subst_empty 0 b). repeat (constructor; auto). rewrite !subst_empty. eapply typing_wf_local in Ht2. - rewrite app_context_assoc in Ht2. eapply All_local_env_app in Ht2 as [Ht2 _]. + rewrite app_context_assoc in Ht2. eapply All_local_env_app_inv in Ht2 as [Ht2 _]. depelim Ht2. apply l0. now rewrite app_context_assoc in Ht2. * intros mdecl idec decli oib. @@ -773,7 +773,7 @@ Proof. now apply is_prop_gt in lt. - rewrite app_context_assoc in eq. pose proof eq as eq'. - eapply All_local_env_app in eq' as [wfΓ wf']. depelim wfΓ; + eapply All_local_env_app_inv in eq' as [wfΓ wf']. depelim wfΓ; rewrite it_mkProd_or_LetIn_app /= /mkProd_or_LetIn /= in X2 |- *. + eapply invert_cumul_prod_l in X2 as (na' & A & B' & (red & conv) & cum). eapply subject_reduction in X1. 3:eassumption. all:auto. @@ -837,7 +837,7 @@ Proof. apply is_prop_gt in lt; auto. - rewrite app_context_assoc in eq. pose proof eq as eq'. - eapply All_local_env_app in eq' as [wfΓ wf']. depelim wfΓ; + eapply All_local_env_app_inv in eq' as [wfΓ wf']. depelim wfΓ; rewrite it_mkProd_or_LetIn_app /= /mkProd_or_LetIn /= in X2 |- *. + eapply invert_cumul_prod_r in X2 as (na' & A' & B' & (red & conv) & cum). eapply subject_reduction in X1. 3:eassumption. all:auto. diff --git a/pcuic/theories/PCUICInductiveInversion.v b/pcuic/theories/PCUICInductiveInversion.v index 75b9b34ed..0dce0721e 100644 --- a/pcuic/theories/PCUICInductiveInversion.v +++ b/pcuic/theories/PCUICInductiveInversion.v @@ -588,7 +588,7 @@ Proof. apply weaken_wf_local => //. rewrite [_ ,,, _]app_context_assoc in wfΓ. - eapply All_local_env_app in wfΓ as [? ?]. + eapply All_local_env_app_inv in wfΓ as [? ?]. apply on_minductive_wf_params_indices => //. pcuic. Qed. @@ -1701,7 +1701,7 @@ Proof. specialize (X Δ ltac:(len; lia) _ _ H). simpl; autorewrite with len in X |- *. destruct X; split; auto. simpl. - eapply All_local_env_app_inv; split. + eapply All_local_env_app; split. constructor; auto. eapply (All_local_env_impl _ _ _ a). intros; auto. now rewrite app_context_assoc. simpl. @@ -2190,7 +2190,7 @@ Proof. rewrite -it_mkProd_or_LetIn_app in cpos. eapply positive_cstr_it_mkProd_or_LetIn in cpos as [hpars _]. rewrite smash_context_app_expand in hpars. - eapply All_local_env_app in hpars as [_hpars hargs]. + eapply All_local_env_app_inv in hpars as [_hpars hargs]. rewrite expand_lets_smash_context /= expand_lets_k_ctx_nil /= in hargs. eapply positive_cstr_closed_args_subst_arities in hargs; eauto. split. @@ -3409,7 +3409,7 @@ Proof. eapply cumul_ctx_subst_instance => //. rewrite -app_context_assoc. eapply weaken_wf_local; eauto. rewrite !subst_instance_context_app in wfargs. - now eapply All_local_env_app in wfargs as [wfargs _]. + now eapply All_local_env_app_inv in wfargs as [wfargs _]. } { rewrite /pargctx. rewrite (smash_context_subst []). @@ -3975,7 +3975,7 @@ Proof. eapply (subst_sorts_local_ctx) in X; simpl in *; eauto. 3:{ eapply subslet_inds; eauto. } 2:{ rewrite app_context_nil_l. - now eapply All_local_env_app in wf as [? ?]. } + now eapply All_local_env_app_inv in wf as [? ?]. } simpl in X. len in X. eapply weaken_sorts_local_ctx in X. 2:eauto. 2:eapply typing_wf_local; eauto. rewrite app_context_nil_l in X. diff --git a/pcuic/theories/PCUICInductives.v b/pcuic/theories/PCUICInductives.v index 0761f8d14..3884bf64b 100644 --- a/pcuic/theories/PCUICInductives.v +++ b/pcuic/theories/PCUICInductives.v @@ -589,7 +589,7 @@ Proof. (arities_context (ind_bodies mdecl))). { eapply wf_arities_context; eauto. } eapply PCUICClosed.sorts_local_ctx_All_local_env in wfargs. - 2:{ eapply All_local_env_app_inv. split; auto. + 2:{ eapply All_local_env_app. split; auto. red in onpars. eapply (All_local_env_impl _ _ _ onpars). intros. destruct T; simpl in *. - eapply weaken_ctx; auto. @@ -676,7 +676,7 @@ Proof. eapply declared_minductive_closed_inds. 2:destruct isdecl as [ [] ?]; eauto. eauto. } rewrite -app_assoc in wfl. - apply All_local_env_app in wfl as [wfctx wfsargs]. + apply All_local_env_app_inv in wfl as [wfctx wfsargs]. rewrite smash_context_app in Heq'. rewrite smash_context_acc in Heq'. rewrite nth_error_app_lt in Heq'. @@ -717,8 +717,8 @@ Proof. { assert(wf_local (Σ.1, ind_universes mdecl) (arities_context (ind_bodies mdecl) ,,, ind_params mdecl ,,, smash_context [] (cshape_args c))). - apply All_local_env_app_inv; split; auto. - now apply All_local_env_app in wfargs as [wfindpars wfargs]. + apply All_local_env_app; split; auto. + now apply All_local_env_app_inv in wfargs as [wfindpars wfargs]. apply wf_local_rel_smash_context; auto. eapply closed_wf_local in X0; auto. eapply (closedn_ctx_decl (n:=idx)) in X0; eauto. @@ -1242,7 +1242,7 @@ Proof. rewrite subst_instance_context_length in subp, suba. subst parctx argctx. repeat split; eauto; rewrite ?subst_instance_context_length => //. - rewrite app_context_assoc in wfcodom. now apply All_local_env_app in wfcodom as [? ?]. + rewrite app_context_assoc in wfcodom. now apply All_local_env_app_inv in wfcodom as [? ?]. simpl. eapply substitution_wf_local; eauto. now rewrite app_context_assoc in wfcodom. unshelve eapply on_inductive_inst in declm; pcuic. diff --git a/pcuic/theories/PCUICPrincipality.v b/pcuic/theories/PCUICPrincipality.v index 214be6a56..50151457a 100644 --- a/pcuic/theories/PCUICPrincipality.v +++ b/pcuic/theories/PCUICPrincipality.v @@ -181,7 +181,7 @@ Section Principality. econstructor. eapply type_reduction; eauto. eapply type_Cumul'; eauto. 2:transitivity dom; auto; now apply conv_cumul. - eapply type_reduction in t0. 3:eapply redA. 2:auto. + eapply type_reduction in t0. 2:eapply redA. eapply validity in t0; auto. eapply isType_tProd in t0 as [? ?]; eauto. eapply typing_wf_local; eauto. @@ -278,7 +278,7 @@ Section Principality. solve_discr. etransitivity; eauto. assert (consistent_instance_ext Σ (ind_universes x0) u'). - { eapply type_reduction in t1. 3:eapply redr. all:pcuic. + { eapply type_reduction in t1. 2:eapply redr. eapply validity in t1; eauto. destruct t1 as [s Hs]. eapply invert_type_mkApps_ind in Hs. intuition eauto. all:auto. eapply d. } @@ -296,7 +296,7 @@ Section Principality. (projection_context x0 x1 ind x2) []); auto. eapply (projection_subslet _ _ _ _ _ _ (ind, k, pars)); eauto. simpl. eapply type_reduction; eauto. simpl. - eapply type_reduction in t0. 3:eapply redr. eapply validity; eauto. auto. + eapply type_reduction in t0. 2:eapply redr. eapply validity; eauto. eapply (projection_subslet _ _ _ _ _ _ (ind, k, pars)); eauto. simpl. eapply validity; eauto. constructor; auto. now apply All2_rev. @@ -309,7 +309,7 @@ Section Principality. eapply (wf_projection_context _ (p:=(ind, k, pars))); pcuic. eapply (projection_subslet _ _ _ _ _ _ (ind, k, pars)); eauto. simpl. eapply type_reduction; eauto. simpl. - eapply type_reduction in t0. 3:eapply redr. all:eauto. + eapply type_reduction in t0. 2:eapply redr. eapply validity; eauto. rewrite e0 in redu'. unshelve epose proof (projection_cumulative_indices wfΣ d _ H H0 redu'). diff --git a/pcuic/theories/PCUICSpine.v b/pcuic/theories/PCUICSpine.v index 314ab52ff..4fd78d885 100644 --- a/pcuic/theories/PCUICSpine.v +++ b/pcuic/theories/PCUICSpine.v @@ -325,12 +325,12 @@ Proof. specialize (IHn (subst_context [b] 0 l)). forward IHn. { rewrite app_context_assoc in wfΓ'. - apply All_local_env_app in wfΓ' as [wfb wfa]. + apply All_local_env_app_inv in wfΓ' as [wfb wfa]. depelim wfb. eapply substitution_wf_local. eauto. epose proof (cons_let_def Σ Γ [] [] na b ty ltac:(constructor)). rewrite !subst_empty in X. eapply X. auto. - eapply All_local_env_app_inv; split. + eapply All_local_env_app; split. constructor; auto. apply wfa. } forward IHn by rewrite subst_context_length; lia. specialize (IHn s inst s' Hsp). @@ -359,14 +359,14 @@ Proof. specialize (IHn (subst_context [hd] 0 l)). forward IHn. { rewrite app_context_assoc in wfΓ'. - apply All_local_env_app in wfΓ' as [wfb wfa]; eauto. + apply All_local_env_app_inv in wfΓ' as [wfb wfa]; eauto. depelim wfb. eapply substitution_wf_local. auto. constructor. constructor. rewrite subst_empty. eapply type_Cumul'. eapply t. eapply l0. eapply conv_cumul; auto. now symmetry. - eapply All_local_env_app_inv; eauto; split. + eapply All_local_env_app; eauto; split. constructor; eauto. eapply isType_tProd in i; intuition eauto. } forward IHn by rewrite subst_context_length; lia. specialize (IHn s tl s'). @@ -650,7 +650,7 @@ Proof. rewrite firstn_0 in csr => //. rewrite app_nil_r in csr. eapply subslet_app_inv in subs as [sl sr]. split; split; auto. rewrite app_context_assoc in wfcodom. - now eapply All_local_env_app in wfcodom as [? ?]. + now eapply All_local_env_app_inv in wfcodom as [? ?]. eapply substitution_wf_local; eauto. now rewrite app_context_assoc in wfcodom. Qed. @@ -1721,8 +1721,8 @@ Proof. * eapply subslet_app => //. eapply sps. rewrite -{1}(subst_empty 0 b). repeat constructor. rewrite !subst_empty. - eapply All_local_env_app in wfΓΔ as [_ wf]. - eapply All_local_env_app in wf as [wfd _]. + eapply All_local_env_app_inv in wfΓΔ as [_ wf]. + eapply All_local_env_app_inv in wf as [wfd _]. depelim wfd. apply l0. * rewrite subst_app_simpl. move: (context_subst_length sps). @@ -1747,7 +1747,7 @@ Proof. 2:{ eauto. } forward X. { pose proof wfΓΔ as wfΓΔ'. - rewrite app_context_assoc in wfΓΔ'. eapply All_local_env_app in wfΓΔ' as [wfΓΔ' _]. + rewrite app_context_assoc in wfΓΔ'. eapply All_local_env_app_inv in wfΓΔ' as [wfΓΔ' _]. eapply (isType_subst wfΣ wfΓΔ') in wat''; eauto. 2:{ repeat constructor. now rewrite subst_empty. } now rewrite subst_it_mkProd_or_LetIn Nat.add_0_r in wat''. } @@ -1889,7 +1889,7 @@ Proof. simpl. rewrite smash_context_acc. simpl. auto. auto. } split; auto. - - eapply All_local_env_app_inv; split; auto. + - eapply All_local_env_app; split; auto. eapply wf_local_rel_smash_context; auto. - induction inst_subslet0 in inst, inst_ctx_subst0, spine_codom_wf0 |- *. depelim inst_ctx_subst0. diff --git a/pcuic/theories/PCUICSubstitution.v b/pcuic/theories/PCUICSubstitution.v index 1fd828974..2a4f0d7e5 100644 --- a/pcuic/theories/PCUICSubstitution.v +++ b/pcuic/theories/PCUICSubstitution.v @@ -2371,20 +2371,20 @@ Proof. - assert (wf_local Σ (Γ ,,, subst_context s 0 Δ ,,, subst_context s #|Δ| (fix_context mfix))). subst types. - apply All_local_env_app in X as [X Hfixc]. - apply All_local_env_app_inv. intuition. + apply All_local_env_app_inv in X as [X Hfixc]. + apply All_local_env_app. intuition. revert Hfixc. clear X0 X H. induction 1; simpl; auto. + destruct t0 as [u [Ht IHt]]. specialize (IHt Γ Γ' (Δ ,,, Γ0) s sub). forward IHt. now rewrite app_context_assoc. rewrite app_context_length subst_context_app app_context_assoc Nat.add_0_r in IHt. unfold snoc; rewrite subst_context_snoc; econstructor; auto. exists u. - apply IHt; apply All_local_env_app_inv; intuition. + apply IHt; apply All_local_env_app; intuition. + destruct t0 as [Ht IHt]. specialize (IHt Γ Γ' (Δ ,,, Γ0) s sub). forward IHt. now rewrite app_context_assoc. rewrite app_context_length subst_context_app app_context_assoc Nat.add_0_r in IHt. unfold snoc; rewrite subst_context_snoc; econstructor; auto; - apply IHt; apply All_local_env_app_inv; intuition. + apply IHt; apply All_local_env_app; intuition. + erewrite map_dtype. eapply type_Fix. * rewrite nth_error_map H. reflexivity. * now rewrite subst_fix_context. @@ -2405,20 +2405,20 @@ Proof. - assert (wf_local Σ (Γ ,,, subst_context s 0 Δ ,,, subst_context s #|Δ| (fix_context mfix))). subst types. - apply All_local_env_app in X as [X Hfixc]. - apply All_local_env_app_inv. intuition. + apply All_local_env_app_inv in X as [X Hfixc]. + apply All_local_env_app. intuition. revert Hfixc. clear X0 X H. induction 1; simpl; auto. + destruct t0 as [u [Ht IHt]]. specialize (IHt Γ Γ' (Δ ,,, Γ0) s sub). forward IHt. now rewrite app_context_assoc. rewrite app_context_length subst_context_app app_context_assoc Nat.add_0_r in IHt. unfold snoc; rewrite subst_context_snoc; econstructor; auto. exists u. - apply IHt; apply All_local_env_app_inv; intuition. + apply IHt; apply All_local_env_app; intuition. + destruct t0 as [Ht IHt]. specialize (IHt Γ Γ' (Δ ,,, Γ0) s sub). forward IHt. now rewrite app_context_assoc. rewrite app_context_length subst_context_app app_context_assoc Nat.add_0_r in IHt. unfold snoc; rewrite subst_context_snoc; econstructor; auto; - apply IHt; apply All_local_env_app_inv; intuition. + apply IHt; apply All_local_env_app; intuition. + erewrite map_dtype. eapply type_CoFix. * rewrite nth_error_map H. reflexivity. * now rewrite subst_fix_context. @@ -2444,7 +2444,7 @@ Proof. pose proof (subst_destArity [] B s #|Δ|). rewrite Hd in H. rewrite H. clear H. split; auto. - apply All_local_env_app_inv; intuition auto. + apply All_local_env_app; intuition auto. clear -sub wfsubs a. induction ctx; try constructor; depelim a. -- rewrite subst_context_snoc. @@ -2455,7 +2455,7 @@ Proof. specialize (t0 _ _ (Δ ,,, ctx) _ sub). forward t0. now rewrite app_context_assoc. simpl in t0. forward t0. rewrite subst_context_app app_context_assoc Nat.add_0_r. - apply All_local_env_app_inv. split; auto. + apply All_local_env_app. split; auto. eapply IHctx. eapply a. now rewrite subst_context_app Nat.add_0_r app_context_assoc app_length in t0. -- rewrite subst_context_snoc. @@ -2466,7 +2466,7 @@ Proof. specialize (t0 _ _ (Δ ,,, ctx) _ sub). forward t0. now rewrite app_context_assoc. simpl in t0. forward t0. rewrite subst_context_app app_context_assoc Nat.add_0_r. - apply All_local_env_app_inv. split; auto. + apply All_local_env_app. split; auto. eapply IHctx. eapply a. now rewrite subst_context_app Nat.add_0_r app_context_assoc app_length in t0. + right; exists u; intuition eauto. @@ -2490,7 +2490,7 @@ Proof. - induction Δ. - + clear X. simpl in *. now apply All_local_env_app in wfΓ0. + + clear X. simpl in *. now apply All_local_env_app_inv in wfΓ0. + rewrite subst_context_snoc. depelim X; simpl; econstructor; eauto. diff --git a/pcuic/theories/PCUICTyping.v b/pcuic/theories/PCUICTyping.v index 39dcf3aa0..85d7372c6 100644 --- a/pcuic/theories/PCUICTyping.v +++ b/pcuic/theories/PCUICTyping.v @@ -604,7 +604,7 @@ Lemma type_Prop `{checker_flags} Σ : Σ ;;; [] |- tSort Universe.lProp : tSort Defined. Lemma env_prop_sigma `{checker_flags} P PΓ : env_prop P PΓ -> - forall Σ (wfΣ : wf Σ), Forall_decls_typing P Σ. + forall (Σ : global_env) (wfΣ : wf Σ), Forall_decls_typing P Σ. Proof. intros. red in X. eapply (X (empty_ext Σ)). apply wfΣ. @@ -622,7 +622,7 @@ Proof. Qed. Lemma size_wf_local_app `{checker_flags} {Σ} (Γ Γ' : context) (Hwf : wf_local Σ (Γ ,,, Γ')) : - wf_local_size Σ (@typing_size _) _ (wf_local_app _ _ _ Hwf) <= + wf_local_size Σ (@typing_size _) _ (wf_local_app_l _ _ _ Hwf) <= wf_local_size Σ (@typing_size _) _ Hwf. Proof. induction Γ' in Γ, Hwf |- *; try lia. simpl. lia. @@ -1130,7 +1130,7 @@ Section All_local_env. apply IHX. simpl in *. lia. Qed. - Lemma lookup_on_global_env P Σ c decl : + Lemma lookup_on_global_env P (Σ : global_env) c decl : on_global_env P Σ -> lookup_env Σ c = Some decl -> { Σ' & { wfΣ' : on_global_env P Σ'.1 & on_global_decl P Σ' c decl } }. @@ -1143,6 +1143,15 @@ Section All_local_env. Qed. Lemma All_local_env_app (P : context -> term -> option term -> Type) l l' : + All_local_env P l * All_local_env (fun Γ t T => P (l ,,, Γ) t T) l' -> + All_local_env P (l ,,, l'). + Proof. + induction l'; simpl; auto. intuition. + intuition. destruct a. destruct decl_body. + inv b. econstructor; eauto. inv b; econstructor; eauto. + Qed. + + Lemma All_local_env_app_inv (P : context -> term -> option term -> Type) l l' : All_local_env P (l ,,, l') -> All_local_env P l * All_local_env (fun Γ t T => P (l ,,, Γ) t T) l'. Proof. @@ -1161,12 +1170,12 @@ Section All_local_env. * apply X1. * apply X2. Qed. - - Definition wf_local_rel_app {Σ Γ1 Γ2 Γ3} : + + Definition wf_local_rel_app_inv {Σ Γ1 Γ2 Γ3} : wf_local_rel Σ Γ1 (Γ2 ,,, Γ3) -> wf_local_rel Σ Γ1 Γ2 * wf_local_rel Σ (Γ1 ,,, Γ2) Γ3. Proof. - intros h. apply All_local_env_app in h as [h1 h2]. + intros h. apply All_local_env_app_inv in h as [h1 h2]. split. - exact h1. - eapply All_local_env_impl. 1: exact h2. @@ -1177,7 +1186,6 @@ Section All_local_env. all: auto. Defined. - Lemma All_local_env_lookup {P Γ n} {decl} : All_local_env P Γ -> nth_error Γ n = Some decl -> @@ -1190,20 +1198,11 @@ Section All_local_env. eapply IHX. Qed. - Lemma All_local_env_app_inv (P : context -> term -> option term -> Type) l l' : - All_local_env P l * All_local_env (fun Γ t T => P (l ,,, Γ) t T) l' -> - All_local_env P (l ,,, l'). - Proof. - induction l'; simpl; auto. intuition. - intuition. destruct a. destruct decl_body. - inv b. econstructor; eauto. inv b; econstructor; eauto. Qed. - - - Definition wf_local_rel_app_inv {Σ Γ1 Γ2 Γ3} : + Definition wf_local_rel_app {Σ Γ1 Γ2 Γ3} : wf_local_rel Σ Γ1 Γ2 -> wf_local_rel Σ (Γ1 ,,, Γ2) Γ3 -> wf_local_rel Σ Γ1 (Γ2 ,,, Γ3). Proof. - intros h1 h2. eapply All_local_env_app_inv. + intros h1 h2. eapply All_local_env_app. split. - assumption. - eapply All_local_env_impl. @@ -1212,7 +1211,28 @@ Section All_local_env. intros Γ t []; cbn; now rewrite app_context_assoc. Defined. + + Definition wf_local_app {Σ Γ1 Γ2} : + wf_local Σ Γ1 -> + wf_local_rel Σ Γ1 Γ2 -> + wf_local Σ (Γ1 ,,, Γ2). + Proof. + intros H1 H2. apply wf_local_local_rel. + apply wf_local_rel_local in H1. + apply wf_local_rel_app; tas. + now rewrite app_context_nil_l. + Qed. + Definition wf_local_app_inv {Σ Γ1 Γ2} : + wf_local Σ (Γ1 ,,, Γ2) -> + wf_local Σ Γ1 * wf_local_rel Σ Γ1 Γ2. + Proof. + intros H. + apply wf_local_rel_local in H. + apply wf_local_rel_app_inv in H as [H H']; tas. + rewrite app_context_nil_l in H'. + now split; [eapply wf_local_local_rel|]. + Qed. Lemma All_local_env_map (P : context -> term -> option term -> Type) f l : (forall u, f (tSort u) = tSort u) -> diff --git a/pcuic/theories/PCUICWeakening.v b/pcuic/theories/PCUICWeakening.v index 80b9b220f..4019419da 100644 --- a/pcuic/theories/PCUICWeakening.v +++ b/pcuic/theories/PCUICWeakening.v @@ -1212,11 +1212,11 @@ Proof. generalize (@nil context_decl) as Δ. rewrite /fix_context_gen. intros Δ wfΔ. - eapply All_local_env_app_inv. split; auto. + eapply All_local_env_app. split; auto. induction a in Δ, wfΔ |- *; simpl; auto. + constructor. + simpl. - eapply All_local_env_app_inv. split; auto. + eapply All_local_env_app. split; auto. * repeat constructor. simpl. destruct p as [s Hs]. diff --git a/safechecker/theories/PCUICSafeChecker.v b/safechecker/theories/PCUICSafeChecker.v index bf074c0b8..144e0e7f8 100644 --- a/safechecker/theories/PCUICSafeChecker.v +++ b/safechecker/theories/PCUICSafeChecker.v @@ -55,7 +55,7 @@ Definition wf_local_rel_app_inv_sq `{cf : checker_flags} {Σ Γ1 Γ2 Γ3} : ∥ wf_local_rel Σ Γ1 Γ2 ∥ -> ∥ wf_local_rel Σ (Γ1 ,,, Γ2) Γ3 ∥ -> ∥ wf_local_rel Σ Γ1 (Γ2 ,,, Γ3) ∥. Proof. - intros; sq; now eapply wf_local_rel_app_inv. + intros; sq; now eapply wf_local_rel_app. Qed. Inductive type_error := @@ -274,7 +274,7 @@ Definition wf_local_app_inv `{cf : checker_flags} {Σ Γ1 Γ2} : -> wf_local Σ (Γ1 ,,, Γ2). Proof. intros H1 H2. - apply wf_local_local_rel, wf_local_rel_app_inv. + apply wf_local_local_rel, wf_local_rel_app. now apply wf_local_rel_local. now rewrite app_context_nil_l. Defined. @@ -2099,7 +2099,7 @@ Section CheckEnv. unfold arities_context. induction 1; simpl; auto. rewrite rev_map_cons /=. - eapply All_local_env_app_inv; split. constructor; pcuic. + eapply All_local_env_app; split. constructor; pcuic. eapply All_local_env_impl; eauto. move=> Γ t [] /=. * move=> ty ht. eapply weaken_ctx; eauto. @@ -2326,8 +2326,8 @@ Section CheckEnv. eapply cumul_Prod_Prod_inv in c as [eqann [eqdom codom]]; auto. rewrite List.rev_app_distr. constructor. - eapply All_local_env_app in wf as [wfΓ wfr]. - eapply All_local_env_app in wfr as [wfd wfΓ0]. + eapply All_local_env_app_inv in wf as [wfΓ wfr]. + eapply All_local_env_app_inv in wfr as [wfd wfΓ0]. depelim wfd. destruct l as [? Hs]. red. eapply type_Cumul'; pcuic. eapply conv_cumul. now symmetry. rewrite subst_telescope_subst_context. eapply X. now len. @@ -2335,8 +2335,8 @@ Section CheckEnv. eapply substitution_wf_local; eauto. 2:rewrite app_context_assoc in wf; eapply wf. repeat constructor. rewrite subst_empty. - eapply All_local_env_app in wf as [wfΓ wfr]. - eapply All_local_env_app in wfr as [wfd wfΓ0]. + eapply All_local_env_app_inv in wf as [wfΓ wfr]. + eapply All_local_env_app_inv in wfr as [wfd wfΓ0]. depelim wfd. destruct l as [? Hs]. eapply type_Cumul'; pcuic. eapply conv_cumul. now symmetry. eapply typing_spine_strengthen; eauto. @@ -2443,7 +2443,7 @@ Section CheckEnv. forward X. rewrite closedn_ctx_app clΓ0 /=. red. rewrite -clΔ''. lia_f_equal. len in X. rewrite app_context_assoc in sp. now specialize (X sp). - rewrite app_context_assoc in wf. now eapply All_local_env_app in wf as [? ?]. + rewrite app_context_assoc in wf. now eapply All_local_env_app_inv in wf as [? ?]. - len in sp. rewrite lift_context_app /= it_mkProd_or_LetIn_app lift_context_app it_mkProd_or_LetIn_app /= -it_mkProd_or_LetIn_app in sp. @@ -2472,7 +2472,7 @@ Section CheckEnv. forward X. rewrite closedn_ctx_app clΓ0 /=. red. rewrite -clΔ''. lia_f_equal. len in X. rewrite app_context_assoc in sp. now specialize (X sp). - rewrite app_context_assoc in wf. now eapply All_local_env_app in wf as [? ?]. + rewrite app_context_assoc in wf. now eapply All_local_env_app_inv in wf as [? ?]. Qed. Lemma typing_spine_it_mkProd_or_LetIn_ext_list_inv {Σ : global_env_ext} (wfΣ : wf Σ) Γ Δ Δ' Δ'' s args s' : @@ -2920,7 +2920,7 @@ Section CheckEnv. rewrite -{1}(subst_empty 0 b). repeat constructor. rewrite !subst_empty. eapply typing_wf_local in h. - rewrite app_context_assoc in h. eapply All_local_env_app in h as [h _]. + rewrite app_context_assoc in h. eapply All_local_env_app_inv in h as [h _]. now depelim h. - intros Γ t T h. rewrite !smash_context_app_ass !expand_lets_vass. diff --git a/template-coq/_PluginProject b/template-coq/_PluginProject index 94b06ed8d..97bcd978c 100644 --- a/template-coq/_PluginProject +++ b/template-coq/_PluginProject @@ -7,6 +7,8 @@ gen-src/signature.mli gen-src/signature.ml gen-src/classes0.mli gen-src/classes0.ml +gen-src/eqDec.mli +gen-src/eqDec.ml gen-src/all_Forall.ml gen-src/all_Forall.mli gen-src/ascii.ml @@ -60,6 +62,8 @@ gen-src/list0.ml gen-src/list0.mli gen-src/logic0.ml gen-src/logic0.mli +gen-src/mCPrelude.mli +gen-src/mCPrelude.ml gen-src/mCCompare.ml gen-src/mCCompare.mli gen-src/mCList.ml diff --git a/template-coq/gen-src/metacoq_template_plugin.mlpack b/template-coq/gen-src/metacoq_template_plugin.mlpack index b3bc6a85c..6bbb09b00 100644 --- a/template-coq/gen-src/metacoq_template_plugin.mlpack +++ b/template-coq/gen-src/metacoq_template_plugin.mlpack @@ -24,8 +24,12 @@ MSetDecide MSetList MSetProperties BinNums +EqDec CRelationClasses Compare_dec +Classes0 +EqDecInstances +MCPrelude MCList MCRelations MCOption @@ -34,7 +38,6 @@ MCCompare MCString MCUtils Signature -Classes0 All_Forall Config0 Universes0 @@ -45,7 +48,6 @@ AstUtils LiftSubst UnivSubst0 Induction -EqDecInstances Reflect Pretty Common0 diff --git a/template-coq/theories/Extraction.v b/template-coq/theories/Extraction.v index ecaf3f522..c90d653ee 100644 --- a/template-coq/theories/Extraction.v +++ b/template-coq/theories/Extraction.v @@ -32,6 +32,7 @@ From MetaCoq.Template Require Import TemplateMonad.Extractable config Induction LiftSubst UnivSubst Pretty. Recursive Extraction Library Extractable. +Extraction Library MCPrelude. Extraction Library MCOption. Extraction Library MCUtils. Extraction Library EqDecInstances. diff --git a/template-coq/theories/Typing.v b/template-coq/theories/Typing.v index 07d592615..a91534b64 100644 --- a/template-coq/theories/Typing.v +++ b/template-coq/theories/Typing.v @@ -1018,7 +1018,6 @@ Proof. apply type_Prop. Defined. - Lemma wf_local_app_l `{checker_flags} Σ (Γ Γ' : context) : wf_local Σ (Γ ,,, Γ') -> wf_local Σ Γ. Proof. induction Γ'. auto. @@ -1567,7 +1566,7 @@ Proof. - apply IHX. Qed. -Lemma All_local_env_app +Lemma All_local_env_app_inv (P : context -> term -> option term -> Type) l l' : All_local_env P (l ,,, l') -> All_local_env P l * All_local_env (fun Γ t T => P (l ,,, Γ) t T) l'. @@ -1603,7 +1602,7 @@ Proof. + apply IHX. Qed. -Lemma All_local_env_app_inv `{checker_flags} (P : context -> term -> option term -> Type) l l' : +Lemma All_local_env_app `{checker_flags} (P : context -> term -> option term -> Type) l l' : All_local_env P l * All_local_env (fun Γ t T => P (l ,,, Γ) t T) l' -> All_local_env P (l ,,, l'). Proof. From c46d77da203563fee632f18b66669c33bbe3c8ac Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Fri, 27 Nov 2020 13:14:39 +0100 Subject: [PATCH 10/70] PCUICCumulativity no longer needed by erasure plugin --- erasure/_PluginProject.in | 4 ++-- erasure/src/metacoq_erasure_plugin.mlpack | 1 - 2 files changed, 2 insertions(+), 3 deletions(-) diff --git a/erasure/_PluginProject.in b/erasure/_PluginProject.in index e47650f5d..6eeb7a21b 100644 --- a/erasure/_PluginProject.in +++ b/erasure/_PluginProject.in @@ -45,8 +45,8 @@ src/pCUICTyping.ml src/pCUICTyping.mli src/pCUICUnivSubst.ml src/pCUICUnivSubst.mli -src/pCUICCumulativity.mli -src/pCUICCumulativity.ml +# src/pCUICCumulativity.mli +# src/pCUICCumulativity.ml src/pCUICPosition.mli src/pCUICPosition.ml src/pCUICNormal.mli diff --git a/erasure/src/metacoq_erasure_plugin.mlpack b/erasure/src/metacoq_erasure_plugin.mlpack index 70bc3cb2e..e6a151957 100644 --- a/erasure/src/metacoq_erasure_plugin.mlpack +++ b/erasure/src/metacoq_erasure_plugin.mlpack @@ -30,7 +30,6 @@ PCUICNormal PCUICPosition PCUICPretty TemplateToPCUIC -PCUICCumulativity PCUICUnivSubst PCUICSafeReduce From 4b52e656c0f01ad83f6c96d350af4cffc4184783 Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Fri, 27 Nov 2020 14:26:36 +0100 Subject: [PATCH 11/70] Split TypeChecker and Environment Checker, move auxilliary lemmas to their right place --- pcuic/theories/PCUICAstUtils.v | 59 +- pcuic/theories/PCUICClosed.v | 3 + pcuic/theories/PCUICGlobalEnv.v | 21 + pcuic/theories/PCUICSafeLemmata.v | 30 +- pcuic/theories/PCUICTyping.v | 7 - pcuic/theories/PCUICUnivSubstitution.v | 115 -- safechecker/theories/PCUICErrors.v | 269 ++++ safechecker/theories/PCUICSafeChecker.v | 1486 +------------------- safechecker/theories/PCUICSafeConversion.v | 90 +- safechecker/theories/PCUICTypeChecker.v | 932 ++++++++++++ safechecker/theories/PCUICWfEnv.v | 62 + template-coq/theories/Universes.v | 84 +- template-coq/theories/monad_utils.v | 80 +- template-coq/theories/utils/All_Forall.v | 15 +- template-coq/theories/utils/MCList.v | 121 +- template-coq/theories/utils/MCPrelude.v | 7 +- template-coq/theories/utils/MCUtils.v | 3 - 17 files changed, 1681 insertions(+), 1703 deletions(-) create mode 100644 safechecker/theories/PCUICErrors.v create mode 100644 safechecker/theories/PCUICTypeChecker.v create mode 100644 safechecker/theories/PCUICWfEnv.v diff --git a/pcuic/theories/PCUICAstUtils.v b/pcuic/theories/PCUICAstUtils.v index 07375fdfe..594847fda 100644 --- a/pcuic/theories/PCUICAstUtils.v +++ b/pcuic/theories/PCUICAstUtils.v @@ -790,6 +790,19 @@ Proof. reflexivity. Qed. +Lemma destArity_mkApps_None ctx t l : + destArity ctx t = None -> destArity ctx (mkApps t l) = None. +Proof. + induction l in t |- *. trivial. + intros H. cbn. apply IHl. reflexivity. +Qed. + +Lemma destArity_mkApps_Ind ctx ind u l : + destArity ctx (mkApps (tInd ind u) l) = None. +Proof. + apply destArity_mkApps_None. reflexivity. +Qed. + (* Helper for nested recursive functions on well-typed terms *) Section MapInP. @@ -828,4 +841,48 @@ Lemma map_InP_length {A B : Type} {P : A -> Type} (f : forall x : A, P x -> B) ( Proof. induction l; simpl; auto. Qed. -Hint Rewrite @map_InP_length : len. \ No newline at end of file +Hint Rewrite @map_InP_length : len. + +(** Views *) + +Definition isSort T := + match T with + | tSort u => true + | _ => false + end. + +Inductive view_sort : term -> Type := +| view_sort_sort s : view_sort (tSort s) +| view_sort_other t : ~ isSort t -> view_sort t. + +Equations view_sortc (t : term) : view_sort t := + view_sortc (tSort s) := view_sort_sort s; + view_sortc t := view_sort_other t _. + +Fixpoint isProd t := + match t with + | tProd na A B => true + | _ => false + end. + +Inductive view_prod : term -> Type := +| view_prod_prod na A b : view_prod (tProd na A b) +| view_prod_other t : ~ isProd t -> view_prod t. + +Equations view_prodc (t : term) : view_prod t := + view_prodc (tProd na A b) := view_prod_prod na A b; + view_prodc t := view_prod_other t _. + +Definition isInd (t : term) : bool := + match t with + | tInd _ _ => true + | _ => false + end. + +Inductive view_ind : term -> Type := +| view_ind_tInd ind u : view_ind (tInd ind u) +| view_ind_other t : negb (isInd t) -> view_ind t. + +Equations view_indc (t : term) : view_ind t := + view_indc (tInd ind u) => view_ind_tInd ind u; + view_indc t => view_ind_other t _. \ No newline at end of file diff --git a/pcuic/theories/PCUICClosed.v b/pcuic/theories/PCUICClosed.v index 7152f08a0..52273ee77 100644 --- a/pcuic/theories/PCUICClosed.v +++ b/pcuic/theories/PCUICClosed.v @@ -997,6 +997,9 @@ Proof. now move: c => [_ /andP [_ ct]]. Qed. +Lemma isType_closed {cf:checker_flags} {Σ Γ T} : wf Σ.1 -> isType Σ Γ T -> closedn #|Γ| T. +Proof. intros wfΣ [s Hs]. now eapply subject_closed in Hs. Qed. + Lemma closed_wf_local `{checker_flags} {Σ Γ} : wf Σ.1 -> wf_local Σ Γ -> diff --git a/pcuic/theories/PCUICGlobalEnv.v b/pcuic/theories/PCUICGlobalEnv.v index 22fc41aa8..bc59d5ee4 100644 --- a/pcuic/theories/PCUICGlobalEnv.v +++ b/pcuic/theories/PCUICGlobalEnv.v @@ -68,6 +68,25 @@ Proof. split; apply LevelSet.union_spec; right; apply XX. Qed. +Lemma wf_consistent {cf:checker_flags} Σ : wf Σ -> consistent (global_constraints Σ). +Proof. + destruct Σ. + - exists {| valuation_mono := fun _ => 1%positive; valuation_poly := fun _ => 0 |}. + intros x Hx; now apply ConstraintSetFact.empty_iff in Hx. + - inversion 1; subst. subst udecl. clear -H2. + destruct H2 as [_ [_ [_ [v Hv]]]]. + exists v. intros ct Hc. apply Hv. simpl in *. + apply ConstraintSet.union_spec in Hc. destruct Hc. + apply ConstraintSet.union_spec; simpl. + + left. destruct d. + destruct c, cst_universes. assumption. + apply ConstraintSetFact.empty_iff in H; contradiction. + destruct m, ind_universes. assumption. + apply ConstraintSetFact.empty_iff in H; contradiction. + + apply ConstraintSet.union_spec; simpl. + now right. +Qed. + Definition global_ext_uctx_consistent {cf:checker_flags} Σ : wf_ext Σ -> consistent (global_ext_uctx Σ).2. Proof. @@ -75,3 +94,5 @@ Proof. unfold wf_ext, on_global_env_ext in HΣ. destruct HΣ as [_ [_ [_ HH]]]. apply HH. Qed. + + diff --git a/pcuic/theories/PCUICSafeLemmata.v b/pcuic/theories/PCUICSafeLemmata.v index 359834dbb..e26ccccb9 100644 --- a/pcuic/theories/PCUICSafeLemmata.v +++ b/pcuic/theories/PCUICSafeLemmata.v @@ -274,8 +274,30 @@ Section Lemmata. Arguments iswelltyped {Σ Γ t A} h. + Definition isType_welltyped {Γ T} + : isType Σ Γ T -> welltyped Σ Γ T. + Proof. + intros []. now econstructor. + Qed. + Hint Resolve isType_welltyped : pcuic. + Context (hΣ : ∥ wf Σ ∥). + Lemma validity_wf {Γ t T} : + ∥ Σ ;;; Γ |- t : T ∥ -> welltyped Σ Γ T. + Proof. + destruct hΣ as [wΣ]. intros [X]. + intros. eapply validity_term in X; try assumption. + destruct X. now exists (tSort x). + Defined. + + Lemma wat_welltyped {Γ T} : + ∥ isType Σ Γ T ∥ -> welltyped Σ Γ T. + Proof. + destruct hΣ as [wΣ]. intros [X]. + now apply isType_welltyped. + Defined. + Lemma welltyped_alpha Γ u v : welltyped Σ Γ u -> eq_term_upto_univ [] eq eq u v -> @@ -871,12 +893,6 @@ Section Lemmata. | _ => false end. - Fixpoint isProd t := - match t with - | tProd na A B => true - | _ => false - end. - Lemma isAppProd_mkApps : forall t l, isAppProd (mkApps t l) = isAppProd t. Proof. @@ -1364,3 +1380,5 @@ Section Lemmata. Qed. End Lemmata. + +Hint Resolve isType_welltyped : pcuic. diff --git a/pcuic/theories/PCUICTyping.v b/pcuic/theories/PCUICTyping.v index 85d7372c6..45b1d7d4d 100644 --- a/pcuic/theories/PCUICTyping.v +++ b/pcuic/theories/PCUICTyping.v @@ -29,13 +29,6 @@ Hint Rewrite subst_context_length subst_instance_context_length map_length app_length lift_context_length @mapi_length @mapi_rec_length List.rev_length Nat.add_0_r : len. - -Definition isSort T := - match T with - | tSort u => True - | _ => False - end. - Fixpoint isArity T := match T with | tSort u => True diff --git a/pcuic/theories/PCUICUnivSubstitution.v b/pcuic/theories/PCUICUnivSubstitution.v index 370f5e8ab..400dd1c60 100644 --- a/pcuic/theories/PCUICUnivSubstitution.v +++ b/pcuic/theories/PCUICUnivSubstitution.v @@ -1889,74 +1889,6 @@ Section SubstIdentity. now rewrite mapi_nth. Qed. - Fixpoint unfold {A} (n : nat) (f : nat -> A) : list A := - match n with - | 0 => [] - | S n => unfold n f ++ [f n] - end. - - Lemma mapi_irrel_list {A B} (f : nat -> A) (l l' : list B) : - #|l| = #|l'| -> - mapi (fun i (x : B) => f i) l = mapi (fun i x => f i) l'. - Proof. - induction l in f, l' |- *; destruct l' => //; simpl; auto. - intros [= eq]. f_equal. - rewrite !mapi_rec_Sk. - now rewrite [mapi_rec _ _ _](IHl (fun x => (f (S x))) l'). - Qed. - - Lemma mapi_unfold {A B} (f : nat -> B) l : mapi (fun i (x : A) => f i) l = unfold #|l| f. - Proof. - induction l in f |- *; simpl; auto. - rewrite mapi_rec_Sk. - rewrite -IHl. rewrite -(mapi_rec_Sk (fun i x => f i) l 0). - change [f #|l|] with (mapi_rec (fun i x => f i) [a] #|l|). - rewrite -(Nat.add_0_r #|l|). rewrite -mapi_rec_app. - change (f 0 :: _) with (mapi (fun i x => f i) (a :: l)). - apply mapi_irrel_list. simpl. rewrite app_length /=; lia. - Qed. - - Lemma forallb_mapi {A B} (p : B -> bool) (f : nat -> B) l : - (forall i, i < #|l| -> p (f i)) -> - forallb p (mapi (fun i (x : A) => f i) l). - Proof. - intros Hp. rewrite (mapi_unfold f). - induction #|l| in *; simpl; auto. - rewrite forallb_app. simpl. now rewrite Hp // !andb_true_r. - Qed. - - Lemma In_unfold n i : In (Level.Var i) (unfold n Level.Var) -> i < n. - Proof. - induction n; simpl => //. - intros H; apply in_app_or in H. - destruct H. - - specialize (IHn H). lia. - - simpl in H. destruct H; [injection H|]. - * intros ->. auto. - * destruct H. - Qed. - - Lemma In_fold_right_add x l : - In x l <-> LevelSet.In x (fold_right LevelSet.add LevelSet.empty l). - Proof. - split. - - induction l; simpl => //. - intros [<-|H]. - * eapply LevelSet.add_spec; left; auto. - * eapply LevelSet.add_spec; right; auto. - - induction l; simpl => //. - * now rewrite LevelSetFact.empty_iff. - * rewrite LevelSet.add_spec. intuition auto. - Qed. - - Lemma CS_For_all_union f cst cst' : ConstraintSet.For_all f (ConstraintSet.union cst cst') -> - ConstraintSet.For_all f cst. - Proof. - unfold CS.For_all. - intros IH x inx. apply (IH x). - now eapply CS.union_spec; left. - Qed. - Lemma declared_inductive_wf_ext_wk Σ mdecl mind : wf Σ -> declared_minductive Σ mind mdecl -> @@ -1981,50 +1913,6 @@ Section SubstIdentity. Hint Resolve declared_inductive_wf_ext_wk declared_inductive_wf_global_ext : pcuic. - Instance For_all_proper P : Morphisms.Proper (CS.Equal ==> iff)%signature (ConstraintSet.For_all P). - Proof. - intros s s' eqs. - unfold CS.For_all. split; intros IH x inxs; apply (IH x); - now apply eqs. - Qed. - - Lemma unfold_length {A} (f : nat -> A) m : #|unfold m f| = m. - Proof. - induction m; simpl; rewrite ?app_length /=; auto. lia. - Qed. - - Lemma nth_error_unfold {A} (f : nat -> A) m n : n < m <-> nth_error (unfold m f) n = Some (f n). - Proof. - induction m in n |- *; split; intros Hn; try lia. - - simpl in Hn. rewrite nth_error_nil in Hn. discriminate. - - destruct (eq_dec n m); [subst|]. - * simpl. rewrite nth_error_app_ge unfold_length // Nat.sub_diag /= //. - * simpl. rewrite nth_error_app_lt ?unfold_length //; try lia. - apply IHm; lia. - - simpl in Hn. eapply nth_error_Some_length in Hn. - rewrite app_length /= unfold_length in Hn. lia. - Qed. - - Lemma nth_error_unfold_inv {A} (f : nat -> A) m n t : nth_error (unfold m f) n = Some t -> t = (f n). - Proof. - induction m in n |- *; intros Hn; try lia. - - simpl in Hn. rewrite nth_error_nil in Hn. discriminate. - - simpl in Hn. - pose proof (nth_error_Some_length Hn). - rewrite app_length /= unfold_length in H. - destruct (eq_dec n m); [subst|]. - * simpl. revert Hn. rewrite nth_error_app_ge unfold_length // Nat.sub_diag /= //; congruence. - * simpl. revert Hn. rewrite nth_error_app_lt ?unfold_length //; try lia. auto. - Qed. - - Lemma CS_For_all_add P x s : CS.For_all P (CS.add x s) -> P x /\ CS.For_all P s. - Proof. - intros. - split. - * apply (H x), CS.add_spec; left => //. - * intros y iny. apply (H y), CS.add_spec; right => //. - Qed. - Lemma subst_instance_level_abs l n Σ : wf Σ -> LevelSet.In l (LevelSet.union @@ -2102,9 +1990,6 @@ Section SubstIdentity. eapply CS_For_all_union. Qed. - Lemma isType_closed {Σ Γ T} : wf Σ.1 -> isType Σ Γ T -> closedn #|Γ| T. - Proof. intros wfΣ [s Hs]. now eapply subject_closed in Hs. Qed. - Lemma udecl_prop_in_var_poly {Σ n} : on_udecl_prop Σ.1 Σ.2 -> LevelSet.In (Level.Var n) (levels_of_udecl Σ.2) -> ∑ ctx, Σ.2 = Polymorphic_ctx ctx. Proof. diff --git a/safechecker/theories/PCUICErrors.v b/safechecker/theories/PCUICErrors.v new file mode 100644 index 000000000..e34b1e5cf --- /dev/null +++ b/safechecker/theories/PCUICErrors.v @@ -0,0 +1,269 @@ + +(* Distributed under the terms of the MIT license. *) +From MetaCoq.Template Require Import config utils uGraph. +From MetaCoq.PCUIC Require Import PCUICAst PCUICAstUtils PCUICPretty. +From Equations Require Import Equations. +Require Import ssreflect ssrbool. + +Local Set Keyed Unification. +Set Equations Transparent. + +Inductive ConversionError := +| NotFoundConstants (c1 c2 : kername) + +| NotFoundConstant (c : kername) + +| LambdaNotConvertibleTypes + (Γ1 : context) (na : aname) (A1 t1 : term) + (Γ2 : context) (na' : aname) (A2 t2 : term) + (e : ConversionError) + +| LambdaNotConvertibleAnn + (Γ1 : context) (na : aname) (A1 t1 : term) + (Γ2 : context) (na' : aname) (A2 t2 : term) + +| ProdNotConvertibleDomains + (Γ1 : context) (na : aname) (A1 B1 : term) + (Γ2 : context) (na' : aname) (A2 B2 : term) + (e : ConversionError) + +| ProdNotConvertibleAnn + (Γ1 : context) (na : aname) (A1 B1 : term) + (Γ2 : context) (na' : aname) (A2 B2 : term) + +| CaseOnDifferentInd + (Γ1 : context) + (ind : inductive) (par : nat) (p c : term) (brs : list (nat × term)) + (Γ2 : context) + (ind' : inductive) (par' : nat) (p' c' : term) (brs' : list (nat × term)) + +| CaseBranchNumMismatch + (ind : inductive) (par : nat) + (Γ : context) (p c : term) (brs1 : list (nat × term)) + (m : nat) (br : term) (brs2 : list (nat × term)) + (Γ' : context) (p' c' : term) (brs1' : list (nat × term)) + (m' : nat) (br' : term) (brs2' : list (nat × term)) + +| DistinctStuckProj + (Γ : context) (p : projection) (c : term) + (Γ' : context) (p' : projection) (c' : term) + +| CannotUnfoldFix + (Γ : context) (mfix : mfixpoint term) (idx : nat) + (Γ' : context) (mfix' : mfixpoint term) (idx' : nat) + +| FixRargMismatch (idx : nat) + (Γ : context) (u : def term) (mfix1 mfix2 : mfixpoint term) + (Γ' : context) (v : def term) (mfix1' mfix2' : mfixpoint term) + +| FixMfixMismatch (idx : nat) + (Γ : context) (mfix : mfixpoint term) + (Γ' : context) (mfix' : mfixpoint term) + +| DistinctCoFix + (Γ : context) (mfix : mfixpoint term) (idx : nat) + (Γ' : context) (mfix' : mfixpoint term) (idx' : nat) + +| CoFixRargMismatch (idx : nat) + (Γ : context) (u : def term) (mfix1 mfix2 : mfixpoint term) + (Γ' : context) (v : def term) (mfix1' mfix2' : mfixpoint term) + +| CoFixMfixMismatch (idx : nat) + (Γ : context) (mfix : mfixpoint term) + (Γ' : context) (mfix' : mfixpoint term) + +| StackHeadError + (leq : conv_pb) + (Γ1 : context) + (t1 : term) (args1 : list term) (u1 : term) (l1 : list term) + (Γ2 : context) + (t2 : term) (u2 : term) (l2 : list term) + (e : ConversionError) + +| StackTailError (leq : conv_pb) + (Γ1 : context) + (t1 : term) (args1 : list term) (u1 : term) (l1 : list term) + (Γ2 : context) + (t2 : term) (u2 : term) (l2 : list term) + (e : ConversionError) + +| StackMismatch + (Γ1 : context) (t1 : term) (args1 l1 : list term) + (Γ2 : context) (t2 : term) (l2 : list term) + +| HeadMismatch + (leq : conv_pb) + (Γ1 : context) (t1 : term) + (Γ2 : context) (t2 : term). + +Inductive type_error := +| UnboundRel (n : nat) +| UnboundVar (id : string) +| UnboundEvar (ev : nat) +| UndeclaredConstant (c : kername) +| UndeclaredInductive (c : inductive) +| UndeclaredConstructor (c : inductive) (i : nat) +| NotCumulSmaller (G : universes_graph) (Γ : context) (t u t' u' : term) (e : ConversionError) +| NotConvertible (G : universes_graph) (Γ : context) (t u : term) +| NotASort (t : term) +| NotAProduct (t t' : term) +| NotAnInductive (t : term) +| NotAnArity (t : term) +| IllFormedFix (m : mfixpoint term) (i : nat) +| UnsatisfiedConstraints (c : ConstraintSet.t) +| Msg (s : string). + +Definition print_level := string_of_level. + +Definition string_of_Z z := + if (z <=? 0)%Z then "-" ^ string_of_nat (Z.to_nat (- z)) else string_of_nat (Z.to_nat z). + +Definition print_edge '(l1, n, l2) + := "(" ^ print_level l1 ^ ", " ^ string_of_Z n ^ ", " + ^ print_level l2 ^ ")". + +Definition print_universes_graph (G : universes_graph) := + let levels := LevelSet.elements G.1.1 in + let edges := wGraph.EdgeSet.elements G.1.2 in + string_of_list print_level levels + ^ "\n" ^ string_of_list print_edge edges. + +Definition string_of_conv_pb (c : conv_pb) : string := + match c with + | Conv => "conversion" + | Cumul => "cumulativity" + end. + +Definition print_term Σ Γ t := + print_term Σ Γ true false t. + +Fixpoint string_of_conv_error Σ (e : ConversionError) : string := + match e with + | NotFoundConstants c1 c2 => + "Both constants " ^ string_of_kername c1 ^ " and " ^ string_of_kername c2 ^ + " are not found in the environment." + | NotFoundConstant c => + "Constant " ^ string_of_kername c ^ + " common in both terms is not found in the environment." + | LambdaNotConvertibleAnn Γ1 na A1 t1 Γ2 na' A2 t2 => + "When comparing\n" ^ print_term Σ Γ1 (tLambda na A1 t1) ^ + "\nand\n" ^ print_term Σ Γ2 (tLambda na' A2 t2) ^ + "\nbinding annotations are not convertible\n" + | LambdaNotConvertibleTypes Γ1 na A1 t1 Γ2 na' A2 t2 e => + "When comparing\n" ^ print_term Σ Γ1 (tLambda na A1 t1) ^ + "\nand\n" ^ print_term Σ Γ2 (tLambda na' A2 t2) ^ + "\ntypes are not convertible:\n" ^ + string_of_conv_error Σ e + | ProdNotConvertibleAnn Γ1 na A1 B1 Γ2 na' A2 B2 => + "When comparing\n" ^ print_term Σ Γ1 (tProd na A1 B1) ^ + "\nand\n" ^ print_term Σ Γ2 (tProd na' A2 B2) ^ + "\nbinding annotations are not convertible:\n" + | ProdNotConvertibleDomains Γ1 na A1 B1 Γ2 na' A2 B2 e => + "When comparing\n" ^ print_term Σ Γ1 (tProd na A1 B1) ^ + "\nand\n" ^ print_term Σ Γ2 (tProd na' A2 B2) ^ + "\ndomains are not convertible:\n" ^ + string_of_conv_error Σ e + | CaseOnDifferentInd Γ ind par p c brs Γ' ind' par' p' c' brs' => + "The two stuck pattern-matching\n" ^ + print_term Σ Γ (tCase (ind, par) p c brs) ^ + "\nand\n" ^ print_term Σ Γ' (tCase (ind', par') p' c' brs') ^ + "\nare done on distinct inductive types." + | CaseBranchNumMismatch + ind par Γ p c brs1 m br brs2 Γ' p' c' brs1' m' br' brs2' => + "The two stuck pattern-matching\n" ^ + print_term Σ Γ (tCase (ind, par) p c (brs1 ++ (m,br) :: brs2)) ^ + "\nand\n" ^ + print_term Σ Γ' (tCase (ind, par) p' c' (brs1' ++ (m',br') :: brs2')) ^ + "\nhave a mistmatch in the branch number " ^ string_of_nat #|brs1| ^ + "\nthe number of parameters do not coincide\n" ^ + print_term Σ Γ br ^ + "\nhas " ^ string_of_nat m ^ " parameters while\n" ^ + print_term Σ Γ br' ^ + "\nhas " ^ string_of_nat m' ^ "." + | DistinctStuckProj Γ p c Γ' p' c' => + "The two stuck projections\n" ^ + print_term Σ Γ (tProj p c) ^ + "\nand\n" ^ + print_term Σ Γ' (tProj p' c') ^ + "\nare syntactically different." + | CannotUnfoldFix Γ mfix idx Γ' mfix' idx' => + "The two fixed-points\n" ^ + print_term Σ Γ (tFix mfix idx) ^ + "\nand\n" ^ print_term Σ Γ' (tFix mfix' idx') ^ + "\ncorrespond to syntactically distinct terms that can't be unfolded." + | FixRargMismatch idx Γ u mfix1 mfix2 Γ' v mfix1' mfix2' => + "The two fixed-points\n" ^ + print_term Σ Γ (tFix (mfix1 ++ u :: mfix2) idx) ^ + "\nand\n" ^ print_term Σ Γ' (tFix (mfix1' ++ v :: mfix2') idx) ^ + "\nhave a mismatch in the function number " ^ string_of_nat #|mfix1| ^ + ": arguments " ^ string_of_nat u.(rarg) ^ + " and " ^ string_of_nat v.(rarg) ^ "are different." + | FixMfixMismatch idx Γ mfix Γ' mfix' => + "The two fixed-points\n" ^ + print_term Σ Γ (tFix mfix idx) ^ + "\nand\n" ^ + print_term Σ Γ' (tFix mfix' idx) ^ + "\nhave a different number of mutually defined functions." + | DistinctCoFix Γ mfix idx Γ' mfix' idx' => + "The two cofixed-points\n" ^ + print_term Σ Γ (tCoFix mfix idx) ^ + "\nand\n" ^ print_term Σ Γ' (tCoFix mfix' idx') ^ + "\ncorrespond to syntactically distinct terms." + | CoFixRargMismatch idx Γ u mfix1 mfix2 Γ' v mfix1' mfix2' => + "The two co-fixed-points\n" ^ + print_term Σ Γ (tCoFix (mfix1 ++ u :: mfix2) idx) ^ + "\nand\n" ^ print_term Σ Γ' (tCoFix (mfix1' ++ v :: mfix2') idx) ^ + "\nhave a mismatch in the function number " ^ string_of_nat #|mfix1| ^ + ": arguments " ^ string_of_nat u.(rarg) ^ + " and " ^ string_of_nat v.(rarg) ^ "are different." + | CoFixMfixMismatch idx Γ mfix Γ' mfix' => + "The two co-fixed-points\n" ^ + print_term Σ Γ (tCoFix mfix idx) ^ + "\nand\n" ^ + print_term Σ Γ' (tCoFix mfix' idx) ^ + "\nhave a different number of mutually defined functions." + | StackHeadError leq Γ1 t1 args1 u1 l1 Γ2 t2 u2 l2 e => + "TODO stackheaderror\n" ^ + string_of_conv_error Σ e + | StackTailError leq Γ1 t1 args1 u1 l1 Γ2 t2 u2 l2 e => + "TODO stacktailerror\n" ^ + string_of_conv_error Σ e + | StackMismatch Γ1 t1 args1 l1 Γ2 t2 l2 => + "Convertible terms\n" ^ + print_term Σ Γ1 t1 ^ + "\nand\n" ^ print_term Σ Γ2 t2 ^ + "are convertible/convertible (TODO) but applied to a different number" ^ + " of arguments." + | HeadMismatch leq Γ1 t1 Γ2 t2 => + "Terms\n" ^ + print_term Σ Γ1 t1 ^ + "\nand\n" ^ print_term Σ Γ2 t2 ^ + "\ndo not have the same head when comparing for " ^ + string_of_conv_pb leq + end. + +Definition string_of_type_error Σ (e : type_error) : string := + match e with + | UnboundRel n => "Unbound rel " ^ string_of_nat n + | UnboundVar id => "Unbound var " ^ id + | UnboundEvar ev => "Unbound evar " ^ string_of_nat ev + | UndeclaredConstant c => "Undeclared constant " ^ string_of_kername c + | UndeclaredInductive c => "Undeclared inductive " ^ string_of_kername (inductive_mind c) + | UndeclaredConstructor c i => "Undeclared inductive " ^ string_of_kername (inductive_mind c) + | NotCumulSmaller G Γ t u t' u' e => "Terms are not <= for cumulativity:\n" ^ + print_term Σ Γ t ^ "\nand:\n" ^ print_term Σ Γ u ^ + "\nafter reduction:\n" ^ + print_term Σ Γ t' ^ "\nand:\n" ^ print_term Σ Γ u' ^ + "\nerror:\n" ^ string_of_conv_error Σ e ^ + "\nin universe graph:\n" ^ print_universes_graph G + | NotConvertible G Γ t u => "Terms are not convertible:\n" ^ + print_term Σ Γ t ^ "\nand:\n" ^ print_term Σ Γ u ^ + "\nin universe graph:\n" ^ print_universes_graph G + | NotASort t => "Not a sort" + | NotAProduct t t' => "Not a product" + | NotAnArity t => print_term Σ [] t ^ " is not an arity" + | NotAnInductive t => "Not an inductive" + | IllFormedFix m i => "Ill-formed recursive definition" + | UnsatisfiedConstraints c => "Unsatisfied constraints" + | Msg s => "Msg: " ^ s + end. diff --git a/safechecker/theories/PCUICSafeChecker.v b/safechecker/theories/PCUICSafeChecker.v index 144e0e7f8..65fcb09c8 100644 --- a/safechecker/theories/PCUICSafeChecker.v +++ b/safechecker/theories/PCUICSafeChecker.v @@ -12,7 +12,8 @@ From MetaCoq.PCUIC Require Import PCUICAst PCUICAstUtils PCUICContexts PCUICSubstitution PCUICSpine PCUICInductiveInversion PCUICClosed PCUICUnivSubstitution PCUICWeakeningEnv. -From MetaCoq.SafeChecker Require Import PCUICSafeReduce PCUICEqualityDec PCUICSafeConversion PCUICWfReduction. +From MetaCoq.SafeChecker Require Import PCUICSafeReduce PCUICErrors PCUICEqualityDec + PCUICSafeConversion PCUICWfReduction PCUICTypeChecker. From Equations Require Import Equations. Require Import ssreflect ssrbool. @@ -29,1301 +30,43 @@ Ltac Coq.Program.Tactics.program_solve_wf ::= end end. -Lemma weakening_sq `{cf : checker_flags} {Σ Γ} Γ' {t T} : - ∥ wf Σ.1 ∥ -> ∥ wf_local Σ (Γ ,,, Γ') ∥ -> - ∥ Σ ;;; Γ |- t : T ∥ -> - ∥ Σ ;;; Γ ,,, Γ' |- lift0 #|Γ'| t : lift0 #|Γ'| T ∥. -Proof. - intros; sq; now eapply weakening. -Defined. - -Definition wf_local_rel_abs_sq `{cf : checker_flags} {Σ Γ Γ' A na} : - ∥ wf_local_rel Σ Γ Γ' ∥ -> {u & ∥ Σ ;;; Γ ,,, Γ' |- A : tSort u ∥ } - -> ∥ wf_local_rel Σ Γ (Γ',, vass na A) ∥. -Proof. - intros H [u Hu]; sq. now eapply wf_local_rel_abs. -Qed. - -Definition wf_local_rel_def_sq `{cf : checker_flags} {Σ Γ Γ' t A na} : - ∥ wf_local_rel Σ Γ Γ' ∥ -> ∥ isType Σ (Γ ,,, Γ') A ∥ -> ∥ Σ ;;; Γ ,,, Γ' |- t : A ∥ - -> ∥ wf_local_rel Σ Γ (Γ',, vdef na t A) ∥. -Proof. - intros; sq. now eapply wf_local_rel_def. -Qed. - -Definition wf_local_rel_app_inv_sq `{cf : checker_flags} {Σ Γ1 Γ2 Γ3} : - ∥ wf_local_rel Σ Γ1 Γ2 ∥ -> ∥ wf_local_rel Σ (Γ1 ,,, Γ2) Γ3 ∥ - -> ∥ wf_local_rel Σ Γ1 (Γ2 ,,, Γ3) ∥. -Proof. - intros; sq; now eapply wf_local_rel_app. -Qed. - -Inductive type_error := -| UnboundRel (n : nat) -| UnboundVar (id : string) -| UnboundEvar (ev : nat) -| UndeclaredConstant (c : kername) -| UndeclaredInductive (c : inductive) -| UndeclaredConstructor (c : inductive) (i : nat) -| NotCumulSmaller (G : universes_graph) (Γ : context) (t u t' u' : term) (e : ConversionError) -| NotConvertible (G : universes_graph) (Γ : context) (t u : term) -| NotASort (t : term) -| NotAProduct (t t' : term) -| NotAnInductive (t : term) -| NotAnArity (t : term) -| IllFormedFix (m : mfixpoint term) (i : nat) -| UnsatisfiedConstraints (c : ConstraintSet.t) -| Msg (s : string). - -Definition print_level := string_of_level. - -Definition string_of_Z z := - if (z <=? 0)%Z then "-" ^ string_of_nat (Z.to_nat (- z)) else string_of_nat (Z.to_nat z). - -Definition print_edge '(l1, n, l2) - := "(" ^ print_level l1 ^ ", " ^ string_of_Z n ^ ", " - ^ print_level l2 ^ ")". - -Definition print_universes_graph (G : universes_graph) := - let levels := LevelSet.elements G.1.1 in - let edges := wGraph.EdgeSet.elements G.1.2 in - string_of_list print_level levels - ^ "\n" ^ string_of_list print_edge edges. - -Definition string_of_conv_pb (c : conv_pb) : string := - match c with - | Conv => "conversion" - | Cumul => "cumulativity" - end. - -Definition print_term Σ Γ t := - print_term Σ Γ true false t. - -Fixpoint string_of_conv_error Σ (e : ConversionError) : string := - match e with - | NotFoundConstants c1 c2 => - "Both constants " ^ string_of_kername c1 ^ " and " ^ string_of_kername c2 ^ - " are not found in the environment." - | NotFoundConstant c => - "Constant " ^ string_of_kername c ^ - " common in both terms is not found in the environment." - | LambdaNotConvertibleAnn Γ1 na A1 t1 Γ2 na' A2 t2 => - "When comparing\n" ^ print_term Σ Γ1 (tLambda na A1 t1) ^ - "\nand\n" ^ print_term Σ Γ2 (tLambda na' A2 t2) ^ - "\nbinding annotations are not convertible\n" - | LambdaNotConvertibleTypes Γ1 na A1 t1 Γ2 na' A2 t2 e => - "When comparing\n" ^ print_term Σ Γ1 (tLambda na A1 t1) ^ - "\nand\n" ^ print_term Σ Γ2 (tLambda na' A2 t2) ^ - "\ntypes are not convertible:\n" ^ - string_of_conv_error Σ e - | ProdNotConvertibleAnn Γ1 na A1 B1 Γ2 na' A2 B2 => - "When comparing\n" ^ print_term Σ Γ1 (tProd na A1 B1) ^ - "\nand\n" ^ print_term Σ Γ2 (tProd na' A2 B2) ^ - "\nbinding annotations are not convertible:\n" - | ProdNotConvertibleDomains Γ1 na A1 B1 Γ2 na' A2 B2 e => - "When comparing\n" ^ print_term Σ Γ1 (tProd na A1 B1) ^ - "\nand\n" ^ print_term Σ Γ2 (tProd na' A2 B2) ^ - "\ndomains are not convertible:\n" ^ - string_of_conv_error Σ e - | CaseOnDifferentInd Γ ind par p c brs Γ' ind' par' p' c' brs' => - "The two stuck pattern-matching\n" ^ - print_term Σ Γ (tCase (ind, par) p c brs) ^ - "\nand\n" ^ print_term Σ Γ' (tCase (ind', par') p' c' brs') ^ - "\nare done on distinct inductive types." - | CaseBranchNumMismatch - ind par Γ p c brs1 m br brs2 Γ' p' c' brs1' m' br' brs2' => - "The two stuck pattern-matching\n" ^ - print_term Σ Γ (tCase (ind, par) p c (brs1 ++ (m,br) :: brs2)) ^ - "\nand\n" ^ - print_term Σ Γ' (tCase (ind, par) p' c' (brs1' ++ (m',br') :: brs2')) ^ - "\nhave a mistmatch in the branch number " ^ string_of_nat #|brs1| ^ - "\nthe number of parameters do not coincide\n" ^ - print_term Σ Γ br ^ - "\nhas " ^ string_of_nat m ^ " parameters while\n" ^ - print_term Σ Γ br' ^ - "\nhas " ^ string_of_nat m' ^ "." - | DistinctStuckProj Γ p c Γ' p' c' => - "The two stuck projections\n" ^ - print_term Σ Γ (tProj p c) ^ - "\nand\n" ^ - print_term Σ Γ' (tProj p' c') ^ - "\nare syntactically different." - | CannotUnfoldFix Γ mfix idx Γ' mfix' idx' => - "The two fixed-points\n" ^ - print_term Σ Γ (tFix mfix idx) ^ - "\nand\n" ^ print_term Σ Γ' (tFix mfix' idx') ^ - "\ncorrespond to syntactically distinct terms that can't be unfolded." - | FixRargMismatch idx Γ u mfix1 mfix2 Γ' v mfix1' mfix2' => - "The two fixed-points\n" ^ - print_term Σ Γ (tFix (mfix1 ++ u :: mfix2) idx) ^ - "\nand\n" ^ print_term Σ Γ' (tFix (mfix1' ++ v :: mfix2') idx) ^ - "\nhave a mismatch in the function number " ^ string_of_nat #|mfix1| ^ - ": arguments " ^ string_of_nat u.(rarg) ^ - " and " ^ string_of_nat v.(rarg) ^ "are different." - | FixMfixMismatch idx Γ mfix Γ' mfix' => - "The two fixed-points\n" ^ - print_term Σ Γ (tFix mfix idx) ^ - "\nand\n" ^ - print_term Σ Γ' (tFix mfix' idx) ^ - "\nhave a different number of mutually defined functions." - | DistinctCoFix Γ mfix idx Γ' mfix' idx' => - "The two cofixed-points\n" ^ - print_term Σ Γ (tCoFix mfix idx) ^ - "\nand\n" ^ print_term Σ Γ' (tCoFix mfix' idx') ^ - "\ncorrespond to syntactically distinct terms." - | CoFixRargMismatch idx Γ u mfix1 mfix2 Γ' v mfix1' mfix2' => - "The two co-fixed-points\n" ^ - print_term Σ Γ (tCoFix (mfix1 ++ u :: mfix2) idx) ^ - "\nand\n" ^ print_term Σ Γ' (tCoFix (mfix1' ++ v :: mfix2') idx) ^ - "\nhave a mismatch in the function number " ^ string_of_nat #|mfix1| ^ - ": arguments " ^ string_of_nat u.(rarg) ^ - " and " ^ string_of_nat v.(rarg) ^ "are different." - | CoFixMfixMismatch idx Γ mfix Γ' mfix' => - "The two co-fixed-points\n" ^ - print_term Σ Γ (tCoFix mfix idx) ^ - "\nand\n" ^ - print_term Σ Γ' (tCoFix mfix' idx) ^ - "\nhave a different number of mutually defined functions." - | StackHeadError leq Γ1 t1 args1 u1 l1 Γ2 t2 u2 l2 e => - "TODO stackheaderror\n" ^ - string_of_conv_error Σ e - | StackTailError leq Γ1 t1 args1 u1 l1 Γ2 t2 u2 l2 e => - "TODO stacktailerror\n" ^ - string_of_conv_error Σ e - | StackMismatch Γ1 t1 args1 l1 Γ2 t2 l2 => - "Convertible terms\n" ^ - print_term Σ Γ1 t1 ^ - "\nand\n" ^ print_term Σ Γ2 t2 ^ - "are convertible/convertible (TODO) but applied to a different number" ^ - " of arguments." - | HeadMismatch leq Γ1 t1 Γ2 t2 => - "Terms\n" ^ - print_term Σ Γ1 t1 ^ - "\nand\n" ^ print_term Σ Γ2 t2 ^ - "\ndo not have the same head when comparing for " ^ - string_of_conv_pb leq - end. +Inductive env_error := +| IllFormedDecl (e : string) (e : type_error) +| AlreadyDeclared (id : string). -Definition string_of_type_error Σ (e : type_error) : string := - match e with - | UnboundRel n => "Unbound rel " ^ string_of_nat n - | UnboundVar id => "Unbound var " ^ id - | UnboundEvar ev => "Unbound evar " ^ string_of_nat ev - | UndeclaredConstant c => "Undeclared constant " ^ string_of_kername c - | UndeclaredInductive c => "Undeclared inductive " ^ string_of_kername (inductive_mind c) - | UndeclaredConstructor c i => "Undeclared inductive " ^ string_of_kername (inductive_mind c) - | NotCumulSmaller G Γ t u t' u' e => "Terms are not <= for cumulativity:\n" ^ - print_term Σ Γ t ^ "\nand:\n" ^ print_term Σ Γ u ^ - "\nafter reduction:\n" ^ - print_term Σ Γ t' ^ "\nand:\n" ^ print_term Σ Γ u' ^ - "\nerror:\n" ^ string_of_conv_error Σ e ^ - "\nin universe graph:\n" ^ print_universes_graph G - | NotConvertible G Γ t u => "Terms are not convertible:\n" ^ - print_term Σ Γ t ^ "\nand:\n" ^ print_term Σ Γ u ^ - "\nin universe graph:\n" ^ print_universes_graph G - | NotASort t => "Not a sort" - | NotAProduct t t' => "Not a product" - | NotAnArity t => print_term Σ [] t ^ " is not an arity" - | NotAnInductive t => "Not an inductive" - | IllFormedFix m i => "Ill-formed recursive definition" - | UnsatisfiedConstraints c => "Unsatisfied constraints" - | Msg s => "Msg: " ^ s - end. +Inductive EnvCheck (A : Type) := +| CorrectDecl (a : A) +| EnvError (Σ : global_env_ext) (e : env_error). +Global Arguments EnvError {A} Σ e. +Global Arguments CorrectDecl {A} a. -Inductive typing_result (A : Type) := -| Checked (a : A) -| TypeError (t : type_error). -Global Arguments Checked {A} a. -Global Arguments TypeError {A} t. - -Instance typing_monad : Monad typing_result := - {| ret A a := Checked a ; - bind A B m f := - match m with - | Checked a => f a - | TypeError t => TypeError t - end +Global Instance envcheck_monad : Monad EnvCheck := + {| ret A a := CorrectDecl a ; + bind A B m f := + match m with + | CorrectDecl a => f a + | EnvError g e => EnvError g e + end |}. -Instance monad_exc : MonadExc type_error typing_result := - { raise A e := TypeError e; +Global Instance envcheck_monad_exc + : MonadExc (global_env_ext * env_error) EnvCheck := + { raise A '(g, e) := EnvError g e; catch A m f := match m with - | Checked a => m - | TypeError t => f t + | CorrectDecl a => m + | EnvError g t => f (g, t) end }. - -Lemma wf_local_rel_inv `{checker_flags} {Σ Γ1 Γ2} (w : wf_local_rel Σ Γ1 Γ2) : - forall d Γ2', Γ2 = Γ2' ,, d -> - wf_local_rel Σ Γ1 Γ2' × (∑ u, Σ ;;; Γ1 ,,, Γ2' |- d.(decl_type) : tSort u) × - match d.(decl_body) with - | Some b => Σ ;;; Γ1 ,,, Γ2' |- b : d.(decl_type) - | None => True - end. -Proof. - intros d Γ. - destruct w; inversion 1; subst; cbn in *. - split; [assumption|]. split; [assumption| trivial]. - split; [assumption|]. split; [assumption| trivial]. -Defined. - -Definition wf_local_app_inv `{cf : checker_flags} {Σ Γ1 Γ2} : - wf_local Σ Γ1 -> wf_local_rel Σ Γ1 Γ2 - -> wf_local Σ (Γ1 ,,, Γ2). -Proof. - intros H1 H2. - apply wf_local_local_rel, wf_local_rel_app. - now apply wf_local_rel_local. - now rewrite app_context_nil_l. -Defined. - -Definition fix_context_i i mfix := - List.rev (mapi_rec (fun i (d : BasicAst.def term) - => vass (dname d) ((lift0 i) (dtype d))) mfix i). - -Lemma lift_fix_context mfix : forall k k' j, j <= k -> - fix_context_i (k + k') mfix = lift_context k' j (fix_context_i k mfix). -Proof. - induction mfix. reflexivity. - intros k k' j Hj. - change ([vass (dname a) ((lift0 (k + k')) (dtype a))] ,,, fix_context_i (S (k + k')) mfix = lift_context k' j ([vass (dname a) ((lift0 k) (dtype a))] ,,, fix_context_i (S k) mfix)). - erewrite lift_context_app, (IHmfix (S k) k' (S j)); cbn. - unfold map_decl, vass; cbn. now rewrite simpl_lift. - now apply le_n_S. -Qed. - -Lemma wf_ext_gc_of_uctx {cf:checker_flags} {Σ : global_env_ext} (HΣ : ∥ wf_ext Σ ∥) - : ∑ uctx', gc_of_uctx (global_ext_uctx Σ) = Some uctx'. -Proof. - assert (consistent (global_ext_uctx Σ).2) as HC. - { sq; apply (global_ext_uctx_consistent _ HΣ). } - destruct Σ as [Σ φ]. - simpl in HC. - unfold gc_of_uctx; simpl in *. - apply gc_consistent_iff in HC. - destruct (gc_of_constraints (global_ext_constraints (Σ, φ))). - eexists; reflexivity. - contradiction HC. -Defined. - -Lemma wf_ext_is_graph {cf:checker_flags} {Σ : global_env_ext} (HΣ : ∥ wf_ext Σ ∥) - : ∑ G, is_graph_of_uctx G (global_ext_uctx Σ). -Proof. - destruct (wf_ext_gc_of_uctx HΣ) as [uctx Huctx]. - exists (make_graph uctx). unfold is_graph_of_uctx. now rewrite Huctx. -Defined. - -Lemma destArity_mkApps_None ctx t l : - destArity ctx t = None -> destArity ctx (mkApps t l) = None. -Proof. - induction l in t |- *. trivial. - intros H. cbn. apply IHl. reflexivity. -Qed. - -Lemma destArity_mkApps_Ind ctx ind u l : - destArity ctx (mkApps (tInd ind u) l) = None. -Proof. - apply destArity_mkApps_None. reflexivity. -Qed. - -Section Typecheck. - Context {cf : checker_flags} {Σ : global_env_ext} (HΣ : ∥ wf Σ ∥) - (Hφ : ∥ on_udecl Σ.1 Σ.2 ∥) - (G : universes_graph) (HG : is_graph_of_uctx G (global_ext_uctx Σ)). - - (* We get stack overflow on Qed after Equations definitions when this is transparent *) - Opaque reduce_stack_full. - - Local Definition HΣ' : ∥ wf_ext Σ ∥. - Proof. - destruct HΣ, Hφ; now constructor. - Defined. - - Definition isType_welltyped {Γ t} - : isType Σ Γ t -> welltyped Σ Γ t. - Proof. - intros []. now econstructor. - Qed. - - Lemma validity_wf {Γ t T} : - ∥ wf_local Σ Γ ∥ -> ∥ Σ ;;; Γ |- t : T ∥ -> welltyped Σ Γ T. - Proof. - destruct HΣ as [wΣ]. intros [wΓ] [X]. - intros. eapply validity_term in X; try assumption. - destruct X. now exists (tSort x). - Defined. - - Lemma wat_welltyped {Γ T} : - ∥ isType Σ Γ T ∥ -> welltyped Σ Γ T. - Proof. - destruct HΣ as [wΣ]. intros [X]. - now apply isType_welltyped. - Defined. - - Definition hnf := reduce_term RedFlags.default Σ HΣ. - - Theorem hnf_sound {Γ t h} : ∥ red (fst Σ) Γ t (hnf Γ t h) ∥. - Proof. - apply reduce_term_sound. - Defined. - - Theorem hnf_complete {Γ t h} : ∥whnf RedFlags.default Σ Γ (hnf Γ t h)∥. - Proof. - apply reduce_term_complete. - Qed. - - Inductive view_sort : term -> Type := - | view_sort_sort s : view_sort (tSort s) - | view_sort_other t : ~isSort t -> view_sort t. - - Equations view_sortc (t : term) : view_sort t := - view_sortc (tSort s) := view_sort_sort s; - view_sortc t := view_sort_other t _. - - Equations? reduce_to_sort (Γ : context) (t : term) (h : welltyped Σ Γ t) - : typing_result (∑ u, ∥ red (fst Σ) Γ t (tSort u) ∥) := - reduce_to_sort Γ t h with view_sortc t := { - | view_sort_sort s => ret (s; sq (refl_red _ _ _)); - | view_sort_other t _ with inspect (hnf Γ t h) := - | exist hnft eq with view_sortc hnft := { - | view_sort_sort s => ret (s; _); - | view_sort_other t _ => raise (NotASort t) - } - }. - Proof. - pose proof (hnf_sound (h:=h)). - now rewrite eq. - Qed. - - Lemma reduce_to_sort_complete {Γ t wt} e : - reduce_to_sort Γ t wt = TypeError e -> - (forall s, red Σ Γ t (tSort s) -> False). - Proof. - funelim (reduce_to_sort Γ t wt); try congruence. - intros _ s r. - pose proof (@hnf_complete Γ t0 h) as [wh]. - pose proof (@hnf_sound Γ t0 h) as [r']. - destruct HΣ. - eapply red_confluence in r as (?&r1&r2); eauto. - apply invert_red_sort in r2 as ->. - eapply whnf_red_inv in r1; eauto. - depelim r1. - clear Heq. - rewrite H in n0. - now cbn in n0. - Qed. - - Inductive view_prod : term -> Type := - | view_prod_prod na A b : view_prod (tProd na A b) - | view_prod_other t : ~isProd t -> view_prod t. - - Equations view_prodc (t : term) : view_prod t := - view_prodc (tProd na A b) := view_prod_prod na A b; - view_prodc t := view_prod_other t _. - - Equations? reduce_to_prod (Γ : context) (t : term) (h : welltyped Σ Γ t) - : typing_result (∑ na a b, ∥ red (fst Σ) Γ t (tProd na a b) ∥) := - reduce_to_prod Γ t h with view_prodc t := { - | view_prod_prod na a b => ret (na; a; b; sq (refl_red _ _ _)); - | view_prod_other t _ with inspect (hnf Γ t h) := - | exist hnft eq with view_prodc hnft := { - | view_prod_prod na a b => ret (na; a; b; _); - | view_prod_other t' _ => raise (NotAProduct t t') - } - }. - Proof. - pose proof (hnf_sound (h:=h)). - now rewrite eq. - Qed. - - Lemma reduce_to_prod_complete {Γ t wt} e : - reduce_to_prod Γ t wt = TypeError e -> - (forall na a b, red Σ Γ t (tProd na a b) -> False). - Proof. - funelim (reduce_to_prod Γ t wt); try congruence. - intros _ na a b r. - pose proof (@hnf_complete Γ t0 h) as [wh]. - pose proof (@hnf_sound Γ t0 h) as [r']. - destruct HΣ. - eapply red_confluence in r as (?&r1&r2); eauto. - apply invert_red_prod in r2 as (?&?&(->&?)&?); auto. - eapply whnf_red_inv in r1; auto. - depelim r1. - clear Heq. - rewrite H in n0. - now cbn in n0. - Qed. - - Definition isInd (t : term) : bool := - match t with - | tInd _ _ => true - | _ => false - end. - - Inductive view_ind : term -> Type := - | view_ind_tInd ind u : view_ind (tInd ind u) - | view_ind_other t : negb (isInd t) -> view_ind t. - - Equations view_indc (t : term) : view_ind t := - view_indc (tInd ind u) => view_ind_tInd ind u; - view_indc t => view_ind_other t _. - - Equations? reduce_to_ind (Γ : context) (t : term) (h : welltyped Σ Γ t) - : typing_result (∑ i u l, ∥ red (fst Σ) Γ t (mkApps (tInd i u) l) ∥) := - reduce_to_ind Γ t h with inspect (decompose_app t) := { - | exist (thd, args) eq_decomp with view_indc thd := { - | view_ind_tInd i u => ret (i; u; args; sq _); - | view_ind_other t _ with inspect (reduce_stack RedFlags.default Σ HΣ Γ t Empty h) := { - | exist (hnft, π) eq with view_indc hnft := { - | view_ind_tInd i u with inspect (decompose_stack π) := { - | exist (l, _) eq_decomp => ret (i; u; l; _) - }; - | view_ind_other _ _ => raise (NotAnInductive t) - } - } - } - }. - Proof. - - assert (X : mkApps (tInd i u) args = t); [|rewrite X; apply refl_red]. - etransitivity. 2: symmetry; eapply mkApps_decompose_app. - now rewrite <- eq_decomp. - - pose proof (reduce_stack_sound RedFlags.default Σ HΣ _ _ Empty h). - rewrite <- eq in H. - cbn in *. - assert (π = appstack l ε) as ->. - 2: { now rewrite zipc_appstack in H. } - unfold reduce_stack in eq. - destruct reduce_stack_full as (?&_&stack_val&?). - subst x. - unfold Pr in stack_val. - cbn in *. - assert (decomp: decompose_stack π = ((decompose_stack π).1, ε)). - { rewrite stack_val. - now destruct decompose_stack. } - apply decompose_stack_eq in decomp as ->. - now rewrite <- eq_decomp0. - Qed. - - Lemma reduce_to_ind_complete Γ ty wat e : - reduce_to_ind Γ ty wat = TypeError e -> - forall ind u args, - red Σ Γ ty (mkApps (tInd ind u) args) -> - False. - Proof. - funelim (reduce_to_ind Γ ty wat); try congruence. - intros _ ind u args r. - pose proof (reduce_stack_whnf RedFlags.default Σ HΣ Γ t ε h) as wh. - unfold reduce_stack in *. - destruct reduce_stack_full as ((hd&π)&r'&stack_valid&(notapp&_)). - destruct wh as [wh]. - apply Req_red in r' as [r']. - unfold Pr in stack_valid. - cbn in *. - destruct HΣ. - eapply red_confluence in r as (?&r1&r2); [|eassumption|exact r']. - assert (exists args, π = appstack args ε) as (?&->). - { exists ((decompose_stack π).1). - assert (decomp: decompose_stack π = ((decompose_stack π).1, ε)). - { now rewrite stack_valid; destruct decompose_stack. } - now apply decompose_stack_eq in decomp. } - - unfold zipp in wh. - rewrite stack_context_appstack decompose_stack_appstack in wh. - rewrite zipc_appstack in r1. - cbn in *. - rewrite app_nil_r in wh. - apply red_mkApps_tInd in r2 as (?&->&?); auto. - eapply whnf_red_inv in r1; eauto. - apply whnf_red_mkApps_inv in r1 as (?&?); auto. - depelim w. - noconf e0. - discriminate i0. - Qed. - - Definition isconv Γ := isconv_term Σ HΣ Hφ G HG Γ Conv. - Definition iscumul Γ := isconv_term Σ HΣ Hφ G HG Γ Cumul. - - Program Definition convert Γ t u - (ht : welltyped Σ Γ t) (hu : welltyped Σ Γ u) - : typing_result (∥ Σ ;;; Γ |- t = u ∥) := - match eqb_term Σ G t u with true => ret _ | false => - match isconv Γ t ht u hu with - | ConvSuccess => ret _ - | ConvError e => (* fallback *) (* nico *) - let t' := hnf Γ t ht in - let u' := hnf Γ u hu in - (* match leq_term (snd Σ) t' u' with true => ret _ | false => *) - raise (NotCumulSmaller G Γ t u t' u' e) - (* end *) - end end. - Next Obligation. - symmetry in Heq_anonymous; eapply eqb_term_spec in Heq_anonymous; tea. - constructor. now constructor. - Qed. - Next Obligation. - symmetry in Heq_anonymous; apply isconv_term_sound in Heq_anonymous. - assumption. - Qed. - - Program Definition convert_leq Γ t u - (ht : welltyped Σ Γ t) (hu : welltyped Σ Γ u) - : typing_result (∥ Σ ;;; Γ |- t <= u ∥) := - match leqb_term Σ G t u with true => ret _ | false => - match iscumul Γ t ht u hu with - | ConvSuccess => ret _ - | ConvError e => (* fallback *) (* nico *) - let t' := hnf Γ t ht in - let u' := hnf Γ u hu in - (* match leq_term (snd Σ) t' u' with true => ret _ | false => *) - raise (NotCumulSmaller G Γ t u t' u' e) - (* end *) - end end. - Next Obligation. - symmetry in Heq_anonymous; eapply leqb_term_spec in Heq_anonymous; tea. - constructor. now constructor. - Qed. - Next Obligation. - symmetry in Heq_anonymous; apply isconv_term_sound in Heq_anonymous. - assumption. - Qed. - - Section InferAux. - Variable (infer : forall Γ (HΓ : ∥ wf_local Σ Γ ∥) (t : term), - typing_result ({ A : term & ∥ Σ ;;; Γ |- t : A ∥ })). - - Program Definition infer_type Γ HΓ t - : typing_result ({u : Universe.t & ∥ Σ ;;; Γ |- t : tSort u ∥}) := - tx <- infer Γ HΓ t ;; - u <- reduce_to_sort Γ tx.π1 _ ;; - ret (u.π1; _). - Next Obligation. - eapply validity_wf; eassumption. - Defined. - Next Obligation. - destruct HΣ, HΓ, X, X0. - now constructor; eapply type_reduction. - Defined. - - Program Definition infer_cumul Γ HΓ t A (hA : ∥ isType Σ Γ A ∥) - : typing_result (∥ Σ ;;; Γ |- t : A ∥) := - A' <- infer Γ HΓ t ;; - X <- convert_leq Γ A'.π1 A _ _ ;; - ret _. - Next Obligation. now eapply validity_wf. Qed. - Next Obligation. destruct hA; now apply wat_welltyped. Qed. - Next Obligation. - destruct HΣ, HΓ, hA, X, X0. constructor. eapply type_Cumul'; eassumption. - Qed. - End InferAux. - - - Program Definition lookup_ind_decl ind - : typing_result - ({decl & {body & declared_inductive (fst Σ) decl ind body}}) := - match lookup_env (fst Σ) ind.(inductive_mind) with - | Some (InductiveDecl decl) => - match nth_error decl.(ind_bodies) ind.(inductive_ind) with - | Some body => ret (decl; body; _) - | None => raise (UndeclaredInductive ind) - end - | _ => raise (UndeclaredInductive ind) - end. - Next Obligation. - split. - - symmetry in Heq_anonymous0. - etransitivity. eassumption. reflexivity. - - now symmetry. - Defined. - - Lemma check_constraints_spec ctrs - : check_constraints G ctrs -> valid_constraints (global_ext_constraints Σ) ctrs. - Proof. - pose proof HΣ'. - intros HH. - refine (check_constraints_spec G (global_ext_uctx Σ) _ _ HG _ HH). - sq; now eapply wf_ext_global_uctx_invariants. - sq; now apply global_ext_uctx_consistent. - Qed. - - Lemma is_graph_of_uctx_levels (l : Level.t) : - LevelSet.mem l (uGraph.wGraph.V G) -> - LevelSet.mem l (global_ext_levels Σ). - Proof. - unfold is_graph_of_uctx in HG. - case_eq (gc_of_uctx (global_ext_uctx Σ)); [intros [lvs cts] XX|intro XX]; - rewrite -> XX in *; simpl in *; [|contradiction]. - unfold gc_of_uctx in XX; simpl in XX. - destruct (gc_of_constraints Σ); [|discriminate]. - inversion XX; subst. generalize (global_ext_levels Σ); intros lvs; cbn. - clear. intro H. apply LevelSet.mem_spec. now apply LevelSet.mem_spec in H. - Qed. - - - Program Definition check_consistent_instance uctx u - : typing_result (consistent_instance_ext Σ uctx u) - := match uctx with - | Monomorphic_ctx _ => - check_eq_nat #|u| 0 (Msg "monomorphic instance should be of length 0") - | Polymorphic_ctx (inst, cstrs) => - let '(inst, cstrs) := AUContext.repr (inst, cstrs) in - check_eq_true (forallb (fun l => LevelSet.mem l (uGraph.wGraph.V G)) u) - (Msg "instance does not have the right length") ;; - (* check_eq_true (forallb (fun l => LevelSet.mem l lvs) u) ;; *) - X <- check_eq_nat #|u| #|inst| - (Msg "instance does not have the right length");; - match check_constraints G (subst_instance_cstrs u cstrs) with - | true => ret (conj _ _) - | false => raise (Msg "ctrs not satisfiable") - end - (* #|u| = #|inst| /\ valid_constraints φ (subst_instance_cstrs u cstrs) *) - end. - Next Obligation. - eapply forallb_All in H. eapply All_forallb'; tea. - clear -cf HG. intros x; simpl. apply is_graph_of_uctx_levels. - Qed. - Next Obligation. - repeat split. - - now rewrite mapi_length in X. - - eapply check_constraints_spec; eauto. - Qed. - - Obligation Tactic := Program.Tactics.program_simplify ; eauto 2. - - Program Definition check_is_allowed_elimination (u : Universe.t) (al : allowed_eliminations) : - typing_result (is_allowed_elimination Σ u al) := - let o := - match al return option (is_allowed_elimination Σ u al) with - | IntoSProp => - match Universe.is_sprop u with - | true => Some _ - | false => None - end - | IntoPropSProp => - match is_propositional u with - | true => Some _ - | false => None - end - | IntoSetPropSProp => - match is_propositional u || check_eqb_universe G u Universe.type0 with - | true => Some _ - | false => None - end - | IntoAny => Some _ - end in - match o with - | Some t => Checked t - | None => TypeError (Msg "Cannot eliminate over this sort") - end. - Next Obligation. - unfold is_allowed_elimination, is_allowed_elimination0. - destruct check_univs; auto. - intros val sat. - symmetry in Heq_anonymous. - apply is_sprop_val with (v := val) in Heq_anonymous. - now rewrite Heq_anonymous. - Qed. - Next Obligation. - unfold is_allowed_elimination, is_allowed_elimination0. - destruct check_univs; auto. - intros val sat. - unfold is_propositional in *. - destruct Universe.is_prop eqn:prop. - - apply is_prop_val with (v := val) in prop; rewrite prop; auto. - - destruct Universe.is_sprop eqn:sprop. - + apply is_sprop_val with (v := val) in sprop; rewrite sprop; auto. - + discriminate. - Qed. - Next Obligation. - unfold is_allowed_elimination, is_allowed_elimination0. - destruct check_univs eqn:cu; auto. - intros val sat. - unfold is_propositional in *. - destruct Universe.is_prop eqn:prop. - - apply is_prop_val with (v := val) in prop; rewrite prop; auto. - - destruct Universe.is_sprop eqn:sprop. - + apply is_sprop_val with (v := val) in sprop; rewrite sprop; auto. - + destruct check_eqb_universe eqn:check; [|discriminate]. - eapply check_eqb_universe_spec' in check; eauto. - * unfold eq_universe, eq_universe0 in check. - rewrite cu in check. - specialize (check val sat). - now rewrite check. - * destruct HΣ, Hφ. - now apply wf_ext_global_uctx_invariants. - * destruct HΣ, Hφ. - now apply global_ext_uctx_consistent. - Qed. - Next Obligation. - unfold is_allowed_elimination, is_allowed_elimination0. - destruct check_univs; auto. - Qed. - - Program Fixpoint infer (Γ : context) (HΓ : ∥ wf_local Σ Γ ∥) (t : term) {struct t} - : typing_result ({ A : term & ∥ Σ ;;; Γ |- t : A ∥ }) := - match t with - | tRel n => - match nth_error Γ n with - | Some c => ret ((lift0 (S n)) (decl_type c); _) - | None => raise (UnboundRel n) - end - - | tVar n => raise (UnboundVar n) - | tEvar ev args => raise (UnboundEvar ev) - - | tSort u => - check_eq_true (wf_universeb Σ u) - (Msg ("Sort contains an undeclared level " ^ string_of_sort u));; - ret (tSort (Universe.super u); _) - - | tProd na A B => - s1 <- infer_type infer Γ HΓ A ;; - s2 <- infer_type infer (Γ ,, vass na A) _ B ;; - ret (tSort (Universe.sort_of_product s1.π1 s2.π1); _) - - | tLambda na A t => - s1 <- infer_type infer Γ HΓ A ;; - B <- infer (Γ ,, vass na A) _ t ;; - ret (tProd na A B.π1; _) - - | tLetIn n b b_ty b' => - infer_type infer Γ HΓ b_ty ;; - infer_cumul infer Γ HΓ b b_ty _ ;; - b'_ty <- infer (Γ ,, vdef n b b_ty) _ b' ;; - ret (tLetIn n b b_ty b'_ty.π1; _) - - | tApp t u => - ty <- infer Γ HΓ t ;; - pi <- reduce_to_prod Γ ty.π1 _ ;; - infer_cumul infer Γ HΓ u pi.π2.π1 _ ;; - ret (subst10 u pi.π2.π2.π1; _) - - | tConst cst u => - match lookup_env (fst Σ) cst with - | Some (ConstantDecl d) => - check_consistent_instance d.(cst_universes) u ;; - let ty := subst_instance_constr u d.(cst_type) in - ret (ty; _) - | _ => raise (UndeclaredConstant cst) - end - - | tInd ind u => - d <- lookup_ind_decl ind ;; - check_consistent_instance d.π1.(ind_universes) u ;; - let ty := subst_instance_constr u d.π2.π1.(ind_type) in - ret (ty; _) - - | tConstruct ind k u => - d <- lookup_ind_decl ind ;; - match nth_error d.π2.π1.(ind_ctors) k with - | Some cdecl => - check_consistent_instance d.π1.(ind_universes) u ;; - ret (type_of_constructor d.π1 cdecl (ind, k) u; _) - | None => raise (UndeclaredConstructor ind k) - end - - | tCase (ind, par) p c brs => - cty <- infer Γ HΓ c ;; - I <- reduce_to_ind Γ cty.π1 _ ;; - let '(ind'; I') := I in let '(u; I'') := I' in let '(args; H) := I'' in - check_eq_true (eqb ind ind') - (* bad case info *) - (NotConvertible G Γ (tInd ind u) (tInd ind' u)) ;; - d <- lookup_ind_decl ind' ;; - let '(decl; d') := d in let '(body; HH) := d' in - check_coind <- check_eq_true (negb (isCoFinite (ind_finite decl))) - (Msg "Case on coinductives disallowed") ;; - check_eq_true (ind_npars decl =? par) - (Msg "not the right number of parameters") ;; - pty <- infer Γ HΓ p ;; - match destArity [] pty.π1 with - | None => raise (Msg "the type of the return predicate of a Case is not an arity") - | Some (pctx, ps) => - check_is_allowed_elimination ps (ind_kelim body);; - let params := firstn par args in - match build_case_predicate_type ind decl body params u ps with - | None => raise (Msg "failure in build_case_predicate_type") - | Some pty' => - (* We could avoid one useless sort comparison by only comparing *) - (* the contexts [pctx] and [indctx] (what is done in Coq). *) - match iscumul Γ pty.π1 _ pty' _ with - | ConvError e => raise (NotCumulSmaller G Γ pty.π1 pty' pty.π1 pty' e) - | ConvSuccess => - match map_option_out (build_branches_type ind decl body params u p) with - | None => raise (Msg "failure in build_branches_type") - | Some btys => - let btyswf : ∥ All (isType Σ Γ ∘ snd) btys ∥ := _ in - (fix check_branches (brs btys : list (nat * term)) - (HH : ∥ All (isType Σ Γ ∘ snd) btys ∥) {struct brs} - : typing_result - (All2 (fun br bty => br.1 = bty.1 /\ ∥ Σ ;;; Γ |- br.2 : bty.2 ∥) brs btys) - := match brs, btys with - | [], [] => ret All2_nil - | (n, t) :: brs , (m, A) :: btys => - W <- check_dec (Msg "not nat eq") - (EqDecInstances.nat_eqdec n m) ;; - Z <- infer_cumul infer Γ HΓ t A _ ;; - X <- check_branches brs btys _ ;; - ret (All2_cons (conj _ _) X) - | [], _ :: _ - | _ :: _, [] => raise (Msg "wrong number of branches") - end) brs btys btyswf ;; - ret (mkApps p (List.skipn par args ++ [c]); _) - end - end - end - end - - | tProj (ind, n, k) c => - d <- lookup_ind_decl ind ;; - match nth_error d.π2.π1.(ind_projs) k with - | Some pdecl => - c_ty <- infer Γ HΓ c ;; - I <- reduce_to_ind Γ c_ty.π1 _ ;; - let '(ind'; I') := I in let '(u; I'') := I' in let '(args; H) := I'' in - check_eq_true (eqb ind ind') - (NotConvertible G Γ (tInd ind u) (tInd ind' u)) ;; - check_eq_true (ind_npars d.π1 =? n) - (Msg "not the right number of parameters") ;; - let ty := snd pdecl in - ret (subst0 (c :: List.rev args) (subst_instance_constr u ty); - _) - | None => raise (Msg "projection not found") - end - - | tFix mfix n => - match nth_error mfix n with - | None => raise (IllFormedFix mfix n) - | Some decl => - XX <- (fix check_types (mfix : mfixpoint term) {struct mfix} - : typing_result (∥ All (fun x => isType Σ Γ (dtype x)) mfix ∥) - := match mfix with - | [] => ret (sq All_nil) - | def :: mfix => - (* probably not tail recursive but needed so that next line terminates *) - W <- infer_type infer Γ HΓ (dtype def) ;; - Z <- check_types mfix ;; - ret _ - end) - mfix ;; - YY <- (fix check_bodies (mfix' : mfixpoint term) - (XX : ∥ All (fun x => isType Σ Γ (dtype x)) mfix' ∥) - {struct mfix'} - : typing_result (All (fun d => - ∥ Σ ;;; Γ ,,, fix_context mfix |- dbody d : (lift0 #|fix_context mfix|) (dtype d) ∥ - /\ isLambda (dbody d) = true) mfix') - := match mfix' with - | [] => ret All_nil - | def :: mfix' => - W1 <- infer_cumul infer (Γ ,,, fix_context mfix) _ (dbody def) - (lift0 #|fix_context mfix| (dtype def)) _ ;; - W2 <- check_eq_true (isLambda (dbody def)) - (Msg "not a lambda") ;; - Z <- check_bodies mfix' _ ;; - ret (All_cons (conj W1 W2) Z) - end) mfix _ ;; - guarded <- check_eq_true (fix_guard mfix) (Msg "Unguarded fixpoint") ;; - wffix <- check_eq_true (wf_fixpoint Σ.1 mfix) (Msg "Ill-formed fixpoint: not defined on a mutually inductive family") ;; - ret (dtype decl; _) - end - - | tCoFix mfix n => - match nth_error mfix n with - | None => raise (IllFormedFix mfix n) - | Some decl => - XX <- (fix check_types (mfix : mfixpoint term) {struct mfix} - : typing_result (∥ All (fun x => isType Σ Γ (dtype x)) mfix ∥) - := match mfix with - | [] => ret (sq All_nil) - | def :: mfix => - (* probably not tail recursive but needed so that next line terminates *) - W <- infer_type infer Γ HΓ (dtype def) ;; - Z <- check_types mfix ;; - ret _ - end) - mfix ;; - YY <- (fix check_bodies (mfix' : mfixpoint term) - (XX' : ∥ All (fun x => isType Σ Γ (dtype x)) mfix' ∥) - {struct mfix'} - : typing_result (All (fun d => - ∥ Σ ;;; Γ ,,, fix_context mfix |- dbody d : (lift0 #|fix_context mfix|) (dtype d) ∥) mfix') - := match mfix' with - | [] => ret All_nil - | def :: mfix' => - W1 <- infer_cumul infer (Γ ,,, fix_context mfix) _ (dbody def) - (lift0 #|fix_context mfix| (dtype def)) _ ;; - Z <- check_bodies mfix' _ ;; - ret (All_cons W1 Z) - end) mfix _ ;; - guarded <- check_eq_true (cofix_guard mfix) (Msg "Unguarded cofixpoint") ;; - wfcofix <- check_eq_true (wf_cofixpoint Σ.1 mfix) (Msg "Ill-formed cofixpoint: not producing values in a mutually coinductive family") ;; - ret (dtype decl; _) - end - end. - - (* tRel *) - Next Obligation. intros; sq; now econstructor. Defined. - (* tSort *) - Next Obligation. - eapply (elimT wf_universe_reflect) in H. - sq; econstructor; tas. - Defined. - (* tProd *) - Next Obligation. - (* intros Γ HΓ t na A B Heq_t [s ?]; *) - sq; econstructor; cbn; easy. Defined. - Next Obligation. - (* intros Γ HΓ t na A B Heq_t [s1 ?] [s2 ?]; *) - sq; econstructor; eassumption. - Defined. - (* tLambda *) - Next Obligation. - (* intros Γ HΓ t0 na A t Heq_t [s ?]; *) - sq; econstructor; cbn; easy. - Defined. - Next Obligation. - (* intros Γ HΓ t0 na A t Heq_t [s ?] [B ?]; *) - sq; econstructor; eassumption. - Defined. - (* tLetIn *) - Next Obligation. - (* intros Γ HΓ t n b b_ty b' Heq_t [? ?]; *) - sq. econstructor; eauto. - Defined. - Next Obligation. - (* intros Γ HΓ t n b b_ty b' Heq_t [? ?] H0; *) - sq; econstructor; cbn; eauto. - Defined. - Next Obligation. - (* intros Γ HΓ t n b b_ty b' Heq_t [? ?] H0 [? ?]; *) - sq; econstructor; eassumption. - Defined. - - (* tApp *) - Next Obligation. simpl; eauto using validity_wf. Qed. - Next Obligation. - cbn in *; sq. - eapply type_reduction in X1 ; try eassumption. - eapply validity_term in X1 ; try assumption. destruct X1 as [s HH]. - eapply inversion_Prod in HH ; try assumption. - destruct HH as [s1 [_ [HH _]]]. - eexists. eassumption. - Defined. - Next Obligation. - cbn in *; sq; econstructor. - 2: eassumption. - eapply type_reduction; eassumption. - Defined. - - (* tConst *) - Next Obligation. - rename Heq_anonymous into HH. - sq; constructor; try assumption. - symmetry in HH. - etransitivity. eassumption. reflexivity. - Defined. - - (* tInd *) - Next Obligation. - sq; econstructor; eassumption. - Defined. - - (* tConstruct *) - Next Obligation. - sq; econstructor; tea. now split. - Defined. - - (* tCase *) - Next Obligation. simpl; eauto using validity_wf. Qed. - Next Obligation. simpl; eauto using validity_wf. Qed. - Next Obligation. - destruct X, X9. sq. - change (eqb ind I = true) in H0. - destruct (eqb_spec ind I) as [e|e]; [destruct e|discriminate]. - change (eqb (ind_npars d) par = true) in H1. - destruct (eqb_spec (ind_npars d) par) as [e|e]; [|discriminate]. - rename Heq_anonymous into HH. symmetry in HH. - simpl in *. - eapply type_reduction in t0; eauto. eapply validity in t0; eauto. - rewrite <- e in HH. - eapply PCUICInductiveInversion.WfArity_build_case_predicate_type in HH; eauto. - destruct HH as [[s Hs] ?]. eexists; eauto. - eapply validity in t; eauto. - generalize (PCUICClosed.destArity_spec [] pty). - rewrite -Heq_anonymous0 /=. intros ->. - eapply PCUICInductives.isType_it_mkProd_or_LetIn_inv in t; eauto. - eapply isType_wf_universes in t. simpl in t. - now exact (elimT wf_universe_reflect t). auto. - Qed. - - Next Obligation. - symmetry in Heq_anonymous2. - unfold iscumul in Heq_anonymous2. simpl in Heq_anonymous2. - apply isconv_term_sound in Heq_anonymous2. - red in Heq_anonymous2. - noconf Heq_I''. - noconf Heq_I'. noconf Heq_I. - noconf Heq_d. noconf Heq_d'. - simpl in *; sq. - change (eqb ind I = true) in H0. - destruct (eqb_spec ind I) as [e|e]; [destruct e|discriminate H0]. - change (eqb (ind_npars d) par = true) in H1. - destruct (eqb_spec (ind_npars d) par) as [e|e]; [|discriminate]; subst. - assert (wfΣ : wf_ext Σ) by (split; auto). - eapply type_reduction in X9; eauto. - have val:= validity_term wfΣ X9. - eapply type_Cumul' in X; [| |eassumption]. - 2:{ eapply PCUICInductiveInversion.WfArity_build_case_predicate_type; eauto. - eapply validity in X; eauto. - generalize (PCUICClosed.destArity_spec [] pty). - rewrite -Heq_anonymous0 /=. intros ->. - eapply PCUICInductives.isType_it_mkProd_or_LetIn_inv in X; eauto. - eapply isType_wf_universes in X. simpl in X. - now exact (elimT wf_universe_reflect X). auto. } - have [pctx' da] : (∑ pctx', destArity [] pty' = Some (pctx', ps)). - { symmetry in Heq_anonymous1. - unshelve eapply (PCUICInductives.build_case_predicate_type_spec (Σ.1, ind_universes d)) in Heq_anonymous1 as [parsubst [_ ->]]. - eauto. eapply (PCUICWeakeningEnv.on_declared_inductive wfΣ) in HH as [? ?]. eauto. - eexists. rewrite !destArity_it_mkProd_or_LetIn; simpl. reflexivity. } - eapply PCUICInductiveInversion.build_branches_type_wt. 6:eapply X. all:eauto. - Defined. - - Obligation Tactic := simpl; intros. - - Next Obligation. - rename Heq_anonymous2 into XX2. - symmetry in XX2. simpl in *. eapply isconv_sound in XX2. - change (eqb ind ind' = true) in H0. - destruct (eqb_spec ind ind') as [e|e]; [destruct e|discriminate H0]. - change (eqb (ind_npars decl) par = true) in H1. - destruct (eqb_spec (ind_npars decl) par) as [e|e]; [|discriminate]; subst. - depelim HH. - sq. auto. now depelim X. - Defined. - Next Obligation. - sq. now depelim HH. - Defined. - - (* The obligation tactic removes a useful let here. *) - Obligation Tactic := idtac. - Next Obligation. - intros. clearbody btyswf. idtac; Program.Tactics.program_simplify. - symmetry in Heq_anonymous2. - unfold iscumul in Heq_anonymous2. simpl in Heq_anonymous2. - apply isconv_term_sound in Heq_anonymous2. - noconf Heq_I''. noconf Heq_I'. noconf Heq_I. - noconf Heq_d. noconf Heq_d'. simpl in *. - assert (∥ All2 (fun x y => ((fst x = fst y) * - (Σ;;; Γ |- snd x : snd y) * isType Σ Γ y.2)%type) brs btys ∥). { - solve_all. simpl in *. - destruct btyswf. eapply All2_sq. solve_all. simpl in *; intuition (sq; auto). } - clear H3. sq. - change (eqb ind I = true) in H0. - destruct (eqb_spec ind I) as [e|e]; [destruct e|discriminate H0]. - change (eqb (ind_npars d) par = true) in H1. - destruct (eqb_spec (ind_npars d) par) as [e|e]; [|discriminate]; subst. - assert (wfΣ : wf_ext Σ) by (split; auto). - eapply type_reduction in X9; eauto. - eapply type_Cumul' in X; eauto. - 2:{ eapply PCUICInductiveInversion.WfArity_build_case_predicate_type; eauto. - now eapply validity in X9. - eapply validity in X; eauto. - generalize (PCUICClosed.destArity_spec [] pty). - rewrite -Heq_anonymous0 /=. intros ->. - eapply PCUICInductives.isType_it_mkProd_or_LetIn_inv in X; eauto. - eapply isType_wf_universes in X. simpl in X. - now exact (elimT wf_universe_reflect X). auto. } - have [pctx' da] : (∑ pctx', destArity [] pty' = Some (pctx', ps)). - { symmetry in Heq_anonymous1. - unshelve eapply (PCUICInductives.build_case_predicate_type_spec (Σ.1, ind_universes d)) in Heq_anonymous1 as [parsubst [_ ->]]. - eauto. eapply (PCUICWeakeningEnv.on_declared_inductive wfΣ) in HH as [? ?]. eauto. - eexists. rewrite !destArity_it_mkProd_or_LetIn; simpl. reflexivity. } - eapply type_Case with (pty0:=pty'); tea. - - reflexivity. - - symmetry; eassumption. - - destruct isCoFinite; auto. - - symmetry; eauto. - Defined. - - Obligation Tactic := Program.Tactics.program_simplify ; eauto 2. - - (* tProj *) - Next Obligation. simpl; eauto using validity_wf. Qed. - Next Obligation. - simpl in *; sq; eapply type_Proj with (pdecl := (i, t0)). - - split. eassumption. split. symmetry; eassumption. cbn in *. - now apply beq_nat_true. - - cbn. destruct (ssrbool.elimT (eqb_spec ind I)); [assumption|]. - eapply type_reduction; eassumption. - - eapply type_reduction in X5; eauto. - eapply validity_term in X5; eauto. - destruct (ssrbool.elimT (eqb_spec ind I)); auto. - unshelve eapply (PCUICInductives.isType_mkApps_Ind _ X7 _) in X5 as [parsubst [argsubst [[sp sp'] cu]]]; eauto. - pose proof (PCUICContexts.context_subst_length2 (PCUICSpine.inst_ctx_subst sp)). - pose proof (PCUICContexts.context_subst_length2 (PCUICSpine.inst_ctx_subst sp')). - autorewrite with len in H, H2. - destruct (PCUICWeakeningEnv.on_declared_inductive HΣ X7) eqn:ond. - rewrite -o.(onNpars) -H. - forward (o0.(onProjections)). - intros H'; rewrite H' nth_error_nil // in Heq_anonymous. - destruct ind_cshapes as [|cs []]; auto. - intros onps. - unshelve epose proof (onps.(on_projs_noidx _ _ _ _ _ _)). - rewrite ond /= in H2. - change (ind_indices o0) with (ind_indices o0) in *. - destruct (ind_indices o0) => //. - simpl in H2. - rewrite List.skipn_length in H2. - rewrite List.firstn_length. lia. - Qed. - - (* tFix *) - Next Obligation. sq. constructor; auto. exists W; auto. Defined. - Next Obligation. sq. now eapply PCUICWeakening.All_mfix_wf in XX0. Defined. - Next Obligation. - sq. cbn in *. depelim XX. - destruct i as [s HH]. - exists s. - change (tSort s) with (lift0 #|fix_context mfix| (tSort s)). - apply weakening; try assumption. - now apply All_mfix_wf. - Defined. - Next Obligation. - clear -XX HΣ. sq. - now depelim XX. - Qed. - Next Obligation. - assert (∥ All (fun d => ((Σ;;; Γ ,,, fix_context mfix |- dbody d : (lift0 #|fix_context mfix|) (dtype d)) * (isLambda (dbody d) = true))%type) mfix ∥). { - eapply All_sq, All_impl. exact YY. - cbn; intros ? []. sq; now constructor. } - sq; econstructor; try eassumption. - symmetry; eassumption. - Qed. - - (* tCoFix *) - Next Obligation. sq. constructor; auto. exists W; auto. Defined. - Next Obligation. sq. now eapply PCUICWeakening.All_mfix_wf in XX. Defined. - Next Obligation. - sq. cbn in *. depelim XX'. - destruct i as [s HH]. - exists s. - change (tSort s) with (lift0 #|fix_context mfix| (tSort s)). - apply weakening; try assumption. - now apply All_mfix_wf. - Defined. - Next Obligation. - clear -XX' HΣ. sq. - now depelim XX'. - Qed. - Next Obligation. - assert (∥ All (fun d => ((Σ;;; Γ ,,, fix_context mfix |- dbody d : (lift0 #|fix_context mfix|) (dtype d)))%type) mfix ∥). { - eapply All_sq, All_impl. exact YY. - now cbn; intros ? []. } - sq; econstructor; try eassumption. - symmetry; eassumption. - Qed. - - Lemma sq_wfl_nil : ∥ wf_local Σ [] ∥. - Proof. - repeat constructor. - Qed. - - Program Fixpoint check_context Γ : typing_result (∥ wf_local Σ Γ ∥) - := match Γ with - | [] => ret sq_wfl_nil - | {| decl_body := None; decl_type := A |} :: Γ => - HΓ <- check_context Γ ;; - XX <- infer_type infer Γ HΓ A ;; - ret _ - | {| decl_body := Some t; decl_type := A |} :: Γ => - HΓ <- check_context Γ ;; - XX <- infer_type infer Γ HΓ A ;; - XX <- infer_cumul infer Γ HΓ t A _ ;; - ret _ - end. - Next Obligation. - sq. econstructor; tas. econstructor; eauto. - Qed. - Next Obligation. - sq. econstructor; tea. - Qed. - Next Obligation. - sq. econstructor; tas. econstructor; eauto. - Qed. - -(* - Program Definition check_isWfArity Γ (HΓ : ∥ wf_local Σ Γ ∥) A - : typing_result (∥ isWfArity Σ Γ A ∥) := - match destArity [] A with - | None => raise (Msg (print_term Σ Γ A ^ " is not an arity")) - | Some (ctx, s) => XX <- check_context (Γ ,,, ctx) ;; - ret _ - end. - Next Obligation. - destruct XX. constructor. exists ctx, s. - split; auto. - Defined. *) - - Program Definition check_isType Γ (HΓ : ∥ wf_local Σ Γ ∥) A - : typing_result (∥ isType Σ Γ A ∥) := - s <- infer Γ HΓ A ;; - s' <- reduce_to_sort Γ s.π1 _ ;; - ret _. - Next Obligation. now eapply validity_wf. Defined. - Next Obligation. destruct X0. sq. eexists. eapply type_reduction; tea. Defined. - - Program Definition check Γ (HΓ : ∥ wf_local Σ Γ ∥) t A - : typing_result (∥ Σ;;; Γ |- t : A ∥) := - check_isType Γ HΓ A ;; - infer_cumul infer Γ HΓ t A _. - -End Typecheck. - - -Definition infer' {cf:checker_flags} {Σ} (HΣ : ∥ wf_ext Σ ∥) - := infer (map_squash fst HΣ) (map_squash snd HΣ). - -Definition make_graph_and_infer {cf:checker_flags} {Σ} (HΣ : ∥ wf_ext Σ ∥) - := let '(G; HG) := wf_ext_is_graph HΣ in infer' HΣ G HG. +Definition wrap_error {A} Σ (id : string) (check : typing_result A) : EnvCheck A := + match check with + | Checked a => CorrectDecl a + | TypeError e => EnvError Σ (IllFormedDecl id e) + end. Section CheckEnv. - Context {cf:checker_flags}. - - Inductive env_error := - | IllFormedDecl (e : string) (e : type_error) - | AlreadyDeclared (id : string). - - Inductive EnvCheck (A : Type) := - | CorrectDecl (a : A) - | EnvError (Σ : global_env_ext) (e : env_error). - Global Arguments EnvError {A} Σ e. - Global Arguments CorrectDecl {A} a. - - Global Instance envcheck_monad : Monad EnvCheck := - {| ret A a := CorrectDecl a ; - bind A B m f := - match m with - | CorrectDecl a => f a - | EnvError g e => EnvError g e - end - |}. - - Global Instance envcheck_monad_exc - : MonadExc (global_env_ext * env_error) EnvCheck := - { raise A '(g, e) := EnvError g e; - catch A m f := - match m with - | CorrectDecl a => m - | EnvError g t => f (g, t) - end - }. - - Definition wrap_error {A} Σ (id : string) (check : typing_result A) : EnvCheck A := - match check with - | Checked a => CorrectDecl a - | TypeError e => EnvError Σ (IllFormedDecl id e) - end. + Context {cf:checker_flags}. Definition check_wf_type kn Σ HΣ HΣ' G HG t : EnvCheck (∑ u, ∥ Σ;;; [] |- t : tSort u ∥) @@ -1378,68 +121,6 @@ Section CheckEnv. 2:split. now eapply eqb_eq in H3. Defined. - Program Fixpoint monad_Alli {T} {M : Monad T} {A} {P} (f : forall n x, T (∥ P n x ∥)) l n - : T (∥ @Alli A P n l ∥) - := match l with - | [] => ret (sq Alli_nil) - | a :: l => X <- f n a ;; - Y <- monad_Alli f l (S n) ;; - ret _ - end. - Next Obligation. - sq. constructor; assumption. - Defined. - - Program Fixpoint monad_Alli_All {T} {M : Monad T} {A} {P} {Q} (f : forall n x, ∥ Q x ∥ -> T (∥ P n x ∥)) l n : - ∥ All Q l ∥ -> T (∥ @Alli A P n l ∥) - := match l with - | [] => fun _ => ret (sq Alli_nil) - | a :: l => fun allq => X <- f n a _ ;; - Y <- monad_Alli_All f l (S n) _ ;; - ret _ - end. - Next Obligation. sq. - now depelim allq. - Qed. - Next Obligation. - sq; now depelim allq. - Qed. - Next Obligation. - sq. constructor; assumption. - Defined. - - Section monad_Alli_nth. - Context {T} {M : Monad T} {A} {P : nat -> A -> Type}. - Program Fixpoint monad_Alli_nth_gen l k - (f : forall n x, nth_error l n = Some x -> T (∥ P (k + n) x ∥)) : - T (∥ @Alli A P k l ∥) - := match l with - | [] => ret (sq Alli_nil) - | a :: l => X <- f 0 a _ ;; - Y <- monad_Alli_nth_gen l (S k) (fun n x hnth => px <- f (S n) x hnth;; ret _) ;; - ret _ - end. - Next Obligation. - sq. now rewrite Nat.add_succ_r in px. - Qed. - Next Obligation. - sq. rewrite Nat.add_0_r in X. constructor; auto. - Qed. - - Definition monad_Alli_nth l (f : forall n x, nth_error l n = Some x -> T (∥ P n x ∥)) : T (∥ @Alli A P 0 l ∥) := - monad_Alli_nth_gen l 0 f. - - End monad_Alli_nth. - - (* Definition Build_on_ind_body Σ mind mdecl i idecl ind_indices ind_sort *) - (* : ind_type idecl = *) - (* it_mkProd_or_LetIn (ind_params mdecl) *) - (* (it_mkProd_or_LetIn ind_indices (tSort ind_sort)) -> *) - (* ∥ on_type (lift_typing typing) Σ [] (ind_type idecl) ∥ -> *) - (* forall onConstructors : on_constructors P Σ mind mdecl i idecl (ind_ctors idecl), *) - (* (ind_projs idecl <> [] -> *) - (* on_projections P Σ mind mdecl i idecl ind_indices (ind_projs idecl)) -> *) - (* check_ind_sorts P onConstructors ind_sort -> on_ind_body P Σ mind mdecl i idecl *) (* We pack up all the information required on the global environment and graph in a single record. *) @@ -1643,34 +324,6 @@ Section CheckEnv. Definition wfnil {Σ : global_env_ext} : ∥ wf_local Σ [] ∥ := sq localenv_nil. Notation " ' pat <- m ;; f " := (bind m (fun pat => f)) (pat pattern, right associativity, at level 100, m at next level). - - Fixpoint split_at_aux {A} (n : nat) (acc : list A) (l : list A) : list A * list A := - match n with - | 0 => (List.rev acc, l) - | S n' => - match l with - | [] => (List.rev acc, []) - | hd :: l' => split_at_aux n' (hd :: acc) l' - end - end. - - Lemma split_at_aux_firstn_skipn {A} n acc (l : list A) : split_at_aux n acc l = (List.rev acc ++ firstn n l, skipn n l). - Proof. - induction n in acc, l |- *; destruct l; simpl; auto. - now rewrite app_nil_r skipn_0. - now rewrite app_nil_r skipn_0. - now rewrite app_nil_r skipn_nil. - rewrite IHn. simpl. - now rewrite -app_assoc skipn_S /=. - Qed. - - Definition split_at {A} (n : nat) (l : list A) : list A * list A := - split_at_aux n [] l. - - Lemma split_at_firstn_skipn {A} n (l : list A) : split_at n l = (firstn n l, skipn n l). - Proof. - now rewrite /split_at split_at_aux_firstn_skipn /= //. - Qed. Lemma inversion_it_mkProd_or_LetIn Σ {wfΣ : wf Σ.1}: forall {Γ Δ s A}, @@ -2703,41 +1356,6 @@ Section CheckEnv. Qed. End PositivityCheck. - Section MonadAllAll. - Context {T} {M : Monad T} {A} {P : A -> Type} {Q} (f : forall x, ∥ Q x ∥ -> T (∥ P x ∥)). - Program Fixpoint monad_All_All l : ∥ All Q l ∥ -> T (∥ All P l ∥) := - match l return ∥ All Q l ∥ -> T (∥ All P l ∥) with - | [] => fun _ => ret (sq All_nil) - | a :: l => fun allq => - X <- f a _ ;; - Y <- monad_All_All l _ ;; - ret _ - end. - Next Obligation. sq. - now depelim allq. - Qed. - Next Obligation. - sq; now depelim allq. - Qed. - Next Obligation. - sq. constructor; assumption. - Defined. - End MonadAllAll. - - (* Does not work due to implicit arguments I guess - Coercion isType_welltyped : isType >-> welltyped. *) - - Lemma forallb_unfold {A} (f : A -> bool) (g : nat -> A) n : - (forall x, x < n -> f (g x)) -> - forallb f (PCUICUnivSubstitution.unfold n g). - Proof. - intros fg. - induction n; simpl; auto. - rewrite forallb_app IHn //. - intros x lt; rewrite fg //. lia. - rewrite /= fg //. - Qed. - Lemma In_Var_global_ext_poly {n Σ inst cstrs} : n < #|inst| -> LevelSet.mem (Level.Var n) (global_ext_levels (Σ, Polymorphic_ctx (inst, cstrs))). @@ -2747,9 +1365,8 @@ Section CheckEnv. apply LevelSet.mem_spec; rewrite LevelSet.union_spec. left. rewrite /AUContext.levels /= PCUICUnivSubstitution.mapi_unfold. apply LevelSetProp.of_list_1, InA_In_eq. - eapply In_unfold_var. exists n. intuition auto. + eapply In_unfold_inj; try congruence. exists n. intuition auto. Qed. - Lemma on_udecl_poly_bounded Σ inst cstrs : wf Σ -> @@ -3228,18 +1845,6 @@ Section CheckEnv. Definition checkb_constructors_smaller (G : universes_graph) (cs : list constructor_shape) (ind_sort : Universe.t) := List.forallb (fun cs => List.forallb (fun argsort => check_leqb_universe G argsort ind_sort) cs.(cshape_sorts)) cs. - Lemma forallbP_cond {A} (P Q : A -> Prop) (p : A -> bool) l : - Forall Q l -> - (forall x, Q x -> reflect (P x) (p x)) -> reflect (Forall P l) (forallb p l). - Proof. - intros HQ Hp. - apply: (iffP idP). - - induction HQ; rewrite /= //. move/andP => [pa pl]. - constructor; auto. now apply/(Hp _). - - induction HQ; intros HP; depelim HP; rewrite /= // IHHQ // andb_true_r. - now apply/(Hp _). - Qed. - Lemma check_constructors_smallerP (Σ : wf_env_ext) cs ind_sort : Forall (fun cs => Forall (wf_universe Σ) cs.(cshape_sorts)) cs -> wf_universe Σ ind_sort -> ∥ reflect (check_constructors_smaller Σ cs ind_sort) (checkb_constructors_smaller Σ cs ind_sort) ∥. @@ -3540,20 +2145,6 @@ Section CheckEnv. Obligation Tactic := Program.Tactics.program_simpl. - Lemma levelset_union_empty s : LevelSet.union LevelSet.empty s = s. - Proof. - apply LevelSet.eq_leibniz. - change LevelSet.eq with LevelSet.Equal. - intros x; rewrite LevelSet.union_spec. lsets. - Qed. - - Lemma constraintset_union_empty s : ConstraintSet.union ConstraintSet.empty s = s. - Proof. - apply ConstraintSet.eq_leibniz. - change ConstraintSet.eq with ConstraintSet.Equal. - intros x; rewrite ConstraintSet.union_spec. lsets. - Qed. - Program Fixpoint check_wf_env (Σ : global_env) : EnvCheck (∑ G, (is_graph_of_uctx G (global_uctx Σ) /\ ∥ wf Σ ∥)) := match Σ with @@ -3710,25 +2301,6 @@ Section CheckEnv. simpl; intros. exact (check_wf_env_bool_spec Σ Γ wfΓ t T eq). Qed. - Lemma wf_consistent Σ : wf Σ -> consistent (global_constraints Σ). - Proof. - destruct Σ. - - exists {| valuation_mono := fun _ => 1%positive; valuation_poly := fun _ => 0 |}. - intros x Hx; now apply ConstraintSetFact.empty_iff in Hx. - - inversion 1; subst. subst udecl. clear -H2. - destruct H2 as [_ [_ [_ [v Hv]]]]. - exists v. intros ct Hc. apply Hv. simpl in *. - apply ConstraintSet.union_spec in Hc. destruct Hc. - apply ConstraintSet.union_spec; simpl. - + left. destruct d. - destruct c, cst_universes. assumption. - apply ConstraintSetFact.empty_iff in H; contradiction. - destruct m, ind_universes. assumption. - apply ConstraintSetFact.empty_iff in H; contradiction. - + apply ConstraintSet.union_spec; simpl. - now right. - Qed. - Obligation Tactic := Program.Tactics.program_simpl. Program Definition typecheck_program (p : program) φ Hφ diff --git a/safechecker/theories/PCUICSafeConversion.v b/safechecker/theories/PCUICSafeConversion.v index d0178386a..21b758aa8 100644 --- a/safechecker/theories/PCUICSafeConversion.v +++ b/safechecker/theories/PCUICSafeConversion.v @@ -7,7 +7,7 @@ From MetaCoq.PCUIC Require Import PCUICAst PCUICAstUtils PCUICSafeLemmata PCUICNormal PCUICInversion PCUICReduction PCUICPosition PCUICPrincipality PCUICContextConversion PCUICSN PCUICUtils PCUICWeakening PCUICConvCumInversion. -From MetaCoq.SafeChecker Require Import PCUICEqualityDec PCUICSafeReduce. +From MetaCoq.SafeChecker Require Import PCUICEqualityDec PCUICErrors PCUICSafeReduce. Require Import Equations.Prop.DepElim. From Equations Require Import Equations. @@ -477,94 +477,6 @@ Section Conversion. (∥ Σ ;;; Γ ,,, stack_context π |- zipp t π = zipp t' π' ∥) (only parsing). - Inductive ConversionError := - | NotFoundConstants (c1 c2 : kername) - - | NotFoundConstant (c : kername) - - | LambdaNotConvertibleTypes - (Γ1 : context) (na : aname) (A1 t1 : term) - (Γ2 : context) (na' : aname) (A2 t2 : term) - (e : ConversionError) - - | LambdaNotConvertibleAnn - (Γ1 : context) (na : aname) (A1 t1 : term) - (Γ2 : context) (na' : aname) (A2 t2 : term) - - | ProdNotConvertibleDomains - (Γ1 : context) (na : aname) (A1 B1 : term) - (Γ2 : context) (na' : aname) (A2 B2 : term) - (e : ConversionError) - - | ProdNotConvertibleAnn - (Γ1 : context) (na : aname) (A1 B1 : term) - (Γ2 : context) (na' : aname) (A2 B2 : term) - - | CaseOnDifferentInd - (Γ1 : context) - (ind : inductive) (par : nat) (p c : term) (brs : list (nat × term)) - (Γ2 : context) - (ind' : inductive) (par' : nat) (p' c' : term) (brs' : list (nat × term)) - - | CaseBranchNumMismatch - (ind : inductive) (par : nat) - (Γ : context) (p c : term) (brs1 : list (nat × term)) - (m : nat) (br : term) (brs2 : list (nat × term)) - (Γ' : context) (p' c' : term) (brs1' : list (nat × term)) - (m' : nat) (br' : term) (brs2' : list (nat × term)) - - | DistinctStuckProj - (Γ : context) (p : projection) (c : term) - (Γ' : context) (p' : projection) (c' : term) - - | CannotUnfoldFix - (Γ : context) (mfix : mfixpoint term) (idx : nat) - (Γ' : context) (mfix' : mfixpoint term) (idx' : nat) - - | FixRargMismatch (idx : nat) - (Γ : context) (u : def term) (mfix1 mfix2 : mfixpoint term) - (Γ' : context) (v : def term) (mfix1' mfix2' : mfixpoint term) - - | FixMfixMismatch (idx : nat) - (Γ : context) (mfix : mfixpoint term) - (Γ' : context) (mfix' : mfixpoint term) - - | DistinctCoFix - (Γ : context) (mfix : mfixpoint term) (idx : nat) - (Γ' : context) (mfix' : mfixpoint term) (idx' : nat) - - | CoFixRargMismatch (idx : nat) - (Γ : context) (u : def term) (mfix1 mfix2 : mfixpoint term) - (Γ' : context) (v : def term) (mfix1' mfix2' : mfixpoint term) - - | CoFixMfixMismatch (idx : nat) - (Γ : context) (mfix : mfixpoint term) - (Γ' : context) (mfix' : mfixpoint term) - - | StackHeadError - (leq : conv_pb) - (Γ1 : context) - (t1 : term) (args1 : list term) (u1 : term) (l1 : list term) - (Γ2 : context) - (t2 : term) (u2 : term) (l2 : list term) - (e : ConversionError) - - | StackTailError (leq : conv_pb) - (Γ1 : context) - (t1 : term) (args1 : list term) (u1 : term) (l1 : list term) - (Γ2 : context) - (t2 : term) (u2 : term) (l2 : list term) - (e : ConversionError) - - | StackMismatch - (Γ1 : context) (t1 : term) (args1 l1 : list term) - (Γ2 : context) (t2 : term) (l2 : list term) - - | HeadMismatch - (leq : conv_pb) - (Γ1 : context) (t1 : term) - (Γ2 : context) (t2 : term). - Inductive ConversionResult (P : Prop) := | Success (h : P) | Error (e : ConversionError) (h : ~P). diff --git a/safechecker/theories/PCUICTypeChecker.v b/safechecker/theories/PCUICTypeChecker.v new file mode 100644 index 000000000..5a92e2a88 --- /dev/null +++ b/safechecker/theories/PCUICTypeChecker.v @@ -0,0 +1,932 @@ +(* Distributed under the terms of the MIT license. *) +From MetaCoq.Template Require Import config utils uGraph. +From MetaCoq.PCUIC Require Import PCUICAst PCUICAstUtils + PCUICLiftSubst PCUICUnivSubst PCUICTyping PCUICNormal PCUICSR + PCUICGeneration PCUICReflect PCUICEquality PCUICInversion PCUICValidity + PCUICWeakening PCUICPosition PCUICCumulativity PCUICSafeLemmata PCUICSN + PCUICPretty PCUICArities PCUICConfluence PCUICSize + PCUICContextConversion PCUICConversion PCUICWfUniverses + PCUICGlobalEnv + (* Used for support lemmas *) + PCUICInductives PCUICWfUniverses + PCUICContexts PCUICSubstitution PCUICSpine PCUICInductiveInversion + PCUICClosed PCUICUnivSubstitution PCUICWeakeningEnv. + +From MetaCoq.SafeChecker Require Import PCUICSafeReduce PCUICErrors PCUICEqualityDec + PCUICSafeConversion PCUICWfReduction. + +From Equations Require Import Equations. +Require Import ssreflect ssrbool. + +Local Set Keyed Unification. +Set Equations Transparent. + +(** It otherwise tries [auto with *], very bad idea. *) +Ltac Coq.Program.Tactics.program_solve_wf ::= + match goal with + | |- @Wf.well_founded _ _ => auto with subterm wf + | |- ?T => match type of T with + | Prop => auto + end + end. + +Inductive typing_result (A : Type) := +| Checked (a : A) +| TypeError (t : type_error). +Global Arguments Checked {A} a. +Global Arguments TypeError {A} t. + +Instance typing_monad : Monad typing_result := + {| ret A a := Checked a ; + bind A B m f := + match m with + | Checked a => f a + | TypeError t => TypeError t + end + |}. + +Instance monad_exc : MonadExc type_error typing_result := + { raise A e := TypeError e; + catch A m f := + match m with + | Checked a => m + | TypeError t => f t + end + }. + +Section Typecheck. + Context {cf : checker_flags} {Σ : global_env_ext} (HΣ : ∥ wf Σ ∥) + (Hφ : ∥ on_udecl Σ.1 Σ.2 ∥) + (G : universes_graph) (HG : is_graph_of_uctx G (global_ext_uctx Σ)). + + (* We get stack overflow on Qed after Equations definitions when this is transparent *) + Opaque reduce_stack_full. + + Local Definition HΣ' : ∥ wf_ext Σ ∥. + Proof. + destruct HΣ, Hφ; now constructor. + Defined. + + Definition hnf := reduce_term RedFlags.default Σ HΣ. + + Theorem hnf_sound {Γ t h} : ∥ red (fst Σ) Γ t (hnf Γ t h) ∥. + Proof. + apply reduce_term_sound. + Defined. + + Theorem hnf_complete {Γ t h} : ∥whnf RedFlags.default Σ Γ (hnf Γ t h)∥. + Proof. + apply reduce_term_complete. + Qed. + + Equations? reduce_to_sort (Γ : context) (t : term) (h : welltyped Σ Γ t) + : typing_result (∑ u, ∥ red (fst Σ) Γ t (tSort u) ∥) := + reduce_to_sort Γ t h with view_sortc t := { + | view_sort_sort s => ret (s; sq (refl_red _ _ _)); + | view_sort_other t _ with inspect (hnf Γ t h) := + | exist hnft eq with view_sortc hnft := { + | view_sort_sort s => ret (s; _); + | view_sort_other t _ => raise (NotASort t) + } + }. + Proof. + pose proof (hnf_sound (h:=h)). + now rewrite eq. + Qed. + + Lemma reduce_to_sort_complete {Γ t wt} e : + reduce_to_sort Γ t wt = TypeError e -> + (forall s, red Σ Γ t (tSort s) -> False). + Proof. + funelim (reduce_to_sort Γ t wt); try congruence. + intros _ s r. + pose proof (@hnf_complete Γ t0 h) as [wh]. + pose proof (@hnf_sound Γ t0 h) as [r']. + destruct HΣ. + eapply red_confluence in r as (?&r1&r2); eauto. + apply invert_red_sort in r2 as ->. + eapply whnf_red_inv in r1; eauto. + depelim r1. + clear Heq. + rewrite H in n0. + now cbn in n0. + Qed. + + Equations? reduce_to_prod (Γ : context) (t : term) (h : welltyped Σ Γ t) + : typing_result (∑ na a b, ∥ red (fst Σ) Γ t (tProd na a b) ∥) := + reduce_to_prod Γ t h with view_prodc t := { + | view_prod_prod na a b => ret (na; a; b; sq (refl_red _ _ _)); + | view_prod_other t _ with inspect (hnf Γ t h) := + | exist hnft eq with view_prodc hnft := { + | view_prod_prod na a b => ret (na; a; b; _); + | view_prod_other t' _ => raise (NotAProduct t t') + } + }. + Proof. + pose proof (hnf_sound (h:=h)). + now rewrite eq. + Qed. + + Lemma reduce_to_prod_complete {Γ t wt} e : + reduce_to_prod Γ t wt = TypeError e -> + (forall na a b, red Σ Γ t (tProd na a b) -> False). + Proof. + funelim (reduce_to_prod Γ t wt); try congruence. + intros _ na a b r. + pose proof (@hnf_complete Γ t0 h) as [wh]. + pose proof (@hnf_sound Γ t0 h) as [r']. + destruct HΣ. + eapply red_confluence in r as (?&r1&r2); eauto. + apply invert_red_prod in r2 as (?&?&(->&?)&?); auto. + eapply whnf_red_inv in r1; auto. + depelim r1. + clear Heq. + rewrite H in n0. + now cbn in n0. + Qed. + + Equations? reduce_to_ind (Γ : context) (t : term) (h : welltyped Σ Γ t) + : typing_result (∑ i u l, ∥ red (fst Σ) Γ t (mkApps (tInd i u) l) ∥) := + reduce_to_ind Γ t h with inspect (decompose_app t) := { + | exist (thd, args) eq_decomp with view_indc thd := { + | view_ind_tInd i u => ret (i; u; args; sq _); + | view_ind_other t _ with inspect (reduce_stack RedFlags.default Σ HΣ Γ t Empty h) := { + | exist (hnft, π) eq with view_indc hnft := { + | view_ind_tInd i u with inspect (decompose_stack π) := { + | exist (l, _) eq_decomp => ret (i; u; l; _) + }; + | view_ind_other _ _ => raise (NotAnInductive t) + } + } + } + }. + Proof. + - assert (X : mkApps (tInd i u) args = t); [|rewrite X; apply refl_red]. + etransitivity. 2: symmetry; eapply mkApps_decompose_app. + now rewrite <- eq_decomp. + - pose proof (reduce_stack_sound RedFlags.default Σ HΣ _ _ Empty h). + rewrite <- eq in H. + cbn in *. + assert (π = appstack l ε) as ->. + 2: { now rewrite zipc_appstack in H. } + unfold reduce_stack in eq. + destruct reduce_stack_full as (?&_&stack_val&?). + subst x. + unfold Pr in stack_val. + cbn in *. + assert (decomp: decompose_stack π = ((decompose_stack π).1, ε)). + { rewrite stack_val. + now destruct decompose_stack. } + apply decompose_stack_eq in decomp as ->. + now rewrite <- eq_decomp0. + Qed. + + Lemma reduce_to_ind_complete Γ ty wat e : + reduce_to_ind Γ ty wat = TypeError e -> + forall ind u args, + red Σ Γ ty (mkApps (tInd ind u) args) -> + False. + Proof. + funelim (reduce_to_ind Γ ty wat); try congruence. + intros _ ind u args r. + pose proof (reduce_stack_whnf RedFlags.default Σ HΣ Γ t ε h) as wh. + unfold reduce_stack in *. + destruct reduce_stack_full as ((hd&π)&r'&stack_valid&(notapp&_)). + destruct wh as [wh]. + apply Req_red in r' as [r']. + unfold Pr in stack_valid. + cbn in *. + destruct HΣ. + eapply red_confluence in r as (?&r1&r2); [|eassumption|exact r']. + assert (exists args, π = appstack args ε) as (?&->). + { exists ((decompose_stack π).1). + assert (decomp: decompose_stack π = ((decompose_stack π).1, ε)). + { now rewrite stack_valid; destruct decompose_stack. } + now apply decompose_stack_eq in decomp. } + + unfold zipp in wh. + rewrite stack_context_appstack decompose_stack_appstack in wh. + rewrite zipc_appstack in r1. + cbn in *. + rewrite app_nil_r in wh. + apply red_mkApps_tInd in r2 as (?&->&?); auto. + eapply whnf_red_inv in r1; eauto. + apply whnf_red_mkApps_inv in r1 as (?&?); auto. + depelim w. + noconf e0. + discriminate i0. + Qed. + + Definition isconv Γ := isconv_term Σ HΣ Hφ G HG Γ Conv. + Definition iscumul Γ := isconv_term Σ HΣ Hφ G HG Γ Cumul. + + Program Definition convert Γ t u + (ht : welltyped Σ Γ t) (hu : welltyped Σ Γ u) + : typing_result (∥ Σ ;;; Γ |- t = u ∥) := + match eqb_term Σ G t u with true => ret _ | false => + match isconv Γ t ht u hu with + | ConvSuccess => ret _ + | ConvError e => (* fallback *) (* nico *) + let t' := hnf Γ t ht in + let u' := hnf Γ u hu in + (* match leq_term (snd Σ) t' u' with true => ret _ | false => *) + raise (NotCumulSmaller G Γ t u t' u' e) + (* end *) + end end. + Next Obligation. + symmetry in Heq_anonymous; eapply eqb_term_spec in Heq_anonymous; tea. + constructor. now constructor. + Qed. + Next Obligation. + symmetry in Heq_anonymous; apply isconv_term_sound in Heq_anonymous. + assumption. + Qed. + + Program Definition convert_leq Γ t u + (ht : welltyped Σ Γ t) (hu : welltyped Σ Γ u) + : typing_result (∥ Σ ;;; Γ |- t <= u ∥) := + match leqb_term Σ G t u with true => ret _ | false => + match iscumul Γ t ht u hu with + | ConvSuccess => ret _ + | ConvError e => (* fallback *) (* nico *) + let t' := hnf Γ t ht in + let u' := hnf Γ u hu in + (* match leq_term (snd Σ) t' u' with true => ret _ | false => *) + raise (NotCumulSmaller G Γ t u t' u' e) + (* end *) + end end. + Next Obligation. + symmetry in Heq_anonymous; eapply leqb_term_spec in Heq_anonymous; tea. + constructor. now constructor. + Qed. + Next Obligation. + symmetry in Heq_anonymous; apply isconv_term_sound in Heq_anonymous. + assumption. + Qed. + + Section InferAux. + Variable (infer : forall Γ (HΓ : ∥ wf_local Σ Γ ∥) (t : term), + typing_result ({ A : term & ∥ Σ ;;; Γ |- t : A ∥ })). + + Program Definition infer_type Γ HΓ t + : typing_result ({u : Universe.t & ∥ Σ ;;; Γ |- t : tSort u ∥}) := + tx <- infer Γ HΓ t ;; + u <- reduce_to_sort Γ tx.π1 _ ;; + ret (u.π1; _). + Next Obligation. + eapply validity_wf; eassumption. + Defined. + Next Obligation. + destruct HΣ, HΓ, X, X0. + now constructor; eapply type_reduction. + Defined. + + Program Definition infer_cumul Γ HΓ t A (hA : ∥ isType Σ Γ A ∥) + : typing_result (∥ Σ ;;; Γ |- t : A ∥) := + A' <- infer Γ HΓ t ;; + X <- convert_leq Γ A'.π1 A _ _ ;; + ret _. + Next Obligation. now eapply validity_wf. Qed. + Next Obligation. destruct hA; now apply wat_welltyped. Qed. + Next Obligation. + destruct HΣ, HΓ, hA, X, X0. constructor. eapply type_Cumul'; eassumption. + Qed. + End InferAux. + + + Program Definition lookup_ind_decl ind + : typing_result + ({decl & {body & declared_inductive (fst Σ) decl ind body}}) := + match lookup_env (fst Σ) ind.(inductive_mind) with + | Some (InductiveDecl decl) => + match nth_error decl.(ind_bodies) ind.(inductive_ind) with + | Some body => ret (decl; body; _) + | None => raise (UndeclaredInductive ind) + end + | _ => raise (UndeclaredInductive ind) + end. + Next Obligation. + split. + - symmetry in Heq_anonymous0. + etransitivity. eassumption. reflexivity. + - now symmetry. + Defined. + + Program Definition check_consistent_instance uctx u + : typing_result (consistent_instance_ext Σ uctx u) + := match uctx with + | Monomorphic_ctx _ => + check_eq_nat #|u| 0 (Msg "monomorphic instance should be of length 0") + | Polymorphic_ctx (inst, cstrs) => + let '(inst, cstrs) := AUContext.repr (inst, cstrs) in + check_eq_true (forallb (fun l => LevelSet.mem l (uGraph.wGraph.V G)) u) + (Msg "instance does not have the right length") ;; + (* check_eq_true (forallb (fun l => LevelSet.mem l lvs) u) ;; *) + X <- check_eq_nat #|u| #|inst| + (Msg "instance does not have the right length");; + match check_constraints G (subst_instance_cstrs u cstrs) with + | true => ret (conj _ _) + | false => raise (Msg "ctrs not satisfiable") + end + (* #|u| = #|inst| /\ valid_constraints φ (subst_instance_cstrs u cstrs) *) + end. + Next Obligation. + eapply forallb_All in H. eapply All_forallb'; tea. + clear -cf HG. intros x; simpl. apply is_graph_of_uctx_levels. + Qed. + Next Obligation. + repeat split. + - now rewrite mapi_length in X. + - eapply check_constraints_spec; eauto. + Qed. + + Obligation Tactic := Program.Tactics.program_simplify ; eauto 2. + + Program Definition check_is_allowed_elimination (u : Universe.t) (al : allowed_eliminations) : + typing_result (is_allowed_elimination Σ u al) := + let o := + match al return option (is_allowed_elimination Σ u al) with + | IntoSProp => + match Universe.is_sprop u with + | true => Some _ + | false => None + end + | IntoPropSProp => + match is_propositional u with + | true => Some _ + | false => None + end + | IntoSetPropSProp => + match is_propositional u || check_eqb_universe G u Universe.type0 with + | true => Some _ + | false => None + end + | IntoAny => Some _ + end in + match o with + | Some t => Checked t + | None => TypeError (Msg "Cannot eliminate over this sort") + end. + Next Obligation. + unfold is_allowed_elimination, is_allowed_elimination0. + destruct check_univs; auto. + intros val sat. + symmetry in Heq_anonymous. + apply is_sprop_val with (v := val) in Heq_anonymous. + now rewrite Heq_anonymous. + Qed. + Next Obligation. + unfold is_allowed_elimination, is_allowed_elimination0. + destruct check_univs; auto. + intros val sat. + unfold is_propositional in *. + destruct Universe.is_prop eqn:prop. + - apply is_prop_val with (v := val) in prop; rewrite prop; auto. + - destruct Universe.is_sprop eqn:sprop. + + apply is_sprop_val with (v := val) in sprop; rewrite sprop; auto. + + discriminate. + Qed. + Next Obligation. + unfold is_allowed_elimination, is_allowed_elimination0. + destruct check_univs eqn:cu; auto. + intros val sat. + unfold is_propositional in *. + destruct Universe.is_prop eqn:prop. + - apply is_prop_val with (v := val) in prop; rewrite prop; auto. + - destruct Universe.is_sprop eqn:sprop. + + apply is_sprop_val with (v := val) in sprop; rewrite sprop; auto. + + destruct check_eqb_universe eqn:check; [|discriminate]. + eapply check_eqb_universe_spec' in check; eauto. + * unfold eq_universe, eq_universe0 in check. + rewrite cu in check. + specialize (check val sat). + now rewrite check. + * destruct HΣ, Hφ. + now apply wf_ext_global_uctx_invariants. + * destruct HΣ, Hφ. + now apply global_ext_uctx_consistent. + Qed. + Next Obligation. + unfold is_allowed_elimination, is_allowed_elimination0. + destruct check_univs; auto. + Qed. + + Program Fixpoint infer (Γ : context) (HΓ : ∥ wf_local Σ Γ ∥) (t : term) {struct t} + : typing_result ({ A : term & ∥ Σ ;;; Γ |- t : A ∥ }) := + match t with + | tRel n => + match nth_error Γ n with + | Some c => ret ((lift0 (S n)) (decl_type c); _) + | None => raise (UnboundRel n) + end + + | tVar n => raise (UnboundVar n) + | tEvar ev args => raise (UnboundEvar ev) + + | tSort u => + check_eq_true (wf_universeb Σ u) + (Msg ("Sort contains an undeclared level " ^ string_of_sort u));; + ret (tSort (Universe.super u); _) + + | tProd na A B => + s1 <- infer_type infer Γ HΓ A ;; + s2 <- infer_type infer (Γ ,, vass na A) _ B ;; + ret (tSort (Universe.sort_of_product s1.π1 s2.π1); _) + + | tLambda na A t => + s1 <- infer_type infer Γ HΓ A ;; + B <- infer (Γ ,, vass na A) _ t ;; + ret (tProd na A B.π1; _) + + | tLetIn n b b_ty b' => + infer_type infer Γ HΓ b_ty ;; + infer_cumul infer Γ HΓ b b_ty _ ;; + b'_ty <- infer (Γ ,, vdef n b b_ty) _ b' ;; + ret (tLetIn n b b_ty b'_ty.π1; _) + + | tApp t u => + ty <- infer Γ HΓ t ;; + pi <- reduce_to_prod Γ ty.π1 _ ;; + infer_cumul infer Γ HΓ u pi.π2.π1 _ ;; + ret (subst10 u pi.π2.π2.π1; _) + + | tConst cst u => + match lookup_env (fst Σ) cst with + | Some (ConstantDecl d) => + check_consistent_instance d.(cst_universes) u ;; + let ty := subst_instance_constr u d.(cst_type) in + ret (ty; _) + | _ => raise (UndeclaredConstant cst) + end + + | tInd ind u => + d <- lookup_ind_decl ind ;; + check_consistent_instance d.π1.(ind_universes) u ;; + let ty := subst_instance_constr u d.π2.π1.(ind_type) in + ret (ty; _) + + | tConstruct ind k u => + d <- lookup_ind_decl ind ;; + match nth_error d.π2.π1.(ind_ctors) k with + | Some cdecl => + check_consistent_instance d.π1.(ind_universes) u ;; + ret (type_of_constructor d.π1 cdecl (ind, k) u; _) + | None => raise (UndeclaredConstructor ind k) + end + + | tCase (ind, par) p c brs => + cty <- infer Γ HΓ c ;; + I <- reduce_to_ind Γ cty.π1 _ ;; + let '(ind'; I') := I in let '(u; I'') := I' in let '(args; H) := I'' in + check_eq_true (eqb ind ind') + (* bad case info *) + (NotConvertible G Γ (tInd ind u) (tInd ind' u)) ;; + d <- lookup_ind_decl ind' ;; + let '(decl; d') := d in let '(body; HH) := d' in + check_coind <- check_eq_true (negb (isCoFinite (ind_finite decl))) + (Msg "Case on coinductives disallowed") ;; + check_eq_true (ind_npars decl =? par) + (Msg "not the right number of parameters") ;; + pty <- infer Γ HΓ p ;; + match destArity [] pty.π1 with + | None => raise (Msg "the type of the return predicate of a Case is not an arity") + | Some (pctx, ps) => + check_is_allowed_elimination ps (ind_kelim body);; + let params := firstn par args in + match build_case_predicate_type ind decl body params u ps with + | None => raise (Msg "failure in build_case_predicate_type") + | Some pty' => + (* We could avoid one useless sort comparison by only comparing *) + (* the contexts [pctx] and [indctx] (what is done in Coq). *) + match iscumul Γ pty.π1 _ pty' _ with + | ConvError e => raise (NotCumulSmaller G Γ pty.π1 pty' pty.π1 pty' e) + | ConvSuccess => + match map_option_out (build_branches_type ind decl body params u p) with + | None => raise (Msg "failure in build_branches_type") + | Some btys => + let btyswf : ∥ All (isType Σ Γ ∘ snd) btys ∥ := _ in + (fix check_branches (brs btys : list (nat * term)) + (HH : ∥ All (isType Σ Γ ∘ snd) btys ∥) {struct brs} + : typing_result + (All2 (fun br bty => br.1 = bty.1 /\ ∥ Σ ;;; Γ |- br.2 : bty.2 ∥) brs btys) + := match brs, btys with + | [], [] => ret All2_nil + | (n, t) :: brs , (m, A) :: btys => + W <- check_dec (Msg "not nat eq") + (EqDecInstances.nat_eqdec n m) ;; + Z <- infer_cumul infer Γ HΓ t A _ ;; + X <- check_branches brs btys _ ;; + ret (All2_cons (conj _ _) X) + | [], _ :: _ + | _ :: _, [] => raise (Msg "wrong number of branches") + end) brs btys btyswf ;; + ret (mkApps p (List.skipn par args ++ [c]); _) + end + end + end + end + + | tProj (ind, n, k) c => + d <- lookup_ind_decl ind ;; + match nth_error d.π2.π1.(ind_projs) k with + | Some pdecl => + c_ty <- infer Γ HΓ c ;; + I <- reduce_to_ind Γ c_ty.π1 _ ;; + let '(ind'; I') := I in let '(u; I'') := I' in let '(args; H) := I'' in + check_eq_true (eqb ind ind') + (NotConvertible G Γ (tInd ind u) (tInd ind' u)) ;; + check_eq_true (ind_npars d.π1 =? n) + (Msg "not the right number of parameters") ;; + let ty := snd pdecl in + ret (subst0 (c :: List.rev args) (subst_instance_constr u ty); + _) + | None => raise (Msg "projection not found") + end + + | tFix mfix n => + match nth_error mfix n with + | None => raise (IllFormedFix mfix n) + | Some decl => + XX <- (fix check_types (mfix : mfixpoint term) {struct mfix} + : typing_result (∥ All (fun x => isType Σ Γ (dtype x)) mfix ∥) + := match mfix with + | [] => ret (sq All_nil) + | def :: mfix => + (* probably not tail recursive but needed so that next line terminates *) + W <- infer_type infer Γ HΓ (dtype def) ;; + Z <- check_types mfix ;; + ret _ + end) + mfix ;; + YY <- (fix check_bodies (mfix' : mfixpoint term) + (XX : ∥ All (fun x => isType Σ Γ (dtype x)) mfix' ∥) + {struct mfix'} + : typing_result (All (fun d => + ∥ Σ ;;; Γ ,,, fix_context mfix |- dbody d : (lift0 #|fix_context mfix|) (dtype d) ∥ + /\ isLambda (dbody d) = true) mfix') + := match mfix' with + | [] => ret All_nil + | def :: mfix' => + W1 <- infer_cumul infer (Γ ,,, fix_context mfix) _ (dbody def) + (lift0 #|fix_context mfix| (dtype def)) _ ;; + W2 <- check_eq_true (isLambda (dbody def)) + (Msg "not a lambda") ;; + Z <- check_bodies mfix' _ ;; + ret (All_cons (conj W1 W2) Z) + end) mfix _ ;; + guarded <- check_eq_true (fix_guard mfix) (Msg "Unguarded fixpoint") ;; + wffix <- check_eq_true (wf_fixpoint Σ.1 mfix) (Msg "Ill-formed fixpoint: not defined on a mutually inductive family") ;; + ret (dtype decl; _) + end + + | tCoFix mfix n => + match nth_error mfix n with + | None => raise (IllFormedFix mfix n) + | Some decl => + XX <- (fix check_types (mfix : mfixpoint term) {struct mfix} + : typing_result (∥ All (fun x => isType Σ Γ (dtype x)) mfix ∥) + := match mfix with + | [] => ret (sq All_nil) + | def :: mfix => + (* probably not tail recursive but needed so that next line terminates *) + W <- infer_type infer Γ HΓ (dtype def) ;; + Z <- check_types mfix ;; + ret _ + end) + mfix ;; + YY <- (fix check_bodies (mfix' : mfixpoint term) + (XX' : ∥ All (fun x => isType Σ Γ (dtype x)) mfix' ∥) + {struct mfix'} + : typing_result (All (fun d => + ∥ Σ ;;; Γ ,,, fix_context mfix |- dbody d : (lift0 #|fix_context mfix|) (dtype d) ∥) mfix') + := match mfix' with + | [] => ret All_nil + | def :: mfix' => + W1 <- infer_cumul infer (Γ ,,, fix_context mfix) _ (dbody def) + (lift0 #|fix_context mfix| (dtype def)) _ ;; + Z <- check_bodies mfix' _ ;; + ret (All_cons W1 Z) + end) mfix _ ;; + guarded <- check_eq_true (cofix_guard mfix) (Msg "Unguarded cofixpoint") ;; + wfcofix <- check_eq_true (wf_cofixpoint Σ.1 mfix) (Msg "Ill-formed cofixpoint: not producing values in a mutually coinductive family") ;; + ret (dtype decl; _) + end + end. + + (* tRel *) + Next Obligation. intros; sq; now econstructor. Defined. + (* tSort *) + Next Obligation. + eapply (elimT wf_universe_reflect) in H. + sq; econstructor; tas. + Defined. + (* tProd *) + Next Obligation. + (* intros Γ HΓ t na A B Heq_t [s ?]; *) + sq; econstructor; cbn; easy. Defined. + Next Obligation. + (* intros Γ HΓ t na A B Heq_t [s1 ?] [s2 ?]; *) + sq; econstructor; eassumption. + Defined. + (* tLambda *) + Next Obligation. + (* intros Γ HΓ t0 na A t Heq_t [s ?]; *) + sq; econstructor; cbn; easy. + Defined. + Next Obligation. + (* intros Γ HΓ t0 na A t Heq_t [s ?] [B ?]; *) + sq; econstructor; eassumption. + Defined. + (* tLetIn *) + Next Obligation. + (* intros Γ HΓ t n b b_ty b' Heq_t [? ?]; *) + sq. econstructor; eauto. + Defined. + Next Obligation. + (* intros Γ HΓ t n b b_ty b' Heq_t [? ?] H0; *) + sq; econstructor; cbn; eauto. + Defined. + Next Obligation. + (* intros Γ HΓ t n b b_ty b' Heq_t [? ?] H0 [? ?]; *) + sq; econstructor; eassumption. + Defined. + + (* tApp *) + Next Obligation. simpl; eauto using validity_wf. Qed. + Next Obligation. + cbn in *; sq. + eapply type_reduction in X1 ; try eassumption. + eapply validity_term in X1 ; try assumption. destruct X1 as [s HH]. + eapply inversion_Prod in HH ; try assumption. + destruct HH as [s1 [_ [HH _]]]. + eexists. eassumption. + Defined. + Next Obligation. + cbn in *; sq; econstructor. + 2: eassumption. + eapply type_reduction; eassumption. + Defined. + + (* tConst *) + Next Obligation. + rename Heq_anonymous into HH. + sq; constructor; try assumption. + symmetry in HH. + etransitivity. eassumption. reflexivity. + Defined. + + (* tInd *) + Next Obligation. + sq; econstructor; eassumption. + Defined. + + (* tConstruct *) + Next Obligation. + sq; econstructor; tea. now split. + Defined. + + (* tCase *) + Next Obligation. simpl; eauto using validity_wf. Qed. + Next Obligation. simpl; eauto using validity_wf. Qed. + Next Obligation. + destruct X, X9. sq. + change (eqb ind I = true) in H0. + destruct (eqb_spec ind I) as [e|e]; [destruct e|discriminate]. + change (eqb (ind_npars d) par = true) in H1. + destruct (eqb_spec (ind_npars d) par) as [e|e]; [|discriminate]. + rename Heq_anonymous into HH. symmetry in HH. + simpl in *. + eapply type_reduction in t0; eauto. eapply validity in t0; eauto. + rewrite <- e in HH. + eapply PCUICInductiveInversion.WfArity_build_case_predicate_type in HH; eauto. + destruct HH as [[s Hs] ?]. eexists; eauto. + eapply validity in t; eauto. + generalize (PCUICClosed.destArity_spec [] pty). + rewrite -Heq_anonymous0 /=. intros ->. + eapply PCUICInductives.isType_it_mkProd_or_LetIn_inv in t; eauto. + eapply isType_wf_universes in t. simpl in t. + now exact (elimT wf_universe_reflect t). auto. + Qed. + + Next Obligation. + symmetry in Heq_anonymous2. + unfold iscumul in Heq_anonymous2. simpl in Heq_anonymous2. + apply isconv_term_sound in Heq_anonymous2. + red in Heq_anonymous2. + noconf Heq_I''. + noconf Heq_I'. noconf Heq_I. + noconf Heq_d. noconf Heq_d'. + simpl in *; sq. + change (eqb ind I = true) in H0. + destruct (eqb_spec ind I) as [e|e]; [destruct e|discriminate H0]. + change (eqb (ind_npars d) par = true) in H1. + destruct (eqb_spec (ind_npars d) par) as [e|e]; [|discriminate]; subst. + assert (wfΣ : wf_ext Σ) by (split; auto). + eapply type_reduction in X9; eauto. + have val:= validity_term wfΣ X9. + eapply type_Cumul' in X; [| |eassumption]. + 2:{ eapply PCUICInductiveInversion.WfArity_build_case_predicate_type; eauto. + eapply validity in X; eauto. + generalize (PCUICClosed.destArity_spec [] pty). + rewrite -Heq_anonymous0 /=. intros ->. + eapply PCUICInductives.isType_it_mkProd_or_LetIn_inv in X; eauto. + eapply isType_wf_universes in X. simpl in X. + now exact (elimT wf_universe_reflect X). auto. } + have [pctx' da] : (∑ pctx', destArity [] pty' = Some (pctx', ps)). + { symmetry in Heq_anonymous1. + unshelve eapply (PCUICInductives.build_case_predicate_type_spec (Σ.1, ind_universes d)) in Heq_anonymous1 as [parsubst [_ ->]]. + eauto. eapply (PCUICWeakeningEnv.on_declared_inductive wfΣ) in HH as [? ?]. eauto. + eexists. rewrite !destArity_it_mkProd_or_LetIn; simpl. reflexivity. } + eapply PCUICInductiveInversion.build_branches_type_wt. 6:eapply X. all:eauto. + Defined. + + Obligation Tactic := simpl; intros. + + Next Obligation. + rename Heq_anonymous2 into XX2. + symmetry in XX2. simpl in *. eapply isconv_sound in XX2. + change (eqb ind ind' = true) in H0. + destruct (eqb_spec ind ind') as [e|e]; [destruct e|discriminate H0]. + change (eqb (ind_npars decl) par = true) in H1. + destruct (eqb_spec (ind_npars decl) par) as [e|e]; [|discriminate]; subst. + depelim HH. + sq. auto. now depelim X. + Defined. + Next Obligation. + sq. now depelim HH. + Defined. + + (* The obligation tactic removes a useful let here. *) + Obligation Tactic := idtac. + Next Obligation. + intros. clearbody btyswf. idtac; Program.Tactics.program_simplify. + symmetry in Heq_anonymous2. + unfold iscumul in Heq_anonymous2. simpl in Heq_anonymous2. + apply isconv_term_sound in Heq_anonymous2. + noconf Heq_I''. noconf Heq_I'. noconf Heq_I. + noconf Heq_d. noconf Heq_d'. simpl in *. + assert (∥ All2 (fun x y => ((fst x = fst y) * + (Σ;;; Γ |- snd x : snd y) * isType Σ Γ y.2)%type) brs btys ∥). { + solve_all. simpl in *. + destruct btyswf. eapply All2_sq. solve_all. simpl in *; intuition (sq; auto). } + clear H3. sq. + change (eqb ind I = true) in H0. + destruct (eqb_spec ind I) as [e|e]; [destruct e|discriminate H0]. + change (eqb (ind_npars d) par = true) in H1. + destruct (eqb_spec (ind_npars d) par) as [e|e]; [|discriminate]; subst. + assert (wfΣ : wf_ext Σ) by (split; auto). + eapply type_reduction in X9; eauto. + eapply type_Cumul' in X; eauto. + 2:{ eapply PCUICInductiveInversion.WfArity_build_case_predicate_type; eauto. + now eapply validity in X9. + eapply validity in X; eauto. + generalize (PCUICClosed.destArity_spec [] pty). + rewrite -Heq_anonymous0 /=. intros ->. + eapply PCUICInductives.isType_it_mkProd_or_LetIn_inv in X; eauto. + eapply isType_wf_universes in X. simpl in X. + now exact (elimT wf_universe_reflect X). auto. } + have [pctx' da] : (∑ pctx', destArity [] pty' = Some (pctx', ps)). + { symmetry in Heq_anonymous1. + unshelve eapply (PCUICInductives.build_case_predicate_type_spec (Σ.1, ind_universes d)) in Heq_anonymous1 as [parsubst [_ ->]]. + eauto. eapply (PCUICWeakeningEnv.on_declared_inductive wfΣ) in HH as [? ?]. eauto. + eexists. rewrite !destArity_it_mkProd_or_LetIn; simpl. reflexivity. } + eapply type_Case with (pty0:=pty'); tea. + - reflexivity. + - symmetry; eassumption. + - destruct isCoFinite; auto. + - symmetry; eauto. + Defined. + + Obligation Tactic := Program.Tactics.program_simplify ; eauto 2. + + (* tProj *) + Next Obligation. simpl; eauto using validity_wf. Qed. + Next Obligation. + simpl in *; sq; eapply type_Proj with (pdecl := (i, t0)). + - split. eassumption. split. symmetry; eassumption. cbn in *. + now apply beq_nat_true. + - cbn. destruct (ssrbool.elimT (eqb_spec ind I)); [assumption|]. + eapply type_reduction; eassumption. + - eapply type_reduction in X5; eauto. + eapply validity_term in X5; eauto. + destruct (ssrbool.elimT (eqb_spec ind I)); auto. + unshelve eapply (PCUICInductives.isType_mkApps_Ind _ X7 _) in X5 as [parsubst [argsubst [[sp sp'] cu]]]; eauto. + pose proof (PCUICContexts.context_subst_length2 (PCUICSpine.inst_ctx_subst sp)). + pose proof (PCUICContexts.context_subst_length2 (PCUICSpine.inst_ctx_subst sp')). + autorewrite with len in H, H2. + destruct (PCUICWeakeningEnv.on_declared_inductive HΣ X7) eqn:ond. + rewrite -o.(onNpars) -H. + forward (o0.(onProjections)). + intros H'; rewrite H' nth_error_nil // in Heq_anonymous. + destruct ind_cshapes as [|cs []]; auto. + intros onps. + unshelve epose proof (onps.(on_projs_noidx _ _ _ _ _ _)). + rewrite ond /= in H2. + change (ind_indices o0) with (ind_indices o0) in *. + destruct (ind_indices o0) => //. + simpl in H2. + rewrite List.skipn_length in H2. + rewrite List.firstn_length. lia. + Qed. + + (* tFix *) + Next Obligation. sq. constructor; auto. exists W; auto. Defined. + Next Obligation. sq. now eapply PCUICWeakening.All_mfix_wf in XX0. Defined. + Next Obligation. + sq. cbn in *. depelim XX. + destruct i as [s HH]. + exists s. + change (tSort s) with (lift0 #|fix_context mfix| (tSort s)). + apply weakening; try assumption. + now apply All_mfix_wf. + Defined. + Next Obligation. + clear -XX HΣ. sq. + now depelim XX. + Qed. + Next Obligation. + assert (∥ All (fun d => ((Σ;;; Γ ,,, fix_context mfix |- dbody d : (lift0 #|fix_context mfix|) (dtype d)) * (isLambda (dbody d) = true))%type) mfix ∥). { + eapply All_sq, All_impl. exact YY. + cbn; intros ? []. sq; now constructor. } + sq; econstructor; try eassumption. + symmetry; eassumption. + Qed. + + (* tCoFix *) + Next Obligation. sq. constructor; auto. exists W; auto. Defined. + Next Obligation. sq. now eapply PCUICWeakening.All_mfix_wf in XX. Defined. + Next Obligation. + sq. cbn in *. depelim XX'. + destruct i as [s HH]. + exists s. + change (tSort s) with (lift0 #|fix_context mfix| (tSort s)). + apply weakening; try assumption. + now apply All_mfix_wf. + Defined. + Next Obligation. + clear -XX' HΣ. sq. + now depelim XX'. + Qed. + Next Obligation. + assert (∥ All (fun d => ((Σ;;; Γ ,,, fix_context mfix |- dbody d : (lift0 #|fix_context mfix|) (dtype d)))%type) mfix ∥). { + eapply All_sq, All_impl. exact YY. + now cbn; intros ? []. } + sq; econstructor; try eassumption. + symmetry; eassumption. + Qed. + + Lemma sq_wfl_nil : ∥ wf_local Σ [] ∥. + Proof. + repeat constructor. + Qed. + + Program Fixpoint check_context Γ : typing_result (∥ wf_local Σ Γ ∥) + := match Γ with + | [] => ret sq_wfl_nil + | {| decl_body := None; decl_type := A |} :: Γ => + HΓ <- check_context Γ ;; + XX <- infer_type infer Γ HΓ A ;; + ret _ + | {| decl_body := Some t; decl_type := A |} :: Γ => + HΓ <- check_context Γ ;; + XX <- infer_type infer Γ HΓ A ;; + XX <- infer_cumul infer Γ HΓ t A _ ;; + ret _ + end. + Next Obligation. + sq. econstructor; tas. econstructor; eauto. + Qed. + Next Obligation. + sq. econstructor; tea. + Qed. + Next Obligation. + sq. econstructor; tas. econstructor; eauto. + Qed. + +(* + Program Definition check_isWfArity Γ (HΓ : ∥ wf_local Σ Γ ∥) A + : typing_result (∥ isWfArity Σ Γ A ∥) := + match destArity [] A with + | None => raise (Msg (print_term Σ Γ A ^ " is not an arity")) + | Some (ctx, s) => XX <- check_context (Γ ,,, ctx) ;; + ret _ + end. + Next Obligation. + destruct XX. constructor. exists ctx, s. + split; auto. + Defined. *) + + Program Definition check_isType Γ (HΓ : ∥ wf_local Σ Γ ∥) A + : typing_result (∥ isType Σ Γ A ∥) := + s <- infer Γ HΓ A ;; + s' <- reduce_to_sort Γ s.π1 _ ;; + ret _. + Next Obligation. now eapply validity_wf. Defined. + Next Obligation. destruct X0. sq. eexists. eapply type_reduction; tea. Defined. + + Program Definition check Γ (HΓ : ∥ wf_local Σ Γ ∥) t A + : typing_result (∥ Σ;;; Γ |- t : A ∥) := + check_isType Γ HΓ A ;; + infer_cumul infer Γ HΓ t A _. + +End Typecheck. diff --git a/safechecker/theories/PCUICWfEnv.v b/safechecker/theories/PCUICWfEnv.v new file mode 100644 index 000000000..3dacd3fc4 --- /dev/null +++ b/safechecker/theories/PCUICWfEnv.v @@ -0,0 +1,62 @@ + +(* Distributed under the terms of the MIT license. *) +From Coq Require Import ProofIrrelevance. +From MetaCoq.Template Require Import config utils uGraph. +From MetaCoq.PCUIC Require Import PCUICAst PCUICAstUtils + PCUICReflect PCUICTyping PCUICGlobalEnv. + +Lemma wf_ext_gc_of_uctx {cf:checker_flags} {Σ : global_env_ext} (HΣ : ∥ wf_ext Σ ∥) + : ∑ uctx', gc_of_uctx (global_ext_uctx Σ) = Some uctx'. +Proof. + assert (consistent (global_ext_uctx Σ).2) as HC. + { sq; apply (global_ext_uctx_consistent _ HΣ). } + destruct Σ as [Σ φ]. + simpl in HC. + unfold gc_of_uctx; simpl in *. + apply gc_consistent_iff in HC. + destruct (gc_of_constraints (global_ext_constraints (Σ, φ))). + eexists; reflexivity. + contradiction HC. +Defined. + +Lemma graph_of_wf_ext {cf:checker_flags} {Σ : global_env_ext} (HΣ : ∥ wf_ext Σ ∥) + : ∑ G, is_graph_of_uctx G (global_ext_uctx Σ). +Proof. + destruct (wf_ext_gc_of_uctx HΣ) as [uctx Huctx]. + exists (make_graph uctx). unfold is_graph_of_uctx. now rewrite Huctx. +Defined. + +Section GraphSpec. + Context {cf:checker_flags} {Σ : global_env_ext} (HΣ : ∥ wf Σ ∥) + (Hφ : ∥ on_udecl Σ.1 Σ.2 ∥) + (G : universes_graph) (HG : is_graph_of_uctx G (global_ext_uctx Σ)). + + Local Definition HΣ' : ∥ wf_ext Σ ∥. + Proof. + destruct HΣ, Hφ; now constructor. + Defined. + + Lemma check_constraints_spec ctrs + : check_constraints G ctrs -> valid_constraints (global_ext_constraints Σ) ctrs. + Proof. + pose proof HΣ'. + intros HH. + refine (check_constraints_spec G (global_ext_uctx Σ) _ _ HG _ HH). + sq; now eapply wf_ext_global_uctx_invariants. + sq; now apply global_ext_uctx_consistent. + Qed. + + Lemma is_graph_of_uctx_levels (l : Level.t) : + LevelSet.mem l (uGraph.wGraph.V G) -> + LevelSet.mem l (global_ext_levels Σ). + Proof. + unfold is_graph_of_uctx in HG. + case_eq (gc_of_uctx (global_ext_uctx Σ)); [intros [lvs cts] XX|intro XX]; + rewrite -> XX in *; simpl in *; [|contradiction]. + unfold gc_of_uctx in XX; simpl in XX. + destruct (gc_of_constraints Σ); [|discriminate]. + inversion XX; subst. generalize (global_ext_levels Σ); intros lvs; cbn. + clear. intro H. apply LevelSet.mem_spec. now apply LevelSet.mem_spec in H. + Qed. + +End GraphSpec. \ No newline at end of file diff --git a/template-coq/theories/Universes.v b/template-coq/theories/Universes.v index 2e759517d..133812223 100644 --- a/template-coq/theories/Universes.v +++ b/template-coq/theories/Universes.v @@ -1,6 +1,7 @@ From Coq Require Import MSetList MSetFacts MSetProperties MSetDecide. From MetaCoq.Template Require Import utils BasicAst config. From Equations Require Import Equations. +Require Import ssreflect. Local Open Scope nat_scope. Local Open Scope string_scope2. @@ -178,6 +179,25 @@ Proof. apply orb_true_iff. Qed. +Lemma LevelSet_In_fold_right_add x l : + In x l <-> LevelSet.In x (fold_right LevelSet.add LevelSet.empty l). +Proof. + split. + - induction l; simpl => //. + intros [<-|H]. + * eapply LevelSet.add_spec; left; auto. + * eapply LevelSet.add_spec; right; auto. + - induction l; simpl => //. + * now rewrite LevelSetFact.empty_iff. + * rewrite LevelSet.add_spec. intuition auto. +Qed. + +Lemma LevelSet_union_empty s : LevelSet.union LevelSet.empty s = s. +Proof. + apply LevelSet.eq_leibniz. + change LevelSet.eq with LevelSet.Equal. + intros x; rewrite LevelSet.union_spec. lsets. +Qed. (* prop level is Prop or SProp *) Module PropLevel. @@ -265,7 +285,7 @@ Module UnivExpr. Qed. Definition lt_compat : Proper (Logic.eq ==> Logic.eq ==> iff) lt. - intros x x' H1 y y' H2; now rewrite H1, H2. + intros x x' H1 y y' H2; now rewrite H1 H2. Qed. Definition compare (x y : t) : comparison := @@ -1152,6 +1172,37 @@ End UnivConstraint. Module ConstraintSet := MSetList.MakeWithLeibniz UnivConstraint. Module ConstraintSetFact := WFactsOn UnivConstraint ConstraintSet. Module ConstraintSetProp := WPropertiesOn UnivConstraint ConstraintSet. +Module CS := ConstraintSet. + +Lemma CS_union_empty s : ConstraintSet.union ConstraintSet.empty s = s. +Proof. + apply ConstraintSet.eq_leibniz. + change ConstraintSet.eq with ConstraintSet.Equal. + intros x; rewrite ConstraintSet.union_spec. lsets. +Qed. + +Lemma CS_For_all_union f cst cst' : ConstraintSet.For_all f (ConstraintSet.union cst cst') -> + ConstraintSet.For_all f cst. +Proof. + unfold CS.For_all. + intros IH x inx. apply (IH x). + now eapply CS.union_spec; left. +Qed. + +Lemma CS_For_all_add P x s : CS.For_all P (CS.add x s) -> P x /\ CS.For_all P s. +Proof. + intros. + split. + * apply (H x), CS.add_spec; left => //. + * intros y iny. apply (H y), CS.add_spec; right => //. +Qed. + +Instance CS_For_all_proper P : Morphisms.Proper (CS.Equal ==> iff)%signature (ConstraintSet.For_all P). +Proof. + intros s s' eqs. + unfold CS.For_all. split; intros IH x inxs; apply (IH x); + now apply eqs. +Qed. (* Being built up from sorted lists without duplicates, constraint sets have decidable equality. This is however not used in the development. *) @@ -1186,8 +1237,6 @@ Module Instance. forallb2 f i j. End Instance. - - Module UContext. Definition t := Instance.t × ConstraintSet.t. @@ -1471,7 +1520,7 @@ Section Univ. Proof. intros H1 H2 v Hv. specialize (is_prop_and_is_sprop_val_false _ H1 H2 v) as [n Hzero]. - rewrite val_universe_sup, Hzero. destruct (Universe.univ_val v s2); simpl; lia. + rewrite val_universe_sup Hzero. destruct (Universe.univ_val v s2); simpl; lia. Qed. Lemma leq_universe0_sup_r φ s1 s2 : @@ -1480,7 +1529,7 @@ Section Univ. Proof. intros H1 H2 v Hv. specialize (is_prop_and_is_sprop_val_false _ H1 H2 v) as [n Hzero]. - rewrite val_universe_sup, Hzero. + rewrite val_universe_sup Hzero. destruct (Universe.univ_val v s1); simpl; lia. Qed. @@ -1711,8 +1760,9 @@ Section UniverseClosedSubst. intro e; split; intro He. - apply Universe.map_spec in He. destruct He as [e' [He' X]]. rewrite closedu_subst_instance_level_expr in X. - now subst. apply UnivExprSet.for_all_spec in H; proper. + apply UnivExprSet.for_all_spec in H; proper. exact (H _ He'). + now subst. - apply Universe.map_spec. exists e; split; tas. symmetry; apply closedu_subst_instance_level_expr. apply UnivExprSet.for_all_spec in H; proper. now apply H. @@ -1792,7 +1842,7 @@ Definition string_of_level (l : Level.t) : string := end. Definition string_of_level_expr (e : UnivExpr.t) : string := - let '(l, b) := e in string_of_level l ^ (if b then "+1" else ""). + let '(l, n) := e in string_of_level l ^ (if n is 0 then "" else "+" ^ string_of_nat n). Definition string_of_sort (u : Universe.t) := match u with @@ -1892,8 +1942,8 @@ Proof. - destruct v;discriminate. - apply is_prop_val with (v:=vv) in e. specialize (is_prop_and_is_sprop_val_false _ f f1 vv) as [n HH]. - rewrite e, HH. - rewrite e, HH in H2. simpl in H2. + rewrite e HH. + rewrite e HH in H2. simpl in H2. simpl. destruct (Universe.univ_val vv u') eqn:eq; simpl; auto. - destruct v';discriminate. - apply is_prop_val with (v:=vv) in f. @@ -1901,13 +1951,13 @@ Proof. rewrite f in H2. eapply univ_le_prop_inv in H2. cong. - apply is_sprop_val with (v:=vv) in e1. specialize (is_prop_and_is_sprop_val_false _ f f1 vv) as [n HH]. - rewrite HH, e1 in H2. now simpl in H2. + rewrite HH e1 in H2. now simpl in H2. - apply is_sprop_val with (v:=vv) in f1. specialize (is_prop_and_is_sprop_val_false _ e e1 vv) as [n HH]. rewrite f1 in H2. apply univ_le_sprop_inv in H2; cong. - specialize (is_prop_and_is_sprop_val_false _ e e1 vv) as [n HH]. specialize (is_prop_and_is_sprop_val_false _ f f1 vv) as [n' HH']. - rewrite HH, HH'. apply univ_val_max_mon; auto. + rewrite HH HH'. apply univ_val_max_mon; auto. now rewrite <- HH, <- HH'. Qed. @@ -1959,7 +2009,7 @@ Section UniverseLemmas. intros s1 s1' H1 s2 s2' H2. unfold_eq_universe. specialize (H1 v Hv). specialize (H2 v Hv). rewrite !val_universe_sup. - now rewrite H1, H2. + now rewrite H1 H2. Qed. Lemma sort_of_product_twice u s : @@ -1968,7 +2018,7 @@ Section UniverseLemmas. Proof. destruct u,s;auto. unfold Universe.sort_of_product;cbn. - now rewrite sup0_assoc, sup0_idem. + now rewrite sup0_assoc sup0_idem. Qed. End UniverseLemmas. @@ -2100,7 +2150,7 @@ Section no_prop_leq_type. Proof. red. destruct check_univs; [|trivial]. intros H1 H2 v Hv. eapply is_prop_val in H1; eapply is_prop_val in H2. - rewrite H1, H2. lled; lia. + rewrite -> H1, H2. lled; lia. Qed. Lemma leq_sprop_sprop {l l'} : @@ -2109,7 +2159,7 @@ Section no_prop_leq_type. Proof. red. destruct check_univs; [|trivial]. intros H1 H2 v Hv. eapply is_sprop_val in H1; eapply is_sprop_val in H2. - rewrite H1, H2. lled; lia. + rewrite -> H1, H2. lled; lia. Qed. Lemma leq_prop_is_prop_sprop {x s} : @@ -2127,7 +2177,7 @@ Section no_prop_leq_type. consistent ϕ -> leq_universe ϕ (Universe.super l) l' -> Universe.is_prop l' -> False. Proof. - intros Hcf [v Hv] H1 H2. unfold leq_universe in *; rewrite Hcf in *. + intros Hcf [v Hv] H1 H2. rewrite /leq_universe Hcf in H1. eapply is_prop_val with (v:=v) in H2. specialize (H1 _ Hv). rewrite H2 in H1. destruct l as [| |]; destruct l'; lled; cbn -[Z.add] in *; lia. Qed. @@ -2137,7 +2187,7 @@ Section no_prop_leq_type. consistent ϕ -> leq_universe ϕ (Universe.super l) l' -> Universe.is_sprop l' -> False. Proof. - intros Hcf [v Hv] H1 H2. unfold leq_universe in *; rewrite Hcf in *. + intros Hcf [v Hv] H1 H2. rewrite /leq_universe Hcf in H1. eapply is_sprop_val with (v:=v) in H2. specialize (H1 _ Hv). rewrite H2 in H1. destruct l as [| |]; destruct l'; lled; cbn -[Z.add] in *; lia. Qed. diff --git a/template-coq/theories/monad_utils.v b/template-coq/theories/monad_utils.v index aa7e8fd45..dc52a1d9a 100644 --- a/template-coq/theories/monad_utils.v +++ b/template-coq/theories/monad_utils.v @@ -1,8 +1,9 @@ (* todo(gmm): This file should really be replaced by a real * monad library. *) -Require Import List. -From MetaCoq.Template Require Import All_Forall. +Require Import Arith List. +From MetaCoq.Template Require Import All_Forall MCSquash. +From Equations Require Import Equations. Coercion is_true : bool >-> Sortclass. Import ListNotations. @@ -147,3 +148,78 @@ Definition check_eq_nat {T E} {M : Monad T} {M' : MonadExc E T} n m (e : E) : T | left p => ret p | right p => raise e end. + +Program Fixpoint monad_Alli {T} {M : Monad T} {A} {P} (f : forall n x, T (∥ P n x ∥)) l n + : T (∥ @Alli A P n l ∥) + := match l with + | [] => ret (sq Alli_nil) + | a :: l => X <- f n a ;; + Y <- monad_Alli f l (S n) ;; + ret _ + end. +Next Obligation. + sq. constructor; assumption. +Defined. + +Program Fixpoint monad_Alli_All {T} {M : Monad T} {A} {P} {Q} (f : forall n x, ∥ Q x ∥ -> T (∥ P n x ∥)) l n : + ∥ All Q l ∥ -> T (∥ @Alli A P n l ∥) + := match l with + | [] => fun _ => ret (sq Alli_nil) + | a :: l => fun allq => X <- f n a _ ;; + Y <- monad_Alli_All f l (S n) _ ;; + ret _ + end. +Next Obligation. sq. + now depelim allq. +Qed. +Next Obligation. + sq; now depelim allq. +Qed. +Next Obligation. + sq. constructor; assumption. +Defined. + +Section monad_Alli_nth. + Context {T} {M : Monad T} {A} {P : nat -> A -> Type}. + Program Fixpoint monad_Alli_nth_gen l k + (f : forall n x, nth_error l n = Some x -> T (∥ P (k + n) x ∥)) : + T (∥ @Alli A P k l ∥) + := match l with + | [] => ret (sq Alli_nil) + | a :: l => X <- f 0 a _ ;; + Y <- monad_Alli_nth_gen l (S k) (fun n x hnth => px <- f (S n) x hnth;; ret _) ;; + ret _ + end. + Next Obligation. + sq. now rewrite Nat.add_succ_r in px. + Qed. + Next Obligation. + sq. rewrite Nat.add_0_r in X. constructor; auto. + Qed. + + Definition monad_Alli_nth l (f : forall n x, nth_error l n = Some x -> T (∥ P n x ∥)) : T (∥ @Alli A P 0 l ∥) := + monad_Alli_nth_gen l 0 f. + +End monad_Alli_nth. + +Section MonadAllAll. + Context {T} {M : Monad T} {A} {P : A -> Type} {Q} (f : forall x, ∥ Q x ∥ -> T (∥ P x ∥)). + Program Fixpoint monad_All_All l : ∥ All Q l ∥ -> T (∥ All P l ∥) := + match l return ∥ All Q l ∥ -> T (∥ All P l ∥) with + | [] => fun _ => ret (sq All_nil) + | a :: l => fun allq => + X <- f a _ ;; + Y <- monad_All_All l _ ;; + ret _ + end. + Next Obligation. sq. + now depelim allq. + Qed. + Next Obligation. + sq; now depelim allq. + Qed. + Next Obligation. + sq. constructor; assumption. + Defined. +End MonadAllAll. + diff --git a/template-coq/theories/utils/All_Forall.v b/template-coq/theories/utils/All_Forall.v index 97b302cfe..aa28009fe 100644 --- a/template-coq/theories/utils/All_Forall.v +++ b/template-coq/theories/utils/All_Forall.v @@ -3,9 +3,6 @@ From MetaCoq.Template Require Import MCPrelude MCList MCRelations MCProd MCOptio From Equations Require Import Equations. Import ListNotations. -Local Ltac inv H := inversion_clear H. -Local Coercion is_true : bool >-> Sortclass. - Derive Signature for Forall Forall2. (** Combinators *) @@ -117,6 +114,18 @@ Proof. constructor; auto. now destruct (Hp a). Qed. +Lemma forallbP_cond {A} (P Q : A -> Prop) (p : A -> bool) l : + Forall Q l -> + (forall x, Q x -> reflect (P x) (p x)) -> reflect (Forall P l) (forallb p l). +Proof. + intros HQ Hp. + apply iff_reflect; split. + - induction HQ; intros HP; depelim HP; rewrite /= // IHHQ // andb_true_r. + now destruct (Hp x H). + - induction HQ; rewrite /= //. move/andb_and => [pa pl]. + constructor; auto. now destruct (Hp _ H). +Qed. + Lemma map_eq_inj {A B} (f g : A -> B) l: map f l = map g l -> All (fun x => f x = g x) l. Proof. diff --git a/template-coq/theories/utils/MCList.v b/template-coq/theories/utils/MCList.v index 626f3c2d6..e3c3b6f24 100644 --- a/template-coq/theories/utils/MCList.v +++ b/template-coq/theories/utils/MCList.v @@ -488,8 +488,6 @@ Proof. eapply IHl1 in H2 as []. split; congruence. Qed. -Arguments skipn : simpl nomatch. - Lemma skipn_all2 : forall {A n} (l : list A), #|l| <= n -> @@ -612,6 +610,34 @@ Proof. * simpl. apply IHn. Qed. +Fixpoint split_at_aux {A} (n : nat) (acc : list A) (l : list A) : list A * list A := + match n with + | 0 => (List.rev acc, l) + | S n' => + match l with + | [] => (List.rev acc, []) + | hd :: l' => split_at_aux n' (hd :: acc) l' + end + end. + +Definition split_at {A} (n : nat) (l : list A) : list A * list A := + split_at_aux n [] l. + +Lemma split_at_aux_firstn_skipn {A} n acc (l : list A) : split_at_aux n acc l = (List.rev acc ++ firstn n l, skipn n l). +Proof. + induction n in acc, l |- *; destruct l; simpl; auto. + now rewrite app_nil_r. + now rewrite app_nil_r. + now rewrite app_nil_r. + rewrite IHn. simpl. + now rewrite -app_assoc /=. +Qed. + +Lemma split_at_firstn_skipn {A} n (l : list A) : split_at n l = (firstn n l, skipn n l). +Proof. + now rewrite /split_at split_at_aux_firstn_skipn /= //. +Qed. + Lemma rev_app : forall A (l l' : list A), (rev (l ++ l') = rev l' ++ rev l)%list. @@ -879,6 +905,97 @@ Proof. now rewrite andb_comm andb_true_r. Qed. +Fixpoint unfold {A} (n : nat) (f : nat -> A) : list A := + match n with + | 0 => [] + | S n => unfold n f ++ [f n] + end. + +Lemma mapi_irrel_list {A B} (f : nat -> A) (l l' : list B) : + #|l| = #|l'| -> + mapi (fun i (x : B) => f i) l = mapi (fun i x => f i) l'. +Proof. + induction l in f, l' |- *; destruct l' => //; simpl; auto. + intros [= eq]. unfold mapi. simpl. f_equal. + rewrite !mapi_rec_Sk. + now rewrite [mapi_rec _ _ _](IHl (fun x => (f (S x))) l'). +Qed. + +Lemma mapi_unfold {A B} (f : nat -> B) l : mapi (fun i (x : A) => f i) l = unfold #|l| f. +Proof. + unfold mapi. + induction l in f |- *; simpl; auto. + rewrite mapi_rec_Sk. + rewrite -IHl. rewrite -(mapi_rec_Sk (fun i x => f i) l 0). + change [f #|l|] with (mapi_rec (fun i x => f i) [a] #|l|). + rewrite -(Nat.add_0_r #|l|). rewrite -mapi_rec_app. + change (f 0 :: _) with (mapi (fun i x => f i) (a :: l)). + apply mapi_irrel_list. simpl. rewrite app_length /=; lia. +Qed. + +Lemma unfold_length {A} (f : nat -> A) m : #|unfold m f| = m. +Proof. + induction m; simpl; rewrite ?app_length /=; auto. lia. +Qed. + +Lemma nth_error_unfold {A} (f : nat -> A) m n : n < m <-> nth_error (unfold m f) n = Some (f n). +Proof. + induction m in n |- *; split; intros Hn; try lia. + - simpl in Hn. rewrite nth_error_nil in Hn. discriminate. + - destruct (Classes.eq_dec n m); [subst|]. + * simpl. rewrite nth_error_app_ge unfold_length // Nat.sub_diag /= //. + * simpl. rewrite nth_error_app_lt ?unfold_length //; try lia. + apply IHm; lia. + - simpl in Hn. eapply nth_error_Some_length in Hn. + rewrite app_length /= unfold_length in Hn. lia. +Qed. + +Lemma nth_error_unfold_inv {A} (f : nat -> A) m n t : nth_error (unfold m f) n = Some t -> t = (f n). +Proof. + induction m in n |- *; intros Hn; try lia. + - simpl in Hn. rewrite nth_error_nil in Hn. discriminate. + - simpl in Hn. + pose proof (nth_error_Some_length Hn). + rewrite app_length /= unfold_length in H. + destruct (Classes.eq_dec n m); [subst|]. + * simpl. revert Hn. rewrite nth_error_app_ge unfold_length // Nat.sub_diag /= //; congruence. + * simpl. revert Hn. rewrite nth_error_app_lt ?unfold_length //; try lia. auto. +Qed. + +Lemma In_unfold_inj {A} (f : nat -> A) n i : + (forall i j, f i = f j -> i = j) -> + In (f i) (unfold n f) -> i < n. +Proof. + intros hf. + induction n; simpl => //. + intros H; apply in_app_or in H. + destruct H. + - specialize (IHn H). lia. + - simpl in H. destruct H; [apply hf in H|]. + * subst. auto. + * destruct H. +Qed. + +Lemma forallb_unfold {A} (f : A -> bool) (g : nat -> A) n : + (forall x, x < n -> f (g x)) -> + forallb f (unfold n g). +Proof. + intros fg. + induction n; simpl; auto. + rewrite forallb_app IHn //. + intros x lt; rewrite fg //. lia. + rewrite /= fg //. +Qed. + +Lemma forallb_mapi {A B} (p : B -> bool) (f : nat -> B) l : + (forall i, i < #|l| -> p (f i)) -> + forallb p (mapi (fun i (x : A) => f i) l). +Proof. + intros Hp. rewrite (mapi_unfold f). + induction #|l| in *; simpl; auto. + rewrite forallb_app. simpl. now rewrite Hp // !andb_true_r. +Qed. + Lemma fold_left_andb_forallb {A} P l x : fold_left (fun b x => P x && b) l (P x) = @forallb A P (x :: l). Proof. diff --git a/template-coq/theories/utils/MCPrelude.v b/template-coq/theories/utils/MCPrelude.v index b53d98f86..6c3fa2b1d 100644 --- a/template-coq/theories/utils/MCPrelude.v +++ b/template-coq/theories/utils/MCPrelude.v @@ -5,6 +5,9 @@ Derive NoConfusion EqDec for Strings.Ascii.ascii string positive Z. Declare Scope metacoq_scope. +(** We cannot use ssrbool currently as it breaks extraction. *) +Coercion is_true : bool >-> Sortclass. + Notation "'eta_compose'" := (fun g f x => g (f x)). (* \circ *) @@ -57,4 +60,6 @@ Hint Extern 10 (_ < _)%nat => lia : terms. Hint Extern 10 (_ <= _)%nat => lia : terms. Hint Extern 10 (@eq nat _ _) => lia : terms. -Ltac easy ::= easy0 || solve [intuition eauto 3 with core terms]. \ No newline at end of file +Ltac easy ::= easy0 || solve [intuition eauto 3 with core terms]. + +Ltac inv H := inversion_clear H. diff --git a/template-coq/theories/utils/MCUtils.v b/template-coq/theories/utils/MCUtils.v index be3d02c58..e6ebf182f 100644 --- a/template-coq/theories/utils/MCUtils.v +++ b/template-coq/theories/utils/MCUtils.v @@ -51,9 +51,6 @@ Ltac rdest := | |- sigT _ => eexists end. -(** We cannot use ssrbool as it breaks extraction. *) -Coercion is_true : bool >-> Sortclass. - Tactic Notation "toProp" ident(H) := match type of H with | is_true (_ apply PeanoNat.Nat.ltb_lt in H From 4d21fb36c2196876f7484909fb4128eac4f9d3c5 Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Fri, 27 Nov 2020 20:34:17 +0100 Subject: [PATCH 12/70] Bundle together the guard axioms in a class --- TODO.md | 7 +- pcuic/theories/PCUICAlpha.v | 4 +- pcuic/theories/PCUICArities.v | 4 +- pcuic/theories/PCUICContextConversion.v | 39 ++-- pcuic/theories/PCUICElimination.v | 6 +- pcuic/theories/PCUICInductiveInversion.v | 2 +- pcuic/theories/PCUICInductives.v | 6 +- pcuic/theories/PCUICInversion.v | 4 +- pcuic/theories/PCUICNameless.v | 10 +- pcuic/theories/PCUICSafeLemmata.v | 2 +- pcuic/theories/PCUICSigmaCalculus.v | 17 +- pcuic/theories/PCUICSubstitution.v | 2 +- pcuic/theories/PCUICToTemplate.v | 2 + pcuic/theories/PCUICToTemplateCorrectness.v | 6 +- pcuic/theories/PCUICTyping.v | 191 +++++++++--------- pcuic/theories/PCUICUnivSubstitution.v | 40 +--- pcuic/theories/PCUICWeakeningEnv.v | 7 +- pcuic/theories/PCUICWfUniverses.v | 2 +- pcuic/theories/TemplateToPCUICCorrectness.v | 4 +- safechecker/_CoqProject.in | 3 + safechecker/_PluginProject.in | 6 + .../src/metacoq_safechecker_plugin.mlpack | 4 +- safechecker/theories/Extraction.v | 4 +- safechecker/theories/PCUICSafeChecker.v | 190 +++++++++-------- safechecker/theories/PCUICSafeRetyping.v | 3 +- safechecker/theories/PCUICTypeChecker.v | 10 +- safechecker/theories/SafeTemplateChecker.v | 4 +- template-coq/theories/EnvironmentTyping.v | 7 +- template-coq/theories/Extraction.v | 1 + template-coq/theories/Universes.v | 2 +- 30 files changed, 319 insertions(+), 270 deletions(-) diff --git a/TODO.md b/TODO.md index 0c158d854..9ccba9f5c 100644 --- a/TODO.md +++ b/TODO.md @@ -29,10 +29,9 @@ - Clean `Derive`s: always derive `Siganture`, `NoConf`, ... directly after the definition of the inductive. (To avoid doing it several times.) - -- Remove `Program` from everywhere. - - + (Mostly done) + +- Finish the PCUICSigmaCalculus proofs. # Big projects diff --git a/pcuic/theories/PCUICAlpha.v b/pcuic/theories/PCUICAlpha.v index d901b0600..d21c1e243 100644 --- a/pcuic/theories/PCUICAlpha.v +++ b/pcuic/theories/PCUICAlpha.v @@ -460,7 +460,7 @@ Section Alpha. { now rewrite !fix_context_length, (All2_length _ _ X). } eapply type_Cumul'. + econstructor. - * eapply (fix_guard_eq_term _ _ n); eauto. + * eapply (fix_guard_eq_term _ _ _ _ n); eauto. constructor. assumption. * eassumption. * assumption. @@ -532,7 +532,7 @@ Section Alpha. { now rewrite !fix_context_length, (All2_length _ _ X). } eapply type_Cumul'. + econstructor. - * eapply (cofix_guard_eq_term _ _ n) ; eauto. + * eapply (cofix_guard_eq_term _ _ _ _ n) ; eauto. constructor. assumption. * eassumption. * eassumption. diff --git a/pcuic/theories/PCUICArities.v b/pcuic/theories/PCUICArities.v index 3f006f21a..a998f28c3 100644 --- a/pcuic/theories/PCUICArities.v +++ b/pcuic/theories/PCUICArities.v @@ -413,7 +413,7 @@ Proof. rewrite (subst_instance_ind_type_id Σ _ {| inductive_mind := inductive_mind ind; inductive_ind := i |}); eauto. destruct isdecl. split; eauto. reflexivity. } clear oind. - revert X. clear onNpars onGuard. + revert X. clear onNpars. generalize (le_n #|ind_bodies mdecl|). generalize (ind_bodies mdecl) at 1 3 4 5. induction l using rev_ind; simpl; first constructor. @@ -448,7 +448,7 @@ Proof. { apply forall_nth_error_Alli. econstructor; eauto. split; eauto. } clear oind. - revert X. clear onNpars onGuard. + revert X. clear onNpars. generalize (le_n #|ind_bodies mdecl|). generalize (ind_bodies mdecl) at 1 3 4 5. induction l using rev_ind; simpl; first constructor. diff --git a/pcuic/theories/PCUICContextConversion.v b/pcuic/theories/PCUICContextConversion.v index 741669314..230dd9dd3 100644 --- a/pcuic/theories/PCUICContextConversion.v +++ b/pcuic/theories/PCUICContextConversion.v @@ -890,6 +890,16 @@ Qed. Hint Extern 4 (eq_term_upto_univ _ _ _ _ _) => reflexivity : pcuic. +Axiom fix_guard_context_cumulativity : forall {cf:checker_flags} Σ Γ Γ' mfix, + cumul_context Σ Γ' Γ -> + fix_guard Σ Γ mfix -> + fix_guard Σ Γ' mfix. + +Axiom cofix_guard_context_cumulativity : forall {cf:checker_flags} Σ Γ Γ' mfix, + cumul_context Σ Γ' Γ -> + cofix_guard Σ Γ mfix -> + cofix_guard Σ Γ' mfix. + Lemma context_cumulativity_prop {cf:checker_flags} : env_prop (fun Σ Γ t T => @@ -951,7 +961,8 @@ Proof. - econstructor; pcuic. intuition auto. eapply isdecl. eapply isdecl. eauto. solve_all. destruct b0 as [? [? ?]]; eauto. - - econstructor; pcuic. + - econstructor. eapply fix_guard_context_cumulativity; eauto. + all:pcuic. eapply (All_impl X0). intros x [s [Hs IH]]. exists s; eauto. @@ -963,18 +974,20 @@ Proof. apply (All_impl X0); simpl. intros x' [s [Hs' IH']]. exists s. eapply IH'; auto. - - econstructor; pcuic. - eapply (All_impl X0). - intros x [s [Hs IH]]. - exists s; eauto. - eapply (All_impl X1). - intros x [Hs IH]. - eapply IH. - now apply cumul_context_app_same. - eapply (All_mfix_wf); auto. - apply (All_impl X0); simpl. - intros x' [s [Hs' IH']]. exists s. - eapply IH'; auto. + - econstructor. + eapply cofix_guard_context_cumulativity; eauto. + all:pcuic. + + eapply (All_impl X0). + intros x [s [Hs IH]]. + exists s; eauto. + + eapply (All_impl X1). + intros x [Hs IH]. + eapply IH. + now apply cumul_context_app_same. + eapply (All_mfix_wf); auto. + apply (All_impl X0); simpl. + intros x' [s [Hs' IH']]. exists s. + eapply IH'; auto. - econstructor; eauto. eapply cumul_cumul_ctx; eauto. diff --git a/pcuic/theories/PCUICElimination.v b/pcuic/theories/PCUICElimination.v index 723d6039b..d1b1d605c 100644 --- a/pcuic/theories/PCUICElimination.v +++ b/pcuic/theories/PCUICElimination.v @@ -19,7 +19,7 @@ Definition SingletonProp `{cf : checker_flags} (Σ : global_env_ext) (ind : indu declared_inductive (fst Σ) mdecl ind idecl -> forall Γ args u n (Σ' : global_env_ext), wf Σ' -> - PCUICWeakeningEnv.extends Σ Σ' -> + extends Σ Σ' -> welltyped Σ' Γ (mkApps (tConstruct ind n u) args) -> ∥Is_proof Σ' Γ (mkApps (tConstruct ind n u) args)∥ /\ #|ind_ctors idecl| <= 1 /\ @@ -30,7 +30,7 @@ Definition Computational `{cf : checker_flags} (Σ : global_env_ext) (ind : indu declared_inductive (fst Σ) mdecl ind idecl -> forall Γ args u n (Σ' : global_env_ext), wf Σ' -> - PCUICWeakeningEnv.extends Σ Σ' -> + extends Σ Σ' -> welltyped Σ' Γ (mkApps (tConstruct ind n u) args) -> Is_proof Σ' Γ (mkApps (tConstruct ind n u) args) -> False. @@ -39,7 +39,7 @@ Definition Informative `{cf : checker_flags} (Σ : global_env_ext) (ind : induct declared_inductive (fst Σ) mdecl ind idecl -> forall Γ args u n (Σ' : global_env_ext), wf_ext Σ' -> - PCUICWeakeningEnv.extends Σ Σ' -> + extends Σ Σ' -> Is_proof Σ' Γ (mkApps (tConstruct ind n u) args) -> #|ind_ctors idecl| <= 1 /\ squash (All (Is_proof Σ' Γ) (skipn (ind_npars mdecl) args)). diff --git a/pcuic/theories/PCUICInductiveInversion.v b/pcuic/theories/PCUICInductiveInversion.v index 0dce0721e..005b3b80a 100644 --- a/pcuic/theories/PCUICInductiveInversion.v +++ b/pcuic/theories/PCUICInductiveInversion.v @@ -379,7 +379,7 @@ Qed. Lemma subslet_cofix {cf:checker_flags} (Σ : global_env_ext) Γ mfix : wf_local Σ Γ -> - cofix_guard mfix -> + cofix_guard Σ Γ mfix -> All (fun d : def term => ∑ s : Universe.t, Σ;;; Γ |- dtype d : tSort s) mfix -> All (fun d : def term => diff --git a/pcuic/theories/PCUICInductives.v b/pcuic/theories/PCUICInductives.v index 3884bf64b..57cd19d59 100644 --- a/pcuic/theories/PCUICInductives.v +++ b/pcuic/theories/PCUICInductives.v @@ -1197,14 +1197,14 @@ Proof. split; auto. destruct (on_declared_inductive wfΣ decli) as [onmind oib]. eapply typing_spine_app; eauto. - - invs H0. destruct (declared_inductive_inj isdecl decli) as [-> ->]. + - invs H0. destruct (declared_inductive_inj d decli) as [-> ->]. clear decli. split; auto. constructor; [|reflexivity]. - destruct (on_declared_inductive wfΣ isdecl) as [onmind oib]. + destruct (on_declared_inductive wfΣ d) as [onmind oib]. pose proof (oib.(onArity)) as ar. eapply isType_weaken; eauto. eapply (isType_subst_instance_decl _ []); eauto. - destruct isdecl; eauto. + destruct d; eauto. eapply oib.(onArity). auto. - specialize (IHtyping1 _ _ wfΣ decli) as [IH cu]; split; auto. eapply typing_spine_weaken_concl; pcuic. diff --git a/pcuic/theories/PCUICInversion.v b/pcuic/theories/PCUICInversion.v index a9a128af3..48e3a037a 100644 --- a/pcuic/theories/PCUICInversion.v +++ b/pcuic/theories/PCUICInversion.v @@ -209,7 +209,7 @@ Section Inversion. Σ ;;; Γ |- tFix mfix n : T -> ∑ decl, let types := fix_context mfix in - fix_guard mfix × + fix_guard Σ Γ mfix × nth_error mfix n = Some decl × All (fun d => isType Σ Γ (dtype d)) mfix × All (fun d => @@ -226,7 +226,7 @@ Section Inversion. forall {Γ mfix idx T}, Σ ;;; Γ |- tCoFix mfix idx : T -> ∑ decl, - cofix_guard mfix × + cofix_guard Σ Γ mfix × let types := fix_context mfix in nth_error mfix idx = Some decl × All (fun d => isType Σ Γ (dtype d)) mfix × diff --git a/pcuic/theories/PCUICNameless.v b/pcuic/theories/PCUICNameless.v index d2bde580c..8bd0d071f 100644 --- a/pcuic/theories/PCUICNameless.v +++ b/pcuic/theories/PCUICNameless.v @@ -1338,10 +1338,11 @@ Proof. = nlctx (Γ ,,, fix_context mfix)) by now rewrite <- nl_fix_context, <- nlctx_app_context. constructor. - + eapply fix_guard_eq_term with (idx:=n). 1: eassumption. + + todo "fix_guard spec". + (*eapply fix_guard_eq_term with (idx:=n). 1: eassumption. constructor. clear. induction mfix. 1: constructor. simpl. constructor; tas. cbn. - repeat split; now apply eq_term_upto_univ_tm_nl. + repeat split; now apply eq_term_upto_univ_tm_nl.*) + now rewrite nth_error_map H0. + auto. + clear -X0. @@ -1361,10 +1362,11 @@ Proof. = nlctx (Γ ,,, fix_context mfix)) by now rewrite <- nl_fix_context, <- nlctx_app_context. constructor; auto. - + eapply cofix_guard_eq_term with (idx:=n). 1: eassumption. + + todo "cofix_guard eq_term". + (* eapply cofix_guard_eq_term with (idx:=n). 1: eassumption. constructor. clear. induction mfix. 1: constructor. simpl. constructor; tas. cbn. - repeat split; now apply eq_term_upto_univ_tm_nl. + repeat split; now apply eq_term_upto_univ_tm_nl.*) + now rewrite nth_error_map H0. + clear -X0. apply All_map. eapply All_impl; tea. diff --git a/pcuic/theories/PCUICSafeLemmata.v b/pcuic/theories/PCUICSafeLemmata.v index e26ccccb9..0cc13c891 100644 --- a/pcuic/theories/PCUICSafeLemmata.v +++ b/pcuic/theories/PCUICSafeLemmata.v @@ -925,7 +925,7 @@ Section Lemmata. induction l ; intros t h. - reflexivity. - cbn in h. specialize IHl with (1 := h). subst. - cbn in h. exfalso. assumption. + cbn in h. exfalso. discriminate. Qed. Lemma isAppProd_isProd : diff --git a/pcuic/theories/PCUICSigmaCalculus.v b/pcuic/theories/PCUICSigmaCalculus.v index b0cb70107..5a36ab61a 100644 --- a/pcuic/theories/PCUICSigmaCalculus.v +++ b/pcuic/theories/PCUICSigmaCalculus.v @@ -12,7 +12,6 @@ Set Equations With UIP. (** * Type preservation for σ-calculus *) - Open Scope sigma_scope. Set Keyed Unification. @@ -1604,6 +1603,20 @@ Proof. + eapply red1_rename. all: try eassumption. Qed. +Lemma fix_guard_rename Σ Γ Δ mfix f : + renaming Σ Γ Δ f -> + let mfix' := map (map_def (rename f) (rename (shiftn (List.length mfix) f))) mfix in + fix_guard Σ Δ mfix -> + fix_guard Σ Γ mfix'. +Admitted. + +Lemma cofix_guard_rename Σ Γ Δ mfix f : + renaming Σ Γ Δ f -> + let mfix' := map (map_def (rename f) (rename (shiftn (List.length mfix) f))) mfix in + cofix_guard Σ Δ mfix -> + cofix_guard Σ Γ mfix'. +Admitted. + Lemma typing_rename_prop : env_prop (fun Σ Γ t A => forall Δ f, @@ -1722,7 +1735,7 @@ Proof. simpl. eapply meta_conv. + eapply type_Fix. - * eapply fix_guard_rename. assumption. + * eapply fix_guard_rename; eauto. * rewrite nth_error_map. rewrite hdecl. simpl. reflexivity. * apply hf. * apply All_map, (All_impl ihmfixt). diff --git a/pcuic/theories/PCUICSubstitution.v b/pcuic/theories/PCUICSubstitution.v index 2a4f0d7e5..0f66fc5ee 100644 --- a/pcuic/theories/PCUICSubstitution.v +++ b/pcuic/theories/PCUICSubstitution.v @@ -2663,7 +2663,7 @@ Proof. - rewrite -> (map_dtype _ (subst s (#|mfix| + #|Δ|))). eapply type_CoFix; auto. - * eapply cofix_guard_subst; auto. + * eapply cofix_guard_subst; eauto. * now rewrite -> nth_error_map, H0. * eapply All_map. eapply (All_impl X0); simpl. diff --git a/pcuic/theories/PCUICToTemplate.v b/pcuic/theories/PCUICToTemplate.v index 7883b7a58..424a06e58 100644 --- a/pcuic/theories/PCUICToTemplate.v +++ b/pcuic/theories/PCUICToTemplate.v @@ -1,6 +1,8 @@ (* Distributed under the terms of the MIT license. *) From MetaCoq.PCUIC Require Import PCUICAst PCUICAstUtils. +Set Warnings "-notation-overridden". From MetaCoq.Template Require Import config utils AstUtils BasicAst Ast. +Set Warnings "+notation-overridden". Fixpoint trans (t : PCUICAst.term) : Ast.term := match t with diff --git a/pcuic/theories/PCUICToTemplateCorrectness.v b/pcuic/theories/PCUICToTemplateCorrectness.v index 76d8e9fa4..b5921b369 100644 --- a/pcuic/theories/PCUICToTemplateCorrectness.v +++ b/pcuic/theories/PCUICToTemplateCorrectness.v @@ -623,10 +623,8 @@ Proof. - apply IHmfix. Qed. - - Lemma trans_wf_local': - forall (Σ : PCUICAst.global_env_ext) Γ (wfΓ : PT.wf_local Σ Γ), + forall (Σ : PCUICAst.global_env_ext) Γ (wfΓ : wf_local Σ Γ), let P := (fun Σ0 Γ0 _ (t T : PCUICAst.term) _ => TT.typing (trans_global Σ0) (trans_local Γ0) (trans t) (trans T)) @@ -757,7 +755,7 @@ Admitted. Lemma All_over_All Σ Γ wfΓ : PT.All_local_env_over PT.typing (fun (Σ : PCUICAst.global_env_ext) (Γ : PCUICAst.context) - (_ : PCUICTyping.wf_local Σ Γ) (t T : PCUICAst.term) + (_ : wf_local Σ Γ) (t T : PCUICAst.term) (_ : PT.typing Σ Γ t T) => TT.typing (trans_global Σ) (trans_local Γ) (trans t) (trans T)) Σ Γ wfΓ -> PT.All_local_env diff --git a/pcuic/theories/PCUICTyping.v b/pcuic/theories/PCUICTyping.v index 45b1d7d4d..444c99784 100644 --- a/pcuic/theories/PCUICTyping.v +++ b/pcuic/theories/PCUICTyping.v @@ -66,93 +66,94 @@ Definition type_of_constructor mdecl (cdecl : ident * term * nat) (c : inductive let mind := inductive_mind (fst c) in subst0 (inds mind u mdecl.(ind_bodies)) (subst_instance_constr u (snd (fst cdecl))). - +Definition extends (Σ Σ' : global_env) := + { Σ'' & Σ' = Σ'' ++ Σ }. + (** ** Typing relation *) Module PCUICEnvTyping := EnvTyping PCUICTerm PCUICEnvironment. Include PCUICEnvTyping. -Derive Signature NoConfusion for All_local_env. +Derive NoConfusion for All_local_env. Derive NoConfusion for context_decl. Derive NoConfusion for list. (* AXIOM GUARD CONDITION *) -Axiom fix_guard : mfixpoint term -> bool. - -Axiom fix_guard_red1 : - forall Σ Γ mfix mfix' idx, - fix_guard mfix -> - red1 Σ Γ (tFix mfix idx) (tFix mfix' idx) -> - fix_guard mfix'. - -Axiom fix_guard_eq_term : - forall mfix mfix' idx, - fix_guard mfix -> - upto_names (tFix mfix idx) (tFix mfix' idx) -> - fix_guard mfix'. - -Axiom fix_guard_rename : - forall mfix f, - let mfix' := - map (map_def (rename f) (rename (shiftn (List.length mfix) f))) mfix - in - fix_guard mfix -> - fix_guard mfix'. - -Axiom fix_guard_lift : - forall mfix n k, - let k' := (#|mfix| + k)%nat in - let mfix' := map (map_def (lift n k) (lift n k')) mfix in - fix_guard mfix -> - fix_guard mfix'. -Axiom fix_guard_subst : - forall mfix s k, +Class GuardChecker := +{ (* Structural recursion check *) + fix_guard : global_env_ext -> context -> mfixpoint term -> bool ; + (* Guarded by destructors check *) + cofix_guard : global_env_ext -> context -> mfixpoint term -> bool ; + + fix_guard_red1 Σ Γ mfix mfix' idx : + fix_guard Σ Γ mfix -> + red1 Σ Γ (tFix mfix idx) (tFix mfix' idx) -> + fix_guard Σ Γ mfix' ; + + fix_guard_eq_term Σ Γ mfix mfix' idx : + fix_guard Σ Γ mfix -> + upto_names (tFix mfix idx) (tFix mfix' idx) -> + fix_guard Σ Γ mfix' ; + + fix_guard_lift Σ Γ Γ' Γ'' mfix : + let k' := (#|mfix| + #|Γ'|)%nat in + let mfix' := map (map_def (lift #|Γ''| #|Γ'|) (lift #|Γ''| k')) mfix in + fix_guard Σ (Γ ,,, Γ') mfix -> + fix_guard Σ (Γ ,,, Γ'' ,,, lift_context #|Γ''| 0 Γ') mfix' ; + + fix_guard_subst Σ Γ Γ' Δ mfix s k : let k' := (#|mfix| + k)%nat in let mfix' := map (map_def (subst s k) (subst s k')) mfix in - fix_guard mfix -> - fix_guard mfix'. - -(* AXIOM Cofix Guard Condition (guarded by constructors) *) - -Axiom cofix_guard : mfixpoint term -> bool. - -Axiom cofix_guard_red1 : - forall Σ Γ mfix mfix' idx, - cofix_guard mfix -> + fix_guard Σ (Γ ,,, Γ' ,,, Δ) mfix -> + fix_guard Σ (Γ ,,, subst_context s 0 Δ) mfix' ; + + fix_guard_subst_instance {cf:checker_flags} Σ Γ mfix u univs : + consistent_instance_ext (Σ.1, univs) Σ.2 u -> + fix_guard Σ Γ mfix -> + fix_guard (Σ.1, univs) (subst_instance_context u Γ) (map (map_def (subst_instance_constr u) (subst_instance_constr u)) + mfix) ; + + fix_guard_extends Σ Γ mfix Σ' : + fix_guard Σ Γ mfix -> + extends Σ.1 Σ' -> + fix_guard Σ' Γ mfix ; + + cofix_guard_red1 Σ Γ mfix mfix' idx : + cofix_guard Σ Γ mfix -> red1 Σ Γ (tCoFix mfix idx) (tCoFix mfix' idx) -> - cofix_guard mfix'. + cofix_guard Σ Γ mfix' ; -Axiom cofix_guard_eq_term : - forall mfix mfix' idx, - cofix_guard mfix -> + cofix_guard_eq_term Σ Γ mfix mfix' idx : + cofix_guard Σ Γ mfix -> upto_names (tCoFix mfix idx) (tCoFix mfix' idx) -> - cofix_guard mfix'. - -Axiom cofix_guard_rename : - forall mfix f, - let mfix' := - map (map_def (rename f) (rename (shiftn (List.length mfix) f))) mfix - in - cofix_guard mfix -> - cofix_guard mfix'. - -Axiom cofix_guard_lift : - forall mfix n k, - let k' := (#|mfix| + k)%nat in - let mfix' := map (map_def (lift n k) (lift n k')) mfix in - cofix_guard mfix -> - cofix_guard mfix'. + cofix_guard Σ Γ mfix' ; + + cofix_guard_lift Σ Γ Γ' Γ'' mfix : + let k' := (#|mfix| + #|Γ'|)%nat in + let mfix' := map (map_def (lift #|Γ''| #|Γ'|) (lift #|Γ''| k')) mfix in + cofix_guard Σ (Γ ,,, Γ') mfix -> + cofix_guard Σ (Γ ,,, Γ'' ,,, lift_context #|Γ''| 0 Γ') mfix' ; -Axiom cofix_guard_subst : - forall mfix s k, + cofix_guard_subst Σ Γ Γ' Δ mfix s k : let k' := (#|mfix| + k)%nat in let mfix' := map (map_def (subst s k) (subst s k')) mfix in - cofix_guard mfix -> - cofix_guard mfix'. + cofix_guard Σ (Γ ,,, Γ' ,,, Δ) mfix -> + cofix_guard Σ (Γ ,,, subst_context s 0 Δ) mfix' ; + + cofix_guard_subst_instance {cf:checker_flags} Σ Γ mfix u univs : + consistent_instance_ext (Σ.1, univs) Σ.2 u -> + cofix_guard Σ Γ mfix -> + cofix_guard (Σ.1, univs) (subst_instance_context u Γ) (map (map_def (subst_instance_constr u) (subst_instance_constr u)) + mfix) ; + + cofix_guard_extends Σ Γ mfix Σ' : + cofix_guard Σ Γ mfix -> + extends Σ.1 Σ' -> + cofix_guard Σ' Γ mfix }. -(* AXIOM INDUCTIVE GUARD CONDITION *) -Axiom ind_guard : mutual_inductive_body -> bool. +Axiom guard_checking : GuardChecker. +Existing Instance guard_checking. (** Compute the type of a case from the predicate [p], actual parameters [pars] and an inductive declaration. *) @@ -326,14 +327,16 @@ Definition wf_universe Σ s := forall l, UnivExprSet.In l u -> LevelSet.In (UnivExpr.get_level l) (global_ext_levels Σ) end. +Reserved Notation "'wf_local' Σ Γ " (at level 9, Σ, Γ at next level). + Inductive typing `{checker_flags} (Σ : global_env_ext) (Γ : context) : term -> term -> Type := | type_Rel n decl : - All_local_env (lift_typing typing Σ) Γ -> + wf_local Σ Γ -> nth_error Γ n = Some decl -> Σ ;;; Γ |- tRel n : lift0 (S n) decl.(decl_type) | type_Sort s : - All_local_env (lift_typing typing Σ) Γ -> + wf_local Σ Γ -> wf_universe Σ s -> Σ ;;; Γ |- tSort s : tSort (Universe.super s) @@ -345,7 +348,7 @@ Inductive typing `{checker_flags} (Σ : global_env_ext) (Γ : context) : term -> | type_Lambda na A t s1 B : Σ ;;; Γ |- A : tSort s1 -> Σ ;;; Γ ,, vass na A |- t : B -> - Σ ;;; Γ |- (tLambda na A t) : tProd na A B + Σ ;;; Γ |- tLambda na A t : tProd na A B | type_LetIn na b B t s1 A : Σ ;;; Γ |- B : tSort s1 -> @@ -359,27 +362,31 @@ Inductive typing `{checker_flags} (Σ : global_env_ext) (Γ : context) : term -> Σ ;;; Γ |- tApp t u : B{0 := u} | type_Const cst u : - All_local_env (lift_typing typing Σ) Γ -> - forall decl (isdecl : declared_constant Σ.1 cst decl), + wf_local Σ Γ -> + forall decl, + declared_constant Σ.1 cst decl -> consistent_instance_ext Σ decl.(cst_universes) u -> Σ ;;; Γ |- (tConst cst u) : subst_instance_constr u decl.(cst_type) | type_Ind ind u : - All_local_env (lift_typing typing Σ) Γ -> - forall mdecl idecl (isdecl : declared_inductive Σ.1 mdecl ind idecl), + wf_local Σ Γ -> + forall mdecl idecl, + declared_inductive Σ.1 mdecl ind idecl -> consistent_instance_ext Σ mdecl.(ind_universes) u -> Σ ;;; Γ |- (tInd ind u) : subst_instance_constr u idecl.(ind_type) | type_Construct ind i u : - All_local_env (lift_typing typing Σ) Γ -> - forall mdecl idecl cdecl (isdecl : declared_constructor Σ.1 mdecl idecl (ind, i) cdecl), + wf_local Σ Γ -> + forall mdecl idecl cdecl, + declared_constructor Σ.1 mdecl idecl (ind, i) cdecl -> consistent_instance_ext Σ mdecl.(ind_universes) u -> Σ ;;; Γ |- (tConstruct ind i u) : type_of_constructor mdecl cdecl (ind, i) u | type_Case indnpar u p c brs args : let ind := indnpar.1 in let npar := indnpar.2 in - forall mdecl idecl (isdecl : declared_inductive Σ.1 mdecl ind idecl), + forall mdecl idecl, + declared_inductive Σ.1 mdecl ind idecl -> mdecl.(ind_npars) = npar -> let params := List.firstn npar args in forall ps pty, build_case_predicate_type ind mdecl idecl params u ps = Some pty -> @@ -392,16 +399,18 @@ Inductive typing `{checker_flags} (Σ : global_env_ext) (Γ : context) : term -> Σ ;;; Γ |- tCase indnpar p c brs : mkApps p (skipn npar args ++ [c]) | type_Proj p c u : - forall mdecl idecl pdecl (isdecl : declared_projection Σ.1 mdecl idecl p pdecl) args, + forall mdecl idecl pdecl, + declared_projection Σ.1 mdecl idecl p pdecl -> + forall args, Σ ;;; Γ |- c : mkApps (tInd (fst (fst p)) u) args -> #|args| = ind_npars mdecl -> let ty := snd pdecl in Σ ;;; Γ |- tProj p c : subst0 (c :: List.rev args) (subst_instance_constr u ty) | type_Fix mfix n decl : - fix_guard mfix -> + fix_guard Σ Γ mfix -> nth_error mfix n = Some decl -> - All_local_env (lift_typing typing Σ) Γ -> + wf_local Σ Γ -> All (fun d => {s & Σ ;;; Γ |- d.(dtype) : tSort s}) mfix -> All (fun d => (Σ ;;; Γ ,,, fix_context mfix |- d.(dbody) : lift0 #|fix_context mfix| d.(dtype)) * (isLambda d.(dbody) = true)%type) mfix -> @@ -409,9 +418,9 @@ Inductive typing `{checker_flags} (Σ : global_env_ext) (Γ : context) : term -> Σ ;;; Γ |- tFix mfix n : decl.(dtype) | type_CoFix mfix n decl : - cofix_guard mfix -> + cofix_guard Σ Γ mfix -> nth_error mfix n = Some decl -> - All_local_env (lift_typing typing Σ) Γ -> + wf_local Σ Γ -> All (fun d => {s & Σ ;;; Γ |- d.(dtype) : tSort s}) mfix -> All (fun d => Σ ;;; Γ ,,, fix_context mfix |- d.(dbody) : lift0 #|fix_context mfix| d.(dtype)) mfix -> wf_cofixpoint Σ.1 mfix -> @@ -422,9 +431,8 @@ Inductive typing `{checker_flags} (Σ : global_env_ext) (Γ : context) : term -> Σ ;;; Γ |- B : tSort s -> Σ ;;; Γ |- A <= B -> Σ ;;; Γ |- t : B -where " Σ ;;; Γ |- t : T " := (typing Σ Γ t T) : type_scope. - -Notation wf_local Σ Γ := (All_local_env (lift_typing typing Σ) Γ). +where " Σ ;;; Γ |- t : T " := (typing Σ Γ t T) +and "'wf_local' Σ Γ " := (All_local_env (lift_typing typing Σ) Γ). Lemma meta_conv {cf : checker_flags} Σ Γ t A B : Σ ;;; Γ |- t : A -> @@ -446,7 +454,6 @@ Definition unlift_opt_pred (P : global_env_ext -> context -> option term -> term Module PCUICTypingDef <: Typing PCUICTerm PCUICEnvironment PCUICEnvTyping. - Definition ind_guard := ind_guard. Definition typing := @typing. Definition wf_universe := @wf_universe. Definition conv := @conv. @@ -503,7 +510,7 @@ Proof. - exact (S (S (wf_local_size _ typing_size _ a))). - exact (S (S (wf_local_size _ typing_size _ a))). - exact (S (S (wf_local_size _ typing_size _ a))). - - exact (S (Nat.max d1 (Nat.max d2 + - exact (S (Nat.max d2 (Nat.max d3 (all2_size _ (fun x y p => Nat.max (typing_size Σ Γ (snd x) (snd y) (snd (fst p))) (typing_size _ _ _ _ (snd p).π2)) a)))). - exact (S (Nat.max (Nat.max (wf_local_size _ typing_size _ a) (all_size _ (fun x p => typing_size Σ _ _ _ p.π2) a0)) (all_size _ (fun x p => typing_size Σ _ _ _ (fst p)) a1))). - exact (S (Nat.max (Nat.max (wf_local_size _ typing_size _ a) (all_size _ (fun x p => typing_size Σ _ _ _ p.π2) a0)) (all_size _ (fun x p => typing_size Σ _ _ _ p) a1))). @@ -778,7 +785,7 @@ Lemma typing_ind_env `{cf : checker_flags} : (forall Σ (wfΣ : wf Σ.1) (Γ : context) (wfΓ : wf_local Σ Γ) (mfix : list (def term)) (n : nat) decl, let types := fix_context mfix in - fix_guard mfix -> + fix_guard Σ Γ mfix -> nth_error mfix n = Some decl -> PΓ Σ Γ wfΓ -> All (fun d => {s & (Σ ;;; Γ |- d.(dtype) : tSort s)%type * P Σ Γ d.(dtype) (tSort s)})%type mfix -> @@ -790,7 +797,7 @@ Lemma typing_ind_env `{cf : checker_flags} : (forall Σ (wfΣ : wf Σ.1) (Γ : context) (wfΓ : wf_local Σ Γ) (mfix : list (def term)) (n : nat) decl, let types := fix_context mfix in - cofix_guard mfix -> + cofix_guard Σ Γ mfix -> nth_error mfix n = Some decl -> PΓ Σ Γ wfΓ -> All (fun d => {s & (Σ ;;; Γ |- d.(dtype) : tSort s)%type * P Σ Γ d.(dtype) (tSort s)})%type mfix -> @@ -1237,7 +1244,7 @@ Section All_local_env. Definition property := forall (Σ : global_env_ext) (Γ : context), - All_local_env (lift_typing typing Σ) Γ -> forall t T : term, typing Σ Γ t T -> Type. + wf_local Σ Γ -> forall t T : term, typing Σ Γ t T -> Type. Definition lookup_wf_local {Γ P} (wfΓ : All_local_env P Γ) (n : nat) (isdecl : n < #|Γ|) : @@ -1296,7 +1303,7 @@ Section All_local_env. | {| decl_name := na; decl_body := None; decl_type := ty |} => fun H => P Σ Γ wfΓ _ _ (projT2 H) end H. - Lemma nth_error_All_local_env_over {P Σ Γ n decl} (eq : nth_error Γ n = Some decl) {wfΓ : All_local_env (lift_typing typing Σ) Γ} : + Lemma nth_error_All_local_env_over {P Σ Γ n decl} (eq : nth_error Γ n = Some decl) {wfΓ : wf_local Σ Γ} : All_local_env_over typing P Σ Γ wfΓ -> let Γ' := skipn (S n) Γ in let p := lookup_wf_local_decl wfΓ n eq in diff --git a/pcuic/theories/PCUICUnivSubstitution.v b/pcuic/theories/PCUICUnivSubstitution.v index 400dd1c60..2c58be262 100644 --- a/pcuic/theories/PCUICUnivSubstitution.v +++ b/pcuic/theories/PCUICUnivSubstitution.v @@ -10,14 +10,10 @@ From Equations Require Import Equations. (** * Universe Substitution lemmas for typing derivations. *) - Local Set Keyed Unification. Set Default Goal Selector "!". -Module CS := ConstraintSet. -Module LS := LevelSet. - Create HintDb univ_subst. Local Ltac aa := rdest; eauto with univ_subst. @@ -442,8 +438,8 @@ Qed. Context {cf : checker_flags}. Lemma consistent_instance_declared lvs φ uctx u : - consistent_instance lvs φ uctx u - -> forallb (fun l => LS.mem l lvs) u. + consistent_instance lvs φ uctx u -> + forallb (fun l => LS.mem l lvs) u. Proof. unfold consistent_instance. destruct uctx as [ctx|ctx]. 1: destruct u; [reflexivity|discriminate]. @@ -1454,20 +1450,6 @@ Proof. destruct destInd as [[i u']|]; simpl; auto. Qed. -Axiom fix_guard_subst_instance : - forall mfix u, - fix_guard mfix -> - fix_guard (map (map_def (subst_instance_constr u) (subst_instance_constr u)) - mfix). - - -Axiom cofix_guard_subst_instance : - forall mfix u, - cofix_guard mfix -> - cofix_guard (map (map_def (subst_instance_constr u) (subst_instance_constr u)) - mfix). - - Lemma All_local_env_over_subst_instance Σ Γ (wfΓ : wf_local Σ Γ) : All_local_env_over typing (fun Σ0 Γ0 (_ : wf_local Σ0 Γ0) t T (_ : Σ0;;; Γ0 |- t : T) => @@ -1664,7 +1646,7 @@ Proof. - intros mfix n decl H H0 H1 X X0 wffix u univs wfΣ' HSub. erewrite map_dtype. econstructor. - + now apply fix_guard_subst_instance. + + now eapply fix_guard_subst_instance. + rewrite nth_error_map, H0. reflexivity. + eapply H1; eauto. + apply All_map, (All_impl X); simpl; intuition auto. @@ -1688,7 +1670,7 @@ Proof. - intros mfix n decl guard H X X0 X1 wfcofix u univs wfΣ' HSub H1. erewrite map_dtype. econstructor; tas. - + now apply cofix_guard_subst_instance. + + now eapply cofix_guard_subst_instance. + rewrite nth_error_map, H. reflexivity. + apply X; eauto. + apply All_map, (All_impl X0); simpl; intuition auto. @@ -1923,9 +1905,9 @@ Section SubstIdentity. intros wfΣ lin. eapply LevelSet.union_spec in lin. destruct lin. - - apply In_fold_right_add in H. + - apply LevelSet_In_fold_right_add in H. destruct l; simpl; auto. - eapply In_unfold in H. + eapply In_unfold_inj in H; [|congruence]. pose proof (proj1 (nth_error_unfold Level.Var n n0) H). now rewrite (nth_error_nth _ _ _ H0). - eapply not_var_global_levels in wfΣ. @@ -1949,7 +1931,7 @@ Section SubstIdentity. apply LevelSet.mem_spec, LevelSet.union_spec. left. unfold levels_of_udecl. simpl. rewrite (mapi_unfold Level.Var). - eapply In_fold_right_add. + eapply LevelSet_In_fold_right_add. induction #|univs| in i, Hi |- *; try lia. simpl. eapply in_or_app. destruct (eq_dec i n). * subst. right; simpl; auto. @@ -2021,8 +2003,8 @@ Section SubstIdentity. destruct (udecl_prop_in_var_poly onu ina) as [[univs csts] eq]. rewrite eq in IHu, ina |- *. simpl in *. rewrite mapi_unfold in IHu, ina |- *. - eapply In_fold_right_add in ina. - eapply In_unfold in ina. + eapply LevelSet_In_fold_right_add in ina. + eapply In_unfold_inj in ina; try congruence. eapply (nth_error_unfold Level.Var) in ina. now rewrite (nth_error_nth _ _ _ ina). Qed. @@ -2039,12 +2021,12 @@ Section SubstIdentity. eapply udecl_prop_in_var_poly in onu as [[ctx cstrs] eq]; eauto. rewrite eq. simpl. rewrite eq in cu. simpl in cu. - apply In_fold_right_add in cu. + apply LevelSet_In_fold_right_add in cu. unfold AUContext.repr in *. rewrite (mapi_unfold Level.Var) in cu |- *. destruct nth_error eqn:hnth. * apply nth_error_unfold_inv in hnth. subst; auto. * apply nth_error_None in hnth. rewrite unfold_length in hnth. - apply In_unfold in cu. lia. + apply In_unfold_inj in cu; try lia. congruence. Qed. Lemma consistent_instance_ext_subst_abs_univ Σ u : diff --git a/pcuic/theories/PCUICWeakeningEnv.v b/pcuic/theories/PCUICWeakeningEnv.v index 56da09a65..c574debd3 100644 --- a/pcuic/theories/PCUICWeakeningEnv.v +++ b/pcuic/theories/PCUICWeakeningEnv.v @@ -4,8 +4,6 @@ From MetaCoq.PCUIC Require Import PCUICAst PCUICEquality PCUICTyping. Require Import ssreflect. -Derive Signature for Alli. - Set Default Goal Selector "!". Lemma global_ext_constraints_app Σ Σ' φ @@ -64,9 +62,6 @@ Qed. Generalizable Variables Σ Γ t T. -Definition extends (Σ Σ' : global_env) := - { Σ'' & Σ' = Σ'' ++ Σ }. - Definition weaken_env_prop_full {cf:checker_flags} (P : global_env_ext -> context -> term -> term -> Type) := forall (Σ : global_env_ext) (Σ' : global_env), wf Σ' -> extends Σ.1 Σ' -> @@ -497,10 +492,12 @@ Proof. close_Forall. intros; intuition eauto with extends. destruct b as [s [Hs IH]]; eauto. - econstructor; eauto with extends. + + eapply fix_guard_extends; eauto. + eapply (All_impl X0); simpl; intuition eauto with extends. destruct X as [s Hs]; exists s. intuition eauto with extends. + eapply All_impl; eauto; simpl; intuition eauto with extends. - econstructor; eauto with extends. + + eapply cofix_guard_extends; eauto. + eapply (All_impl X0); simpl; intuition eauto with extends. destruct X as [s Hs]; exists s. intuition eauto with extends. + eapply All_impl; eauto; simpl; intuition eauto with extends. diff --git a/pcuic/theories/PCUICWfUniverses.v b/pcuic/theories/PCUICWfUniverses.v index e5bfaa299..c0d345cf3 100644 --- a/pcuic/theories/PCUICWfUniverses.v +++ b/pcuic/theories/PCUICWfUniverses.v @@ -259,7 +259,7 @@ Section CheckerFlags. rewrite mapi_unfold in wfx. eapply (proj1 (LevelSetProp.of_list_1 _ _)) in wfx. apply SetoidList.InA_alt in wfx as [? [<- wfx]]. simpl in wfx. - eapply In_unfold in wfx. + eapply In_unfold_inj in wfx; [|congruence]. destruct (nth_in_or_default n u (Level.lSet)). red in cu. eapply Forall_In in cu; eauto. rewrite e. red. eapply LS.union_spec. right. eapply global_levels_Set. diff --git a/pcuic/theories/TemplateToPCUICCorrectness.v b/pcuic/theories/TemplateToPCUICCorrectness.v index 17f3312af..9fa9a87bb 100644 --- a/pcuic/theories/TemplateToPCUICCorrectness.v +++ b/pcuic/theories/TemplateToPCUICCorrectness.v @@ -1125,9 +1125,9 @@ Admitted. Hint Resolve trans_wf_local : trans. Axiom fix_guard_trans : - forall mfix, + forall Σ Γ mfix, TTy.fix_guard mfix -> - fix_guard (map (map_def trans trans) mfix). + fix_guard Σ Γ (map (map_def trans trans) mfix). Lemma isWFArity_wf (Σ : Ast.global_env_ext) Γ T : Typing.wf Σ -> TTy.isWfArity TTy.typing Σ Γ T -> T.wf T. Proof. diff --git a/safechecker/_CoqProject.in b/safechecker/_CoqProject.in index 08d8cbe7d..29115f2f4 100644 --- a/safechecker/_CoqProject.in +++ b/safechecker/_CoqProject.in @@ -1,9 +1,12 @@ -R theories MetaCoq.SafeChecker +theories/PCUICErrors.v theories/PCUICSafeReduce.v theories/PCUICEqualityDec.v theories/PCUICSafeConversion.v theories/PCUICWfReduction.v +theories/PCUICWfEnv.v +theories/PCUICTypeChecker.v theories/PCUICSafeChecker.v theories/SafeTemplateChecker.v theories/PCUICSafeRetyping.v diff --git a/safechecker/_PluginProject.in b/safechecker/_PluginProject.in index cfeeda7dd..d4ffe1b33 100644 --- a/safechecker/_PluginProject.in +++ b/safechecker/_PluginProject.in @@ -83,12 +83,18 @@ src/pCUICPretty.mli src/pCUICPretty.ml # From SafeChecker +src/pCUICErrors.mli +src/pCUICErrors.ml src/pCUICSafeReduce.mli src/pCUICSafeReduce.ml src/pCUICEqualityDec.mli src/pCUICEqualityDec.ml src/pCUICSafeConversion.mli src/pCUICSafeConversion.ml +# src/pCUICWfEnv.mli +# src/pCUICWfEnv.ml +src/pCUICTypeChecker.mli +src/pCUICTypeChecker.ml src/pCUICSafeChecker.mli src/pCUICSafeChecker.ml src/safeTemplateChecker.mli diff --git a/safechecker/src/metacoq_safechecker_plugin.mlpack b/safechecker/src/metacoq_safechecker_plugin.mlpack index 4d1b6a859..9233d9ebc 100644 --- a/safechecker/src/metacoq_safechecker_plugin.mlpack +++ b/safechecker/src/metacoq_safechecker_plugin.mlpack @@ -30,11 +30,13 @@ PCUICPosition PCUICPretty TemplateToPCUIC PCUICCumulativity - PCUICUnivSubst + +PCUICErrors PCUICSafeReduce PCUICEqualityDec PCUICSafeConversion +PCUICTypeChecker PCUICSafeChecker SafeTemplateChecker diff --git a/safechecker/theories/Extraction.v b/safechecker/theories/Extraction.v index aa416b31b..abfa71959 100644 --- a/safechecker/theories/Extraction.v +++ b/safechecker/theories/Extraction.v @@ -31,9 +31,7 @@ Extract Constant Equations.Init.pr2 => "snd". Extraction Inline Equations.Init.pr1 Equations.Init.pr2. Extraction Inline Equations.Prop.Logic.transport Equations.Prop.Logic.transport_r MCEquality.transport. -Extract Constant PCUICTyping.fix_guard => "(fun x -> true)". -Extract Constant PCUICTyping.cofix_guard => "(fun x -> true)". -Extract Constant PCUICTyping.ind_guard => "(fun x -> true)". +Extract Constant PCUICTyping.guard_checking => "{ fix_guard = (fun _ _ _ -> true); cofix_guard = (fun _ _ _ -> true) }". Cd "src". diff --git a/safechecker/theories/PCUICSafeChecker.v b/safechecker/theories/PCUICSafeChecker.v index 65fcb09c8..1d38c4739 100644 --- a/safechecker/theories/PCUICSafeChecker.v +++ b/safechecker/theories/PCUICSafeChecker.v @@ -13,7 +13,7 @@ From MetaCoq.PCUIC Require Import PCUICAst PCUICAstUtils PCUICClosed PCUICUnivSubstitution PCUICWeakeningEnv. From MetaCoq.SafeChecker Require Import PCUICSafeReduce PCUICErrors PCUICEqualityDec - PCUICSafeConversion PCUICWfReduction PCUICTypeChecker. + PCUICSafeConversion PCUICWfReduction PCUICWfEnv PCUICTypeChecker. From Equations Require Import Equations. Require Import ssreflect ssrbool. @@ -110,15 +110,14 @@ Section CheckEnv. : ∥ Alli (on_ind_body (lift_typing typing) Σ ind mdecl) 0 (ind_bodies mdecl) ∥ -> ∥ wf_local Σ (ind_params mdecl) ∥ -> context_assumptions (ind_params mdecl) = ind_npars mdecl -> - ind_guard mdecl -> check_variance (ind_universes mdecl) (ind_variance mdecl) -> ∥ on_inductive (lift_typing typing) Σ ind mdecl ∥. Proof. - intros H H0 H1 H2 H3. sq. econstructor; try eassumption. - unfold check_variance in H3. unfold on_variance. + intros H H0 H1 H2. sq. econstructor; try eassumption. + unfold check_variance in H2. unfold on_variance. destruct (ind_universes mdecl) eqn:E; destruct (ind_variance mdecl) eqn:E'; try congruence. - 2:split. now eapply eqb_eq in H3. + 2:split. now eapply eqb_eq in H2. Defined. @@ -444,8 +443,6 @@ Section CheckEnv. wf_local Σ Γ * wt_decl Σ Γ d. Proof. intros wfd; depelim wfd; split; simpl; pcuic. - destruct l as [s Hs]. now exists (tSort s). - destruct l as [s Hs]. now exists (tSort s). now exists t. Qed. @@ -573,9 +570,9 @@ Section CheckEnv. Next Obligation. destruct Σ as [Σ wfΣ G wfG]; simpl in *. sq. destruct le; simpl. - - eapply leqb_term_spec in check0; sq; auto. + - eapply leqb_term_spec in check; sq; auto. eapply wfΣ. - - eapply eqb_term_spec in check0; sq; auto. + - eapply eqb_term_spec in check; sq; auto. apply wfΣ. Qed. @@ -1356,6 +1353,19 @@ Section CheckEnv. Qed. End PositivityCheck. + Lemma In_unfold_inj {A} (f : nat -> A) n i : + (forall i j, f i = f j -> i = j) -> + In (f i) (unfold n f) <-> i < n. + Proof. + intros hf. split. + now apply In_unfold_inj. + intros. + induction n in i, H |- *; simpl => //. lia. + eapply in_app_iff. + destruct (eq_dec i n). subst. right; left; auto. + left. eapply IHn. lia. + Qed. + Lemma In_Var_global_ext_poly {n Σ inst cstrs} : n < #|inst| -> LevelSet.mem (Level.Var n) (global_ext_levels (Σ, Polymorphic_ctx (inst, cstrs))). @@ -1363,9 +1373,9 @@ Section CheckEnv. intros Hn. unfold global_ext_levels; simpl. apply LevelSet.mem_spec; rewrite LevelSet.union_spec. left. - rewrite /AUContext.levels /= PCUICUnivSubstitution.mapi_unfold. + rewrite /AUContext.levels /= mapi_unfold. apply LevelSetProp.of_list_1, InA_In_eq. - eapply In_unfold_inj; try congruence. exists n. intuition auto. + eapply In_unfold_inj; try congruence. Qed. Lemma on_udecl_poly_bounded Σ inst cstrs : @@ -1591,6 +1601,68 @@ Section CheckEnv. eapply All2_refl. intros. simpl. eapply (eq_decl_upto_refl Σ). Qed. + Lemma wt_cstrs {Σ : wf_env_ext} {n mdecl cstrs cs} : + ∥ All2 + (fun (cstr : (ident × term) × nat) (cs0 : constructor_shape) => + check_constructor_spec Σ n mdecl cstr cs0) cstrs cs ∥ -> + ∥ All (fun cstr => welltyped Σ (arities_context mdecl.(ind_bodies)) cstr.1.2) cstrs ∥. + Proof. + intros; sq. + solve_all. simpl. + destruct X as [[[isTy _] _] _]. simpl in isTy. + now eapply isType_welltyped in isTy. + Qed. + + Lemma get_wt_indices {Σ : wf_env_ext} {mdecl cstrs cs} + (wfar : ∥ wf_ind_types Σ mdecl ∥) + (wfpars : ∥ wf_local Σ (ind_params mdecl) ∥) + (n : nat) (idecl : one_inductive_body) (indices : context) + (hnth : nth_error mdecl.(ind_bodies) n = Some idecl) + (heq : ∥ ∑ inds, idecl.(ind_type) = it_mkProd_or_LetIn (mdecl.(ind_params) ,,, indices) (tSort inds) ∥) : + ∥ All2 + (fun (cstr : (ident × term) × nat) (cs0 : constructor_shape) => + check_constructor_spec Σ (S n) mdecl cstr cs0) cstrs cs ∥ -> + ∥ All (fun cs => wt_indices Σ mdecl indices cs) cs ∥. + Proof. + destruct Σ as [Σ wfΣ G wfG]; simpl in *. destruct wfΣ. + intros; sq. + solve_all. simpl. + destruct X as [[[isTy eq] sorts] eq']. simpl in *. + assert(wf_local Σ (ind_params mdecl,,, indices)). + { eapply nth_error_all in wfar; eauto. simpl in wfar. + destruct heq as [s Hs]. rewrite Hs in wfar. + eapply isType_it_mkProd_or_LetIn_wf_local in wfar. + now rewrite app_context_nil_l in wfar. auto. } + red. rewrite eq in isTy. + eapply isType_it_mkProd_or_LetIn_inv in isTy; auto. + eapply isType_mkApps_inv in isTy as [fty [s [Hf Hsp]]]; auto. + eapply inversion_Rel in Hf as [decl [wfctx [Hnth cum]]]; auto. + rewrite nth_error_app_ge in Hnth. lia. + split. now rewrite app_context_assoc in wfctx. + replace (#|ind_params mdecl,,, cshape_args y| + (#|ind_bodies mdecl| - S n) - + #|ind_params mdecl,,, cshape_args y|) with (#|ind_bodies mdecl| - S n) in Hnth by lia. + pose proof (nth_error_Some_length hnth). + rewrite nth_error_rev in hnth => //. + eapply nth_error_arities_context in hnth. rewrite Hnth in hnth. + noconf hnth; simpl in *. clear Hnth. + eapply PCUICSpine.typing_spine_strengthen in Hsp; eauto. + clear cum. + destruct heq as [inds eqind]. + move: Hsp. rewrite eqind. + rewrite lift_it_mkProd_or_LetIn /= => Hs. + rewrite closed_ctx_lift in Hs. eapply PCUICClosed.closed_wf_local; eauto. + rewrite app_context_assoc in Hs wfctx. + eapply typing_spine_it_mkProd_or_LetIn_ext_list_inv in Hs; auto. + 2:{ eapply PCUICWeakening.weaken_wf_local; pcuic. + now eapply wf_ind_types_wf_arities. } + 2:{ eapply PCUICClosed.closed_wf_local; eauto. } + eapply typing_spine_it_mkProd_or_LetIn_inv in Hs => //. auto. + eapply weakening_wf_local; eauto. + rewrite -app_context_assoc. + eapply PCUICWeakening.weaken_wf_local; eauto. + now eapply wf_ind_types_wf_arities. + Qed. + Program Definition check_cstr_variance (Σ : wf_env) mdecl (id : kername) indices (mdeclvar : check_variance mdecl.(ind_universes) mdecl.(ind_variance) = true) cs (wfΣ : ∥ wf_ext (Σ, ind_universes mdecl) ∥) @@ -1655,67 +1727,27 @@ Section CheckEnv. destruct ind_universes as [|[]] => //. Qed. - Lemma wt_cstrs {Σ : wf_env_ext} {n mdecl cstrs cs} : - ∥ All2 - (fun (cstr : (ident × term) × nat) (cs0 : constructor_shape) => - check_constructor_spec Σ n mdecl cstr cs0) cstrs cs ∥ -> - ∥ All (fun cstr => welltyped Σ (arities_context mdecl.(ind_bodies)) cstr.1.2) cstrs ∥. - Proof. - intros; sq. - solve_all. simpl. - destruct X as [[[isTy _] _] _]. simpl in isTy. - apply (isType_welltyped isTy). - Qed. - - Lemma get_wt_indices {Σ : wf_env_ext} {mdecl cstrs cs} - (wfar : ∥ wf_ind_types Σ mdecl ∥) - (wfpars : ∥ wf_local Σ (ind_params mdecl) ∥) - (n : nat) (idecl : one_inductive_body) (indices : context) - (hnth : nth_error mdecl.(ind_bodies) n = Some idecl) - (heq : ∥ ∑ inds, idecl.(ind_type) = it_mkProd_or_LetIn (mdecl.(ind_params) ,,, indices) (tSort inds) ∥) : - ∥ All2 - (fun (cstr : (ident × term) × nat) (cs0 : constructor_shape) => - check_constructor_spec Σ (S n) mdecl cstr cs0) cstrs cs ∥ -> - ∥ All (fun cs => wt_indices Σ mdecl indices cs) cs ∥. - Proof. - destruct Σ as [Σ wfΣ G wfG]; simpl in *. destruct wfΣ. - intros; sq. - solve_all. simpl. - destruct X as [[[isTy eq] sorts] eq']. simpl in *. - assert(wf_local Σ (ind_params mdecl,,, indices)). - { eapply nth_error_all in wfar; eauto. simpl in wfar. - destruct heq as [s Hs]. rewrite Hs in wfar. - eapply isType_it_mkProd_or_LetIn_wf_local in wfar. - now rewrite app_context_nil_l in wfar. auto. } - red. rewrite eq in isTy. - eapply isType_it_mkProd_or_LetIn_inv in isTy; auto. - eapply isType_mkApps_inv in isTy as [fty [s [Hf Hsp]]]; auto. - eapply inversion_Rel in Hf as [decl [wfctx [Hnth cum]]]; auto. - rewrite nth_error_app_ge in Hnth. lia. - split. now rewrite app_context_assoc in wfctx. - replace (#|ind_params mdecl,,, cshape_args y| + (#|ind_bodies mdecl| - S n) - - #|ind_params mdecl,,, cshape_args y|) with (#|ind_bodies mdecl| - S n) in Hnth by lia. - pose proof (nth_error_Some_length hnth). - rewrite nth_error_rev in hnth => //. - eapply nth_error_arities_context in hnth. rewrite Hnth in hnth. - noconf hnth; simpl in *. clear Hnth. - eapply PCUICSpine.typing_spine_strengthen in Hsp; eauto. - clear cum. - destruct heq as [inds eqind]. - move: Hsp. rewrite eqind. - rewrite lift_it_mkProd_or_LetIn /= => Hs. - rewrite closed_ctx_lift in Hs. eapply PCUICClosed.closed_wf_local; eauto. - rewrite app_context_assoc in Hs wfctx. - eapply typing_spine_it_mkProd_or_LetIn_ext_list_inv in Hs; auto. - 2:{ eapply PCUICWeakening.weaken_wf_local; pcuic. - now eapply wf_ind_types_wf_arities. } - 2:{ eapply PCUICClosed.closed_wf_local; eauto. } - eapply typing_spine_it_mkProd_or_LetIn_inv in Hs => //. auto. - eapply weakening_wf_local; eauto. - rewrite -app_context_assoc. - eapply PCUICWeakening.weaken_wf_local; eauto. - now eapply wf_ind_types_wf_arities. - Qed. + (** Moving it causes a universe bug... *) + Section MonadAllAll. + Context {T : Type -> Type} {M : Monad T} {A} {P : A -> Type} {Q : A -> Type} (f : forall x, ∥ Q x ∥ -> T (∥ P x ∥)). + Program Fixpoint monad_All_All l : ∥ All Q l ∥ -> T (∥ All P l ∥) := + match l return ∥ All Q l ∥ -> T (∥ All P l ∥) with + | [] => fun _ => ret (sq All_nil) + | a :: l => fun allq => + X <- f a _ ;; + Y <- monad_All_All l _ ;; + ret _ + end. + Next Obligation. sq. + now depelim allq. + Qed. + Next Obligation. + sq; now depelim allq. + Qed. + Next Obligation. + sq. constructor; assumption. + Defined. + End MonadAllAll. Program Definition check_constructors (Σ0 : wf_env) (Σ : wf_env_ext) (id : kername) (mdecl : mutual_inductive_body) (HΣ : Σ.(wf_env_ext_env) = (Σ0, ind_universes mdecl)) @@ -1738,7 +1770,6 @@ Section CheckEnv. Next Obligation. now sq. Qed. Next Obligation. apply wf_env_ext_wf. Qed. - Next Obligation. epose proof (get_wt_indices wfar wfpars _ _ _ hnth heq Hcs). destruct Σ as [Σ wfΣ G wfG]; simpl in *. clear X. @@ -2118,15 +2149,14 @@ Section CheckEnv. let wfΣ : wf_env_ext := {| wf_env_ext_env := Σ; wf_env_ext_wf := _; wf_env_ext_graph := G; wf_env_ext_graph_wf := HG |} in let id := string_of_kername kn in - X5 <- wrap_error Σ id (check_eq_true (check_variance mdecl.(ind_universes) mdecl.(ind_variance)) (Msg "variance"));; - X2 <- wrap_error Σ id (check_context HΣ HΣ' G HG (ind_params mdecl)) ;; - X3 <- wrap_error Σ id (check_eq_nat (context_assumptions (ind_params mdecl)) + check_var <- wrap_error Σ id (check_eq_true (check_variance mdecl.(ind_universes) mdecl.(ind_variance)) (Msg "variance"));; + check_pars <- wrap_error Σ id (check_context HΣ HΣ' G HG (ind_params mdecl)) ;; + check_npars <- wrap_error Σ id (check_eq_nat (context_assumptions (ind_params mdecl)) (ind_npars mdecl) (Msg "wrong number of parameters")) ;; onarities <- check_ind_types wfΣ mdecl ;; - X1 <- monad_Alli_nth mdecl.(ind_bodies) (fun i oib Hoib => check_one_ind_body Σ0 wfΣ kn mdecl eq X2 onarities X5 i oib Hoib);; - X4 <- wrap_error Σ id (check_eq_true (ind_guard mdecl) (Msg "guard"));; - ret (Build_on_inductive_sq X1 X2 X3 X4 X5) + check_bodies <- monad_Alli_nth mdecl.(ind_bodies) (fun i oib Hoib => check_one_ind_body Σ0 wfΣ kn mdecl eq check_pars onarities check_var i oib Hoib);; + ret (Build_on_inductive_sq check_bodies check_pars check_npars check_var) end. Next Obligation. sq. unfold on_constant_decl; rewrite <- Heq_anonymous; tas. @@ -2232,7 +2262,7 @@ Section CheckEnv. destruct g. destruct c, cst_universes; try discriminate; reflexivity. destruct m, ind_universes; try discriminate; reflexivity. } rewrite eq1; clear eq1. - now rewrite levelset_union_empty constraintset_union_empty. + now rewrite LevelSet_union_empty CS_union_empty. Qed. Obligation Tactic := idtac. diff --git a/safechecker/theories/PCUICSafeRetyping.v b/safechecker/theories/PCUICSafeRetyping.v index 5a32c8965..d7f51457e 100644 --- a/safechecker/theories/PCUICSafeRetyping.v +++ b/safechecker/theories/PCUICSafeRetyping.v @@ -10,7 +10,8 @@ From MetaCoq.PCUIC Require Import PCUICAst PCUICAstUtils PCUICArities PCUICInduc PCUICGeneration PCUICInversion PCUICValidity PCUICInductives PCUICInductiveInversion PCUICSpine PCUICSR PCUICCumulativity PCUICConversion PCUICConfluence PCUICArities PCUICWeakeningEnv PCUICContexts. -From MetaCoq.SafeChecker Require Import PCUICSafeReduce PCUICSafeChecker. +From MetaCoq.SafeChecker Require Import PCUICErrors PCUICSafeReduce PCUICTypeChecker. (* for reduce_to_sort... *) + PCUICSafeChecker. Local Open Scope string_scope. Set Asymmetric Patterns. Import monad_utils.MonadNotation. diff --git a/safechecker/theories/PCUICTypeChecker.v b/safechecker/theories/PCUICTypeChecker.v index 5a92e2a88..d64028dd5 100644 --- a/safechecker/theories/PCUICTypeChecker.v +++ b/safechecker/theories/PCUICTypeChecker.v @@ -6,14 +6,14 @@ From MetaCoq.PCUIC Require Import PCUICAst PCUICAstUtils PCUICWeakening PCUICPosition PCUICCumulativity PCUICSafeLemmata PCUICSN PCUICPretty PCUICArities PCUICConfluence PCUICSize PCUICContextConversion PCUICConversion PCUICWfUniverses - PCUICGlobalEnv + PCUICGlobalEnv (* Used for support lemmas *) PCUICInductives PCUICWfUniverses PCUICContexts PCUICSubstitution PCUICSpine PCUICInductiveInversion PCUICClosed PCUICUnivSubstitution PCUICWeakeningEnv. From MetaCoq.SafeChecker Require Import PCUICSafeReduce PCUICErrors PCUICEqualityDec - PCUICSafeConversion PCUICWfReduction. + PCUICSafeConversion PCUICWfReduction PCUICWfEnv. From Equations Require Import Equations. Require Import ssreflect ssrbool. @@ -332,7 +332,7 @@ Section Typecheck. end. Next Obligation. eapply forallb_All in H. eapply All_forallb'; tea. - clear -cf HG. intros x; simpl. apply is_graph_of_uctx_levels. + clear -cf HG. intros x; simpl. now apply is_graph_of_uctx_levels. Qed. Next Obligation. repeat split. @@ -574,7 +574,7 @@ Section Typecheck. Z <- check_bodies mfix' _ ;; ret (All_cons (conj W1 W2) Z) end) mfix _ ;; - guarded <- check_eq_true (fix_guard mfix) (Msg "Unguarded fixpoint") ;; + guarded <- check_eq_true (fix_guard Σ Γ mfix) (Msg "Unguarded fixpoint") ;; wffix <- check_eq_true (wf_fixpoint Σ.1 mfix) (Msg "Ill-formed fixpoint: not defined on a mutually inductive family") ;; ret (dtype decl; _) end @@ -607,7 +607,7 @@ Section Typecheck. Z <- check_bodies mfix' _ ;; ret (All_cons W1 Z) end) mfix _ ;; - guarded <- check_eq_true (cofix_guard mfix) (Msg "Unguarded cofixpoint") ;; + guarded <- check_eq_true (cofix_guard Σ Γ mfix) (Msg "Unguarded cofixpoint") ;; wfcofix <- check_eq_true (wf_cofixpoint Σ.1 mfix) (Msg "Ill-formed cofixpoint: not producing values in a mutually coinductive family") ;; ret (dtype decl; _) end diff --git a/safechecker/theories/SafeTemplateChecker.v b/safechecker/theories/SafeTemplateChecker.v index e07ebaff0..e0f230ec5 100644 --- a/safechecker/theories/SafeTemplateChecker.v +++ b/safechecker/theories/SafeTemplateChecker.v @@ -4,7 +4,7 @@ From MetaCoq.Template Require Import config utils. From MetaCoq.Template Require AstUtils Typing. From MetaCoq.PCUIC Require Import PCUICAst PCUICAstUtils PCUICTyping TemplateToPCUIC. -From MetaCoq.SafeChecker Require Import PCUICSafeReduce PCUICSafeChecker. +From MetaCoq.SafeChecker Require Import PCUICErrors PCUICSafeChecker. Program Definition infer_template_program {cf : checker_flags} (p : Ast.program) φ Hφ @@ -107,7 +107,7 @@ Program Definition infer_and_print_template_program {cf : checker_flags} (p : As | EnvError Σ (AlreadyDeclared id) => inr ("Already declared: " ^ id) | EnvError Σ (IllFormedDecl id e) => - inr ("Type error: " ^ PCUICSafeChecker.string_of_type_error Σ e ^ ", while checking " ^ id) + inr ("Type error: " ^ string_of_type_error Σ e ^ ", while checking " ^ id) end. (* Program Definition check_template_program {cf : checker_flags} (p : Ast.program) (ty : Ast.term) *) diff --git a/template-coq/theories/EnvironmentTyping.v b/template-coq/theories/EnvironmentTyping.v index 11b631490..f8a8b8d0c 100644 --- a/template-coq/theories/EnvironmentTyping.v +++ b/template-coq/theories/EnvironmentTyping.v @@ -123,7 +123,6 @@ Module EnvTyping (T : Term) (E : EnvironmentSig T). Import T E. Section TypeLocal. - Context (typing : forall (Γ : context), term -> option term -> Type). Inductive All_local_env : context -> Type := @@ -140,7 +139,7 @@ Module EnvTyping (T : Term) (E : EnvironmentSig T). typing Γ t None -> typing Γ b (Some t) -> All_local_env (Γ ,, vdef na b t). - + Derive Signature for All_local_env. End TypeLocal. Arguments localenv_nil {_}. @@ -289,8 +288,6 @@ Module Type Typing (T : Term) (E : EnvironmentSig T) (ET : EnvTypingSig T E). Import T E ET. - Parameter (ind_guard : mutual_inductive_body -> bool). - Parameter (conv : forall `{checker_flags}, global_env_ext -> context -> term -> term -> Type). Parameter (cumul : forall `{checker_flags}, global_env_ext -> context -> term -> term -> Type). @@ -819,7 +816,6 @@ Module DeclarationTyping (T : Term) (E : EnvironmentSig T) onParams : on_context Σ mdecl.(ind_params); onNpars : context_assumptions mdecl.(ind_params) = mdecl.(ind_npars); onVariance : on_variance mdecl.(ind_universes) mdecl.(ind_variance); - onGuard : ind_guard mdecl }. (** *** Typing of constant declarations *) @@ -905,7 +901,6 @@ Module DeclarationTyping (T : Term) (E : EnvironmentSig T) Arguments onParams {_ P Σ mind mdecl}. Arguments onNpars {_ P Σ mind mdecl}. Arguments onVariance {_ P Σ mind mdecl}. - Arguments onGuard {_ P Σ mind mdecl}. Lemma All_local_env_impl (P Q : context -> term -> option term -> Type) l : All_local_env P l -> diff --git a/template-coq/theories/Extraction.v b/template-coq/theories/Extraction.v index c90d653ee..f7a6482e3 100644 --- a/template-coq/theories/Extraction.v +++ b/template-coq/theories/Extraction.v @@ -35,6 +35,7 @@ Recursive Extraction Library Extractable. Extraction Library MCPrelude. Extraction Library MCOption. Extraction Library MCUtils. +Extraction Library MCList. Extraction Library EqDecInstances. Extraction Library Induction. Extraction Library LiftSubst. diff --git a/template-coq/theories/Universes.v b/template-coq/theories/Universes.v index 133812223..6c4bc0004 100644 --- a/template-coq/theories/Universes.v +++ b/template-coq/theories/Universes.v @@ -159,6 +159,7 @@ Module LevelSet := MSetList.MakeWithLeibniz Level. Module LevelSetFact := WFactsOn Level LevelSet. Module LevelSetProp := WPropertiesOn Level LevelSet. Module LevelSetDecide := WDecide (LevelSet). +Module LS := LevelSet. Ltac lsets := LevelSetDecide.fsetdec. Definition LevelSet_pair x y @@ -1196,7 +1197,6 @@ Proof. * apply (H x), CS.add_spec; left => //. * intros y iny. apply (H y), CS.add_spec; right => //. Qed. - Instance CS_For_all_proper P : Morphisms.Proper (CS.Equal ==> iff)%signature (ConstraintSet.For_all P). Proof. intros s s' eqs. From 27922a14d56b62827ebe5d4b97c2df3d1732591a Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Fri, 27 Nov 2020 22:09:19 +0100 Subject: [PATCH 13/70] Try to reduce coupling of files in safechecker and erasure --- .gitignore | 4 + dependency-graph/depgraph-2020-11-27.dot | 346 ++++ dependency-graph/depgraph-2020-11-27.png | Bin 0 -> 1176066 bytes dependency-graph/depgraph-2020-11-27.svg | 2083 +++++++++++++++++++++ erasure/_PluginProject.in | 4 + erasure/src/metacoq_erasure_plugin.mlpack | 2 + erasure/theories/Erasure.v | 4 +- erasure/theories/ErasureCorrectness.v | 14 +- erasure/theories/ErasureFunction.v | 2 +- erasure/theories/Extraction.v | 5 +- erasure/theories/Prelim.v | 2 +- safechecker/theories/PCUICErrors.v | 25 + safechecker/theories/PCUICSafeRetyping.v | 4 +- safechecker/theories/PCUICTypeChecker.v | 24 - 14 files changed, 2478 insertions(+), 41 deletions(-) create mode 100644 dependency-graph/depgraph-2020-11-27.dot create mode 100644 dependency-graph/depgraph-2020-11-27.png create mode 100644 dependency-graph/depgraph-2020-11-27.svg diff --git a/.gitignore b/.gitignore index 08e40751d..7f8e6dcb8 100644 --- a/.gitignore +++ b/.gitignore @@ -412,3 +412,7 @@ erasure/src/signature.ml erasure/src/signature.mli erasure/src/eOptimizePropDiscr.ml erasure/src/eOptimizePropDiscr.mli +erasure/src/pCUICErrors.ml +erasure/src/pCUICErrors.mli +erasure/src/pCUICTypeChecker.ml +erasure/src/pCUICTypeChecker.mli diff --git a/dependency-graph/depgraph-2020-11-27.dot b/dependency-graph/depgraph-2020-11-27.dot new file mode 100644 index 000000000..e3f2dd61c --- /dev/null +++ b/dependency-graph/depgraph-2020-11-27.dot @@ -0,0 +1,346 @@ +digraph dependencies { +node[style=filled] +"safechecker/Extraction"[label="Extraction", color=paleturquoise1] +"safechecker/PCUICSafeRetyping"[label="PCUICSafeRetyping", color=paleturquoise1] +"safechecker/SafeTemplateChecker"[label="SafeTemplateChecker", color=paleturquoise1] +"safechecker/PCUICSafeChecker"[label="PCUICSafeChecker", color=paleturquoise1] +"safechecker/PCUICTypeChecker"[label="PCUICTypeChecker", color=paleturquoise1] +"safechecker/PCUICWfEnv"[label="PCUICWfEnv", color=paleturquoise1] +"safechecker/PCUICWfReduction"[label="PCUICWfReduction", color=paleturquoise1] +"safechecker/PCUICSafeConversion"[label="PCUICSafeConversion", color=paleturquoise1] +"safechecker/PCUICEqualityDec"[label="PCUICEqualityDec", color=paleturquoise1] +"safechecker/PCUICSafeReduce"[label="PCUICSafeReduce", color=paleturquoise1] +"safechecker/PCUICErrors"[label="PCUICErrors", color=paleturquoise1] +"pcuic/PCUICValidity" -> "pcuic/PCUICAlpha" +"pcuic/PCUICWfUniverses" -> "pcuic/PCUICArities" +"template-coq/EnvironmentTyping" -> "pcuic/PCUICAst" +"pcuic/PCUICSize" -> "pcuic/PCUICAstUtils" +"template-coq/Reflect" -> "pcuic/PCUICAstUtils" +"template-coq/common/uGraph" -> "pcuic/PCUICAstUtils" +"pcuic/PCUICClosed" -> "pcuic/PCUICCSubst" +"pcuic/PCUICElimination" -> "pcuic/PCUICCanonicity" +"pcuic/PCUICSN" -> "pcuic/PCUICCanonicity" +"pcuic/PCUICWcbvEval" -> "pcuic/PCUICCanonicity" +"pcuic/PCUICWeakeningEnv" -> "pcuic/PCUICClosed" +"pcuic/PCUICParallelReductionConfluence" -> "pcuic/PCUICConfluence" +"pcuic/PCUICConfluence" -> "pcuic/PCUICContextConversion" +"pcuic/PCUICContextRelation" -> "pcuic/PCUICContextConversion" +"pcuic/PCUICTyping" -> "pcuic/PCUICContextRelation" +"pcuic/PCUICCtxShape" -> "pcuic/PCUICContexts" +"pcuic/PCUICCumulProp" -> "pcuic/PCUICConvCumInversion" +"pcuic/PCUICContextConversion" -> "pcuic/PCUICConversion" +"pcuic/PCUICInversion" -> "pcuic/PCUICCtxShape" +"pcuic/PCUICNameless" -> "pcuic/PCUICCtxShape" +"template-coq/UnivSubst" -> "pcuic/PCUICCtxShape" +"pcuic/PCUICSafeLemmata" -> "pcuic/PCUICCumulProp" +"pcuic/PCUICReduction" -> "pcuic/PCUICCumulativity" +"pcuic/PCUICCumulProp" -> "pcuic/PCUICElimination" +"pcuic/PCUICLiftSubst" -> "pcuic/PCUICEquality" +"pcuic/PCUICReflect" -> "pcuic/PCUICEquality" +"pcuic/PCUICTyping" -> "pcuic/PCUICGeneration" +"pcuic/PCUICTyping" -> "pcuic/PCUICGlobalEnv" +"pcuic/PCUICAstUtils" -> "pcuic/PCUICInduction" +"pcuic/PCUICValidity" -> "pcuic/PCUICInductiveInversion" +"pcuic/PCUICSpine" -> "pcuic/PCUICInductives" +"pcuic/PCUICConversion" -> "pcuic/PCUICInversion" +"pcuic/PCUICInduction" -> "pcuic/PCUICLiftSubst" +"pcuic/PCUICTyping" -> "pcuic/PCUICNameless" +"pcuic/PCUICContextRelation" -> "pcuic/PCUICNormal" +"template-coq/UnivSubst" -> "pcuic/PCUICNormal" +"pcuic/PCUICSubstitution" -> "pcuic/PCUICParallelReduction" +"pcuic/PCUICParallelReduction" -> "pcuic/PCUICParallelReductionConfluence" +"pcuic/PCUICEquality" -> "pcuic/PCUICPosition" +"pcuic/PCUICLiftSubst" -> "pcuic/PCUICPretty" +"pcuic/PCUICCumulProp" -> "pcuic/PCUICPrincipality" +"pcuic/PCUICPosition" -> "pcuic/PCUICReduction" +"pcuic/PCUICRelations" -> "pcuic/PCUICReduction" +"pcuic/PCUICUnivSubst" -> "pcuic/PCUICReduction" +"pcuic/PCUICInduction" -> "pcuic/PCUICReflect" +"pcuic/PCUICSafeLemmata" -> "pcuic/PCUICSN" +"pcuic/PCUICAlpha" -> "pcuic/PCUICSR" +"pcuic/PCUICInductiveInversion" -> "pcuic/PCUICSR" +"pcuic/PCUICNormal" -> "pcuic/PCUICSafeLemmata" +"pcuic/PCUICSR" -> "pcuic/PCUICSafeLemmata" +"pcuic/PCUICWeakening" -> "pcuic/PCUICSigmaCalculus" +"pcuic/PCUICAst" -> "pcuic/PCUICSize" +"pcuic/PCUICArities" -> "pcuic/PCUICSpine" +"pcuic/PCUICSigmaCalculus" -> "pcuic/PCUICSubstitution" +"pcuic/PCUICUnivSubstitution" -> "pcuic/PCUICSubstitution" +"pcuic/PCUICCumulativity" -> "pcuic/PCUICTyping" +"pcuic/PCUICUtils" -> "pcuic/PCUICTyping" +"template-coq/utils/LibHypsNaming" -> "pcuic/PCUICTyping" +"pcuic/PCUICLiftSubst" -> "pcuic/PCUICUnivSubst" +"pcuic/PCUICWeakening" -> "pcuic/PCUICUnivSubstitution" +"pcuic/PCUICAstUtils" -> "pcuic/PCUICUtils" +"pcuic/PCUICInductives" -> "pcuic/PCUICValidity" +"pcuic/PCUICCSubst" -> "pcuic/PCUICWcbvEval" +"pcuic/PCUICSR" -> "pcuic/PCUICWcbvEval" +"pcuic/PCUICClosed" -> "pcuic/PCUICWeakening" +"pcuic/PCUICGeneration" -> "pcuic/PCUICWeakening" +"pcuic/PCUICTyping" -> "pcuic/PCUICWeakeningEnv" +"pcuic/PCUICContexts" -> "pcuic/PCUICWfUniverses" +"pcuic/PCUICAst" -> "pcuic/TemplateToPCUIC" +"template-coq/Environment" -> "template-coq/Ast" +"template-coq/Ast" -> "template-coq/AstUtils" +"template-coq/utils" -> "template-coq/BasicAst" +"template-coq/Universes" -> "template-coq/Environment" +"template-coq/AstUtils" -> "template-coq/EnvironmentTyping" +"template-coq/AstUtils" -> "template-coq/Induction" +"template-coq/Induction" -> "template-coq/LiftSubst" +"template-coq/Induction" -> "template-coq/Reflect" +"template-coq/EnvironmentTyping" -> "template-coq/Typing" +"template-coq/UnivSubst" -> "template-coq/Typing" +"template-coq/LiftSubst" -> "template-coq/UnivSubst" +"template-coq/BasicAst" -> "template-coq/Universes" +"template-coq/config" -> "template-coq/Universes" +"template-coq/Universes" -> "template-coq/common/uGraph" +"template-coq/utils/wGraph" -> "template-coq/common/uGraph" +"template-coq/utils/All_Forall" -> "template-coq/monad_utils" +"template-coq/monad_utils" -> "template-coq/utils" +"template-coq/utils/MCUtils" -> "template-coq/utils" +"template-coq/utils/MCOption" -> "template-coq/utils/All_Forall" +"template-coq/utils/MCSquash" -> "template-coq/utils/All_Forall" +"template-coq/utils/MCPrelude" -> "template-coq/utils/MCList" +"template-coq/utils/MCRelations" -> "template-coq/utils/MCList" +"template-coq/utils/MCList" -> "template-coq/utils/MCOption" +"template-coq/utils/MCProd" -> "template-coq/utils/MCOption" +"template-coq/utils/MCCompare" -> "template-coq/utils/MCString" +"template-coq/utils/All_Forall" -> "template-coq/utils/MCUtils" +"template-coq/utils/MCArith" -> "template-coq/utils/MCUtils" +"template-coq/utils/MCEquality" -> "template-coq/utils/MCUtils" +"template-coq/utils/MCString" -> "template-coq/utils/MCUtils" +"template-coq/utils/MCUtils" -> "template-coq/utils/wGraph" +"safechecker/SafeTemplateChecker" -> "safechecker/Extraction" +"pcuic/PCUICGlobalEnv" -> "safechecker/PCUICEqualityDec" +"pcuic/PCUICPretty" -> "safechecker/PCUICErrors" +"safechecker/PCUICTypeChecker" -> "safechecker/PCUICSafeChecker" +"pcuic/PCUICConvCumInversion" -> "safechecker/PCUICSafeConversion" +"pcuic/PCUICPrincipality" -> "safechecker/PCUICSafeConversion" +"safechecker/PCUICEqualityDec" -> "safechecker/PCUICSafeConversion" +"safechecker/PCUICErrors" -> "safechecker/PCUICSafeConversion" +"safechecker/PCUICSafeReduce" -> "safechecker/PCUICSafeConversion" +"pcuic/PCUICCanonicity" -> "safechecker/PCUICSafeReduce" +"safechecker/PCUICTypeChecker" -> "safechecker/PCUICSafeRetyping" +"safechecker/PCUICWfEnv" -> "safechecker/PCUICTypeChecker" +"safechecker/PCUICWfReduction" -> "safechecker/PCUICTypeChecker" +"pcuic/PCUICGlobalEnv" -> "safechecker/PCUICWfEnv" +"safechecker/PCUICSafeConversion" -> "safechecker/PCUICWfReduction" +"pcuic/TemplateToPCUIC" -> "safechecker/SafeTemplateChecker" +"template-coq/Typing" -> "safechecker/SafeTemplateChecker" +"safechecker/PCUICSafeChecker" -> "safechecker/SafeTemplateChecker" +"template-coq/Extraction"[label="Extraction", color=aquamarine] +"template-coq/Constants"[label="Constants", color=aquamarine] +"template-coq/monad_utils"[label="monad_utils", color=aquamarine] +"template-coq/TemplateMonad/Extractable"[label="Extractable", color=aquamarine] +"template-coq/TemplateMonad/Core"[label="Core", color=aquamarine] +"template-coq/TemplateMonad/Common"[label="Common", color=aquamarine] +"template-coq/TemplateMonad"[label="TemplateMonad", color=aquamarine] +"template-coq/TypingWf"[label="TypingWf", color=aquamarine] +"template-coq/Typing"[label="Typing", color=aquamarine] +"template-coq/WfInv"[label="WfInv", color=aquamarine] +"template-coq/EnvironmentTyping"[label="EnvironmentTyping", color=aquamarine] +"template-coq/Pretty"[label="Pretty", color=aquamarine] +"template-coq/UnivSubst"[label="UnivSubst", color=aquamarine] +"template-coq/LiftSubst"[label="LiftSubst", color=aquamarine] +"template-coq/Induction"[label="Induction", color=aquamarine] +"template-coq/Kernames"[label="Kernames", color=aquamarine] +"template-coq/Reflect"[label="Reflect", color=aquamarine] +"template-coq/AstUtils"[label="AstUtils", color=aquamarine] +"template-coq/Ast"[label="Ast", color=aquamarine] +"template-coq/Environment"[label="Environment", color=aquamarine] +"template-coq/BasicAst"[label="BasicAst", color=aquamarine] +"template-coq/Universes"[label="Universes", color=aquamarine] +"template-coq/config"[label="config", color=aquamarine] +"template-coq/utils"[label="utils", color=aquamarine] +"template-coq/common/uGraph"[label="uGraph", color=aquamarine] +"template-coq/utils/MCUtils"[label="MCUtils", color=aquamarine] +"template-coq/utils/wGraph"[label="wGraph", color=aquamarine] +"template-coq/utils/MCString"[label="MCString", color=aquamarine] +"template-coq/utils/MCSquash"[label="MCSquash", color=aquamarine] +"template-coq/utils/MCRelations"[label="MCRelations", color=aquamarine] +"template-coq/utils/MCProd"[label="MCProd", color=aquamarine] +"template-coq/utils/MCOption"[label="MCOption", color=aquamarine] +"template-coq/utils/MCList"[label="MCList", color=aquamarine] +"template-coq/utils/LibHypsNaming"[label="LibHypsNaming", color=aquamarine] +"template-coq/utils/MCEquality"[label="MCEquality", color=aquamarine] +"template-coq/utils/MCCompare"[label="MCCompare", color=aquamarine] +"template-coq/utils/MCArith"[label="MCArith", color=aquamarine] +"template-coq/utils/All_Forall"[label="All_Forall", color=aquamarine] +"template-coq/utils/MCPrelude"[label="MCPrelude", color=aquamarine] +"template-coq/TemplateMonad" -> "template-coq/Constants" +"template-coq/TemplateMonad/Extractable" -> "template-coq/Constants" +"template-coq/common/uGraph" -> "template-coq/Constants" +"template-coq/Pretty" -> "template-coq/Extraction" +"template-coq/Reflect" -> "template-coq/Extraction" +"template-coq/TemplateMonad/Extractable" -> "template-coq/Extraction" +"template-coq/UnivSubst" -> "template-coq/Extraction" +"template-coq/AstUtils" -> "template-coq/Kernames" +"template-coq/LiftSubst" -> "template-coq/Pretty" +"template-coq/TemplateMonad/Core" -> "template-coq/TemplateMonad" +"template-coq/Ast" -> "template-coq/TemplateMonad/Common" +"template-coq/AstUtils" -> "template-coq/TemplateMonad/Core" +"template-coq/TemplateMonad/Common" -> "template-coq/TemplateMonad/Core" +"template-coq/AstUtils" -> "template-coq/TemplateMonad/Extractable" +"template-coq/TemplateMonad/Common" -> "template-coq/TemplateMonad/Extractable" +"template-coq/Typing" -> "template-coq/TypingWf" +"template-coq/AstUtils" -> "template-coq/WfInv" +"checker/All"[label="All", color=seagreen3] +"checker/Normal"[label="Normal", color=seagreen3] +"checker/Retyping"[label="Retyping", color=seagreen3] +"checker/WcbvEval"[label="WcbvEval", color=seagreen3] +"checker/Checker"[label="Checker", color=seagreen3] +"checker/Substitution"[label="Substitution", color=seagreen3] +"checker/Weakening"[label="Weakening", color=seagreen3] +"checker/Closed"[label="Closed", color=seagreen3] +"checker/WeakeningEnv"[label="WeakeningEnv", color=seagreen3] +"checker/Generation"[label="Generation", color=seagreen3] +"template-coq/Loader" -> "template-coq/All" +"template-coq/Typing" -> "template-coq/All" +"template-coq/Constants" -> "template-coq/Loader" +"template-coq/All" -> "checker/All" +"checker/Retyping" -> "checker/All" +"checker/Substitution" -> "checker/All" +"template-coq/Typing" -> "checker/Checker" +"template-coq/common/uGraph" -> "checker/Checker" +"template-coq/Reflect" -> "checker/Closed" +"template-coq/TypingWf" -> "checker/Closed" +"checker/WeakeningEnv" -> "checker/Closed" +"template-coq/Reflect" -> "checker/Generation" +"template-coq/Typing" -> "checker/Generation" +"template-coq/Typing" -> "checker/Normal" +"checker/Checker" -> "checker/Retyping" +"checker/Generation" -> "checker/Substitution" +"checker/Weakening" -> "checker/Substitution" +"template-coq/Reflect" -> "checker/WcbvEval" +"template-coq/Typing" -> "checker/WcbvEval" +"template-coq/WfInv" -> "checker/WcbvEval" +"checker/Closed" -> "checker/Weakening" +"template-coq/Typing" -> "checker/WeakeningEnv" +"template-coq/utils/LibHypsNaming" -> "checker/WeakeningEnv" +"erasure/Erasure"[label="Erasure", color=tan] +"erasure/EOptimizePropDiscr"[label="EOptimizePropDiscr", color=tan] +"erasure/ErasureFunction"[label="ErasureFunction", color=tan] +"erasure/ErasureCorrectness"[label="ErasureCorrectness", color=tan] +"erasure/EArities"[label="EArities", color=tan] +"erasure/EInversion"[label="EInversion", color=tan] +"erasure/ESubstitution"[label="ESubstitution", color=tan] +"erasure/Prelim"[label="Prelim", color=tan] +"erasure/Extraction"[label="Extraction", color=tan] +"erasure/EAll"[label="EAll", color=tan] +"erasure/EDeps"[label="EDeps", color=tan] +"erasure/Extract"[label="Extract", color=tan] +"erasure/ETyping"[label="ETyping", color=tan] +"erasure/EWndEval"[label="EWndEval", color=tan] +"erasure/EWcbvEval"[label="EWcbvEval", color=tan] +"erasure/ECSubst"[label="ECSubst", color=tan] +"erasure/EPretty"[label="EPretty", color=tan] +"erasure/EReflect"[label="EReflect", color=tan] +"erasure/ELiftSubst"[label="ELiftSubst", color=tan] +"erasure/EInduction"[label="EInduction", color=tan] +"erasure/EAstUtils"[label="EAstUtils", color=tan] +"erasure/EAst"[label="EAst", color=tan] +"erasure/EWcbvEval" -> "erasure/EAll" +"erasure/EWndEval" -> "erasure/EAll" +"erasure/Extract" -> "erasure/EAll" +"pcuic/PCUICCanonicity" -> "erasure/EArities" +"pcuic/PCUICPrincipality" -> "erasure/EArities" +"erasure/Extract" -> "erasure/EArities" +"template-coq/Universes" -> "erasure/EAst" +"template-coq/Kernames" -> "erasure/EAstUtils" +"erasure/EAst" -> "erasure/EAstUtils" +"erasure/ELiftSubst" -> "erasure/ECSubst" +"erasure/ESubstitution" -> "erasure/EDeps" +"erasure/EAst" -> "erasure/EInduction" +"erasure/Prelim" -> "erasure/EInversion" +"erasure/EInduction" -> "erasure/ELiftSubst" +"erasure/ErasureFunction" -> "erasure/EOptimizePropDiscr" +"erasure/ETyping" -> "erasure/EPretty" +"pcuic/PCUICReflect" -> "erasure/EReflect" +"erasure/EInduction" -> "erasure/EReflect" +"erasure/Prelim" -> "erasure/ESubstitution" +"erasure/EAstUtils" -> "erasure/ETyping" +"erasure/ELiftSubst" -> "erasure/ETyping" +"erasure/EReflect" -> "erasure/ETyping" +"pcuic/PCUICWcbvEval" -> "erasure/EWcbvEval" +"erasure/ECSubst" -> "erasure/EWcbvEval" +"erasure/ETyping" -> "erasure/EWcbvEval" +"erasure/ETyping" -> "erasure/EWndEval" +"safechecker/SafeTemplateChecker" -> "erasure/Erasure" +"template-coq/Pretty" -> "erasure/Erasure" +"erasure/EOptimizePropDiscr" -> "erasure/Erasure" +"erasure/EPretty" -> "erasure/Erasure" +"erasure/EDeps" -> "erasure/ErasureCorrectness" +"erasure/EInversion" -> "erasure/ErasureCorrectness" +"safechecker/PCUICSafeRetyping" -> "erasure/ErasureFunction" +"erasure/ErasureCorrectness" -> "erasure/ErasureFunction" +"pcuic/PCUICElimination" -> "erasure/Extract" +"erasure/ETyping" -> "erasure/Extract" +"erasure/Erasure" -> "erasure/Extraction" +"safechecker/PCUICSafeChecker" -> "erasure/Prelim" +"erasure/EArities" -> "erasure/Prelim" +"erasure/EWcbvEval" -> "erasure/Prelim" +"pcuic/PCUICToTemplateCorrectness"[label="PCUICToTemplateCorrectness", color=lemonchiffon1] +"pcuic/PCUICToTemplate"[label="PCUICToTemplate", color=lemonchiffon1] +"pcuic/TemplateToPCUICCorrectness"[label="TemplateToPCUICCorrectness", color=lemonchiffon1] +"pcuic/TemplateToPCUIC"[label="TemplateToPCUIC", color=lemonchiffon1] +"pcuic/PCUICSafeLemmata"[label="PCUICSafeLemmata", color=lemonchiffon1] +"pcuic/PCUICSigmaCalculus"[label="PCUICSigmaCalculus", color=lemonchiffon1] +"pcuic/PCUICPrincipality"[label="PCUICPrincipality", color=lemonchiffon1] +"pcuic/PCUICSN"[label="PCUICSN", color=lemonchiffon1] +"pcuic/PCUICElimination"[label="PCUICElimination", color=lemonchiffon1] +"pcuic/PCUICCumulProp"[label="PCUICCumulProp", color=lemonchiffon1] +"pcuic/PCUICPretty"[label="PCUICPretty", color=lemonchiffon1] +"pcuic/PCUICWcbvEval"[label="PCUICWcbvEval", color=lemonchiffon1] +"pcuic/PCUICCSubst"[label="PCUICCSubst", color=lemonchiffon1] +"pcuic/PCUICCanonicity"[label="PCUICCanonicity", color=lemonchiffon1] +"pcuic/PCUICSR"[label="PCUICSR", color=lemonchiffon1] +"pcuic/PCUICInductiveInversion"[label="PCUICInductiveInversion", color=lemonchiffon1] +"pcuic/PCUICValidity"[label="PCUICValidity", color=lemonchiffon1] +"pcuic/PCUICInductives"[label="PCUICInductives", color=lemonchiffon1] +"pcuic/PCUICSpine"[label="PCUICSpine", color=lemonchiffon1] +"pcuic/PCUICWfUniverses"[label="PCUICWfUniverses", color=lemonchiffon1] +"pcuic/PCUICArities"[label="PCUICArities", color=lemonchiffon1] +"pcuic/PCUICContexts"[label="PCUICContexts", color=lemonchiffon1] +"pcuic/PCUICCtxShape"[label="PCUICCtxShape", color=lemonchiffon1] +"pcuic/PCUICAlpha"[label="PCUICAlpha", color=lemonchiffon1] +"pcuic/PCUICGeneration"[label="PCUICGeneration", color=lemonchiffon1] +"pcuic/PCUICConvCumInversion"[label="PCUICConvCumInversion", color=lemonchiffon1] +"pcuic/PCUICConversion"[label="PCUICConversion", color=lemonchiffon1] +"pcuic/PCUICContextConversion"[label="PCUICContextConversion", color=lemonchiffon1] +"pcuic/PCUICContextRelation"[label="PCUICContextRelation", color=lemonchiffon1] +"pcuic/PCUICConfluence"[label="PCUICConfluence", color=lemonchiffon1] +"pcuic/PCUICParallelReductionConfluence"[label="PCUICParallelReductionConfluence", color=lemonchiffon1] +"pcuic/PCUICParallelReduction"[label="PCUICParallelReduction", color=lemonchiffon1] +"pcuic/PCUICReduction"[label="PCUICReduction", color=lemonchiffon1] +"pcuic/PCUICCumulativity"[label="PCUICCumulativity", color=lemonchiffon1] +"pcuic/PCUICSubstitution"[label="PCUICSubstitution", color=lemonchiffon1] +"pcuic/PCUICUnivSubstitution"[label="PCUICUnivSubstitution", color=lemonchiffon1] +"pcuic/PCUICWeakening"[label="PCUICWeakening", color=lemonchiffon1] +"pcuic/PCUICClosed"[label="PCUICClosed", color=lemonchiffon1] +"pcuic/PCUICWeakeningEnv"[label="PCUICWeakeningEnv", color=lemonchiffon1] +"pcuic/PCUICEquality"[label="PCUICEquality", color=lemonchiffon1] +"pcuic/PCUICNameless"[label="PCUICNameless", color=lemonchiffon1] +"pcuic/PCUICNormal"[label="PCUICNormal", color=lemonchiffon1] +"pcuic/PCUICPosition"[label="PCUICPosition", color=lemonchiffon1] +"pcuic/PCUICInversion"[label="PCUICInversion", color=lemonchiffon1] +"pcuic/PCUICGlobalEnv"[label="PCUICGlobalEnv", color=lemonchiffon1] +"pcuic/PCUICTyping"[label="PCUICTyping", color=lemonchiffon1] +"pcuic/PCUICUnivSubst"[label="PCUICUnivSubst", color=lemonchiffon1] +"pcuic/PCUICLiftSubst"[label="PCUICLiftSubst", color=lemonchiffon1] +"pcuic/PCUICReflect"[label="PCUICReflect", color=lemonchiffon1] +"pcuic/PCUICInduction"[label="PCUICInduction", color=lemonchiffon1] +"pcuic/PCUICAstUtils"[label="PCUICAstUtils", color=lemonchiffon1] +"pcuic/PCUICSize"[label="PCUICSize", color=lemonchiffon1] +"pcuic/PCUICAst"[label="PCUICAst", color=lemonchiffon1] +"pcuic/PCUICRelations"[label="PCUICRelations", color=lemonchiffon1] +"pcuic/PCUICUtils"[label="PCUICUtils", color=lemonchiffon1] +"pcuic/PCUICAstUtils" -> "pcuic/PCUICToTemplate" +"template-coq/TypingWf" -> "pcuic/PCUICToTemplateCorrectness" +"template-coq/WfInv" -> "pcuic/PCUICToTemplateCorrectness" +"pcuic/PCUICGeneration" -> "pcuic/PCUICToTemplateCorrectness" +"pcuic/PCUICToTemplate" -> "pcuic/PCUICToTemplateCorrectness" +"template-coq/TypingWf" -> "pcuic/TemplateToPCUICCorrectness" +"template-coq/WfInv" -> "pcuic/TemplateToPCUICCorrectness" +"pcuic/PCUICSubstitution" -> "pcuic/TemplateToPCUICCorrectness" +"pcuic/TemplateToPCUIC" -> "pcuic/TemplateToPCUICCorrectness" +} diff --git a/dependency-graph/depgraph-2020-11-27.png b/dependency-graph/depgraph-2020-11-27.png new file mode 100644 index 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+erasure/EPretty + +EPretty + + + +erasure/ETyping->erasure/EPretty + + + + + +erasure/EWndEval->erasure/EAll + + + + + +erasure/EWcbvEval->erasure/Prelim + + + + + +erasure/EWcbvEval->erasure/EAll + + + + + +erasure/ECSubst + +ECSubst + + + +erasure/ECSubst->erasure/EWcbvEval + + + + + +erasure/EPretty->erasure/Erasure + + + + + +erasure/EReflect->erasure/ETyping + + + + + +erasure/ELiftSubst + +ELiftSubst + + + +erasure/ELiftSubst->erasure/ETyping + + + + + +erasure/ELiftSubst->erasure/ECSubst + + + + + +erasure/EInduction + +EInduction + + + +erasure/EInduction->erasure/EReflect + + + + + +erasure/EInduction->erasure/ELiftSubst + + + + + +erasure/EAstUtils->erasure/ETyping + + + + + +erasure/EAst->erasure/EInduction + + + + + +erasure/EAst->erasure/EAstUtils + + + + + +pcuic/PCUICToTemplate->pcuic/PCUICToTemplateCorrectness + + + + + diff --git a/erasure/_PluginProject.in b/erasure/_PluginProject.in index 6eeb7a21b..175a348f1 100644 --- a/erasure/_PluginProject.in +++ b/erasure/_PluginProject.in @@ -77,10 +77,14 @@ src/templateToPCUIC.mli src/templateToPCUIC.ml # From SafeChecker +src/pCUICErrors.mli +src/pCUICErrors.ml src/pCUICSafeReduce.mli src/pCUICSafeReduce.ml src/pCUICSafeConversion.mli src/pCUICSafeConversion.ml +src/pCUICTypeChecker.mli +src/pCUICTypeChecker.ml src/pCUICSafeChecker.mli src/pCUICSafeChecker.ml src/pCUICSafeRetyping.ml diff --git a/erasure/src/metacoq_erasure_plugin.mlpack b/erasure/src/metacoq_erasure_plugin.mlpack index e6a151957..3f1b5fbfa 100644 --- a/erasure/src/metacoq_erasure_plugin.mlpack +++ b/erasure/src/metacoq_erasure_plugin.mlpack @@ -31,9 +31,11 @@ PCUICPosition PCUICPretty TemplateToPCUIC +PCUICErrors PCUICUnivSubst PCUICSafeReduce PCUICSafeConversion +PCUICTypeChecker PCUICSafeChecker PCUICSafeRetyping SafeTemplateChecker diff --git a/erasure/theories/Erasure.v b/erasure/theories/Erasure.v index 04df96f6a..0a0fe60ff 100644 --- a/erasure/theories/Erasure.v +++ b/erasure/theories/Erasure.v @@ -3,7 +3,7 @@ From Coq Require Import Program. From MetaCoq.Template Require Import config utils uGraph Pretty. From MetaCoq.PCUIC Require Import PCUICAst PCUICAstUtils PCUICTyping TemplateToPCUIC. -From MetaCoq.SafeChecker Require Import PCUICSafeReduce PCUICSafeChecker +From MetaCoq.SafeChecker Require Import PCUICErrors PCUICSafeReduce PCUICSafeChecker SafeTemplateChecker. From MetaCoq.Erasure Require Import EAstUtils ErasureFunction EPretty. From MetaCoq.Erasure Require ErasureFunction EOptimizePropDiscr. @@ -127,7 +127,7 @@ Program Fixpoint check_wf_env_only_univs (Σ : global_env) destruct g. destruct c, cst_universes; try discriminate; reflexivity. destruct m, ind_universes; try discriminate; reflexivity. } rewrite eq1; clear eq1. - now rewrite levelset_union_empty, constraintset_union_empty. + now rewrite LevelSet_union_empty, CS_union_empty. Qed. (* This is the total erasure function + the optimization that removes all diff --git a/erasure/theories/ErasureCorrectness.v b/erasure/theories/ErasureCorrectness.v index e490a3f9a..c207da5b2 100644 --- a/erasure/theories/ErasureCorrectness.v +++ b/erasure/theories/ErasureCorrectness.v @@ -86,17 +86,17 @@ Proof. - econstructor. - econstructor; eauto. cbn in *. destruct t0. exists x. eapply PCUICContextConversion.context_conversion with (Γ ,,, Γ0); eauto. - * eapply PCUICSafeChecker.wf_local_app_inv; eauto. + * eapply wf_local_app; eauto. * eapply conv_context_app; eauto. eapply typing_wf_local; eauto. - econstructor; eauto. + cbn in *. destruct t0. exists x. eapply PCUICContextConversion.context_conversion with (Γ ,,, Γ0); eauto. - * eapply PCUICSafeChecker.wf_local_app_inv; eauto. + * eapply wf_local_app; eauto. * eapply conv_context_app; eauto. eapply typing_wf_local; eauto. + cbn in *. eapply PCUICContextConversion.context_conversion with (Γ ,,, Γ0); eauto. - * eapply PCUICSafeChecker.wf_local_app_inv; eauto. + * eapply wf_local_app; eauto. * eapply conv_context_app; eauto. eapply typing_wf_local; eauto. Qed. @@ -152,7 +152,7 @@ Proof. eapply PCUICContextConversion.context_conversion with (Γ ,,, Γ0); eauto. 2:{ eapply conv_context_app; auto. eapply typing_wf_local; eauto. } eapply typing_wf_local in X3. - eapply PCUICSafeChecker.wf_local_app_inv. + eapply wf_local_app. eauto. eapply wf_local_rel_local in X3. eapply wf_local_rel_app_inv in X3 as []. rewrite app_context_nil_l in w0. eapply wf_local_rel_conv; eauto. @@ -161,7 +161,7 @@ Proof. 2:{ eapply conv_context_app; auto. eapply typing_wf_local; eauto. } eapply typing_wf_local in t0. - eapply PCUICSafeChecker.wf_local_app_inv. + eapply wf_local_app. eauto. eapply wf_local_rel_local in t0. eapply wf_local_rel_app_inv in t0 as []. rewrite app_context_nil_l in w0. eapply wf_local_rel_conv; eauto. @@ -185,7 +185,7 @@ Proof. eapply PCUICContextConversion.context_conversion with (Γ ,,, Γ0); eauto. 2:{ eapply conv_context_app; auto. eapply typing_wf_local; eauto. } eapply typing_wf_local in X3. - eapply PCUICSafeChecker.wf_local_app_inv. + eapply wf_local_app. eauto. eapply wf_local_rel_local in X3. eapply wf_local_rel_app_inv in X3 as []. rewrite app_context_nil_l in w0. @@ -196,7 +196,7 @@ Proof. 2:{ eapply conv_context_app; auto. eapply typing_wf_local; eauto. } eapply typing_wf_local in t0. - eapply PCUICSafeChecker.wf_local_app_inv. + eapply wf_local_app. eauto. eapply wf_local_rel_local in t0. eapply wf_local_rel_app_inv in t0 as []. rewrite app_context_nil_l in w0. eapply wf_local_rel_conv; eauto. diff --git a/erasure/theories/ErasureFunction.v b/erasure/theories/ErasureFunction.v index 035b9fa4f..d3993f5f4 100644 --- a/erasure/theories/ErasureFunction.v +++ b/erasure/theories/ErasureFunction.v @@ -8,7 +8,7 @@ From MetaCoq.PCUIC Require Import PCUICAst PCUICAstUtils PCUICCumulativity PCUICSR PCUICSafeLemmata PCUICValidity PCUICPrincipality PCUICElimination PCUICSN. -From MetaCoq.SafeChecker Require Import PCUICSafeReduce PCUICSafeChecker PCUICSafeRetyping. +From MetaCoq.SafeChecker Require Import PCUICErrors PCUICSafeReduce PCUICTypeChecker PCUICSafeRetyping. From MetaCoq.Erasure Require Import EAstUtils EArities Extract Prelim ErasureCorrectness EDeps. Local Open Scope string_scope. diff --git a/erasure/theories/Extraction.v b/erasure/theories/Extraction.v index 63a8da240..57b9bfd0a 100644 --- a/erasure/theories/Extraction.v +++ b/erasure/theories/Extraction.v @@ -36,10 +36,7 @@ Extract Constant Equations.Init.pr1 => "fst". Extract Constant Equations.Init.pr2 => "snd". Extraction Inline Equations.Init.pr1 Equations.Init.pr2. -Extract Constant PCUICTyping.fix_guard => "(fun x -> true)". -Extract Constant PCUICTyping.cofix_guard => "(fun x -> true)". -Extract Constant PCUICTyping.ind_guard => "(fun x -> true)". -(* Extract Constant erase_mfix_obligation_1 => "(fun _ _ _ _ => ret typing_monad __)". *) +Extract Constant PCUICTyping.guard_checking => "{ fix_guard = (fun _ _ _ -> true); cofix_guard = (fun _ _ _ -> true) }". Cd "src". diff --git a/erasure/theories/Prelim.v b/erasure/theories/Prelim.v index f8fa1ba89..3746e7034 100644 --- a/erasure/theories/Prelim.v +++ b/erasure/theories/Prelim.v @@ -5,7 +5,7 @@ From MetaCoq.PCUIC Require Import PCUICTyping PCUICAst PCUICAstUtils PCUICSubstitution PCUICLiftSubst PCUICClosed PCUICWcbvEval PCUICSR PCUICInversion PCUICGeneration PCUICContextConversion PCUICCanonicity. -From MetaCoq.SafeChecker Require Import PCUICSafeReduce PCUICSafeChecker. +From MetaCoq.SafeChecker Require Import PCUICErrors. From Coq Require Import Program ssreflect. diff --git a/safechecker/theories/PCUICErrors.v b/safechecker/theories/PCUICErrors.v index e34b1e5cf..516a360e2 100644 --- a/safechecker/theories/PCUICErrors.v +++ b/safechecker/theories/PCUICErrors.v @@ -112,6 +112,7 @@ Inductive type_error := | IllFormedFix (m : mfixpoint term) (i : nat) | UnsatisfiedConstraints (c : ConstraintSet.t) | Msg (s : string). +Derive NoConfusion for type_error. Definition print_level := string_of_level. @@ -267,3 +268,27 @@ Definition string_of_type_error Σ (e : type_error) : string := | UnsatisfiedConstraints c => "Unsatisfied constraints" | Msg s => "Msg: " ^ s end. + +Inductive typing_result (A : Type) := +| Checked (a : A) +| TypeError (t : type_error). +Global Arguments Checked {A} a. +Global Arguments TypeError {A} t. + +Instance typing_monad : Monad typing_result := + {| ret A a := Checked a ; + bind A B m f := + match m with + | Checked a => f a + | TypeError t => TypeError t + end + |}. + +Instance monad_exc : MonadExc type_error typing_result := + { raise A e := TypeError e; + catch A m f := + match m with + | Checked a => m + | TypeError t => f t + end + }. \ No newline at end of file diff --git a/safechecker/theories/PCUICSafeRetyping.v b/safechecker/theories/PCUICSafeRetyping.v index d7f51457e..107719083 100644 --- a/safechecker/theories/PCUICSafeRetyping.v +++ b/safechecker/theories/PCUICSafeRetyping.v @@ -10,8 +10,8 @@ From MetaCoq.PCUIC Require Import PCUICAst PCUICAstUtils PCUICArities PCUICInduc PCUICGeneration PCUICInversion PCUICValidity PCUICInductives PCUICInductiveInversion PCUICSpine PCUICSR PCUICCumulativity PCUICConversion PCUICConfluence PCUICArities PCUICWeakeningEnv PCUICContexts. -From MetaCoq.SafeChecker Require Import PCUICErrors PCUICSafeReduce PCUICTypeChecker. (* for reduce_to_sort... *) - PCUICSafeChecker. +From MetaCoq.SafeChecker Require Import PCUICErrors PCUICSafeReduce + (* For reduce function TODO: move *) PCUICTypeChecker PCUICSafeChecker. Local Open Scope string_scope. Set Asymmetric Patterns. Import monad_utils.MonadNotation. diff --git a/safechecker/theories/PCUICTypeChecker.v b/safechecker/theories/PCUICTypeChecker.v index d64028dd5..2852ccd0b 100644 --- a/safechecker/theories/PCUICTypeChecker.v +++ b/safechecker/theories/PCUICTypeChecker.v @@ -30,30 +30,6 @@ Ltac Coq.Program.Tactics.program_solve_wf ::= end end. -Inductive typing_result (A : Type) := -| Checked (a : A) -| TypeError (t : type_error). -Global Arguments Checked {A} a. -Global Arguments TypeError {A} t. - -Instance typing_monad : Monad typing_result := - {| ret A a := Checked a ; - bind A B m f := - match m with - | Checked a => f a - | TypeError t => TypeError t - end - |}. - -Instance monad_exc : MonadExc type_error typing_result := - { raise A e := TypeError e; - catch A m f := - match m with - | Checked a => m - | TypeError t => f t - end - }. - Section Typecheck. Context {cf : checker_flags} {Σ : global_env_ext} (HΣ : ∥ wf Σ ∥) (Hφ : ∥ on_udecl Σ.1 Σ.2 ∥) From 70c97ddc46109ba07bd6d7eea9f8f84d8d4b2d0c Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Fri, 27 Nov 2020 22:30:21 +0100 Subject: [PATCH 14/70] typing_correctness broken for now --- examples/typing_correctness.v | 11 +++++++---- 1 file changed, 7 insertions(+), 4 deletions(-) diff --git a/examples/typing_correctness.v b/examples/typing_correctness.v index 3d7eb9a77..171955738 100644 --- a/examples/typing_correctness.v +++ b/examples/typing_correctness.v @@ -1,7 +1,7 @@ (* Distributed under the terms of the MIT license. *) From MetaCoq.Template Require Import config Universes All. From MetaCoq.PCUIC Require Import PCUICAst PCUICAstUtils PCUICTyping PCUICLiftSubst. -From MetaCoq.SafeChecker Require Import PCUICSafeChecker. +From MetaCoq.SafeChecker Require Import PCUICErrors PCUICTypeChecker PCUICSafeChecker. From Equations Require Import Equations. Existing Instance default_checker_flags. @@ -51,9 +51,11 @@ Proof. end. Defined. + + (** There is always a proof of `forall x : Sort s, x -> x` *) -Definition inh {cf:checker_flags} (Σ : wf_env_ext) Γ T := ∑ t, ∥ Σ ;;; Γ |- t : T ∥. +Definition inh {cf:checker_flags} (Σ : wf_env_ext) Γ T := ∑ t, ∥ typing Σ Γ t T ∥. Definition check_inh {cf:checker_flags} (Σ : wf_env_ext) Γ (wfΓ : ∥ wf_local Σ Γ ∥) t {T} : typing_result (inh Σ Γ T) := prf <- check_type_wf_env_fast Σ Γ wfΓ t (T := T) ;; @@ -78,8 +80,9 @@ Lemma identity_typing (u := Universe.make univ): inh gctx_wf_env [] (tProd (bNam Proof. set (impl := tLambda (bNamed "s") (tSort u) (tLambda bAnon (tRel 0) (tRel 0))). assert (wfΓ : ∥ wf_local gctx_wf_env [] ∥) by do 2 constructor. - (** All immediate now *) +Admitted. +(* (** All immediate now *) Time fill_inh impl. Time Qed. - +*) Print identity_typing. From 3c6db117cdcfa2993ebe5786feebb94b45f58cc7 Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Fri, 27 Nov 2020 23:00:41 +0100 Subject: [PATCH 15/70] Disable erasure_live_test for now --- test-suite/_CoqProject | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/test-suite/_CoqProject b/test-suite/_CoqProject index 86f9eaa69..990a5214f 100644 --- a/test-suite/_CoqProject +++ b/test-suite/_CoqProject @@ -22,7 +22,7 @@ case.v castprop.v # CheckerTest.v disabled cofix.v -erasure_live_test.v +# erasure_live_test.v erasure_test.v evars.v extractable.v From a54f1b59831704e29a5d531d0547cee536abb30d Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Fri, 27 Nov 2020 23:44:20 +0100 Subject: [PATCH 16/70] SafeConversion no longer needed --- erasure/_PluginProject.in | 4 ++-- erasure/src/metacoq_erasure_plugin.mlpack | 1 - 2 files changed, 2 insertions(+), 3 deletions(-) diff --git a/erasure/_PluginProject.in b/erasure/_PluginProject.in index 175a348f1..51a2114a4 100644 --- a/erasure/_PluginProject.in +++ b/erasure/_PluginProject.in @@ -81,8 +81,8 @@ src/pCUICErrors.mli src/pCUICErrors.ml src/pCUICSafeReduce.mli src/pCUICSafeReduce.ml -src/pCUICSafeConversion.mli -src/pCUICSafeConversion.ml +# src/pCUICSafeConversion.mli +# src/pCUICSafeConversion.ml src/pCUICTypeChecker.mli src/pCUICTypeChecker.ml src/pCUICSafeChecker.mli diff --git a/erasure/src/metacoq_erasure_plugin.mlpack b/erasure/src/metacoq_erasure_plugin.mlpack index 3f1b5fbfa..bb3b67945 100644 --- a/erasure/src/metacoq_erasure_plugin.mlpack +++ b/erasure/src/metacoq_erasure_plugin.mlpack @@ -34,7 +34,6 @@ TemplateToPCUIC PCUICErrors PCUICUnivSubst PCUICSafeReduce -PCUICSafeConversion PCUICTypeChecker PCUICSafeChecker PCUICSafeRetyping From c27c0bb4243065b9b2dca0ca3cee4eed6a33b9a6 Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Fri, 27 Nov 2020 23:46:21 +0100 Subject: [PATCH 17/70] Remove unnecessary depgraphs --- dependency-graph/depgraph-2020-11-26.dot | 339 ---- dependency-graph/depgraph-2020-11-26.png | Bin 1158736 -> 0 bytes dependency-graph/depgraph-2020-11-26.svg | 2041 --------------------- dependency-graph/depgraph-2020-11-27.dot | 346 ---- dependency-graph/depgraph-2020-11-27.png | Bin 1176066 -> 0 bytes dependency-graph/depgraph-2020-11-27.svg | 2083 ---------------------- 6 files changed, 4809 deletions(-) delete mode 100644 dependency-graph/depgraph-2020-11-26.dot delete mode 100644 dependency-graph/depgraph-2020-11-26.png delete mode 100644 dependency-graph/depgraph-2020-11-26.svg delete mode 100644 dependency-graph/depgraph-2020-11-27.dot delete mode 100644 dependency-graph/depgraph-2020-11-27.png delete mode 100644 dependency-graph/depgraph-2020-11-27.svg diff --git a/dependency-graph/depgraph-2020-11-26.dot b/dependency-graph/depgraph-2020-11-26.dot deleted file mode 100644 index 4a2d876ba..000000000 --- a/dependency-graph/depgraph-2020-11-26.dot +++ /dev/null @@ -1,339 +0,0 @@ -digraph dependencies { -node[style=filled] -"safechecker/Extraction"[label="Extraction", color=paleturquoise1] -"safechecker/PCUICSafeRetyping"[label="PCUICSafeRetyping", color=paleturquoise1] -"safechecker/SafeTemplateChecker"[label="SafeTemplateChecker", color=paleturquoise1] -"safechecker/PCUICSafeChecker"[label="PCUICSafeChecker", color=paleturquoise1] -"safechecker/PCUICWfReduction"[label="PCUICWfReduction", color=paleturquoise1] -"safechecker/PCUICSafeConversion"[label="PCUICSafeConversion", color=paleturquoise1] -"safechecker/PCUICEqualityDec"[label="PCUICEqualityDec", color=paleturquoise1] -"safechecker/PCUICSafeReduce"[label="PCUICSafeReduce", color=paleturquoise1] -"pcuic/PCUICValidity" -> "pcuic/PCUICAlpha" -"pcuic/PCUICWfUniverses" -> "pcuic/PCUICArities" -"template-coq/EnvironmentTyping" -> "pcuic/PCUICAst" -"pcuic/PCUICSize" -> "pcuic/PCUICAstUtils" -"template-coq/Reflect" -> "pcuic/PCUICAstUtils" -"template-coq/common/uGraph" -> "pcuic/PCUICAstUtils" -"pcuic/PCUICClosed" -> "pcuic/PCUICCSubst" -"pcuic/PCUICElimination" -> "pcuic/PCUICCanonicity" -"pcuic/PCUICSN" -> "pcuic/PCUICCanonicity" -"pcuic/PCUICWcbvEval" -> "pcuic/PCUICCanonicity" -"pcuic/PCUICWeakeningEnv" -> "pcuic/PCUICClosed" -"pcuic/PCUICParallelReductionConfluence" -> "pcuic/PCUICConfluence" -"pcuic/PCUICConfluence" -> "pcuic/PCUICContextConversion" -"pcuic/PCUICContextRelation" -> "pcuic/PCUICContextConversion" -"pcuic/PCUICTyping" -> "pcuic/PCUICContextRelation" -"pcuic/PCUICCtxShape" -> "pcuic/PCUICContexts" -"pcuic/PCUICCumulProp" -> "pcuic/PCUICConvCumInversion" -"pcuic/PCUICContextConversion" -> "pcuic/PCUICConversion" -"pcuic/PCUICInversion" -> "pcuic/PCUICCtxShape" -"pcuic/PCUICNameless" -> "pcuic/PCUICCtxShape" -"template-coq/UnivSubst" -> "pcuic/PCUICCtxShape" -"pcuic/PCUICSafeLemmata" -> "pcuic/PCUICCumulProp" -"pcuic/PCUICReduction" -> "pcuic/PCUICCumulativity" -"pcuic/PCUICCumulProp" -> "pcuic/PCUICElimination" -"pcuic/PCUICLiftSubst" -> "pcuic/PCUICEquality" -"pcuic/PCUICReflect" -> "pcuic/PCUICEquality" -"pcuic/PCUICTyping" -> "pcuic/PCUICGeneration" -"pcuic/PCUICTyping" -> "pcuic/PCUICGlobalEnv" -"pcuic/PCUICAstUtils" -> "pcuic/PCUICInduction" -"pcuic/PCUICValidity" -> "pcuic/PCUICInductiveInversion" -"pcuic/PCUICSpine" -> "pcuic/PCUICInductives" -"pcuic/PCUICConversion" -> "pcuic/PCUICInversion" -"pcuic/PCUICInduction" -> "pcuic/PCUICLiftSubst" -"pcuic/PCUICTyping" -> "pcuic/PCUICNameless" -"pcuic/PCUICContextRelation" -> "pcuic/PCUICNormal" -"template-coq/UnivSubst" -> "pcuic/PCUICNormal" -"pcuic/PCUICSubstitution" -> "pcuic/PCUICParallelReduction" -"pcuic/PCUICParallelReduction" -> "pcuic/PCUICParallelReductionConfluence" -"pcuic/PCUICEquality" -> "pcuic/PCUICPosition" -"pcuic/PCUICLiftSubst" -> "pcuic/PCUICPretty" -"pcuic/PCUICCumulProp" -> "pcuic/PCUICPrincipality" -"pcuic/PCUICPosition" -> "pcuic/PCUICReduction" -"pcuic/PCUICRelations" -> "pcuic/PCUICReduction" -"pcuic/PCUICUnivSubst" -> "pcuic/PCUICReduction" -"pcuic/PCUICInduction" -> "pcuic/PCUICReflect" -"pcuic/PCUICSafeLemmata" -> "pcuic/PCUICSN" -"pcuic/PCUICAlpha" -> "pcuic/PCUICSR" -"pcuic/PCUICInductiveInversion" -> "pcuic/PCUICSR" -"pcuic/PCUICNormal" -> "pcuic/PCUICSafeLemmata" -"pcuic/PCUICSR" -> "pcuic/PCUICSafeLemmata" -"pcuic/PCUICWeakening" -> "pcuic/PCUICSigmaCalculus" -"pcuic/PCUICAst" -> "pcuic/PCUICSize" -"pcuic/PCUICArities" -> "pcuic/PCUICSpine" -"pcuic/PCUICSigmaCalculus" -> "pcuic/PCUICSubstitution" -"pcuic/PCUICUnivSubstitution" -> "pcuic/PCUICSubstitution" -"pcuic/PCUICCumulativity" -> "pcuic/PCUICTyping" -"pcuic/PCUICUtils" -> "pcuic/PCUICTyping" -"template-coq/utils/LibHypsNaming" -> "pcuic/PCUICTyping" -"pcuic/PCUICLiftSubst" -> "pcuic/PCUICUnivSubst" -"pcuic/PCUICWeakening" -> "pcuic/PCUICUnivSubstitution" -"pcuic/PCUICAstUtils" -> "pcuic/PCUICUtils" -"pcuic/PCUICInductives" -> "pcuic/PCUICValidity" -"pcuic/PCUICCSubst" -> "pcuic/PCUICWcbvEval" -"pcuic/PCUICSR" -> "pcuic/PCUICWcbvEval" -"pcuic/PCUICClosed" -> "pcuic/PCUICWeakening" -"pcuic/PCUICGeneration" -> "pcuic/PCUICWeakening" -"pcuic/PCUICTyping" -> "pcuic/PCUICWeakeningEnv" -"pcuic/PCUICContexts" -> "pcuic/PCUICWfUniverses" -"pcuic/PCUICAst" -> "pcuic/TemplateToPCUIC" -"template-coq/Environment" -> "template-coq/Ast" -"template-coq/Ast" -> "template-coq/AstUtils" -"template-coq/utils" -> "template-coq/BasicAst" -"template-coq/Universes" -> "template-coq/Environment" -"template-coq/AstUtils" -> "template-coq/EnvironmentTyping" -"template-coq/AstUtils" -> "template-coq/Induction" -"template-coq/Induction" -> "template-coq/LiftSubst" -"template-coq/Induction" -> "template-coq/Reflect" -"template-coq/EnvironmentTyping" -> "template-coq/Typing" -"template-coq/UnivSubst" -> "template-coq/Typing" -"template-coq/LiftSubst" -> "template-coq/UnivSubst" -"template-coq/BasicAst" -> "template-coq/Universes" -"template-coq/config" -> "template-coq/Universes" -"template-coq/Universes" -> "template-coq/common/uGraph" -"template-coq/utils/wGraph" -> 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-"template-coq/AstUtils"[label="AstUtils", color=aquamarine] -"template-coq/Ast"[label="Ast", color=aquamarine] -"template-coq/Environment"[label="Environment", color=aquamarine] -"template-coq/BasicAst"[label="BasicAst", color=aquamarine] -"template-coq/Universes"[label="Universes", color=aquamarine] -"template-coq/config"[label="config", color=aquamarine] -"template-coq/utils"[label="utils", color=aquamarine] -"template-coq/common/uGraph"[label="uGraph", color=aquamarine] -"template-coq/utils/MCUtils"[label="MCUtils", color=aquamarine] -"template-coq/utils/wGraph"[label="wGraph", color=aquamarine] -"template-coq/utils/MCString"[label="MCString", color=aquamarine] -"template-coq/utils/MCSquash"[label="MCSquash", color=aquamarine] -"template-coq/utils/MCRelations"[label="MCRelations", color=aquamarine] -"template-coq/utils/MCProd"[label="MCProd", color=aquamarine] -"template-coq/utils/MCOption"[label="MCOption", color=aquamarine] -"template-coq/utils/MCList"[label="MCList", color=aquamarine] -"template-coq/utils/LibHypsNaming"[label="LibHypsNaming", color=aquamarine] -"template-coq/utils/MCEquality"[label="MCEquality", color=aquamarine] -"template-coq/utils/MCCompare"[label="MCCompare", color=aquamarine] -"template-coq/utils/MCArith"[label="MCArith", color=aquamarine] -"template-coq/utils/All_Forall"[label="All_Forall", color=aquamarine] -"template-coq/utils/MCPrelude"[label="MCPrelude", color=aquamarine] -"template-coq/TemplateMonad" -> "template-coq/Constants" -"template-coq/TemplateMonad/Extractable" -> "template-coq/Constants" -"template-coq/common/uGraph" -> "template-coq/Constants" -"template-coq/Pretty" -> "template-coq/Extraction" -"template-coq/Reflect" -> "template-coq/Extraction" -"template-coq/TemplateMonad/Extractable" -> "template-coq/Extraction" -"template-coq/UnivSubst" -> "template-coq/Extraction" -"template-coq/AstUtils" -> "template-coq/Kernames" -"template-coq/LiftSubst" -> "template-coq/Pretty" -"template-coq/TemplateMonad/Core" -> "template-coq/TemplateMonad" -"template-coq/Ast" -> "template-coq/TemplateMonad/Common" -"template-coq/AstUtils" -> "template-coq/TemplateMonad/Core" -"template-coq/TemplateMonad/Common" -> "template-coq/TemplateMonad/Core" -"template-coq/AstUtils" -> "template-coq/TemplateMonad/Extractable" -"template-coq/TemplateMonad/Common" -> "template-coq/TemplateMonad/Extractable" -"template-coq/Typing" -> "template-coq/TypingWf" -"template-coq/AstUtils" -> "template-coq/WfInv" -"checker/All"[label="All", color=seagreen3] -"checker/Normal"[label="Normal", color=seagreen3] -"checker/Retyping"[label="Retyping", color=seagreen3] -"checker/WcbvEval"[label="WcbvEval", color=seagreen3] -"checker/Checker"[label="Checker", color=seagreen3] -"checker/Substitution"[label="Substitution", color=seagreen3] -"checker/Weakening"[label="Weakening", color=seagreen3] -"checker/Closed"[label="Closed", color=seagreen3] -"checker/WeakeningEnv"[label="WeakeningEnv", color=seagreen3] -"checker/Generation"[label="Generation", color=seagreen3] -"template-coq/Loader" -> "template-coq/All" -"template-coq/Typing" -> "template-coq/All" -"template-coq/Constants" -> "template-coq/Loader" -"template-coq/All" -> "checker/All" -"checker/Retyping" -> "checker/All" -"checker/Substitution" -> "checker/All" -"template-coq/Typing" -> "checker/Checker" -"template-coq/common/uGraph" -> "checker/Checker" -"template-coq/Reflect" -> "checker/Closed" -"template-coq/TypingWf" -> "checker/Closed" -"checker/WeakeningEnv" -> "checker/Closed" -"template-coq/Reflect" -> "checker/Generation" -"template-coq/Typing" -> "checker/Generation" -"template-coq/Typing" -> "checker/Normal" -"checker/Checker" -> "checker/Retyping" -"checker/Generation" -> "checker/Substitution" -"checker/Weakening" -> "checker/Substitution" -"template-coq/Reflect" -> "checker/WcbvEval" -"template-coq/Typing" -> "checker/WcbvEval" -"template-coq/WfInv" -> "checker/WcbvEval" -"checker/Closed" -> "checker/Weakening" -"template-coq/Typing" -> "checker/WeakeningEnv" -"template-coq/utils/LibHypsNaming" -> "checker/WeakeningEnv" -"erasure/Erasure"[label="Erasure", color=tan] -"erasure/EOptimizePropDiscr"[label="EOptimizePropDiscr", color=tan] -"erasure/ErasureFunction"[label="ErasureFunction", color=tan] -"erasure/ErasureCorrectness"[label="ErasureCorrectness", color=tan] -"erasure/EArities"[label="EArities", color=tan] -"erasure/EInversion"[label="EInversion", color=tan] -"erasure/ESubstitution"[label="ESubstitution", color=tan] -"erasure/Prelim"[label="Prelim", color=tan] -"erasure/Extraction"[label="Extraction", color=tan] -"erasure/EAll"[label="EAll", color=tan] -"erasure/EDeps"[label="EDeps", color=tan] -"erasure/Extract"[label="Extract", color=tan] -"erasure/ETyping"[label="ETyping", color=tan] -"erasure/EWndEval"[label="EWndEval", color=tan] -"erasure/EWcbvEval"[label="EWcbvEval", color=tan] -"erasure/ECSubst"[label="ECSubst", color=tan] -"erasure/EPretty"[label="EPretty", color=tan] -"erasure/EReflect"[label="EReflect", color=tan] -"erasure/ELiftSubst"[label="ELiftSubst", color=tan] -"erasure/EInduction"[label="EInduction", color=tan] -"erasure/EAstUtils"[label="EAstUtils", color=tan] -"erasure/EAst"[label="EAst", color=tan] -"erasure/EWcbvEval" -> "erasure/EAll" -"erasure/EWndEval" -> "erasure/EAll" -"erasure/Extract" -> "erasure/EAll" -"pcuic/PCUICCanonicity" -> "erasure/EArities" -"pcuic/PCUICPrincipality" -> "erasure/EArities" -"erasure/Extract" -> "erasure/EArities" -"template-coq/Universes" -> "erasure/EAst" -"template-coq/Kernames" -> "erasure/EAstUtils" -"erasure/EAst" -> "erasure/EAstUtils" -"erasure/ELiftSubst" -> "erasure/ECSubst" -"erasure/ESubstitution" -> "erasure/EDeps" -"erasure/EAst" -> "erasure/EInduction" -"erasure/Prelim" -> "erasure/EInversion" -"erasure/EInduction" -> "erasure/ELiftSubst" -"erasure/ErasureFunction" -> "erasure/EOptimizePropDiscr" -"erasure/ETyping" -> "erasure/EPretty" -"pcuic/PCUICReflect" -> "erasure/EReflect" -"erasure/EInduction" -> "erasure/EReflect" -"erasure/Prelim" -> "erasure/ESubstitution" -"erasure/EAstUtils" -> "erasure/ETyping" -"erasure/ELiftSubst" -> "erasure/ETyping" -"erasure/EReflect" -> "erasure/ETyping" -"pcuic/PCUICWcbvEval" -> "erasure/EWcbvEval" -"erasure/ECSubst" -> "erasure/EWcbvEval" -"erasure/ETyping" -> "erasure/EWcbvEval" -"erasure/ETyping" -> "erasure/EWndEval" -"safechecker/SafeTemplateChecker" -> "erasure/Erasure" -"template-coq/Pretty" -> "erasure/Erasure" -"erasure/EOptimizePropDiscr" -> "erasure/Erasure" -"erasure/EPretty" -> "erasure/Erasure" -"erasure/EDeps" -> "erasure/ErasureCorrectness" -"erasure/EInversion" -> "erasure/ErasureCorrectness" -"safechecker/PCUICSafeRetyping" -> "erasure/ErasureFunction" -"erasure/ErasureCorrectness" -> "erasure/ErasureFunction" -"pcuic/PCUICElimination" -> "erasure/Extract" -"erasure/ETyping" -> "erasure/Extract" -"erasure/Erasure" -> "erasure/Extraction" -"safechecker/PCUICSafeChecker" -> "erasure/Prelim" -"erasure/EArities" -> "erasure/Prelim" -"erasure/EWcbvEval" -> "erasure/Prelim" -"pcuic/PCUICToTemplateCorrectness"[label="PCUICToTemplateCorrectness", color=lemonchiffon1] -"pcuic/PCUICToTemplate"[label="PCUICToTemplate", color=lemonchiffon1] -"pcuic/TemplateToPCUICCorrectness"[label="TemplateToPCUICCorrectness", color=lemonchiffon1] -"pcuic/TemplateToPCUIC"[label="TemplateToPCUIC", color=lemonchiffon1] -"pcuic/PCUICSafeLemmata"[label="PCUICSafeLemmata", color=lemonchiffon1] -"pcuic/PCUICSigmaCalculus"[label="PCUICSigmaCalculus", color=lemonchiffon1] -"pcuic/PCUICPrincipality"[label="PCUICPrincipality", color=lemonchiffon1] -"pcuic/PCUICSN"[label="PCUICSN", color=lemonchiffon1] -"pcuic/PCUICElimination"[label="PCUICElimination", color=lemonchiffon1] -"pcuic/PCUICCumulProp"[label="PCUICCumulProp", color=lemonchiffon1] -"pcuic/PCUICPretty"[label="PCUICPretty", color=lemonchiffon1] -"pcuic/PCUICWcbvEval"[label="PCUICWcbvEval", color=lemonchiffon1] -"pcuic/PCUICCSubst"[label="PCUICCSubst", color=lemonchiffon1] -"pcuic/PCUICCanonicity"[label="PCUICCanonicity", color=lemonchiffon1] -"pcuic/PCUICSR"[label="PCUICSR", color=lemonchiffon1] -"pcuic/PCUICInductiveInversion"[label="PCUICInductiveInversion", color=lemonchiffon1] -"pcuic/PCUICValidity"[label="PCUICValidity", color=lemonchiffon1] -"pcuic/PCUICInductives"[label="PCUICInductives", color=lemonchiffon1] -"pcuic/PCUICSpine"[label="PCUICSpine", color=lemonchiffon1] -"pcuic/PCUICWfUniverses"[label="PCUICWfUniverses", color=lemonchiffon1] -"pcuic/PCUICArities"[label="PCUICArities", color=lemonchiffon1] -"pcuic/PCUICContexts"[label="PCUICContexts", color=lemonchiffon1] -"pcuic/PCUICCtxShape"[label="PCUICCtxShape", color=lemonchiffon1] -"pcuic/PCUICAlpha"[label="PCUICAlpha", color=lemonchiffon1] -"pcuic/PCUICGeneration"[label="PCUICGeneration", color=lemonchiffon1] -"pcuic/PCUICConvCumInversion"[label="PCUICConvCumInversion", color=lemonchiffon1] -"pcuic/PCUICConversion"[label="PCUICConversion", color=lemonchiffon1] -"pcuic/PCUICContextConversion"[label="PCUICContextConversion", color=lemonchiffon1] -"pcuic/PCUICContextRelation"[label="PCUICContextRelation", color=lemonchiffon1] -"pcuic/PCUICConfluence"[label="PCUICConfluence", color=lemonchiffon1] -"pcuic/PCUICParallelReductionConfluence"[label="PCUICParallelReductionConfluence", color=lemonchiffon1] -"pcuic/PCUICParallelReduction"[label="PCUICParallelReduction", color=lemonchiffon1] -"pcuic/PCUICReduction"[label="PCUICReduction", color=lemonchiffon1] -"pcuic/PCUICCumulativity"[label="PCUICCumulativity", color=lemonchiffon1] -"pcuic/PCUICSubstitution"[label="PCUICSubstitution", color=lemonchiffon1] -"pcuic/PCUICUnivSubstitution"[label="PCUICUnivSubstitution", color=lemonchiffon1] -"pcuic/PCUICWeakening"[label="PCUICWeakening", color=lemonchiffon1] -"pcuic/PCUICClosed"[label="PCUICClosed", color=lemonchiffon1] -"pcuic/PCUICWeakeningEnv"[label="PCUICWeakeningEnv", color=lemonchiffon1] -"pcuic/PCUICEquality"[label="PCUICEquality", color=lemonchiffon1] -"pcuic/PCUICNameless"[label="PCUICNameless", color=lemonchiffon1] -"pcuic/PCUICNormal"[label="PCUICNormal", color=lemonchiffon1] -"pcuic/PCUICPosition"[label="PCUICPosition", color=lemonchiffon1] -"pcuic/PCUICInversion"[label="PCUICInversion", color=lemonchiffon1] -"pcuic/PCUICGlobalEnv"[label="PCUICGlobalEnv", color=lemonchiffon1] -"pcuic/PCUICTyping"[label="PCUICTyping", color=lemonchiffon1] -"pcuic/PCUICUnivSubst"[label="PCUICUnivSubst", color=lemonchiffon1] -"pcuic/PCUICLiftSubst"[label="PCUICLiftSubst", color=lemonchiffon1] -"pcuic/PCUICReflect"[label="PCUICReflect", color=lemonchiffon1] -"pcuic/PCUICInduction"[label="PCUICInduction", color=lemonchiffon1] -"pcuic/PCUICAstUtils"[label="PCUICAstUtils", color=lemonchiffon1] -"pcuic/PCUICSize"[label="PCUICSize", color=lemonchiffon1] -"pcuic/PCUICAst"[label="PCUICAst", color=lemonchiffon1] -"pcuic/PCUICRelations"[label="PCUICRelations", color=lemonchiffon1] -"pcuic/PCUICUtils"[label="PCUICUtils", color=lemonchiffon1] -"pcuic/PCUICAstUtils" -> "pcuic/PCUICToTemplate" -"template-coq/TypingWf" -> "pcuic/PCUICToTemplateCorrectness" -"template-coq/WfInv" -> "pcuic/PCUICToTemplateCorrectness" -"pcuic/PCUICGeneration" -> "pcuic/PCUICToTemplateCorrectness" -"pcuic/PCUICToTemplate" -> "pcuic/PCUICToTemplateCorrectness" -"template-coq/TypingWf" -> "pcuic/TemplateToPCUICCorrectness" -"template-coq/WfInv" -> "pcuic/TemplateToPCUICCorrectness" -"pcuic/PCUICSubstitution" -> "pcuic/TemplateToPCUICCorrectness" -"pcuic/TemplateToPCUIC" -> "pcuic/TemplateToPCUICCorrectness" -} diff --git a/dependency-graph/depgraph-2020-11-26.png b/dependency-graph/depgraph-2020-11-26.png deleted file mode 100644 index 3dfdcae3699d5ba5a470c03ce53be00cc13188d2..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 1158736 zcmZsD1z43?v^F48f+CG{gLHT2q068_N?N)@L?k7pn?obrsq~>6C8fK&|L@?;z`g%{ 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b/dependency-graph/depgraph-2020-11-26.svg deleted file mode 100644 index 08ce288db..000000000 --- a/dependency-graph/depgraph-2020-11-26.svg +++ /dev/null @@ -1,2041 +0,0 @@ - - - - - - -dependencies - - - -safechecker/Extraction - -Extraction - - - -safechecker/PCUICSafeRetyping - -PCUICSafeRetyping - - - -erasure/ErasureFunction - -ErasureFunction - - - -safechecker/PCUICSafeRetyping->erasure/ErasureFunction - - - - - -safechecker/SafeTemplateChecker - -SafeTemplateChecker - - - -safechecker/SafeTemplateChecker->safechecker/Extraction - - - - - -erasure/Erasure - -Erasure - - - -safechecker/SafeTemplateChecker->erasure/Erasure - - - - - -safechecker/PCUICSafeChecker - -PCUICSafeChecker - - - -safechecker/PCUICSafeChecker->safechecker/PCUICSafeRetyping - - - - - -safechecker/PCUICSafeChecker->safechecker/SafeTemplateChecker - - - - - -erasure/Prelim - -Prelim - - - -safechecker/PCUICSafeChecker->erasure/Prelim - - - - - -safechecker/PCUICWfReduction - -PCUICWfReduction - - - -safechecker/PCUICWfReduction->safechecker/PCUICSafeChecker - - - - - -safechecker/PCUICSafeConversion - -PCUICSafeConversion - - - -safechecker/PCUICSafeConversion->safechecker/PCUICWfReduction - - - - - -safechecker/PCUICEqualityDec - -PCUICEqualityDec - - - -safechecker/PCUICEqualityDec->safechecker/PCUICSafeConversion - - - - - -safechecker/PCUICSafeReduce - -PCUICSafeReduce - - - -safechecker/PCUICSafeReduce->safechecker/PCUICSafeConversion - - - - - -pcuic/PCUICValidity - -PCUICValidity - - - -pcuic/PCUICAlpha - -PCUICAlpha - - - -pcuic/PCUICValidity->pcuic/PCUICAlpha - - - - - -pcuic/PCUICInductiveInversion - -PCUICInductiveInversion - - - -pcuic/PCUICValidity->pcuic/PCUICInductiveInversion - - - - - -pcuic/PCUICSR - -PCUICSR - - - -pcuic/PCUICAlpha->pcuic/PCUICSR - - - - - -pcuic/PCUICWfUniverses - -PCUICWfUniverses - - - -pcuic/PCUICArities - -PCUICArities - - - -pcuic/PCUICWfUniverses->pcuic/PCUICArities - - - - - -pcuic/PCUICSpine - -PCUICSpine - - - -pcuic/PCUICArities->pcuic/PCUICSpine - - - - - -template-coq/EnvironmentTyping - -EnvironmentTyping - - - -pcuic/PCUICAst - -PCUICAst - - - -template-coq/EnvironmentTyping->pcuic/PCUICAst - - - - - -template-coq/Typing - -Typing - - - -template-coq/EnvironmentTyping->template-coq/Typing - - - - - -pcuic/PCUICSize - -PCUICSize - - - -pcuic/PCUICAst->pcuic/PCUICSize - - - - - -pcuic/TemplateToPCUIC - -TemplateToPCUIC - - - -pcuic/PCUICAst->pcuic/TemplateToPCUIC - - - - - -pcuic/PCUICAstUtils - -PCUICAstUtils - - - -pcuic/PCUICSize->pcuic/PCUICAstUtils - - - - - -pcuic/PCUICInduction - -PCUICInduction - - - -pcuic/PCUICAstUtils->pcuic/PCUICInduction - - - - - -pcuic/PCUICUtils - -PCUICUtils - - - -pcuic/PCUICAstUtils->pcuic/PCUICUtils - - - - - -pcuic/PCUICToTemplate - -PCUICToTemplate - - - -pcuic/PCUICAstUtils->pcuic/PCUICToTemplate - - - - - -template-coq/Reflect - -Reflect - - - -template-coq/Reflect->pcuic/PCUICAstUtils - - - - - -template-coq/Extraction - -Extraction - - - -template-coq/Reflect->template-coq/Extraction - - - - - -checker/WcbvEval - -WcbvEval - - - -template-coq/Reflect->checker/WcbvEval - - - - - -checker/Closed - -Closed - - - -template-coq/Reflect->checker/Closed - - - - - -checker/Generation - -Generation - - - -template-coq/Reflect->checker/Generation - - - - - -template-coq/common/uGraph - -uGraph - - - -template-coq/common/uGraph->pcuic/PCUICAstUtils - - - - - -template-coq/Constants - -Constants - - - -template-coq/common/uGraph->template-coq/Constants - - - - - -checker/Checker - -Checker - - - -template-coq/common/uGraph->checker/Checker - - - - - -pcuic/PCUICClosed - -PCUICClosed - - - -pcuic/PCUICCSubst - -PCUICCSubst - - - -pcuic/PCUICClosed->pcuic/PCUICCSubst - - - - - -pcuic/PCUICWeakening - -PCUICWeakening - - - -pcuic/PCUICClosed->pcuic/PCUICWeakening - - - - - -pcuic/PCUICWcbvEval - -PCUICWcbvEval - - - -pcuic/PCUICCSubst->pcuic/PCUICWcbvEval - - - - - -pcuic/PCUICElimination - -PCUICElimination - - - -pcuic/PCUICCanonicity - -PCUICCanonicity - - - -pcuic/PCUICElimination->pcuic/PCUICCanonicity - - - - - -erasure/Extract - -Extract - - - -pcuic/PCUICElimination->erasure/Extract - - - - - -pcuic/PCUICCanonicity->safechecker/PCUICSafeReduce - - - - - -erasure/EArities - -EArities - - - -pcuic/PCUICCanonicity->erasure/EArities - - - - - -pcuic/PCUICSN - -PCUICSN - - - -pcuic/PCUICSN->pcuic/PCUICCanonicity - - - - - -pcuic/PCUICWcbvEval->pcuic/PCUICCanonicity - - - - - -erasure/EWcbvEval - -EWcbvEval - - - -pcuic/PCUICWcbvEval->erasure/EWcbvEval - - - - - -pcuic/PCUICWeakeningEnv - -PCUICWeakeningEnv - - - -pcuic/PCUICWeakeningEnv->pcuic/PCUICClosed - - - - - -pcuic/PCUICParallelReductionConfluence - -PCUICParallelReductionConfluence - - - -pcuic/PCUICConfluence - -PCUICConfluence - - - -pcuic/PCUICParallelReductionConfluence->pcuic/PCUICConfluence - - - - - -pcuic/PCUICContextConversion - -PCUICContextConversion - - - -pcuic/PCUICConfluence->pcuic/PCUICContextConversion - - - - - -pcuic/PCUICConversion - -PCUICConversion - - - -pcuic/PCUICContextConversion->pcuic/PCUICConversion - - - - - -pcuic/PCUICContextRelation - -PCUICContextRelation - - - -pcuic/PCUICContextRelation->pcuic/PCUICContextConversion - - - - - -pcuic/PCUICNormal - -PCUICNormal - - - -pcuic/PCUICContextRelation->pcuic/PCUICNormal - - - - - -pcuic/PCUICTyping - -PCUICTyping - - - -pcuic/PCUICTyping->pcuic/PCUICWeakeningEnv - - - - - -pcuic/PCUICTyping->pcuic/PCUICContextRelation - - - - - -pcuic/PCUICNameless - -PCUICNameless - - - -pcuic/PCUICTyping->pcuic/PCUICNameless - - - - - -pcuic/PCUICGeneration - -PCUICGeneration - - - -pcuic/PCUICTyping->pcuic/PCUICGeneration - - - - - -pcuic/PCUICGlobalEnv - -PCUICGlobalEnv - - - -pcuic/PCUICTyping->pcuic/PCUICGlobalEnv - - - - - -pcuic/PCUICCtxShape - -PCUICCtxShape - - - -pcuic/PCUICContexts - -PCUICContexts - - - -pcuic/PCUICCtxShape->pcuic/PCUICContexts - - - - - -pcuic/PCUICContexts->pcuic/PCUICWfUniverses - - - - - -pcuic/PCUICCumulProp - -PCUICCumulProp - - - -pcuic/PCUICCumulProp->pcuic/PCUICElimination - - - - - -pcuic/PCUICConvCumInversion - -PCUICConvCumInversion - - - -pcuic/PCUICCumulProp->pcuic/PCUICConvCumInversion - - - - - -pcuic/PCUICPrincipality - -PCUICPrincipality - - - -pcuic/PCUICCumulProp->pcuic/PCUICPrincipality - - - - - -pcuic/PCUICConvCumInversion->safechecker/PCUICSafeConversion - - - - - -pcuic/PCUICInversion - -PCUICInversion - - - -pcuic/PCUICConversion->pcuic/PCUICInversion - - - - - -pcuic/PCUICInversion->pcuic/PCUICCtxShape - - - - - -pcuic/PCUICNameless->pcuic/PCUICCtxShape - - - - - -template-coq/UnivSubst - -UnivSubst - - - -template-coq/UnivSubst->pcuic/PCUICCtxShape - - - - - -template-coq/UnivSubst->pcuic/PCUICNormal - - - - - -template-coq/UnivSubst->template-coq/Typing - - - - - -template-coq/UnivSubst->template-coq/Extraction - - - - - -pcuic/PCUICSafeLemmata - -PCUICSafeLemmata - - - -pcuic/PCUICSafeLemmata->pcuic/PCUICSN - - - - - -pcuic/PCUICSafeLemmata->pcuic/PCUICCumulProp - - - - - -pcuic/PCUICReduction - -PCUICReduction - - - -pcuic/PCUICCumulativity - -PCUICCumulativity - - - -pcuic/PCUICReduction->pcuic/PCUICCumulativity - - - - - -pcuic/PCUICCumulativity->pcuic/PCUICTyping - - - - - -pcuic/PCUICLiftSubst - -PCUICLiftSubst - - - -pcuic/PCUICEquality - -PCUICEquality - - - -pcuic/PCUICLiftSubst->pcuic/PCUICEquality - - - - - -pcuic/PCUICPretty - -PCUICPretty - - - -pcuic/PCUICLiftSubst->pcuic/PCUICPretty - - - - - -pcuic/PCUICUnivSubst - -PCUICUnivSubst - - - -pcuic/PCUICLiftSubst->pcuic/PCUICUnivSubst - - - - - -pcuic/PCUICPosition - -PCUICPosition - - - -pcuic/PCUICEquality->pcuic/PCUICPosition - - - - - -pcuic/PCUICReflect - -PCUICReflect - - - -pcuic/PCUICReflect->pcuic/PCUICEquality - - - - - -erasure/EReflect - -EReflect - - - -pcuic/PCUICReflect->erasure/EReflect - - - - - -pcuic/PCUICGeneration->pcuic/PCUICWeakening - - - - - -pcuic/PCUICToTemplateCorrectness - -PCUICToTemplateCorrectness - - - -pcuic/PCUICGeneration->pcuic/PCUICToTemplateCorrectness - - - - - -pcuic/PCUICGlobalEnv->safechecker/PCUICEqualityDec - - - - - -pcuic/PCUICInduction->pcuic/PCUICLiftSubst - - - - - -pcuic/PCUICInduction->pcuic/PCUICReflect - - - - - -pcuic/PCUICInductiveInversion->pcuic/PCUICSR - - - - - -pcuic/PCUICInductives - -PCUICInductives - - - -pcuic/PCUICSpine->pcuic/PCUICInductives - - - - - -pcuic/PCUICInductives->pcuic/PCUICValidity - - - - - -pcuic/PCUICNormal->pcuic/PCUICSafeLemmata - - - - - -pcuic/PCUICSubstitution - -PCUICSubstitution - - - -pcuic/PCUICParallelReduction - -PCUICParallelReduction - - - -pcuic/PCUICSubstitution->pcuic/PCUICParallelReduction - - - - - -pcuic/TemplateToPCUICCorrectness - -TemplateToPCUICCorrectness - - - -pcuic/PCUICSubstitution->pcuic/TemplateToPCUICCorrectness - - - - - -pcuic/PCUICParallelReduction->pcuic/PCUICParallelReductionConfluence - - - - - -pcuic/PCUICPosition->pcuic/PCUICReduction - - - - - -pcuic/PCUICPretty->safechecker/PCUICWfReduction - - - - - -pcuic/PCUICPrincipality->safechecker/PCUICSafeConversion - - - - - -pcuic/PCUICPrincipality->erasure/EArities - - - - - -pcuic/PCUICRelations - -PCUICRelations - - - -pcuic/PCUICRelations->pcuic/PCUICReduction - - - - - -pcuic/PCUICUnivSubst->pcuic/PCUICReduction - - - - - -pcuic/PCUICSR->pcuic/PCUICWcbvEval - - - - - -pcuic/PCUICSR->pcuic/PCUICSafeLemmata - - - - - -pcuic/PCUICSigmaCalculus - -PCUICSigmaCalculus - - - -pcuic/PCUICWeakening->pcuic/PCUICSigmaCalculus - - - - - -pcuic/PCUICUnivSubstitution - -PCUICUnivSubstitution - - - -pcuic/PCUICWeakening->pcuic/PCUICUnivSubstitution - - - - - -pcuic/PCUICSigmaCalculus->pcuic/PCUICSubstitution - - - - - -pcuic/PCUICUnivSubstitution->pcuic/PCUICSubstitution - - - - - -pcuic/PCUICUtils->pcuic/PCUICTyping - - - - - -template-coq/utils/LibHypsNaming - -LibHypsNaming - - - -template-coq/utils/LibHypsNaming->pcuic/PCUICTyping - - - - - -checker/WeakeningEnv - -WeakeningEnv - - - -template-coq/utils/LibHypsNaming->checker/WeakeningEnv - - - - - -pcuic/TemplateToPCUIC->safechecker/SafeTemplateChecker - - - - - -pcuic/TemplateToPCUIC->pcuic/TemplateToPCUICCorrectness - - - - - -template-coq/Environment - -Environment - - - -template-coq/Ast - -Ast - - - -template-coq/Environment->template-coq/Ast - - - - - -template-coq/AstUtils - -AstUtils - - - -template-coq/Ast->template-coq/AstUtils - - - - - -template-coq/TemplateMonad/Common - -Common - - - -template-coq/Ast->template-coq/TemplateMonad/Common - - - - - -template-coq/AstUtils->template-coq/EnvironmentTyping - - - - - -template-coq/Induction - -Induction - - - -template-coq/AstUtils->template-coq/Induction - - - - - -template-coq/TemplateMonad/Extractable - -Extractable - - - -template-coq/AstUtils->template-coq/TemplateMonad/Extractable - - - - - -template-coq/TemplateMonad/Core - -Core - - - -template-coq/AstUtils->template-coq/TemplateMonad/Core - - - - - -template-coq/WfInv - -WfInv - - - -template-coq/AstUtils->template-coq/WfInv - - - - - -template-coq/Kernames - -Kernames - - - -template-coq/AstUtils->template-coq/Kernames - - - - - -template-coq/utils - -utils - - - -template-coq/BasicAst - -BasicAst - - - -template-coq/utils->template-coq/BasicAst - - - - - -template-coq/Universes - -Universes - - - -template-coq/BasicAst->template-coq/Universes - - - - - -template-coq/Universes->template-coq/common/uGraph - - - - - -template-coq/Universes->template-coq/Environment - - - - - -erasure/EAst - -EAst - - - -template-coq/Universes->erasure/EAst - - - - - -template-coq/Induction->template-coq/Reflect - - - - - -template-coq/LiftSubst - -LiftSubst - - - -template-coq/Induction->template-coq/LiftSubst - - - - - -template-coq/LiftSubst->template-coq/UnivSubst - - - - - -template-coq/Pretty - -Pretty - - - -template-coq/LiftSubst->template-coq/Pretty - - - - - -template-coq/Typing->safechecker/SafeTemplateChecker - - - - - -template-coq/TypingWf - -TypingWf - - - -template-coq/Typing->template-coq/TypingWf - - - - - -checker/Normal - -Normal - - - -template-coq/Typing->checker/Normal - - - - - -template-coq/Typing->checker/WcbvEval - - - - - -template-coq/Typing->checker/Checker - - - - - -template-coq/Typing->checker/WeakeningEnv - - - - - -template-coq/Typing->checker/Generation - - - - - -template-coq/All - -template-coq/All - - - -template-coq/Typing->template-coq/All - - - - - -template-coq/config - -config - - - -template-coq/config->template-coq/Universes - - - - - -template-coq/utils/wGraph - -wGraph - - - -template-coq/utils/wGraph->template-coq/common/uGraph - - - - - -template-coq/utils/All_Forall - -All_Forall - - - -template-coq/monad_utils - -monad_utils - - - -template-coq/utils/All_Forall->template-coq/monad_utils - - - - - -template-coq/utils/MCUtils - -MCUtils - - - -template-coq/utils/All_Forall->template-coq/utils/MCUtils - - - - - -template-coq/monad_utils->template-coq/utils - - - - - -template-coq/utils/MCUtils->template-coq/utils - - - - - -template-coq/utils/MCUtils->template-coq/utils/wGraph - - - - - -template-coq/utils/MCOption - -MCOption - - - -template-coq/utils/MCOption->template-coq/utils/All_Forall - - - - - -template-coq/utils/MCSquash - -MCSquash - - - -template-coq/utils/MCSquash->template-coq/utils/All_Forall - - - - - -template-coq/utils/MCPrelude - -MCPrelude - - - -template-coq/utils/MCList - -MCList - - - -template-coq/utils/MCPrelude->template-coq/utils/MCList - - - - - -template-coq/utils/MCList->template-coq/utils/MCOption - - - - - -template-coq/utils/MCRelations - -MCRelations - - - -template-coq/utils/MCRelations->template-coq/utils/MCList - - - - - -template-coq/utils/MCProd - -MCProd - - - -template-coq/utils/MCProd->template-coq/utils/MCOption - - - - - -template-coq/utils/MCCompare - -MCCompare - - - -template-coq/utils/MCString - -MCString - - - -template-coq/utils/MCCompare->template-coq/utils/MCString - - - - - -template-coq/utils/MCString->template-coq/utils/MCUtils - - - - - -template-coq/utils/MCArith - -MCArith - - - -template-coq/utils/MCArith->template-coq/utils/MCUtils - - - - - -template-coq/utils/MCEquality - -MCEquality - - - -template-coq/utils/MCEquality->template-coq/utils/MCUtils - - - - - -template-coq/Loader - -template-coq/Loader - - - -template-coq/Constants->template-coq/Loader - - - - - -template-coq/TemplateMonad/Extractable->template-coq/Extraction - - - - - -template-coq/TemplateMonad/Extractable->template-coq/Constants - - - - - -template-coq/TemplateMonad - -TemplateMonad - - - -template-coq/TemplateMonad/Core->template-coq/TemplateMonad - - - - - -template-coq/TemplateMonad/Common->template-coq/TemplateMonad/Extractable - - - - - -template-coq/TemplateMonad/Common->template-coq/TemplateMonad/Core - - - - - -template-coq/TemplateMonad->template-coq/Constants - - - - - -template-coq/TypingWf->checker/Closed - - - - - -template-coq/TypingWf->pcuic/PCUICToTemplateCorrectness - - - - - -template-coq/TypingWf->pcuic/TemplateToPCUICCorrectness - - - - - -template-coq/WfInv->checker/WcbvEval - - - - - -template-coq/WfInv->pcuic/PCUICToTemplateCorrectness - - - - - -template-coq/WfInv->pcuic/TemplateToPCUICCorrectness - - - - - -template-coq/Pretty->template-coq/Extraction - - - - - -template-coq/Pretty->erasure/Erasure - - - - - -erasure/EAstUtils - -EAstUtils - - - -template-coq/Kernames->erasure/EAstUtils - - - - - -checker/All - -All - - - -checker/Retyping - -Retyping - - - -checker/Retyping->checker/All - - - - - -checker/Checker->checker/Retyping - - - - - -checker/Substitution - -Substitution - - - -checker/Substitution->checker/All - - - - - -checker/Weakening - -Weakening - - - -checker/Weakening->checker/Substitution - - - - - -checker/Closed->checker/Weakening - - - - - -checker/WeakeningEnv->checker/Closed - - - - - -checker/Generation->checker/Substitution - - - - - -template-coq/Loader->template-coq/All - - - - - -template-coq/All->checker/All - - - - - -erasure/Extraction - -Extraction - - - -erasure/Erasure->erasure/Extraction - - - - - -erasure/EOptimizePropDiscr - -EOptimizePropDiscr - - - -erasure/EOptimizePropDiscr->erasure/Erasure - - - - - -erasure/ErasureFunction->erasure/EOptimizePropDiscr - - - - - -erasure/ErasureCorrectness - -ErasureCorrectness - - - -erasure/ErasureCorrectness->erasure/ErasureFunction - - - - - -erasure/EArities->erasure/Prelim - - - - - -erasure/EInversion - -EInversion - - - -erasure/EInversion->erasure/ErasureCorrectness - - - - - -erasure/ESubstitution - -ESubstitution - - - -erasure/EDeps - -EDeps - - - -erasure/ESubstitution->erasure/EDeps - - - - - -erasure/Prelim->erasure/EInversion - - - - - -erasure/Prelim->erasure/ESubstitution - - - - - -erasure/EAll - -EAll - - - -erasure/EDeps->erasure/ErasureCorrectness - - - - - -erasure/Extract->erasure/EArities - - - - - -erasure/Extract->erasure/EAll - - - - - -erasure/ETyping - -ETyping - - - -erasure/ETyping->erasure/Extract - - - - - -erasure/EWndEval - -EWndEval - - - -erasure/ETyping->erasure/EWndEval - - - - - -erasure/ETyping->erasure/EWcbvEval - - - - - -erasure/EPretty - -EPretty - - - -erasure/ETyping->erasure/EPretty - - - - - -erasure/EWndEval->erasure/EAll - - - - - -erasure/EWcbvEval->erasure/Prelim - - - - - -erasure/EWcbvEval->erasure/EAll - - - - - -erasure/ECSubst - -ECSubst - - - -erasure/ECSubst->erasure/EWcbvEval - - - - - -erasure/EPretty->erasure/Erasure - - - - - -erasure/EReflect->erasure/ETyping - - - - - -erasure/ELiftSubst - -ELiftSubst - - - -erasure/ELiftSubst->erasure/ETyping - - - - - -erasure/ELiftSubst->erasure/ECSubst - - - - - -erasure/EInduction - -EInduction - - - -erasure/EInduction->erasure/EReflect - - - - - -erasure/EInduction->erasure/ELiftSubst - - - - - -erasure/EAstUtils->erasure/ETyping - - - - - -erasure/EAst->erasure/EInduction - - - - - -erasure/EAst->erasure/EAstUtils - - - - - -pcuic/PCUICToTemplate->pcuic/PCUICToTemplateCorrectness - - - - - diff --git a/dependency-graph/depgraph-2020-11-27.dot b/dependency-graph/depgraph-2020-11-27.dot deleted file mode 100644 index e3f2dd61c..000000000 --- a/dependency-graph/depgraph-2020-11-27.dot +++ /dev/null @@ -1,346 +0,0 @@ -digraph dependencies { -node[style=filled] -"safechecker/Extraction"[label="Extraction", color=paleturquoise1] -"safechecker/PCUICSafeRetyping"[label="PCUICSafeRetyping", color=paleturquoise1] -"safechecker/SafeTemplateChecker"[label="SafeTemplateChecker", color=paleturquoise1] -"safechecker/PCUICSafeChecker"[label="PCUICSafeChecker", color=paleturquoise1] -"safechecker/PCUICTypeChecker"[label="PCUICTypeChecker", color=paleturquoise1] -"safechecker/PCUICWfEnv"[label="PCUICWfEnv", color=paleturquoise1] -"safechecker/PCUICWfReduction"[label="PCUICWfReduction", color=paleturquoise1] -"safechecker/PCUICSafeConversion"[label="PCUICSafeConversion", color=paleturquoise1] -"safechecker/PCUICEqualityDec"[label="PCUICEqualityDec", color=paleturquoise1] -"safechecker/PCUICSafeReduce"[label="PCUICSafeReduce", color=paleturquoise1] -"safechecker/PCUICErrors"[label="PCUICErrors", color=paleturquoise1] -"pcuic/PCUICValidity" -> "pcuic/PCUICAlpha" -"pcuic/PCUICWfUniverses" -> "pcuic/PCUICArities" -"template-coq/EnvironmentTyping" -> "pcuic/PCUICAst" -"pcuic/PCUICSize" -> "pcuic/PCUICAstUtils" -"template-coq/Reflect" -> "pcuic/PCUICAstUtils" -"template-coq/common/uGraph" -> "pcuic/PCUICAstUtils" -"pcuic/PCUICClosed" -> "pcuic/PCUICCSubst" -"pcuic/PCUICElimination" -> "pcuic/PCUICCanonicity" -"pcuic/PCUICSN" -> "pcuic/PCUICCanonicity" -"pcuic/PCUICWcbvEval" -> "pcuic/PCUICCanonicity" -"pcuic/PCUICWeakeningEnv" -> "pcuic/PCUICClosed" -"pcuic/PCUICParallelReductionConfluence" -> "pcuic/PCUICConfluence" -"pcuic/PCUICConfluence" -> "pcuic/PCUICContextConversion" -"pcuic/PCUICContextRelation" -> "pcuic/PCUICContextConversion" -"pcuic/PCUICTyping" -> "pcuic/PCUICContextRelation" -"pcuic/PCUICCtxShape" -> "pcuic/PCUICContexts" -"pcuic/PCUICCumulProp" -> "pcuic/PCUICConvCumInversion" -"pcuic/PCUICContextConversion" -> "pcuic/PCUICConversion" -"pcuic/PCUICInversion" -> "pcuic/PCUICCtxShape" -"pcuic/PCUICNameless" -> "pcuic/PCUICCtxShape" -"template-coq/UnivSubst" -> "pcuic/PCUICCtxShape" -"pcuic/PCUICSafeLemmata" -> "pcuic/PCUICCumulProp" -"pcuic/PCUICReduction" -> "pcuic/PCUICCumulativity" -"pcuic/PCUICCumulProp" -> "pcuic/PCUICElimination" -"pcuic/PCUICLiftSubst" -> "pcuic/PCUICEquality" -"pcuic/PCUICReflect" -> "pcuic/PCUICEquality" -"pcuic/PCUICTyping" -> "pcuic/PCUICGeneration" -"pcuic/PCUICTyping" -> "pcuic/PCUICGlobalEnv" -"pcuic/PCUICAstUtils" -> "pcuic/PCUICInduction" -"pcuic/PCUICValidity" -> "pcuic/PCUICInductiveInversion" -"pcuic/PCUICSpine" -> "pcuic/PCUICInductives" -"pcuic/PCUICConversion" -> "pcuic/PCUICInversion" -"pcuic/PCUICInduction" -> "pcuic/PCUICLiftSubst" -"pcuic/PCUICTyping" -> "pcuic/PCUICNameless" -"pcuic/PCUICContextRelation" -> "pcuic/PCUICNormal" -"template-coq/UnivSubst" -> "pcuic/PCUICNormal" -"pcuic/PCUICSubstitution" -> "pcuic/PCUICParallelReduction" -"pcuic/PCUICParallelReduction" -> "pcuic/PCUICParallelReductionConfluence" -"pcuic/PCUICEquality" -> "pcuic/PCUICPosition" -"pcuic/PCUICLiftSubst" -> "pcuic/PCUICPretty" -"pcuic/PCUICCumulProp" -> "pcuic/PCUICPrincipality" -"pcuic/PCUICPosition" -> "pcuic/PCUICReduction" -"pcuic/PCUICRelations" -> "pcuic/PCUICReduction" -"pcuic/PCUICUnivSubst" -> "pcuic/PCUICReduction" -"pcuic/PCUICInduction" -> "pcuic/PCUICReflect" -"pcuic/PCUICSafeLemmata" -> "pcuic/PCUICSN" -"pcuic/PCUICAlpha" -> "pcuic/PCUICSR" -"pcuic/PCUICInductiveInversion" -> "pcuic/PCUICSR" -"pcuic/PCUICNormal" -> "pcuic/PCUICSafeLemmata" -"pcuic/PCUICSR" -> "pcuic/PCUICSafeLemmata" -"pcuic/PCUICWeakening" -> "pcuic/PCUICSigmaCalculus" -"pcuic/PCUICAst" -> "pcuic/PCUICSize" -"pcuic/PCUICArities" -> "pcuic/PCUICSpine" -"pcuic/PCUICSigmaCalculus" -> "pcuic/PCUICSubstitution" -"pcuic/PCUICUnivSubstitution" -> "pcuic/PCUICSubstitution" -"pcuic/PCUICCumulativity" -> "pcuic/PCUICTyping" -"pcuic/PCUICUtils" -> "pcuic/PCUICTyping" -"template-coq/utils/LibHypsNaming" -> "pcuic/PCUICTyping" -"pcuic/PCUICLiftSubst" -> "pcuic/PCUICUnivSubst" -"pcuic/PCUICWeakening" -> "pcuic/PCUICUnivSubstitution" -"pcuic/PCUICAstUtils" -> "pcuic/PCUICUtils" -"pcuic/PCUICInductives" -> "pcuic/PCUICValidity" -"pcuic/PCUICCSubst" -> "pcuic/PCUICWcbvEval" -"pcuic/PCUICSR" -> "pcuic/PCUICWcbvEval" -"pcuic/PCUICClosed" -> "pcuic/PCUICWeakening" -"pcuic/PCUICGeneration" -> "pcuic/PCUICWeakening" -"pcuic/PCUICTyping" -> "pcuic/PCUICWeakeningEnv" -"pcuic/PCUICContexts" -> "pcuic/PCUICWfUniverses" -"pcuic/PCUICAst" -> "pcuic/TemplateToPCUIC" -"template-coq/Environment" -> "template-coq/Ast" -"template-coq/Ast" -> "template-coq/AstUtils" -"template-coq/utils" -> "template-coq/BasicAst" -"template-coq/Universes" -> "template-coq/Environment" -"template-coq/AstUtils" -> "template-coq/EnvironmentTyping" -"template-coq/AstUtils" -> "template-coq/Induction" -"template-coq/Induction" -> "template-coq/LiftSubst" -"template-coq/Induction" -> "template-coq/Reflect" -"template-coq/EnvironmentTyping" -> "template-coq/Typing" -"template-coq/UnivSubst" -> "template-coq/Typing" -"template-coq/LiftSubst" -> "template-coq/UnivSubst" -"template-coq/BasicAst" -> "template-coq/Universes" -"template-coq/config" -> "template-coq/Universes" -"template-coq/Universes" -> "template-coq/common/uGraph" -"template-coq/utils/wGraph" -> "template-coq/common/uGraph" -"template-coq/utils/All_Forall" -> "template-coq/monad_utils" -"template-coq/monad_utils" -> "template-coq/utils" -"template-coq/utils/MCUtils" -> "template-coq/utils" -"template-coq/utils/MCOption" -> "template-coq/utils/All_Forall" -"template-coq/utils/MCSquash" -> "template-coq/utils/All_Forall" -"template-coq/utils/MCPrelude" -> "template-coq/utils/MCList" -"template-coq/utils/MCRelations" -> "template-coq/utils/MCList" -"template-coq/utils/MCList" -> "template-coq/utils/MCOption" -"template-coq/utils/MCProd" -> "template-coq/utils/MCOption" -"template-coq/utils/MCCompare" -> "template-coq/utils/MCString" -"template-coq/utils/All_Forall" -> "template-coq/utils/MCUtils" -"template-coq/utils/MCArith" -> "template-coq/utils/MCUtils" -"template-coq/utils/MCEquality" -> "template-coq/utils/MCUtils" -"template-coq/utils/MCString" -> "template-coq/utils/MCUtils" -"template-coq/utils/MCUtils" -> "template-coq/utils/wGraph" -"safechecker/SafeTemplateChecker" -> "safechecker/Extraction" -"pcuic/PCUICGlobalEnv" -> "safechecker/PCUICEqualityDec" -"pcuic/PCUICPretty" -> "safechecker/PCUICErrors" -"safechecker/PCUICTypeChecker" -> "safechecker/PCUICSafeChecker" -"pcuic/PCUICConvCumInversion" -> "safechecker/PCUICSafeConversion" -"pcuic/PCUICPrincipality" -> "safechecker/PCUICSafeConversion" -"safechecker/PCUICEqualityDec" -> "safechecker/PCUICSafeConversion" -"safechecker/PCUICErrors" -> "safechecker/PCUICSafeConversion" -"safechecker/PCUICSafeReduce" -> "safechecker/PCUICSafeConversion" -"pcuic/PCUICCanonicity" -> "safechecker/PCUICSafeReduce" -"safechecker/PCUICTypeChecker" -> "safechecker/PCUICSafeRetyping" -"safechecker/PCUICWfEnv" -> "safechecker/PCUICTypeChecker" -"safechecker/PCUICWfReduction" -> "safechecker/PCUICTypeChecker" -"pcuic/PCUICGlobalEnv" -> "safechecker/PCUICWfEnv" -"safechecker/PCUICSafeConversion" -> "safechecker/PCUICWfReduction" -"pcuic/TemplateToPCUIC" -> "safechecker/SafeTemplateChecker" -"template-coq/Typing" -> "safechecker/SafeTemplateChecker" -"safechecker/PCUICSafeChecker" -> "safechecker/SafeTemplateChecker" -"template-coq/Extraction"[label="Extraction", color=aquamarine] -"template-coq/Constants"[label="Constants", color=aquamarine] -"template-coq/monad_utils"[label="monad_utils", color=aquamarine] -"template-coq/TemplateMonad/Extractable"[label="Extractable", color=aquamarine] -"template-coq/TemplateMonad/Core"[label="Core", color=aquamarine] -"template-coq/TemplateMonad/Common"[label="Common", color=aquamarine] -"template-coq/TemplateMonad"[label="TemplateMonad", color=aquamarine] -"template-coq/TypingWf"[label="TypingWf", color=aquamarine] -"template-coq/Typing"[label="Typing", color=aquamarine] -"template-coq/WfInv"[label="WfInv", color=aquamarine] -"template-coq/EnvironmentTyping"[label="EnvironmentTyping", color=aquamarine] -"template-coq/Pretty"[label="Pretty", color=aquamarine] -"template-coq/UnivSubst"[label="UnivSubst", color=aquamarine] -"template-coq/LiftSubst"[label="LiftSubst", color=aquamarine] -"template-coq/Induction"[label="Induction", color=aquamarine] -"template-coq/Kernames"[label="Kernames", color=aquamarine] -"template-coq/Reflect"[label="Reflect", color=aquamarine] -"template-coq/AstUtils"[label="AstUtils", color=aquamarine] -"template-coq/Ast"[label="Ast", color=aquamarine] -"template-coq/Environment"[label="Environment", color=aquamarine] -"template-coq/BasicAst"[label="BasicAst", color=aquamarine] -"template-coq/Universes"[label="Universes", color=aquamarine] -"template-coq/config"[label="config", color=aquamarine] -"template-coq/utils"[label="utils", color=aquamarine] -"template-coq/common/uGraph"[label="uGraph", color=aquamarine] -"template-coq/utils/MCUtils"[label="MCUtils", color=aquamarine] -"template-coq/utils/wGraph"[label="wGraph", color=aquamarine] -"template-coq/utils/MCString"[label="MCString", color=aquamarine] -"template-coq/utils/MCSquash"[label="MCSquash", color=aquamarine] -"template-coq/utils/MCRelations"[label="MCRelations", color=aquamarine] -"template-coq/utils/MCProd"[label="MCProd", color=aquamarine] -"template-coq/utils/MCOption"[label="MCOption", color=aquamarine] -"template-coq/utils/MCList"[label="MCList", color=aquamarine] -"template-coq/utils/LibHypsNaming"[label="LibHypsNaming", color=aquamarine] -"template-coq/utils/MCEquality"[label="MCEquality", color=aquamarine] -"template-coq/utils/MCCompare"[label="MCCompare", color=aquamarine] -"template-coq/utils/MCArith"[label="MCArith", color=aquamarine] -"template-coq/utils/All_Forall"[label="All_Forall", color=aquamarine] -"template-coq/utils/MCPrelude"[label="MCPrelude", color=aquamarine] -"template-coq/TemplateMonad" -> "template-coq/Constants" -"template-coq/TemplateMonad/Extractable" -> "template-coq/Constants" -"template-coq/common/uGraph" -> "template-coq/Constants" -"template-coq/Pretty" -> "template-coq/Extraction" -"template-coq/Reflect" -> "template-coq/Extraction" -"template-coq/TemplateMonad/Extractable" -> "template-coq/Extraction" -"template-coq/UnivSubst" -> "template-coq/Extraction" -"template-coq/AstUtils" -> "template-coq/Kernames" -"template-coq/LiftSubst" -> "template-coq/Pretty" -"template-coq/TemplateMonad/Core" -> "template-coq/TemplateMonad" -"template-coq/Ast" -> "template-coq/TemplateMonad/Common" -"template-coq/AstUtils" -> "template-coq/TemplateMonad/Core" -"template-coq/TemplateMonad/Common" -> "template-coq/TemplateMonad/Core" -"template-coq/AstUtils" -> "template-coq/TemplateMonad/Extractable" -"template-coq/TemplateMonad/Common" -> "template-coq/TemplateMonad/Extractable" -"template-coq/Typing" -> "template-coq/TypingWf" -"template-coq/AstUtils" -> "template-coq/WfInv" -"checker/All"[label="All", color=seagreen3] -"checker/Normal"[label="Normal", color=seagreen3] -"checker/Retyping"[label="Retyping", color=seagreen3] -"checker/WcbvEval"[label="WcbvEval", color=seagreen3] -"checker/Checker"[label="Checker", color=seagreen3] -"checker/Substitution"[label="Substitution", color=seagreen3] -"checker/Weakening"[label="Weakening", color=seagreen3] -"checker/Closed"[label="Closed", color=seagreen3] -"checker/WeakeningEnv"[label="WeakeningEnv", color=seagreen3] -"checker/Generation"[label="Generation", color=seagreen3] -"template-coq/Loader" -> "template-coq/All" -"template-coq/Typing" -> "template-coq/All" -"template-coq/Constants" -> "template-coq/Loader" -"template-coq/All" -> "checker/All" -"checker/Retyping" -> "checker/All" -"checker/Substitution" -> "checker/All" -"template-coq/Typing" -> "checker/Checker" -"template-coq/common/uGraph" -> "checker/Checker" -"template-coq/Reflect" -> "checker/Closed" -"template-coq/TypingWf" -> "checker/Closed" -"checker/WeakeningEnv" -> "checker/Closed" -"template-coq/Reflect" -> "checker/Generation" -"template-coq/Typing" -> "checker/Generation" -"template-coq/Typing" -> "checker/Normal" -"checker/Checker" -> "checker/Retyping" -"checker/Generation" -> "checker/Substitution" -"checker/Weakening" -> "checker/Substitution" -"template-coq/Reflect" -> "checker/WcbvEval" -"template-coq/Typing" -> "checker/WcbvEval" -"template-coq/WfInv" -> "checker/WcbvEval" -"checker/Closed" -> "checker/Weakening" -"template-coq/Typing" -> "checker/WeakeningEnv" -"template-coq/utils/LibHypsNaming" -> "checker/WeakeningEnv" -"erasure/Erasure"[label="Erasure", color=tan] -"erasure/EOptimizePropDiscr"[label="EOptimizePropDiscr", color=tan] -"erasure/ErasureFunction"[label="ErasureFunction", color=tan] -"erasure/ErasureCorrectness"[label="ErasureCorrectness", color=tan] -"erasure/EArities"[label="EArities", color=tan] -"erasure/EInversion"[label="EInversion", color=tan] -"erasure/ESubstitution"[label="ESubstitution", color=tan] -"erasure/Prelim"[label="Prelim", color=tan] -"erasure/Extraction"[label="Extraction", color=tan] -"erasure/EAll"[label="EAll", color=tan] -"erasure/EDeps"[label="EDeps", color=tan] -"erasure/Extract"[label="Extract", color=tan] -"erasure/ETyping"[label="ETyping", color=tan] -"erasure/EWndEval"[label="EWndEval", color=tan] -"erasure/EWcbvEval"[label="EWcbvEval", color=tan] -"erasure/ECSubst"[label="ECSubst", color=tan] -"erasure/EPretty"[label="EPretty", color=tan] -"erasure/EReflect"[label="EReflect", color=tan] -"erasure/ELiftSubst"[label="ELiftSubst", color=tan] -"erasure/EInduction"[label="EInduction", color=tan] -"erasure/EAstUtils"[label="EAstUtils", color=tan] -"erasure/EAst"[label="EAst", color=tan] -"erasure/EWcbvEval" -> "erasure/EAll" -"erasure/EWndEval" -> "erasure/EAll" -"erasure/Extract" -> "erasure/EAll" -"pcuic/PCUICCanonicity" -> "erasure/EArities" -"pcuic/PCUICPrincipality" -> "erasure/EArities" -"erasure/Extract" -> "erasure/EArities" -"template-coq/Universes" -> "erasure/EAst" -"template-coq/Kernames" -> "erasure/EAstUtils" -"erasure/EAst" -> "erasure/EAstUtils" -"erasure/ELiftSubst" -> "erasure/ECSubst" -"erasure/ESubstitution" -> "erasure/EDeps" -"erasure/EAst" -> "erasure/EInduction" -"erasure/Prelim" -> "erasure/EInversion" -"erasure/EInduction" -> "erasure/ELiftSubst" -"erasure/ErasureFunction" -> "erasure/EOptimizePropDiscr" -"erasure/ETyping" -> "erasure/EPretty" -"pcuic/PCUICReflect" -> "erasure/EReflect" -"erasure/EInduction" -> "erasure/EReflect" -"erasure/Prelim" -> "erasure/ESubstitution" -"erasure/EAstUtils" -> "erasure/ETyping" -"erasure/ELiftSubst" -> "erasure/ETyping" -"erasure/EReflect" -> "erasure/ETyping" -"pcuic/PCUICWcbvEval" -> "erasure/EWcbvEval" -"erasure/ECSubst" -> "erasure/EWcbvEval" -"erasure/ETyping" -> "erasure/EWcbvEval" -"erasure/ETyping" -> "erasure/EWndEval" -"safechecker/SafeTemplateChecker" -> "erasure/Erasure" -"template-coq/Pretty" -> "erasure/Erasure" -"erasure/EOptimizePropDiscr" -> "erasure/Erasure" -"erasure/EPretty" -> "erasure/Erasure" -"erasure/EDeps" -> "erasure/ErasureCorrectness" -"erasure/EInversion" -> "erasure/ErasureCorrectness" -"safechecker/PCUICSafeRetyping" -> "erasure/ErasureFunction" -"erasure/ErasureCorrectness" -> "erasure/ErasureFunction" -"pcuic/PCUICElimination" -> "erasure/Extract" -"erasure/ETyping" -> "erasure/Extract" -"erasure/Erasure" -> "erasure/Extraction" -"safechecker/PCUICSafeChecker" -> "erasure/Prelim" -"erasure/EArities" -> "erasure/Prelim" -"erasure/EWcbvEval" -> "erasure/Prelim" -"pcuic/PCUICToTemplateCorrectness"[label="PCUICToTemplateCorrectness", color=lemonchiffon1] -"pcuic/PCUICToTemplate"[label="PCUICToTemplate", color=lemonchiffon1] -"pcuic/TemplateToPCUICCorrectness"[label="TemplateToPCUICCorrectness", color=lemonchiffon1] -"pcuic/TemplateToPCUIC"[label="TemplateToPCUIC", color=lemonchiffon1] -"pcuic/PCUICSafeLemmata"[label="PCUICSafeLemmata", color=lemonchiffon1] -"pcuic/PCUICSigmaCalculus"[label="PCUICSigmaCalculus", color=lemonchiffon1] -"pcuic/PCUICPrincipality"[label="PCUICPrincipality", color=lemonchiffon1] -"pcuic/PCUICSN"[label="PCUICSN", color=lemonchiffon1] -"pcuic/PCUICElimination"[label="PCUICElimination", color=lemonchiffon1] -"pcuic/PCUICCumulProp"[label="PCUICCumulProp", color=lemonchiffon1] -"pcuic/PCUICPretty"[label="PCUICPretty", color=lemonchiffon1] -"pcuic/PCUICWcbvEval"[label="PCUICWcbvEval", color=lemonchiffon1] -"pcuic/PCUICCSubst"[label="PCUICCSubst", color=lemonchiffon1] -"pcuic/PCUICCanonicity"[label="PCUICCanonicity", color=lemonchiffon1] -"pcuic/PCUICSR"[label="PCUICSR", color=lemonchiffon1] -"pcuic/PCUICInductiveInversion"[label="PCUICInductiveInversion", color=lemonchiffon1] -"pcuic/PCUICValidity"[label="PCUICValidity", color=lemonchiffon1] -"pcuic/PCUICInductives"[label="PCUICInductives", color=lemonchiffon1] -"pcuic/PCUICSpine"[label="PCUICSpine", color=lemonchiffon1] -"pcuic/PCUICWfUniverses"[label="PCUICWfUniverses", color=lemonchiffon1] -"pcuic/PCUICArities"[label="PCUICArities", color=lemonchiffon1] -"pcuic/PCUICContexts"[label="PCUICContexts", color=lemonchiffon1] -"pcuic/PCUICCtxShape"[label="PCUICCtxShape", color=lemonchiffon1] -"pcuic/PCUICAlpha"[label="PCUICAlpha", color=lemonchiffon1] -"pcuic/PCUICGeneration"[label="PCUICGeneration", color=lemonchiffon1] -"pcuic/PCUICConvCumInversion"[label="PCUICConvCumInversion", color=lemonchiffon1] -"pcuic/PCUICConversion"[label="PCUICConversion", color=lemonchiffon1] -"pcuic/PCUICContextConversion"[label="PCUICContextConversion", color=lemonchiffon1] -"pcuic/PCUICContextRelation"[label="PCUICContextRelation", color=lemonchiffon1] -"pcuic/PCUICConfluence"[label="PCUICConfluence", color=lemonchiffon1] -"pcuic/PCUICParallelReductionConfluence"[label="PCUICParallelReductionConfluence", color=lemonchiffon1] -"pcuic/PCUICParallelReduction"[label="PCUICParallelReduction", color=lemonchiffon1] -"pcuic/PCUICReduction"[label="PCUICReduction", color=lemonchiffon1] -"pcuic/PCUICCumulativity"[label="PCUICCumulativity", color=lemonchiffon1] -"pcuic/PCUICSubstitution"[label="PCUICSubstitution", color=lemonchiffon1] -"pcuic/PCUICUnivSubstitution"[label="PCUICUnivSubstitution", color=lemonchiffon1] -"pcuic/PCUICWeakening"[label="PCUICWeakening", color=lemonchiffon1] -"pcuic/PCUICClosed"[label="PCUICClosed", color=lemonchiffon1] -"pcuic/PCUICWeakeningEnv"[label="PCUICWeakeningEnv", color=lemonchiffon1] -"pcuic/PCUICEquality"[label="PCUICEquality", color=lemonchiffon1] -"pcuic/PCUICNameless"[label="PCUICNameless", color=lemonchiffon1] -"pcuic/PCUICNormal"[label="PCUICNormal", color=lemonchiffon1] -"pcuic/PCUICPosition"[label="PCUICPosition", color=lemonchiffon1] -"pcuic/PCUICInversion"[label="PCUICInversion", color=lemonchiffon1] -"pcuic/PCUICGlobalEnv"[label="PCUICGlobalEnv", color=lemonchiffon1] -"pcuic/PCUICTyping"[label="PCUICTyping", color=lemonchiffon1] -"pcuic/PCUICUnivSubst"[label="PCUICUnivSubst", color=lemonchiffon1] -"pcuic/PCUICLiftSubst"[label="PCUICLiftSubst", color=lemonchiffon1] -"pcuic/PCUICReflect"[label="PCUICReflect", color=lemonchiffon1] -"pcuic/PCUICInduction"[label="PCUICInduction", color=lemonchiffon1] -"pcuic/PCUICAstUtils"[label="PCUICAstUtils", color=lemonchiffon1] -"pcuic/PCUICSize"[label="PCUICSize", color=lemonchiffon1] -"pcuic/PCUICAst"[label="PCUICAst", color=lemonchiffon1] -"pcuic/PCUICRelations"[label="PCUICRelations", color=lemonchiffon1] -"pcuic/PCUICUtils"[label="PCUICUtils", color=lemonchiffon1] -"pcuic/PCUICAstUtils" -> "pcuic/PCUICToTemplate" -"template-coq/TypingWf" -> "pcuic/PCUICToTemplateCorrectness" -"template-coq/WfInv" -> "pcuic/PCUICToTemplateCorrectness" -"pcuic/PCUICGeneration" -> 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-template-coq/utils/MCOption->template-coq/utils/All_Forall - - - - - -template-coq/utils/MCSquash - -MCSquash - - - -template-coq/utils/MCSquash->template-coq/utils/All_Forall - - - - - -template-coq/utils/MCPrelude - -MCPrelude - - - -template-coq/utils/MCList - -MCList - - - -template-coq/utils/MCPrelude->template-coq/utils/MCList - - - - - -template-coq/utils/MCList->template-coq/utils/MCOption - - - - - -template-coq/utils/MCRelations - -MCRelations - - - -template-coq/utils/MCRelations->template-coq/utils/MCList - - - - - -template-coq/utils/MCProd - -MCProd - - - -template-coq/utils/MCProd->template-coq/utils/MCOption - - - - - -template-coq/utils/MCCompare - -MCCompare - - - -template-coq/utils/MCString - -MCString - - - -template-coq/utils/MCCompare->template-coq/utils/MCString - - - - - -template-coq/utils/MCString->template-coq/utils/MCUtils - - - - - -template-coq/utils/MCArith - -MCArith - - - -template-coq/utils/MCArith->template-coq/utils/MCUtils - - - - - -template-coq/utils/MCEquality - -MCEquality - - - -template-coq/utils/MCEquality->template-coq/utils/MCUtils - - - - - -template-coq/Loader - -template-coq/Loader - - - -template-coq/Constants->template-coq/Loader - - - - - -template-coq/TemplateMonad/Extractable->template-coq/Extraction - - - - - -template-coq/TemplateMonad/Extractable->template-coq/Constants - - - - - -template-coq/TemplateMonad - -TemplateMonad - - - -template-coq/TemplateMonad/Core->template-coq/TemplateMonad - - - - - -template-coq/TemplateMonad/Common->template-coq/TemplateMonad/Extractable - - - - - -template-coq/TemplateMonad/Common->template-coq/TemplateMonad/Core - - - - - -template-coq/TemplateMonad->template-coq/Constants - - - - - -template-coq/TypingWf->checker/Closed - - - - - -template-coq/TypingWf->pcuic/PCUICToTemplateCorrectness - - - - - -template-coq/TypingWf->pcuic/TemplateToPCUICCorrectness - - - - - -template-coq/WfInv->checker/WcbvEval - - - - - -template-coq/WfInv->pcuic/PCUICToTemplateCorrectness - - - - - -template-coq/WfInv->pcuic/TemplateToPCUICCorrectness - - - - - -template-coq/Pretty->template-coq/Extraction - - - - - -template-coq/Pretty->erasure/Erasure - - - - - -erasure/EAstUtils - -EAstUtils - - - -template-coq/Kernames->erasure/EAstUtils - - - - - -checker/All - -All - - - -checker/Retyping - -Retyping - - - -checker/Retyping->checker/All - - - - - -checker/Checker->checker/Retyping - - - - - -checker/Substitution - -Substitution - - - -checker/Substitution->checker/All - - - - - -checker/Weakening - -Weakening - - - -checker/Weakening->checker/Substitution - - - - - -checker/Closed->checker/Weakening - - - - - -checker/WeakeningEnv->checker/Closed - - - - - -checker/Generation->checker/Substitution - - - - - -template-coq/Loader->template-coq/All - - - - - -template-coq/All->checker/All - - - - - -erasure/Extraction - -Extraction - - - -erasure/Erasure->erasure/Extraction - - - - - -erasure/EOptimizePropDiscr - -EOptimizePropDiscr - - - -erasure/EOptimizePropDiscr->erasure/Erasure - - - - - -erasure/ErasureFunction->erasure/EOptimizePropDiscr - - - - - -erasure/ErasureCorrectness - -ErasureCorrectness - - - -erasure/ErasureCorrectness->erasure/ErasureFunction - - - - - -erasure/EArities->erasure/Prelim - - - - - -erasure/EInversion - -EInversion - - - -erasure/EInversion->erasure/ErasureCorrectness - - - - - -erasure/ESubstitution - -ESubstitution - - - -erasure/EDeps - -EDeps - - - -erasure/ESubstitution->erasure/EDeps - - - - - -erasure/Prelim->erasure/EInversion - - - - - -erasure/Prelim->erasure/ESubstitution - - - - - -erasure/EAll - -EAll - - - -erasure/EDeps->erasure/ErasureCorrectness - - - - - -erasure/Extract->erasure/EArities - - - - - -erasure/Extract->erasure/EAll - - - - - -erasure/ETyping - -ETyping - - - -erasure/ETyping->erasure/Extract - - - - - -erasure/EWndEval - -EWndEval - - - -erasure/ETyping->erasure/EWndEval - - - - - -erasure/ETyping->erasure/EWcbvEval - - - - - -erasure/EPretty - -EPretty - - - -erasure/ETyping->erasure/EPretty - - - - - -erasure/EWndEval->erasure/EAll - - - - - -erasure/EWcbvEval->erasure/Prelim - - - - - -erasure/EWcbvEval->erasure/EAll - - - - - -erasure/ECSubst - -ECSubst - - - -erasure/ECSubst->erasure/EWcbvEval - - - - - -erasure/EPretty->erasure/Erasure - - - - - -erasure/EReflect->erasure/ETyping - - - - - -erasure/ELiftSubst - -ELiftSubst - - - -erasure/ELiftSubst->erasure/ETyping - - - - - -erasure/ELiftSubst->erasure/ECSubst - - - - - -erasure/EInduction - -EInduction - - - -erasure/EInduction->erasure/EReflect - - - - - -erasure/EInduction->erasure/ELiftSubst - - - - - -erasure/EAstUtils->erasure/ETyping - - - - - -erasure/EAst->erasure/EInduction - - - - - -erasure/EAst->erasure/EAstUtils - - - - - -pcuic/PCUICToTemplate->pcuic/PCUICToTemplateCorrectness - - - - - From b526cec8e8dd48f2a28edc00f4c5e6c8bb4bbc94 Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Sat, 28 Nov 2020 15:07:26 +0100 Subject: [PATCH 18/70] Finish decoupling of Type/SafeChecker and erasure: only retyping needed to compile it --- erasure/theories/EOptimizePropDiscr.v | 2 + erasure/theories/ErasureFunction.v | 7 +- pcuic/theories/PCUICAstUtils.v | 4 +- safechecker/theories/PCUICErrors.v | 37 ++++- safechecker/theories/PCUICSafeChecker.v | 37 +---- safechecker/theories/PCUICSafeReduce.v | 161 ++++++++++++++++++++++ safechecker/theories/PCUICSafeRetyping.v | 3 +- safechecker/theories/PCUICTypeChecker.v | 163 +---------------------- test-suite/erasure_live_test.v | 22 +++ 9 files changed, 237 insertions(+), 199 deletions(-) diff --git a/erasure/theories/EOptimizePropDiscr.v b/erasure/theories/EOptimizePropDiscr.v index f3b752fa0..1f871b672 100644 --- a/erasure/theories/EOptimizePropDiscr.v +++ b/erasure/theories/EOptimizePropDiscr.v @@ -28,7 +28,9 @@ Ltac introdep := let H := fresh in intros H; depelim H. Hint Constructors Ee.eval : core. +Set Warnings "-notation-overridden". Import E. +Set Warnings "+notation-overridden". Section optimize. Context (Σ : global_context). diff --git a/erasure/theories/ErasureFunction.v b/erasure/theories/ErasureFunction.v index d3993f5f4..410c5e4e8 100644 --- a/erasure/theories/ErasureFunction.v +++ b/erasure/theories/ErasureFunction.v @@ -8,8 +8,8 @@ From MetaCoq.PCUIC Require Import PCUICAst PCUICAstUtils PCUICCumulativity PCUICSR PCUICSafeLemmata PCUICValidity PCUICPrincipality PCUICElimination PCUICSN. -From MetaCoq.SafeChecker Require Import PCUICErrors PCUICSafeReduce PCUICTypeChecker PCUICSafeRetyping. -From MetaCoq.Erasure Require Import EAstUtils EArities Extract Prelim ErasureCorrectness EDeps. +From MetaCoq.SafeChecker Require Import PCUICErrors PCUICSafeReduce PCUICSafeRetyping. +From MetaCoq.Erasure Require Import EAstUtils EArities Extract Prelim EDeps ErasureCorrectness. Local Open Scope string_scope. Set Asymmetric Patterns. @@ -20,7 +20,7 @@ Set Equations Transparent. Local Set Keyed Unification. Require Import ssreflect. -Derive Signature for on_global_env. +Derive Signature for PCUICTyping.on_global_env. (* To debug performance issues *) (* @@ -1117,6 +1117,7 @@ Proof. sq. destruct X0 as [bod [bodty [[Hbod Hebod] Heqdeps]]]. eapply (erase_global_erases_deps (Σ := (Σ, cst_universes c))); simpl; auto. constructor; simpl; auto. + red in w. depelim w. auto. eauto. eauto. eapply IHΣ. diff --git a/pcuic/theories/PCUICAstUtils.v b/pcuic/theories/PCUICAstUtils.v index 594847fda..aa8e5ea87 100644 --- a/pcuic/theories/PCUICAstUtils.v +++ b/pcuic/theories/PCUICAstUtils.v @@ -4,6 +4,7 @@ From MetaCoq.PCUIC Require Import PCUICAst PCUICSize. Require Import ssreflect. From Equations Require Import Equations. +Set Equations Transparent. Derive Signature for All All2. @@ -814,7 +815,6 @@ Section MapInP. map_InP nil _ := nil; map_InP (cons x xs) H := cons (f x (H x (or_introl eq_refl))) (map_InP xs (fun x inx => H x _)). End MapInP. -Global Transparent map_InP. Lemma map_InP_spec {A B : Type} {P : A -> Type} (f : A -> B) (l : list A) (H : forall x, In x l -> P x) : map_InP (fun (x : A) (_ : P x) => f x) l H = List.map f l. @@ -885,4 +885,4 @@ Inductive view_ind : term -> Type := Equations view_indc (t : term) : view_ind t := view_indc (tInd ind u) => view_ind_tInd ind u; - view_indc t => view_ind_other t _. \ No newline at end of file + view_indc t => view_ind_other t _. diff --git a/safechecker/theories/PCUICErrors.v b/safechecker/theories/PCUICErrors.v index 516a360e2..6136f62fb 100644 --- a/safechecker/theories/PCUICErrors.v +++ b/safechecker/theories/PCUICErrors.v @@ -291,4 +291,39 @@ Instance monad_exc : MonadExc type_error typing_result := | Checked a => m | TypeError t => f t end - }. \ No newline at end of file + }. + +Inductive env_error := +| IllFormedDecl (e : string) (e : type_error) +| AlreadyDeclared (id : string). + +Inductive EnvCheck (A : Type) := +| CorrectDecl (a : A) +| EnvError (Σ : global_env_ext) (e : env_error). +Global Arguments EnvError {A} Σ e. +Global Arguments CorrectDecl {A} a. + +Global Instance envcheck_monad : Monad EnvCheck := + {| ret A a := CorrectDecl a ; + bind A B m f := + match m with + | CorrectDecl a => f a + | EnvError g e => EnvError g e + end + |}. + +Global Instance envcheck_monad_exc + : MonadExc (global_env_ext * env_error) EnvCheck := + { raise A '(g, e) := EnvError g e; + catch A m f := + match m with + | CorrectDecl a => m + | EnvError g t => f (g, t) + end + }. + +Definition wrap_error {A} Σ (id : string) (check : typing_result A) : EnvCheck A := + match check with + | Checked a => CorrectDecl a + | TypeError e => EnvError Σ (IllFormedDecl id e) + end. \ No newline at end of file diff --git a/safechecker/theories/PCUICSafeChecker.v b/safechecker/theories/PCUICSafeChecker.v index 1d38c4739..fef3c99dd 100644 --- a/safechecker/theories/PCUICSafeChecker.v +++ b/safechecker/theories/PCUICSafeChecker.v @@ -30,41 +30,6 @@ Ltac Coq.Program.Tactics.program_solve_wf ::= end end. -Inductive env_error := -| IllFormedDecl (e : string) (e : type_error) -| AlreadyDeclared (id : string). - -Inductive EnvCheck (A : Type) := -| CorrectDecl (a : A) -| EnvError (Σ : global_env_ext) (e : env_error). -Global Arguments EnvError {A} Σ e. -Global Arguments CorrectDecl {A} a. - -Global Instance envcheck_monad : Monad EnvCheck := - {| ret A a := CorrectDecl a ; - bind A B m f := - match m with - | CorrectDecl a => f a - | EnvError g e => EnvError g e - end - |}. - -Global Instance envcheck_monad_exc - : MonadExc (global_env_ext * env_error) EnvCheck := - { raise A '(g, e) := EnvError g e; - catch A m f := - match m with - | CorrectDecl a => m - | EnvError g t => f (g, t) - end - }. - -Definition wrap_error {A} Σ (id : string) (check : typing_result A) : EnvCheck A := - match check with - | Checked a => CorrectDecl a - | TypeError e => EnvError Σ (IllFormedDecl id e) - end. - Section CheckEnv. Context {cf:checker_flags}. @@ -1927,6 +1892,8 @@ Section CheckEnv. (Msg ("Incorrect inductive sort: The constructor arguments universes are not smaller than the declared inductive sort")) ;; match indices_matter with | true => + (* FIXME this is wrong, we should use sorts_local_ctx as the indices might be + in sorts which don't necessarily have a sup. *) tyloc <- check_type_local_ctx Σ params indices ind_sort wfparams ;; ret _ | false => ret _ diff --git a/safechecker/theories/PCUICSafeReduce.v b/safechecker/theories/PCUICSafeReduce.v index 3a90d1f79..12226aa5a 100644 --- a/safechecker/theories/PCUICSafeReduce.v +++ b/safechecker/theories/PCUICSafeReduce.v @@ -1721,3 +1721,164 @@ Section Reduce. Qed. End Reduce. + +From MetaCoq.PCUIC Require Import PCUICConfluence PCUICConversion. +From MetaCoq.SafeChecker Require Import PCUICErrors. + +Section ReduceFns. + Context {cf : checker_flags} {Σ : global_env_ext} (HΣ : ∥ wf Σ ∥). + + (* We get stack overflow on Qed after Equations definitions when this is transparent *) + Opaque reduce_stack_full. + + Definition hnf := reduce_term RedFlags.default Σ HΣ. + + Theorem hnf_sound {Γ t h} : ∥ red (fst Σ) Γ t (hnf Γ t h) ∥. + Proof. + apply reduce_term_sound. + Defined. + + Theorem hnf_complete {Γ t h} : ∥whnf RedFlags.default Σ Γ (hnf Γ t h)∥. + Proof. + apply reduce_term_complete. + Qed. + + Equations? reduce_to_sort (Γ : context) (t : term) (h : welltyped Σ Γ t) + : typing_result (∑ u, ∥ red (fst Σ) Γ t (tSort u) ∥) := + reduce_to_sort Γ t h with view_sortc t := { + | view_sort_sort s => ret (s; sq (refl_red _ _ _)); + | view_sort_other t _ with inspect (hnf Γ t h) := + | exist hnft eq with view_sortc hnft := { + | view_sort_sort s => ret (s; _); + | view_sort_other t _ => raise (NotASort t) + } + }. + Proof. + pose proof (hnf_sound (h:=h)). + now rewrite eq. + Qed. + + Lemma reduce_to_sort_complete {Γ t wt} e : + reduce_to_sort Γ t wt = TypeError e -> + (forall s, red Σ Γ t (tSort s) -> False). + Proof. + funelim (reduce_to_sort Γ t wt); try congruence. + intros _ s r. + pose proof (@hnf_complete Γ t0 h) as [wh]. + pose proof (@hnf_sound Γ t0 h) as [r']. + destruct HΣ. + eapply red_confluence in r as (?&r1&r2); eauto. + apply invert_red_sort in r2 as ->. + eapply whnf_red_inv in r1; eauto. + depelim r1. + clear Heq. + rewrite H in n0. + now cbn in n0. + Qed. + + Equations? reduce_to_prod (Γ : context) (t : term) (h : welltyped Σ Γ t) + : typing_result (∑ na a b, ∥ red (fst Σ) Γ t (tProd na a b) ∥) := + reduce_to_prod Γ t h with view_prodc t := { + | view_prod_prod na a b => ret (na; a; b; sq (refl_red _ _ _)); + | view_prod_other t _ with inspect (hnf Γ t h) := + | exist hnft eq with view_prodc hnft := { + | view_prod_prod na a b => ret (na; a; b; _); + | view_prod_other t' _ => raise (NotAProduct t t') + } + }. + Proof. + pose proof (hnf_sound (h:=h)). + now rewrite eq. + Qed. + + Lemma reduce_to_prod_complete {Γ t wt} e : + reduce_to_prod Γ t wt = TypeError e -> + (forall na a b, red Σ Γ t (tProd na a b) -> False). + Proof. + funelim (reduce_to_prod Γ t wt); try congruence. + intros _ na a b r. + pose proof (@hnf_complete Γ t0 h) as [wh]. + pose proof (@hnf_sound Γ t0 h) as [r']. + destruct HΣ. + eapply red_confluence in r as (?&r1&r2); eauto. + apply invert_red_prod in r2 as (?&?&(->&?)&?); auto. + eapply whnf_red_inv in r1; auto. + depelim r1. + clear Heq. + rewrite H in n0. + now cbn in n0. + Qed. + + Equations? reduce_to_ind (Γ : context) (t : term) (h : welltyped Σ Γ t) + : typing_result (∑ i u l, ∥ red (fst Σ) Γ t (mkApps (tInd i u) l) ∥) := + reduce_to_ind Γ t h with inspect (decompose_app t) := { + | exist (thd, args) eq_decomp with view_indc thd := { + | view_ind_tInd i u => ret (i; u; args; sq _); + | view_ind_other t _ with inspect (reduce_stack RedFlags.default Σ HΣ Γ t Empty h) := { + | exist (hnft, π) eq with view_indc hnft := { + | view_ind_tInd i u with inspect (decompose_stack π) := { + | exist (l, _) eq_decomp => ret (i; u; l; _) + }; + | view_ind_other _ _ => raise (NotAnInductive t) + } + } + } + }. + Proof. + - assert (X : mkApps (tInd i u) args = t); [|rewrite X; apply refl_red]. + etransitivity. 2: symmetry; eapply mkApps_decompose_app. + now rewrite <- eq_decomp. + - pose proof (reduce_stack_sound RedFlags.default Σ HΣ _ _ Empty h). + rewrite <- eq in H. + cbn in *. + assert (π = appstack l ε) as ->. + 2: { now rewrite zipc_appstack in H. } + unfold reduce_stack in eq. + destruct reduce_stack_full as (?&_&stack_val&?). + subst x. + unfold Pr in stack_val. + cbn in *. + assert (decomp: decompose_stack π = ((decompose_stack π).1, ε)). + { rewrite stack_val. + now destruct decompose_stack. } + apply decompose_stack_eq in decomp as ->. + now rewrite <- eq_decomp0. + Qed. + + Lemma reduce_to_ind_complete Γ ty wat e : + reduce_to_ind Γ ty wat = TypeError e -> + forall ind u args, + red Σ Γ ty (mkApps (tInd ind u) args) -> + False. + Proof. + funelim (reduce_to_ind Γ ty wat); try congruence. + intros _ ind u args r. + pose proof (reduce_stack_whnf RedFlags.default Σ HΣ Γ t ε h) as wh. + unfold reduce_stack in *. + destruct reduce_stack_full as ((hd&π)&r'&stack_valid&(notapp&_)). + destruct wh as [wh]. + apply Req_red in r' as [r']. + unfold Pr in stack_valid. + cbn in *. + destruct HΣ. + eapply red_confluence in r as (?&r1&r2); [|eassumption|exact r']. + assert (exists args, π = appstack args ε) as (?&->). + { exists ((decompose_stack π).1). + assert (decomp: decompose_stack π = ((decompose_stack π).1, ε)). + { now rewrite stack_valid; destruct decompose_stack. } + now apply decompose_stack_eq in decomp. } + + unfold zipp in wh. + rewrite stack_context_appstack, decompose_stack_appstack in wh. + rewrite zipc_appstack in r1. + cbn in *. + rewrite app_nil_r in wh. + apply red_mkApps_tInd in r2 as (?&->&?); auto. + eapply whnf_red_inv in r1; eauto. + apply whnf_red_mkApps_inv in r1 as (?&?); auto. + depelim w. + noconf e0. + discriminate i0. + Qed. + +End ReduceFns. \ No newline at end of file diff --git a/safechecker/theories/PCUICSafeRetyping.v b/safechecker/theories/PCUICSafeRetyping.v index 107719083..ee891f44f 100644 --- a/safechecker/theories/PCUICSafeRetyping.v +++ b/safechecker/theories/PCUICSafeRetyping.v @@ -10,8 +10,7 @@ From MetaCoq.PCUIC Require Import PCUICAst PCUICAstUtils PCUICArities PCUICInduc PCUICGeneration PCUICInversion PCUICValidity PCUICInductives PCUICInductiveInversion PCUICSpine PCUICSR PCUICCumulativity PCUICConversion PCUICConfluence PCUICArities PCUICWeakeningEnv PCUICContexts. -From MetaCoq.SafeChecker Require Import PCUICErrors PCUICSafeReduce - (* For reduce function TODO: move *) PCUICTypeChecker PCUICSafeChecker. +From MetaCoq.SafeChecker Require Import PCUICErrors PCUICSafeReduce. Local Open Scope string_scope. Set Asymmetric Patterns. Import monad_utils.MonadNotation. diff --git a/safechecker/theories/PCUICTypeChecker.v b/safechecker/theories/PCUICTypeChecker.v index 2852ccd0b..315cd9e0d 100644 --- a/safechecker/theories/PCUICTypeChecker.v +++ b/safechecker/theories/PCUICTypeChecker.v @@ -43,155 +43,7 @@ Section Typecheck. destruct HΣ, Hφ; now constructor. Defined. - Definition hnf := reduce_term RedFlags.default Σ HΣ. - - Theorem hnf_sound {Γ t h} : ∥ red (fst Σ) Γ t (hnf Γ t h) ∥. - Proof. - apply reduce_term_sound. - Defined. - - Theorem hnf_complete {Γ t h} : ∥whnf RedFlags.default Σ Γ (hnf Γ t h)∥. - Proof. - apply reduce_term_complete. - Qed. - - Equations? reduce_to_sort (Γ : context) (t : term) (h : welltyped Σ Γ t) - : typing_result (∑ u, ∥ red (fst Σ) Γ t (tSort u) ∥) := - reduce_to_sort Γ t h with view_sortc t := { - | view_sort_sort s => ret (s; sq (refl_red _ _ _)); - | view_sort_other t _ with inspect (hnf Γ t h) := - | exist hnft eq with view_sortc hnft := { - | view_sort_sort s => ret (s; _); - | view_sort_other t _ => raise (NotASort t) - } - }. - Proof. - pose proof (hnf_sound (h:=h)). - now rewrite eq. - Qed. - - Lemma reduce_to_sort_complete {Γ t wt} e : - reduce_to_sort Γ t wt = TypeError e -> - (forall s, red Σ Γ t (tSort s) -> False). - Proof. - funelim (reduce_to_sort Γ t wt); try congruence. - intros _ s r. - pose proof (@hnf_complete Γ t0 h) as [wh]. - pose proof (@hnf_sound Γ t0 h) as [r']. - destruct HΣ. - eapply red_confluence in r as (?&r1&r2); eauto. - apply invert_red_sort in r2 as ->. - eapply whnf_red_inv in r1; eauto. - depelim r1. - clear Heq. - rewrite H in n0. - now cbn in n0. - Qed. - - Equations? reduce_to_prod (Γ : context) (t : term) (h : welltyped Σ Γ t) - : typing_result (∑ na a b, ∥ red (fst Σ) Γ t (tProd na a b) ∥) := - reduce_to_prod Γ t h with view_prodc t := { - | view_prod_prod na a b => ret (na; a; b; sq (refl_red _ _ _)); - | view_prod_other t _ with inspect (hnf Γ t h) := - | exist hnft eq with view_prodc hnft := { - | view_prod_prod na a b => ret (na; a; b; _); - | view_prod_other t' _ => raise (NotAProduct t t') - } - }. - Proof. - pose proof (hnf_sound (h:=h)). - now rewrite eq. - Qed. - - Lemma reduce_to_prod_complete {Γ t wt} e : - reduce_to_prod Γ t wt = TypeError e -> - (forall na a b, red Σ Γ t (tProd na a b) -> False). - Proof. - funelim (reduce_to_prod Γ t wt); try congruence. - intros _ na a b r. - pose proof (@hnf_complete Γ t0 h) as [wh]. - pose proof (@hnf_sound Γ t0 h) as [r']. - destruct HΣ. - eapply red_confluence in r as (?&r1&r2); eauto. - apply invert_red_prod in r2 as (?&?&(->&?)&?); auto. - eapply whnf_red_inv in r1; auto. - depelim r1. - clear Heq. - rewrite H in n0. - now cbn in n0. - Qed. - - Equations? reduce_to_ind (Γ : context) (t : term) (h : welltyped Σ Γ t) - : typing_result (∑ i u l, ∥ red (fst Σ) Γ t (mkApps (tInd i u) l) ∥) := - reduce_to_ind Γ t h with inspect (decompose_app t) := { - | exist (thd, args) eq_decomp with view_indc thd := { - | view_ind_tInd i u => ret (i; u; args; sq _); - | view_ind_other t _ with inspect (reduce_stack RedFlags.default Σ HΣ Γ t Empty h) := { - | exist (hnft, π) eq with view_indc hnft := { - | view_ind_tInd i u with inspect (decompose_stack π) := { - | exist (l, _) eq_decomp => ret (i; u; l; _) - }; - | view_ind_other _ _ => raise (NotAnInductive t) - } - } - } - }. - Proof. - - assert (X : mkApps (tInd i u) args = t); [|rewrite X; apply refl_red]. - etransitivity. 2: symmetry; eapply mkApps_decompose_app. - now rewrite <- eq_decomp. - - pose proof (reduce_stack_sound RedFlags.default Σ HΣ _ _ Empty h). - rewrite <- eq in H. - cbn in *. - assert (π = appstack l ε) as ->. - 2: { now rewrite zipc_appstack in H. } - unfold reduce_stack in eq. - destruct reduce_stack_full as (?&_&stack_val&?). - subst x. - unfold Pr in stack_val. - cbn in *. - assert (decomp: decompose_stack π = ((decompose_stack π).1, ε)). - { rewrite stack_val. - now destruct decompose_stack. } - apply decompose_stack_eq in decomp as ->. - now rewrite <- eq_decomp0. - Qed. - - Lemma reduce_to_ind_complete Γ ty wat e : - reduce_to_ind Γ ty wat = TypeError e -> - forall ind u args, - red Σ Γ ty (mkApps (tInd ind u) args) -> - False. - Proof. - funelim (reduce_to_ind Γ ty wat); try congruence. - intros _ ind u args r. - pose proof (reduce_stack_whnf RedFlags.default Σ HΣ Γ t ε h) as wh. - unfold reduce_stack in *. - destruct reduce_stack_full as ((hd&π)&r'&stack_valid&(notapp&_)). - destruct wh as [wh]. - apply Req_red in r' as [r']. - unfold Pr in stack_valid. - cbn in *. - destruct HΣ. - eapply red_confluence in r as (?&r1&r2); [|eassumption|exact r']. - assert (exists args, π = appstack args ε) as (?&->). - { exists ((decompose_stack π).1). - assert (decomp: decompose_stack π = ((decompose_stack π).1, ε)). - { now rewrite stack_valid; destruct decompose_stack. } - now apply decompose_stack_eq in decomp. } - - unfold zipp in wh. - rewrite stack_context_appstack decompose_stack_appstack in wh. - rewrite zipc_appstack in r1. - cbn in *. - rewrite app_nil_r in wh. - apply red_mkApps_tInd in r2 as (?&->&?); auto. - eapply whnf_red_inv in r1; eauto. - apply whnf_red_mkApps_inv in r1 as (?&?); auto. - depelim w. - noconf e0. - discriminate i0. - Qed. + Notation hnf := (hnf HΣ). Definition isconv Γ := isconv_term Σ HΣ Hφ G HG Γ Conv. Definition iscumul Γ := isconv_term Σ HΣ Hφ G HG Γ Cumul. @@ -247,7 +99,7 @@ Section Typecheck. Program Definition infer_type Γ HΓ t : typing_result ({u : Universe.t & ∥ Σ ;;; Γ |- t : tSort u ∥}) := tx <- infer Γ HΓ t ;; - u <- reduce_to_sort Γ tx.π1 _ ;; + u <- reduce_to_sort HΣ Γ tx.π1 _ ;; ret (u.π1; _). Next Obligation. eapply validity_wf; eassumption. @@ -296,8 +148,7 @@ Section Typecheck. | Polymorphic_ctx (inst, cstrs) => let '(inst, cstrs) := AUContext.repr (inst, cstrs) in check_eq_true (forallb (fun l => LevelSet.mem l (uGraph.wGraph.V G)) u) - (Msg "instance does not have the right length") ;; - (* check_eq_true (forallb (fun l => LevelSet.mem l lvs) u) ;; *) + (Msg "undeclared level in instance") ;; X <- check_eq_nat #|u| #|inst| (Msg "instance does not have the right length");; match check_constraints G (subst_instance_cstrs u cstrs) with @@ -422,7 +273,7 @@ Section Typecheck. | tApp t u => ty <- infer Γ HΓ t ;; - pi <- reduce_to_prod Γ ty.π1 _ ;; + pi <- reduce_to_prod HΣ Γ ty.π1 _ ;; infer_cumul infer Γ HΓ u pi.π2.π1 _ ;; ret (subst10 u pi.π2.π2.π1; _) @@ -452,7 +303,7 @@ Section Typecheck. | tCase (ind, par) p c brs => cty <- infer Γ HΓ c ;; - I <- reduce_to_ind Γ cty.π1 _ ;; + I <- reduce_to_ind HΣ Γ cty.π1 _ ;; let '(ind'; I') := I in let '(u; I'') := I' in let '(args; H) := I'' in check_eq_true (eqb ind ind') (* bad case info *) @@ -507,7 +358,7 @@ Section Typecheck. match nth_error d.π2.π1.(ind_projs) k with | Some pdecl => c_ty <- infer Γ HΓ c ;; - I <- reduce_to_ind Γ c_ty.π1 _ ;; + I <- reduce_to_ind HΣ Γ c_ty.π1 _ ;; let '(ind'; I') := I in let '(u; I'') := I' in let '(args; H) := I'' in check_eq_true (eqb ind ind') (NotConvertible G Γ (tInd ind u) (tInd ind' u)) ;; @@ -895,7 +746,7 @@ Section Typecheck. Program Definition check_isType Γ (HΓ : ∥ wf_local Σ Γ ∥) A : typing_result (∥ isType Σ Γ A ∥) := s <- infer Γ HΓ A ;; - s' <- reduce_to_sort Γ s.π1 _ ;; + s' <- reduce_to_sort HΣ Γ s.π1 _ ;; ret _. Next Obligation. now eapply validity_wf. Defined. Next Obligation. destruct X0. sq. eexists. eapply type_reduction; tea. Defined. diff --git a/test-suite/erasure_live_test.v b/test-suite/erasure_live_test.v index 4144a6acf..b82cd6676 100644 --- a/test-suite/erasure_live_test.v +++ b/test-suite/erasure_live_test.v @@ -1,5 +1,7 @@ From Coq Require Import Recdef. From MetaCoq.Template Require Import Loader. +From MetaCoq.SafeChecker Require Import SafeTemplateChecker. +From MetaCoq.PCUIC Require Import PCUICAstUtils. From MetaCoq.Erasure Require Import Erasure. From Coq Require Import String. Local Open Scope string_scope. @@ -10,6 +12,26 @@ Definition test (p : Ast.program) : string := erase_and_print_template_program p. MetaCoq Quote Recursively Definition zero := 0. + +(* Definition zerocst_test : ∑ s, test zero = s. +Proof. + eexists. + unfold test, erase_and_print_template_program. + set(e := fix_program_universes zero). + cbn in e. + unfold erase_template_program. + set (foo := ErasureFunction.erase _ _ _ _ _). + hnf in foo. + unfold ErasureFunction.is_erasable in foo. + set (isa := ErasureFunction.is_arity _ _ _ _ _ _) in *. + hnf in isa. + set (rs := PCUICTypeChecker.reduce_to_sort _ _ _ _) in *. + elimtype False. clear foo isa. + hnf in rs. + + + simpl in foo. *) + Definition zerocst := Eval lazy in test zero. MetaCoq Quote Recursively Definition exproof := I. From ccb388219d276154f3d37b5495dcb516112f92d1 Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Sat, 28 Nov 2020 15:10:06 +0100 Subject: [PATCH 19/70] typing_correctness and erasure_live_test reducing again. --- examples/typing_correctness.v | 6 ++---- test-suite/_CoqProject | 2 +- 2 files changed, 3 insertions(+), 5 deletions(-) diff --git a/examples/typing_correctness.v b/examples/typing_correctness.v index 171955738..c14492b2b 100644 --- a/examples/typing_correctness.v +++ b/examples/typing_correctness.v @@ -80,9 +80,7 @@ Lemma identity_typing (u := Universe.make univ): inh gctx_wf_env [] (tProd (bNam Proof. set (impl := tLambda (bNamed "s") (tSort u) (tLambda bAnon (tRel 0) (tRel 0))). assert (wfΓ : ∥ wf_local gctx_wf_env [] ∥) by do 2 constructor. -Admitted. -(* (** All immediate now *) Time fill_inh impl. Time Qed. -*) -Print identity_typing. + +Print identity_typing. (* Still a huge wf_env proof unfolded *) diff --git a/test-suite/_CoqProject b/test-suite/_CoqProject index 990a5214f..86f9eaa69 100644 --- a/test-suite/_CoqProject +++ b/test-suite/_CoqProject @@ -22,7 +22,7 @@ case.v castprop.v # CheckerTest.v disabled cofix.v -# erasure_live_test.v +erasure_live_test.v erasure_test.v evars.v extractable.v From 9df4b96f2764b612a4e3a6351486c22bf73f8034 Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Sat, 28 Nov 2020 15:24:58 +0100 Subject: [PATCH 20/70] Decouple SafeChecker completely from erasure, at the ML level too --- dependency-graph/depgraph-2020-11-28.dot | 346 ++++ dependency-graph/depgraph-2020-11-28.png | Bin 0 -> 1151726 bytes dependency-graph/depgraph-2020-11-28.svg | 2083 ++++++++++++++++++++ erasure/_PluginProject.in | 6 - erasure/src/g_metacoq_erasure.mlg | 1 - erasure/src/metacoq_erasure_plugin.mlpack | 3 - erasure/theories/EOptimizePropDiscr.v | 1 - erasure/theories/Erasure.v | 5 +- safechecker/theories/SafeTemplateChecker.v | 4 +- 9 files changed, 2432 insertions(+), 17 deletions(-) create mode 100644 dependency-graph/depgraph-2020-11-28.dot create mode 100644 dependency-graph/depgraph-2020-11-28.png create mode 100644 dependency-graph/depgraph-2020-11-28.svg diff --git a/dependency-graph/depgraph-2020-11-28.dot b/dependency-graph/depgraph-2020-11-28.dot new file mode 100644 index 000000000..c103181dd --- /dev/null +++ b/dependency-graph/depgraph-2020-11-28.dot @@ -0,0 +1,346 @@ +digraph dependencies { +node[style=filled] +"safechecker/Extraction"[label="Extraction", color=paleturquoise1] +"safechecker/PCUICSafeRetyping"[label="PCUICSafeRetyping", color=paleturquoise1] +"safechecker/SafeTemplateChecker"[label="SafeTemplateChecker", color=paleturquoise1] +"safechecker/PCUICSafeChecker"[label="PCUICSafeChecker", color=paleturquoise1] +"safechecker/PCUICTypeChecker"[label="PCUICTypeChecker", color=paleturquoise1] +"safechecker/PCUICWfEnv"[label="PCUICWfEnv", color=paleturquoise1] +"safechecker/PCUICWfReduction"[label="PCUICWfReduction", color=paleturquoise1] +"safechecker/PCUICSafeConversion"[label="PCUICSafeConversion", color=paleturquoise1] +"safechecker/PCUICEqualityDec"[label="PCUICEqualityDec", color=paleturquoise1] +"safechecker/PCUICSafeReduce"[label="PCUICSafeReduce", color=paleturquoise1] +"safechecker/PCUICErrors"[label="PCUICErrors", color=paleturquoise1] +"pcuic/PCUICValidity" -> "pcuic/PCUICAlpha" +"pcuic/PCUICWfUniverses" -> "pcuic/PCUICArities" +"template-coq/EnvironmentTyping" -> "pcuic/PCUICAst" +"pcuic/PCUICSize" -> "pcuic/PCUICAstUtils" +"template-coq/Reflect" -> "pcuic/PCUICAstUtils" +"template-coq/common/uGraph" -> "pcuic/PCUICAstUtils" +"pcuic/PCUICClosed" -> "pcuic/PCUICCSubst" +"pcuic/PCUICElimination" -> "pcuic/PCUICCanonicity" +"pcuic/PCUICSN" -> "pcuic/PCUICCanonicity" +"pcuic/PCUICWcbvEval" -> "pcuic/PCUICCanonicity" +"pcuic/PCUICWeakeningEnv" -> "pcuic/PCUICClosed" +"pcuic/PCUICParallelReductionConfluence" -> "pcuic/PCUICConfluence" +"pcuic/PCUICConfluence" -> "pcuic/PCUICContextConversion" +"pcuic/PCUICContextRelation" -> "pcuic/PCUICContextConversion" +"pcuic/PCUICTyping" -> "pcuic/PCUICContextRelation" +"pcuic/PCUICCtxShape" -> "pcuic/PCUICContexts" +"pcuic/PCUICCumulProp" -> "pcuic/PCUICConvCumInversion" +"pcuic/PCUICContextConversion" -> "pcuic/PCUICConversion" +"pcuic/PCUICInversion" -> "pcuic/PCUICCtxShape" +"pcuic/PCUICNameless" -> "pcuic/PCUICCtxShape" +"template-coq/UnivSubst" -> "pcuic/PCUICCtxShape" +"pcuic/PCUICSafeLemmata" -> "pcuic/PCUICCumulProp" +"pcuic/PCUICReduction" -> "pcuic/PCUICCumulativity" +"pcuic/PCUICCumulProp" -> "pcuic/PCUICElimination" +"pcuic/PCUICLiftSubst" -> "pcuic/PCUICEquality" +"pcuic/PCUICReflect" -> "pcuic/PCUICEquality" +"pcuic/PCUICTyping" -> "pcuic/PCUICGeneration" +"pcuic/PCUICTyping" -> "pcuic/PCUICGlobalEnv" +"pcuic/PCUICAstUtils" -> "pcuic/PCUICInduction" +"pcuic/PCUICValidity" -> "pcuic/PCUICInductiveInversion" +"pcuic/PCUICSpine" -> "pcuic/PCUICInductives" +"pcuic/PCUICConversion" -> "pcuic/PCUICInversion" +"pcuic/PCUICInduction" -> "pcuic/PCUICLiftSubst" +"pcuic/PCUICTyping" -> "pcuic/PCUICNameless" +"pcuic/PCUICContextRelation" -> "pcuic/PCUICNormal" +"template-coq/UnivSubst" -> "pcuic/PCUICNormal" +"pcuic/PCUICSubstitution" -> "pcuic/PCUICParallelReduction" +"pcuic/PCUICParallelReduction" -> "pcuic/PCUICParallelReductionConfluence" +"pcuic/PCUICEquality" -> "pcuic/PCUICPosition" +"pcuic/PCUICLiftSubst" -> "pcuic/PCUICPretty" +"pcuic/PCUICCumulProp" -> "pcuic/PCUICPrincipality" +"pcuic/PCUICPosition" -> "pcuic/PCUICReduction" +"pcuic/PCUICRelations" -> "pcuic/PCUICReduction" +"pcuic/PCUICUnivSubst" -> "pcuic/PCUICReduction" +"pcuic/PCUICInduction" -> "pcuic/PCUICReflect" +"pcuic/PCUICSafeLemmata" -> "pcuic/PCUICSN" +"pcuic/PCUICAlpha" -> "pcuic/PCUICSR" +"pcuic/PCUICInductiveInversion" -> "pcuic/PCUICSR" +"pcuic/PCUICNormal" -> "pcuic/PCUICSafeLemmata" +"pcuic/PCUICSR" -> "pcuic/PCUICSafeLemmata" +"pcuic/PCUICWeakening" -> "pcuic/PCUICSigmaCalculus" +"pcuic/PCUICAst" -> "pcuic/PCUICSize" +"pcuic/PCUICArities" -> "pcuic/PCUICSpine" +"pcuic/PCUICSigmaCalculus" -> "pcuic/PCUICSubstitution" +"pcuic/PCUICUnivSubstitution" -> "pcuic/PCUICSubstitution" +"pcuic/PCUICCumulativity" -> "pcuic/PCUICTyping" +"pcuic/PCUICUtils" -> "pcuic/PCUICTyping" +"template-coq/utils/LibHypsNaming" -> "pcuic/PCUICTyping" +"pcuic/PCUICLiftSubst" -> "pcuic/PCUICUnivSubst" +"pcuic/PCUICWeakening" -> "pcuic/PCUICUnivSubstitution" +"pcuic/PCUICAstUtils" -> "pcuic/PCUICUtils" +"pcuic/PCUICInductives" -> "pcuic/PCUICValidity" +"pcuic/PCUICCSubst" -> "pcuic/PCUICWcbvEval" +"pcuic/PCUICSR" -> "pcuic/PCUICWcbvEval" +"pcuic/PCUICClosed" -> "pcuic/PCUICWeakening" +"pcuic/PCUICGeneration" -> "pcuic/PCUICWeakening" +"pcuic/PCUICTyping" -> "pcuic/PCUICWeakeningEnv" +"pcuic/PCUICContexts" -> "pcuic/PCUICWfUniverses" +"pcuic/PCUICAst" -> "pcuic/TemplateToPCUIC" +"template-coq/Environment" -> "template-coq/Ast" +"template-coq/Ast" -> "template-coq/AstUtils" +"template-coq/utils" -> "template-coq/BasicAst" +"template-coq/Universes" -> "template-coq/Environment" +"template-coq/AstUtils" -> "template-coq/EnvironmentTyping" +"template-coq/AstUtils" -> "template-coq/Induction" +"template-coq/Induction" -> "template-coq/LiftSubst" +"template-coq/Induction" -> "template-coq/Reflect" +"template-coq/EnvironmentTyping" -> "template-coq/Typing" +"template-coq/UnivSubst" -> "template-coq/Typing" +"template-coq/LiftSubst" -> "template-coq/UnivSubst" +"template-coq/BasicAst" -> "template-coq/Universes" +"template-coq/config" -> "template-coq/Universes" +"template-coq/Universes" -> "template-coq/common/uGraph" +"template-coq/utils/wGraph" -> "template-coq/common/uGraph" +"template-coq/utils/All_Forall" -> "template-coq/monad_utils" +"template-coq/monad_utils" -> "template-coq/utils" +"template-coq/utils/MCUtils" -> "template-coq/utils" +"template-coq/utils/MCOption" -> "template-coq/utils/All_Forall" +"template-coq/utils/MCSquash" -> "template-coq/utils/All_Forall" +"template-coq/utils/MCPrelude" -> "template-coq/utils/MCList" +"template-coq/utils/MCRelations" -> "template-coq/utils/MCList" +"template-coq/utils/MCList" -> "template-coq/utils/MCOption" +"template-coq/utils/MCProd" -> "template-coq/utils/MCOption" +"template-coq/utils/MCCompare" -> "template-coq/utils/MCString" +"template-coq/utils/All_Forall" -> "template-coq/utils/MCUtils" +"template-coq/utils/MCArith" -> "template-coq/utils/MCUtils" +"template-coq/utils/MCEquality" -> "template-coq/utils/MCUtils" +"template-coq/utils/MCString" -> "template-coq/utils/MCUtils" +"template-coq/utils/MCUtils" -> "template-coq/utils/wGraph" +"safechecker/SafeTemplateChecker" -> "safechecker/Extraction" +"pcuic/PCUICGlobalEnv" -> "safechecker/PCUICEqualityDec" +"pcuic/PCUICPretty" -> "safechecker/PCUICErrors" +"safechecker/PCUICTypeChecker" -> "safechecker/PCUICSafeChecker" +"pcuic/PCUICConvCumInversion" -> "safechecker/PCUICSafeConversion" +"pcuic/PCUICPrincipality" -> "safechecker/PCUICSafeConversion" +"safechecker/PCUICEqualityDec" -> "safechecker/PCUICSafeConversion" +"safechecker/PCUICSafeReduce" -> "safechecker/PCUICSafeConversion" +"pcuic/PCUICCanonicity" -> "safechecker/PCUICSafeReduce" +"safechecker/PCUICErrors" -> "safechecker/PCUICSafeReduce" +"safechecker/PCUICSafeReduce" -> "safechecker/PCUICSafeRetyping" +"safechecker/PCUICWfEnv" -> "safechecker/PCUICTypeChecker" +"safechecker/PCUICWfReduction" -> "safechecker/PCUICTypeChecker" +"pcuic/PCUICGlobalEnv" -> "safechecker/PCUICWfEnv" +"safechecker/PCUICSafeConversion" -> "safechecker/PCUICWfReduction" +"pcuic/TemplateToPCUIC" -> "safechecker/SafeTemplateChecker" +"template-coq/Typing" -> "safechecker/SafeTemplateChecker" +"safechecker/PCUICSafeChecker" -> "safechecker/SafeTemplateChecker" +"template-coq/Extraction"[label="Extraction", color=aquamarine] +"template-coq/Constants"[label="Constants", color=aquamarine] +"template-coq/monad_utils"[label="monad_utils", color=aquamarine] +"template-coq/TemplateMonad/Extractable"[label="Extractable", color=aquamarine] +"template-coq/TemplateMonad/Core"[label="Core", color=aquamarine] +"template-coq/TemplateMonad/Common"[label="Common", color=aquamarine] +"template-coq/TemplateMonad"[label="TemplateMonad", color=aquamarine] +"template-coq/TypingWf"[label="TypingWf", color=aquamarine] +"template-coq/Typing"[label="Typing", color=aquamarine] +"template-coq/WfInv"[label="WfInv", color=aquamarine] +"template-coq/EnvironmentTyping"[label="EnvironmentTyping", color=aquamarine] +"template-coq/Pretty"[label="Pretty", color=aquamarine] +"template-coq/UnivSubst"[label="UnivSubst", color=aquamarine] +"template-coq/LiftSubst"[label="LiftSubst", color=aquamarine] +"template-coq/Induction"[label="Induction", color=aquamarine] +"template-coq/Kernames"[label="Kernames", color=aquamarine] +"template-coq/Reflect"[label="Reflect", color=aquamarine] +"template-coq/AstUtils"[label="AstUtils", color=aquamarine] +"template-coq/Ast"[label="Ast", color=aquamarine] +"template-coq/Environment"[label="Environment", color=aquamarine] +"template-coq/BasicAst"[label="BasicAst", color=aquamarine] +"template-coq/Universes"[label="Universes", color=aquamarine] +"template-coq/config"[label="config", color=aquamarine] +"template-coq/utils"[label="utils", color=aquamarine] +"template-coq/common/uGraph"[label="uGraph", color=aquamarine] +"template-coq/utils/MCUtils"[label="MCUtils", color=aquamarine] +"template-coq/utils/wGraph"[label="wGraph", color=aquamarine] +"template-coq/utils/MCString"[label="MCString", color=aquamarine] +"template-coq/utils/MCSquash"[label="MCSquash", color=aquamarine] +"template-coq/utils/MCRelations"[label="MCRelations", color=aquamarine] +"template-coq/utils/MCProd"[label="MCProd", color=aquamarine] +"template-coq/utils/MCOption"[label="MCOption", color=aquamarine] +"template-coq/utils/MCList"[label="MCList", color=aquamarine] +"template-coq/utils/LibHypsNaming"[label="LibHypsNaming", color=aquamarine] +"template-coq/utils/MCEquality"[label="MCEquality", color=aquamarine] +"template-coq/utils/MCCompare"[label="MCCompare", color=aquamarine] +"template-coq/utils/MCArith"[label="MCArith", color=aquamarine] +"template-coq/utils/All_Forall"[label="All_Forall", color=aquamarine] +"template-coq/utils/MCPrelude"[label="MCPrelude", color=aquamarine] +"template-coq/TemplateMonad" -> "template-coq/Constants" +"template-coq/TemplateMonad/Extractable" -> "template-coq/Constants" +"template-coq/common/uGraph" -> "template-coq/Constants" +"template-coq/Pretty" -> "template-coq/Extraction" +"template-coq/Reflect" -> "template-coq/Extraction" +"template-coq/TemplateMonad/Extractable" -> "template-coq/Extraction" +"template-coq/UnivSubst" -> "template-coq/Extraction" +"template-coq/AstUtils" -> "template-coq/Kernames" +"template-coq/LiftSubst" -> "template-coq/Pretty" +"template-coq/TemplateMonad/Core" -> "template-coq/TemplateMonad" +"template-coq/Ast" -> "template-coq/TemplateMonad/Common" +"template-coq/AstUtils" -> "template-coq/TemplateMonad/Core" +"template-coq/TemplateMonad/Common" -> "template-coq/TemplateMonad/Core" +"template-coq/AstUtils" -> "template-coq/TemplateMonad/Extractable" +"template-coq/TemplateMonad/Common" -> "template-coq/TemplateMonad/Extractable" +"template-coq/Typing" -> "template-coq/TypingWf" +"template-coq/AstUtils" -> "template-coq/WfInv" +"checker/All"[label="All", color=seagreen3] +"checker/Normal"[label="Normal", color=seagreen3] +"checker/Retyping"[label="Retyping", color=seagreen3] +"checker/WcbvEval"[label="WcbvEval", color=seagreen3] +"checker/Checker"[label="Checker", color=seagreen3] +"checker/Substitution"[label="Substitution", color=seagreen3] +"checker/Weakening"[label="Weakening", color=seagreen3] +"checker/Closed"[label="Closed", color=seagreen3] +"checker/WeakeningEnv"[label="WeakeningEnv", color=seagreen3] +"checker/Generation"[label="Generation", color=seagreen3] +"template-coq/Loader" -> "template-coq/All" +"template-coq/Typing" -> "template-coq/All" +"template-coq/Constants" -> "template-coq/Loader" +"template-coq/All" -> "checker/All" +"checker/Retyping" -> "checker/All" +"checker/Substitution" -> "checker/All" +"template-coq/Typing" -> "checker/Checker" +"template-coq/common/uGraph" -> "checker/Checker" +"template-coq/Reflect" -> "checker/Closed" +"template-coq/TypingWf" -> "checker/Closed" +"checker/WeakeningEnv" -> "checker/Closed" +"template-coq/Reflect" -> "checker/Generation" +"template-coq/Typing" -> "checker/Generation" +"template-coq/Typing" -> "checker/Normal" +"checker/Checker" -> "checker/Retyping" +"checker/Generation" -> "checker/Substitution" +"checker/Weakening" -> "checker/Substitution" +"template-coq/Reflect" -> "checker/WcbvEval" +"template-coq/Typing" -> "checker/WcbvEval" +"template-coq/WfInv" -> "checker/WcbvEval" +"checker/Closed" -> "checker/Weakening" +"template-coq/Typing" -> "checker/WeakeningEnv" +"template-coq/utils/LibHypsNaming" -> "checker/WeakeningEnv" +"erasure/Erasure"[label="Erasure", color=tan] +"erasure/EOptimizePropDiscr"[label="EOptimizePropDiscr", color=tan] +"erasure/ErasureFunction"[label="ErasureFunction", color=tan] +"erasure/ErasureCorrectness"[label="ErasureCorrectness", color=tan] +"erasure/EArities"[label="EArities", color=tan] +"erasure/EInversion"[label="EInversion", color=tan] +"erasure/ESubstitution"[label="ESubstitution", color=tan] +"erasure/Prelim"[label="Prelim", color=tan] +"erasure/Extraction"[label="Extraction", color=tan] +"erasure/EAll"[label="EAll", color=tan] +"erasure/EDeps"[label="EDeps", color=tan] +"erasure/Extract"[label="Extract", color=tan] +"erasure/ETyping"[label="ETyping", color=tan] +"erasure/EWndEval"[label="EWndEval", color=tan] +"erasure/EWcbvEval"[label="EWcbvEval", color=tan] +"erasure/ECSubst"[label="ECSubst", color=tan] +"erasure/EPretty"[label="EPretty", color=tan] +"erasure/EReflect"[label="EReflect", color=tan] +"erasure/ELiftSubst"[label="ELiftSubst", color=tan] +"erasure/EInduction"[label="EInduction", color=tan] +"erasure/EAstUtils"[label="EAstUtils", color=tan] +"erasure/EAst"[label="EAst", color=tan] +"erasure/EWcbvEval" -> "erasure/EAll" +"erasure/EWndEval" -> "erasure/EAll" +"erasure/Extract" -> "erasure/EAll" +"pcuic/PCUICCanonicity" -> "erasure/EArities" +"pcuic/PCUICPrincipality" -> "erasure/EArities" +"erasure/Extract" -> "erasure/EArities" +"template-coq/Universes" -> "erasure/EAst" +"template-coq/Kernames" -> "erasure/EAstUtils" +"erasure/EAst" -> "erasure/EAstUtils" +"erasure/ELiftSubst" -> "erasure/ECSubst" +"erasure/ESubstitution" -> "erasure/EDeps" +"erasure/EAst" -> "erasure/EInduction" +"erasure/Prelim" -> "erasure/EInversion" +"erasure/EInduction" -> "erasure/ELiftSubst" +"erasure/ErasureFunction" -> "erasure/EOptimizePropDiscr" +"erasure/ETyping" -> "erasure/EPretty" +"pcuic/PCUICReflect" -> "erasure/EReflect" +"erasure/EInduction" -> "erasure/EReflect" +"erasure/Prelim" -> "erasure/ESubstitution" +"erasure/EAstUtils" -> "erasure/ETyping" +"erasure/ELiftSubst" -> "erasure/ETyping" +"erasure/EReflect" -> "erasure/ETyping" +"pcuic/PCUICWcbvEval" -> "erasure/EWcbvEval" +"erasure/ECSubst" -> "erasure/EWcbvEval" +"erasure/ETyping" -> "erasure/EWcbvEval" +"erasure/ETyping" -> "erasure/EWndEval" +"pcuic/TemplateToPCUIC" -> "erasure/Erasure" +"template-coq/Pretty" -> "erasure/Erasure" +"erasure/EOptimizePropDiscr" -> "erasure/Erasure" +"erasure/EPretty" -> "erasure/Erasure" +"erasure/EDeps" -> "erasure/ErasureCorrectness" +"erasure/EInversion" -> "erasure/ErasureCorrectness" +"safechecker/PCUICSafeRetyping" -> "erasure/ErasureFunction" +"erasure/ErasureCorrectness" -> "erasure/ErasureFunction" +"pcuic/PCUICElimination" -> "erasure/Extract" +"erasure/ETyping" -> "erasure/Extract" +"erasure/Erasure" -> "erasure/Extraction" +"safechecker/PCUICErrors" -> "erasure/Prelim" +"erasure/EArities" -> "erasure/Prelim" +"erasure/EWcbvEval" -> "erasure/Prelim" +"pcuic/PCUICToTemplateCorrectness"[label="PCUICToTemplateCorrectness", color=lemonchiffon1] +"pcuic/PCUICToTemplate"[label="PCUICToTemplate", color=lemonchiffon1] +"pcuic/TemplateToPCUICCorrectness"[label="TemplateToPCUICCorrectness", color=lemonchiffon1] +"pcuic/TemplateToPCUIC"[label="TemplateToPCUIC", color=lemonchiffon1] +"pcuic/PCUICSafeLemmata"[label="PCUICSafeLemmata", color=lemonchiffon1] +"pcuic/PCUICSigmaCalculus"[label="PCUICSigmaCalculus", color=lemonchiffon1] +"pcuic/PCUICPrincipality"[label="PCUICPrincipality", color=lemonchiffon1] +"pcuic/PCUICSN"[label="PCUICSN", color=lemonchiffon1] +"pcuic/PCUICElimination"[label="PCUICElimination", color=lemonchiffon1] +"pcuic/PCUICCumulProp"[label="PCUICCumulProp", color=lemonchiffon1] +"pcuic/PCUICPretty"[label="PCUICPretty", color=lemonchiffon1] +"pcuic/PCUICWcbvEval"[label="PCUICWcbvEval", color=lemonchiffon1] +"pcuic/PCUICCSubst"[label="PCUICCSubst", color=lemonchiffon1] 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color=lemonchiffon1] +"pcuic/PCUICNameless"[label="PCUICNameless", color=lemonchiffon1] +"pcuic/PCUICNormal"[label="PCUICNormal", color=lemonchiffon1] +"pcuic/PCUICPosition"[label="PCUICPosition", color=lemonchiffon1] +"pcuic/PCUICInversion"[label="PCUICInversion", color=lemonchiffon1] +"pcuic/PCUICGlobalEnv"[label="PCUICGlobalEnv", color=lemonchiffon1] +"pcuic/PCUICTyping"[label="PCUICTyping", color=lemonchiffon1] +"pcuic/PCUICUnivSubst"[label="PCUICUnivSubst", color=lemonchiffon1] +"pcuic/PCUICLiftSubst"[label="PCUICLiftSubst", color=lemonchiffon1] +"pcuic/PCUICReflect"[label="PCUICReflect", color=lemonchiffon1] +"pcuic/PCUICInduction"[label="PCUICInduction", color=lemonchiffon1] +"pcuic/PCUICAstUtils"[label="PCUICAstUtils", color=lemonchiffon1] +"pcuic/PCUICSize"[label="PCUICSize", color=lemonchiffon1] +"pcuic/PCUICAst"[label="PCUICAst", color=lemonchiffon1] +"pcuic/PCUICRelations"[label="PCUICRelations", color=lemonchiffon1] +"pcuic/PCUICUtils"[label="PCUICUtils", color=lemonchiffon1] +"pcuic/PCUICAstUtils" -> "pcuic/PCUICToTemplate" +"template-coq/TypingWf" -> "pcuic/PCUICToTemplateCorrectness" +"template-coq/WfInv" -> "pcuic/PCUICToTemplateCorrectness" +"pcuic/PCUICGeneration" -> "pcuic/PCUICToTemplateCorrectness" +"pcuic/PCUICToTemplate" -> "pcuic/PCUICToTemplateCorrectness" +"template-coq/TypingWf" -> "pcuic/TemplateToPCUICCorrectness" +"template-coq/WfInv" -> "pcuic/TemplateToPCUICCorrectness" +"pcuic/PCUICSubstitution" -> "pcuic/TemplateToPCUICCorrectness" +"pcuic/TemplateToPCUIC" -> "pcuic/TemplateToPCUICCorrectness" +} diff --git a/dependency-graph/depgraph-2020-11-28.png b/dependency-graph/depgraph-2020-11-28.png new file mode 100644 index 0000000000000000000000000000000000000000..bee4f97f04bee70cd51c5ef84b7788bf5fe47e74 GIT binary patch literal 1151726 zcmbrmby!u~7cLBf($Xc;-2&1L5}TBe5CQ21r5gmK8}%<;a9ke5m_7^qKB;o#sfK(a4X;owkN;Nb8)kRJh`cyss> z0)IR*l$Ut{cMJJ1voS9Y4vqp2^g>+SHTCbDo2UA5G>Dh5mJ 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+erasure/EInduction->erasure/EReflect + + + + + +erasure/EInduction->erasure/ELiftSubst + + + + + +erasure/EAstUtils->erasure/ETyping + + + + + +erasure/EAst->erasure/EInduction + + + + + +erasure/EAst->erasure/EAstUtils + + + + + +pcuic/PCUICToTemplate->pcuic/PCUICToTemplateCorrectness + + + + + diff --git a/erasure/_PluginProject.in b/erasure/_PluginProject.in index 51a2114a4..4a9aa57a8 100644 --- a/erasure/_PluginProject.in +++ b/erasure/_PluginProject.in @@ -83,14 +83,8 @@ src/pCUICSafeReduce.mli src/pCUICSafeReduce.ml # src/pCUICSafeConversion.mli # src/pCUICSafeConversion.ml -src/pCUICTypeChecker.mli -src/pCUICTypeChecker.ml -src/pCUICSafeChecker.mli -src/pCUICSafeChecker.ml src/pCUICSafeRetyping.ml src/pCUICSafeRetyping.mli -src/safeTemplateChecker.mli -src/safeTemplateChecker.ml # src/ssreflect.mli # src/ssreflect.ml diff --git a/erasure/src/g_metacoq_erasure.mlg b/erasure/src/g_metacoq_erasure.mlg index cb88f4803..2a545d0a5 100644 --- a/erasure/src/g_metacoq_erasure.mlg +++ b/erasure/src/g_metacoq_erasure.mlg @@ -7,7 +7,6 @@ open Stdarg open Pp open PeanoNat.Nat open Datatypes -open PCUICSafeChecker let pr_char c = str (Char.escaped c) diff --git a/erasure/src/metacoq_erasure_plugin.mlpack b/erasure/src/metacoq_erasure_plugin.mlpack index bb3b67945..9b773b89d 100644 --- a/erasure/src/metacoq_erasure_plugin.mlpack +++ b/erasure/src/metacoq_erasure_plugin.mlpack @@ -34,10 +34,7 @@ TemplateToPCUIC PCUICErrors PCUICUnivSubst PCUICSafeReduce -PCUICTypeChecker -PCUICSafeChecker PCUICSafeRetyping -SafeTemplateChecker EAst EAstUtils diff --git a/erasure/theories/EOptimizePropDiscr.v b/erasure/theories/EOptimizePropDiscr.v index 1f871b672..a507445a8 100644 --- a/erasure/theories/EOptimizePropDiscr.v +++ b/erasure/theories/EOptimizePropDiscr.v @@ -8,7 +8,6 @@ From MetaCoq.PCUIC Require Import PCUICAst PCUICAstUtils PCUICCumulativity PCUICSR PCUICSafeLemmata PCUICValidity PCUICPrincipality PCUICElimination PCUICSN. -From MetaCoq.SafeChecker Require Import PCUICSafeReduce PCUICSafeChecker PCUICSafeRetyping. From MetaCoq.Erasure Require Import EAstUtils EArities Extract Prelim ErasureCorrectness EDeps ErasureFunction ELiftSubst. diff --git a/erasure/theories/Erasure.v b/erasure/theories/Erasure.v index 0a0fe60ff..308c1e0c2 100644 --- a/erasure/theories/Erasure.v +++ b/erasure/theories/Erasure.v @@ -3,12 +3,10 @@ From Coq Require Import Program. From MetaCoq.Template Require Import config utils uGraph Pretty. From MetaCoq.PCUIC Require Import PCUICAst PCUICAstUtils PCUICTyping TemplateToPCUIC. -From MetaCoq.SafeChecker Require Import PCUICErrors PCUICSafeReduce PCUICSafeChecker - SafeTemplateChecker. +From MetaCoq.SafeChecker Require Import PCUICErrors. From MetaCoq.Erasure Require Import EAstUtils ErasureFunction EPretty. From MetaCoq.Erasure Require ErasureFunction EOptimizePropDiscr. -Existing Instance envcheck_monad. Existing Instance extraction_checker_flags. (** This is a hack to avoid having to handle template polymorphism and make @@ -159,7 +157,6 @@ Local Open Scope string_scope. (** This uses the retyping-based erasure *) Program Definition erase_and_print_template_program {cf : checker_flags} (p : Ast.program) : string := - let p := fix_program_universes p in let (Σ', t) := erase_template_program p in "Environment is well-formed and " ^ Pretty.print_term (Ast.empty_ext p.1) [] true p.2 ^ " erases to: " ^ nl ^ print_term Σ' [] true false t. diff --git a/safechecker/theories/SafeTemplateChecker.v b/safechecker/theories/SafeTemplateChecker.v index e0f230ec5..18bc180ef 100644 --- a/safechecker/theories/SafeTemplateChecker.v +++ b/safechecker/theories/SafeTemplateChecker.v @@ -12,6 +12,7 @@ Program Definition infer_template_program {cf : checker_flags} (p : Ast.program) p <- typecheck_program (cf:=cf) (trans_global_decls p.1, trans p.2) φ Hφ ;; ret (p.π1 ; _). +(* (** In Coq until 8.10, programs can be ill-formed w.r.t. universes as they don't include all declarations of universes and constraints coming from section variable declarations. We hence write a program that computes the dangling universes in an Ast.program and registers @@ -96,10 +97,9 @@ Definition fix_global_env_universes (Σ : Ast.global_env) : Ast.global_env := Definition fix_program_universes (p : Ast.program) : Ast.program := let '(Σ, t) := p in (fix_global_env_universes Σ, t). - +*) Program Definition infer_and_print_template_program {cf : checker_flags} (p : Ast.program) φ Hφ : string + string := - let p := fix_program_universes p in match infer_template_program (cf:=cf) p φ Hφ return string + string with | CorrectDecl t => inl ("Environment is well-formed and " ^ string_of_term (trans p.2) ^ From a39dff31ba7dda1531e32f4683664cd3f5a8c4e8 Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Tue, 1 Dec 2020 14:39:53 +0100 Subject: [PATCH 21/70] Some defs were blocking execution inside coq --- Makefile | 2 +- pcuic/theories/PCUICCumulativity.v | 1 + template-coq/theories/utils/MCPrelude.v | 1 + test-suite/erasure_live_test.v | 19 ------------------- 4 files changed, 3 insertions(+), 20 deletions(-) diff --git a/Makefile b/Makefile index ad2c5d82a..89b059dd3 100644 --- a/Makefile +++ b/Makefile @@ -90,7 +90,7 @@ cleanplugins: ci-local: ./configure.sh local - $(MAKE) all test-suite TIMED=pretty-timed + $(MAKE) all test-suite ci-opam: # Use -v so that regular output is produced diff --git a/pcuic/theories/PCUICCumulativity.v b/pcuic/theories/PCUICCumulativity.v index 0d55590d5..9d453ce23 100644 --- a/pcuic/theories/PCUICCumulativity.v +++ b/pcuic/theories/PCUICCumulativity.v @@ -53,6 +53,7 @@ Section ConvCumulDefs. End ConvCumulDefs. +(* todo mode typing notation *) Reserved Notation " Σ ;;; Γ |- t : T " (at level 50, Γ, t, T at next level). Reserved Notation " Σ ;;; Γ |- t <= u " (at level 50, Γ, t, u at next level). Reserved Notation " Σ ;;; Γ |- t = u " (at level 50, Γ, t, u at next level). diff --git a/template-coq/theories/utils/MCPrelude.v b/template-coq/theories/utils/MCPrelude.v index 6c3fa2b1d..81f3ffe07 100644 --- a/template-coq/theories/utils/MCPrelude.v +++ b/template-coq/theories/utils/MCPrelude.v @@ -1,5 +1,6 @@ Require Import String ZArith Lia. From Equations Require Import Equations. +Set Equations Transparent. Derive NoConfusion EqDec for Strings.Ascii.ascii string positive Z. diff --git a/test-suite/erasure_live_test.v b/test-suite/erasure_live_test.v index b82cd6676..02b4cf88d 100644 --- a/test-suite/erasure_live_test.v +++ b/test-suite/erasure_live_test.v @@ -13,25 +13,6 @@ Definition test (p : Ast.program) : string := MetaCoq Quote Recursively Definition zero := 0. -(* Definition zerocst_test : ∑ s, test zero = s. -Proof. - eexists. - unfold test, erase_and_print_template_program. - set(e := fix_program_universes zero). - cbn in e. - unfold erase_template_program. - set (foo := ErasureFunction.erase _ _ _ _ _). - hnf in foo. - unfold ErasureFunction.is_erasable in foo. - set (isa := ErasureFunction.is_arity _ _ _ _ _ _) in *. - hnf in isa. - set (rs := PCUICTypeChecker.reduce_to_sort _ _ _ _) in *. - elimtype False. clear foo isa. - hnf in rs. - - - simpl in foo. *) - Definition zerocst := Eval lazy in test zero. MetaCoq Quote Recursively Definition exproof := I. From 49f9f734588691eca0ff6d37b0b2a6d9fe41d757 Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Wed, 2 Dec 2020 18:13:47 +0100 Subject: [PATCH 22/70] Fix pr_char_list in safechecker to not use Scanf.unescaped, and add back fixing of universes, still needed in 8.11 --- safechecker/src/g_metacoq_safechecker.mlg | 13 ++++++++++++- safechecker/theories/SafeTemplateChecker.v | 6 +++--- 2 files changed, 15 insertions(+), 4 deletions(-) diff --git a/safechecker/src/g_metacoq_safechecker.mlg b/safechecker/src/g_metacoq_safechecker.mlg index 599c8641e..06637500b 100644 --- a/safechecker/src/g_metacoq_safechecker.mlg +++ b/safechecker/src/g_metacoq_safechecker.mlg @@ -9,7 +9,18 @@ open PeanoNat.Nat open Datatypes open PCUICSafeChecker -let pr_char_list l = str (Scanf.unescaped (Tm_util.list_to_string l)) +let bytes_of_list l = + let bytes = Bytes.create (List.length l) in + let rec fill acc = function + | [] -> bytes + | c :: cs -> + Bytes.set bytes acc c; + fill (1 + acc) cs + in fill 0 l + +let pr_char_list l = + (* We allow utf8 encoding *) + str (Bytes.to_string (bytes_of_list l)) let time prefix f x = let start = Unix.gettimeofday () in diff --git a/safechecker/theories/SafeTemplateChecker.v b/safechecker/theories/SafeTemplateChecker.v index 18bc180ef..737e3f9d6 100644 --- a/safechecker/theories/SafeTemplateChecker.v +++ b/safechecker/theories/SafeTemplateChecker.v @@ -12,8 +12,7 @@ Program Definition infer_template_program {cf : checker_flags} (p : Ast.program) p <- typecheck_program (cf:=cf) (trans_global_decls p.1, trans p.2) φ Hφ ;; ret (p.π1 ; _). -(* -(** In Coq until 8.10, programs can be ill-formed w.r.t. universes as they don't include +(** In Coq until 8.11 at least, programs can be ill-formed w.r.t. universes as they don't include all declarations of universes and constraints coming from section variable declarations. We hence write a program that computes the dangling universes in an Ast.program and registers them appropriately. *) @@ -97,9 +96,10 @@ Definition fix_global_env_universes (Σ : Ast.global_env) : Ast.global_env := Definition fix_program_universes (p : Ast.program) : Ast.program := let '(Σ, t) := p in (fix_global_env_universes Σ, t). -*) + Program Definition infer_and_print_template_program {cf : checker_flags} (p : Ast.program) φ Hφ : string + string := + let p := fix_program_universes p in match infer_template_program (cf:=cf) p φ Hφ return string + string with | CorrectDecl t => inl ("Environment is well-formed and " ^ string_of_term (trans p.2) ^ From 74084cd541ffb2976f9d2ec7d095f6cb81042bce Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Wed, 2 Dec 2020 21:09:45 +0100 Subject: [PATCH 23/70] Clean Erasure.v to use "todos" only for the ultimate definition for testing erasure. --- erasure/theories/Erasure.v | 151 ++-------- pcuic/theories/TemplateToPCUICCorrectness.v | 317 +++++++++++++++----- 2 files changed, 261 insertions(+), 207 deletions(-) diff --git a/erasure/theories/Erasure.v b/erasure/theories/Erasure.v index 308c1e0c2..4defe8095 100644 --- a/erasure/theories/Erasure.v +++ b/erasure/theories/Erasure.v @@ -1,137 +1,20 @@ (* Distributed under the terms of the MIT license. *) From Coq Require Import Program. -From MetaCoq.Template Require Import config utils uGraph Pretty. +From MetaCoq.Template Require Import config utils uGraph Pretty Environment Typing. From MetaCoq.PCUIC Require Import PCUICAst PCUICAstUtils PCUICTyping - TemplateToPCUIC. + TemplateToPCUIC TemplateToPCUICCorrectness. From MetaCoq.SafeChecker Require Import PCUICErrors. From MetaCoq.Erasure Require Import EAstUtils ErasureFunction EPretty. From MetaCoq.Erasure Require ErasureFunction EOptimizePropDiscr. Existing Instance extraction_checker_flags. -(** This is a hack to avoid having to handle template polymorphism and make - erasure fast: we actually admit the proof of wf Σ and never build it. *) - -Definition assume_wf_decl {cf : checker_flags} (Σ : global_env_ext) : - ∥ wf Σ ∥ -> - ∥ on_udecl Σ.1 Σ.2 ∥ -> - forall G : universes_graph, - is_graph_of_uctx G (global_ext_uctx Σ) -> - forall kn (d : global_decl), EnvCheck (∥ on_global_decl (lift_typing typing) Σ kn d ∥). -Proof. - intros. apply CorrectDecl. constructor. todo "assumed correct global declaration". -Defined. - -Definition assume_fresh id env : EnvCheck (∥ fresh_global id env ∥). -Proof. - left. todo "assumed fresh". -Defined. - -Program Definition compute_udecl (id : string) (Σ : global_env) (HΣ : ∥ wf Σ ∥) G - (HG : is_graph_of_uctx G (global_uctx Σ)) (udecl : universes_decl) - : EnvCheck (∑ uctx', gc_of_uctx (uctx_of_udecl udecl) = Some uctx' /\ - ∥ on_udecl Σ udecl ∥) := - match gc_of_uctx (uctx_of_udecl udecl) with - | Some uctx => ret (uctx; conj _ _) - | None => raise (empty_ext Σ, IllFormedDecl id (Msg "constraints not satisfiable")) - end. - Next Obligation. - constructor. todo "assume udecl is ok". - Defined. - -Program Fixpoint check_wf_env_only_univs (Σ : global_env) - : EnvCheck (∑ G, (is_graph_of_uctx G (global_uctx Σ) /\ ∥ wf Σ ∥)) := - match Σ with - | nil => ret (init_graph; _) - | d :: Σ => - G <- check_wf_env_only_univs Σ ;; - assume_fresh d.1 Σ ;; - let udecl := universes_decl_of_decl d.2 in - uctx <- compute_udecl (string_of_kername d.1) Σ _ G.π1 (proj1 G.π2) udecl ;; - let G' := add_uctx uctx.π1 G.π1 in - assume_wf_decl (Σ, udecl) _ _ G' _ d.1 d.2 ;; - match udecl with - | Monomorphic_ctx _ => ret (G'; _) - | Polymorphic_ctx _ => ret (G.π1; _) - end - end. - Next Obligation. - repeat constructor. - Qed. - Next Obligation. - sq. unfold is_graph_of_uctx, gc_of_uctx; simpl. - unfold gc_of_uctx in e. simpl in e. - case_eq (gc_of_constraints (constraints_of_udecl (universes_decl_of_decl g))); - [|intro HH; rewrite HH in e; discriminate e]. - intros ctrs' Hctrs'. rewrite Hctrs' in e. - cbn in e. inversion e; subst; clear e. - unfold global_ext_constraints; simpl. - pose proof (gc_of_constraints_union - (constraints_of_udecl (universes_decl_of_decl g)) (global_constraints Σ)). - rewrite Hctrs' in H0. simpl in H0. - red in i. unfold gc_of_uctx in i; simpl in i. - case_eq (gc_of_constraints (global_constraints Σ)); - [|intro HH; rewrite HH in i; cbn in i; contradiction i]. - intros Σctrs HΣctrs; rewrite HΣctrs in H0, i; simpl in *. - destruct (gc_of_constraints (ConstraintSet.union _ _)). - simpl in H0. - subst G. unfold global_ext_levels; simpl. - symmetry. rewrite add_uctx_make_graph. - apply graph_eq. simpl. reflexivity. - simpl. now rewrite H0. simpl. reflexivity. - now simpl in H0. - Qed. - Next Obligation. - split; sq. 2: constructor; tas. - unfold is_graph_of_uctx, gc_of_uctx; simpl. - unfold gc_of_uctx in e. simpl in e. - case_eq (gc_of_constraints (constraints_of_udecl (universes_decl_of_decl g))); - [|intro HH; rewrite HH in e; discriminate e]. - intros ctrs' Hctrs'. rewrite Hctrs' in e. - cbn in e. inversion e; subst; clear e. - unfold global_ext_constraints; simpl. - pose proof (gc_of_constraints_union - (constraints_of_udecl (universes_decl_of_decl g)) (global_constraints Σ)). - rewrite Hctrs' in H1; simpl in H1. - red in i. unfold gc_of_uctx in i; simpl in i. - assert (eq: monomorphic_constraints_decl g - = constraints_of_udecl (universes_decl_of_decl g)). { - destruct g. destruct c, cst_universes; try discriminate; reflexivity. - destruct m, ind_universes; try discriminate; reflexivity. } - rewrite eq; clear eq. - case_eq (gc_of_constraints (global_constraints Σ)); - [|intro HH; rewrite HH in i; cbn in i; contradiction i]. - intros Σctrs HΣctrs; rewrite HΣctrs in H1, i; simpl in *. - destruct (gc_of_constraints (ConstraintSet.union _ _)). - simpl in H1. - subst G. unfold global_ext_levels; simpl. - assert (eq: monomorphic_levels_decl g - = levels_of_udecl (universes_decl_of_decl g)). { - destruct g. destruct c, cst_universes; try discriminate; reflexivity. - destruct m, ind_universes; try discriminate; reflexivity. } - rewrite eq. simpl. rewrite add_uctx_make_graph. - apply graph_eq; try reflexivity. - simpl. now rewrite H1. - now simpl in H1. - Qed. - Next Obligation. - split; sq. 2: constructor; tas. - unfold global_uctx; simpl. - assert (eq1: monomorphic_levels_decl g = LevelSet.empty). { - destruct g. destruct c, cst_universes; try discriminate; reflexivity. - destruct m, ind_universes; try discriminate; reflexivity. } - rewrite eq1; clear eq1. - assert (eq1: monomorphic_constraints_decl g = ConstraintSet.empty). { - destruct g. destruct c, cst_universes; try discriminate; reflexivity. - destruct m, ind_universes; try discriminate; reflexivity. } - rewrite eq1; clear eq1. - now rewrite LevelSet_union_empty, CS_union_empty. - Qed. - (* This is the total erasure function + the optimization that removes all pattern-matches on propositions. *) Program Definition erase_template_program (p : Ast.program) + (wfΣ : ∥ Typing.wf_ext (Ast.empty_ext p.1) ∥) + (wt : ∥ ∑ T, Typing.typing (Ast.empty_ext p.1) [] p.2 T ∥) : (EAst.global_context * EAst.term) := let Σ := (trans_global (Ast.empty_ext p.1)).1 in let t := ErasureFunction.erase (empty_ext Σ) _ nil (trans p.2) _ in @@ -139,24 +22,28 @@ Program Definition erase_template_program (p : Ast.program) (EOptimizePropDiscr.optimize_env Σ', EOptimizePropDiscr.optimize Σ' t). Next Obligation. - unfold trans_global. - simpl. unfold wf_ext, empty_ext. simpl. - unfold on_global_env_ext. constructor. todo "assuming wf environment". -Defined. + sq. + apply (template_to_pcuic_env (Ast.empty_ext p.1) wfΣ). +Qed. Next Obligation. - unfold trans_global. - simpl. unfold wf_ext, empty_ext. simpl. - unfold on_global_env_ext. todo "assuming well-typedness". + sq. destruct wt as [T Ht]. exists (trans T). + change (@nil context_decl) with (trans_local []). + change (empty_ext (trans_global_decls p.1)) with (trans_global (Ast.empty_ext p.1)). + eapply template_to_pcuic_typing; simpl. apply wfΣ. + apply Ht. Defined. Next Obligation. - constructor. todo "assuming wf environment". + sq. apply (template_to_pcuic_env (Ast.empty_ext p.1) wfΣ). Defined. Local Open Scope string_scope. -(** This uses the retyping-based erasure *) +(** This uses the retyping-based erasure and assumes that the global environment and term + are welltyped (for speed). As such this should only be used for testing, or when we know that + the environment is wellformed and the term well-typed (e.g. when it comes directly from a + Coq definition). *) Program Definition erase_and_print_template_program {cf : checker_flags} (p : Ast.program) : string := - let (Σ', t) := erase_template_program p in - "Environment is well-formed and " ^ Pretty.print_term (Ast.empty_ext p.1) [] true p.2 ^ + let (Σ', t) := erase_template_program p (todo "wf_env") (todo "welltyped") in + Pretty.print_term (Ast.empty_ext p.1) [] true p.2 ^ nl ^ " erases to: " ^ nl ^ print_term Σ' [] true false t. diff --git a/pcuic/theories/TemplateToPCUICCorrectness.v b/pcuic/theories/TemplateToPCUICCorrectness.v index 9fa9a87bb..b2eff5476 100644 --- a/pcuic/theories/TemplateToPCUICCorrectness.v +++ b/pcuic/theories/TemplateToPCUICCorrectness.v @@ -8,13 +8,12 @@ Set Warnings "+notation-overridden". From Equations.Prop Require Import DepElim. +Implicit Types cf : checker_flags. Module T := Template.Ast. Module TTy := Template.Typing. Module TEnv := Template.Ast.TemplateEnvironment. -Local Existing Instance default_checker_flags. - Module TL := Template.LiftSubst. Lemma mkApps_morphism (f : term -> term) u v : @@ -59,7 +58,7 @@ Proof. rewrite mkApps_app. reflexivity. Qed. -Lemma trans_mkApps u v : T.wf u -> List.Forall T.wf v -> +Lemma trans_mkApps u v : trans (T.mkApps u v) = mkApps (trans u) (List.map trans v). Proof. revert u; induction v. @@ -68,16 +67,12 @@ Proof. rewrite <- Template.LiftSubst.mkApps_mkApp; auto. rewrite IHv. simpl. f_equal. apply trans_mkApp. - - apply Template.LiftSubst.wf_mkApp; auto. inversion_clear H0. auto. - inversion_clear H0. auto. Qed. -Lemma trans_subst t k u : All T.wf t -> T.wf u -> +Lemma trans_subst t k u : trans (TL.subst t k u) = subst (map trans t) k (trans u). Proof. - intros wft wfu. - revert k. induction wfu using Template.Induction.term_wf_forall_list_ind; simpl; intros; try congruence. + revert k. induction u using Template.Induction.term_forall_list_ind; simpl; intros; try congruence. - repeat nth_leb_simpl; auto. rewrite trans_lift. @@ -86,11 +81,9 @@ Proof. - f_equal; solve_list. - - rewrite subst_mkApps. rewrite <- IHwfu. + - rewrite subst_mkApps. rewrite <- IHu. rewrite trans_mkApps. f_equal. solve_list. - apply Template.LiftSubst.wf_subst; auto. - solve_all. solve_all. apply Template.LiftSubst.wf_subst; auto. solve_all. - f_equal; auto; solve_list. - f_equal; auto; solve_list. @@ -266,7 +259,6 @@ Proof. erewrite <- IHparams. f_equal. 5:eauto. simpl. rewrite trans_subst; auto. inv Hparams. red in H. simpl in H. intuition auto. - now (inv Hparams). constructor; auto. inv Hparams; red in H; simpl in H; intuition auto. apply Template.LiftSubst.wf_subst; auto. solve_all. @@ -306,8 +298,6 @@ Proof. rewrite map_rev in e. rewrite e. f_equal. symmetry. apply trans_subst. - - apply Forall_All. assumption. - - assumption. Qed. Lemma trans_it_mkProd_or_LetIn ctx t : @@ -530,7 +520,7 @@ Qed. Derive Signature for TTy.eq_term_upto_univ. -Lemma leq_term_mkApps Σ ϕ t u t' u' : +Lemma leq_term_mkApps {cf} Σ ϕ t u t' u' : eq_term Σ ϕ t t' -> All2 (eq_term Σ ϕ) u u' -> leq_term Σ ϕ (mkApps t u) (mkApps t' u'). Proof. @@ -574,7 +564,7 @@ Proof. Qed. (* TODO update Template Coq's eq_term to reflect PCUIC's cumulativity *) -Lemma trans_eq_term_upto_univ : +Lemma trans_eq_term_upto_univ {cf} : forall Σ Re Rle t u napp, T.wf t -> T.wf u -> @@ -710,7 +700,7 @@ Admitted. intuition eauto. Qed. *) -Lemma trans_leq_term Σ ϕ T U : +Lemma trans_leq_term {cf} Σ ϕ T U : T.wf T -> T.wf U -> TTy.leq_term ϕ T U -> leq_term Σ ϕ (trans T) (trans U). Proof. @@ -718,7 +708,7 @@ Proof. eapply trans_eq_term_upto_univ ; eauto. Qed. -Lemma trans_eq_term Σ φ t u : +Lemma trans_eq_term {cf} Σ φ t u : T.wf t -> T.wf u -> TTy.eq_term φ t u -> eq_term Σ φ (trans t) (trans u). Proof. @@ -726,7 +716,7 @@ Proof. eapply trans_eq_term_upto_univ ; eauto. Qed. -Lemma trans_eq_term_list : +Lemma trans_eq_term_list {cf}: forall Σ φ l l', List.Forall T.wf l -> List.Forall T.wf l' -> @@ -763,20 +753,13 @@ Proof. simpl in *. congruence. Qed. -Lemma trans_iota_red pars ind c u args brs : - T.wf (Template.Ast.mkApps (Template.Ast.tConstruct ind c u) args) -> - List.Forall (T.wf ∘ snd) brs -> +Lemma trans_iota_red pars c args brs : trans (TTy.iota_red pars c args brs) = iota_red pars c (List.map trans args) (List.map (on_snd trans) brs). Proof. - unfold TTy.iota_red, iota_red. intros wfapp wfbrs. + unfold TTy.iota_red, iota_red. rewrite trans_mkApps. - - - induction wfbrs in c |- *. - destruct c; simpl; constructor. - destruct c; simpl; try constructor; auto with wf. - - apply wf_mkApps_napp in wfapp. solve_all. apply All_skipn. solve_all. constructor. - - f_equal. induction brs in c |- *; simpl; destruct c; trivial. + f_equal. induction brs in c |- *; simpl; destruct c; trivial. now rewrite map_skipn. Qed. @@ -801,10 +784,7 @@ Proof. destruct (Ast.isLambda (dbody d)); [|discriminate]. intros [= <- <-]. simpl. repeat f_equal. - rewrite trans_subst. clear Hdef. - unfold TTy.fix_subst. generalize mfix at 2. - induction mfix0. constructor. simpl. repeat (constructor; auto). - apply (nth_error_forall Hdef) in wffix. simpl in wffix; intuition. + rewrite trans_subst. f_equal. clear Hdef. unfold fix_subst, TTy.fix_subst. rewrite map_length. generalize mfix at 1 3. @@ -821,10 +801,7 @@ Proof. unfold TTy.unfold_cofix, unfold_cofix. intros wffix. rewrite nth_error_map. destruct (nth_error mfix idx) eqn:Hdef. intros [= <- <-]. simpl. repeat f_equal. - rewrite trans_subst. clear Hdef. - unfold TTy.cofix_subst. generalize mfix at 2. - induction mfix0. constructor. simpl. repeat (constructor; auto). - apply (nth_error_forall Hdef) in wffix. simpl in wffix; intuition. + rewrite trans_subst. f_equal. clear Hdef. unfold cofix_subst, TTy.cofix_subst. rewrite map_length. generalize mfix at 1 3. @@ -860,7 +837,7 @@ Proof. Qed. Ltac wf_inv H := try apply wf_inv in H; simpl in H; rdest. -Lemma trans_red1 Σ Γ T U : +Lemma trans_red1 {cf} Σ Γ T U : TTy.on_global_env (fun Σ => wf_decl_pred) Σ -> List.Forall wf_decl Γ -> T.wf T -> @@ -872,8 +849,7 @@ Proof. try solve [econstructor; eauto]. - simpl. wf_inv H1. apply Forall_All in H2. inv H2. - rewrite trans_mkApps; auto. apply Template.LiftSubst.wf_subst; auto with wf; solve_all. - apply All_Forall. auto. + rewrite trans_mkApps; auto. rewrite trans_subst; auto. apply red1_mkApps_l. constructor. - rewrite trans_subst; eauto. repeat constructor. @@ -1009,16 +985,21 @@ Proof. + simpl. inversion b0. reflexivity. Qed. +Lemma global_levels_trans Σ + : global_levels (trans_global_decls Σ) = TTy.global_levels Σ. +Proof. + induction Σ; simpl; auto. + rewrite IHΣ. f_equal. clear. + destruct a as [? []]; reflexivity. +Qed. + Lemma global_ext_levels_trans Σ : global_ext_levels (trans_global Σ) = TTy.global_ext_levels Σ. Proof. destruct Σ. unfold trans_global, TTy.global_ext_levels, global_ext_levels; simpl. f_equal. clear u. - induction g. - - reflexivity. - - simpl. rewrite IHg. f_equal. clear. - destruct a as [? []]; reflexivity. + now rewrite global_levels_trans. Qed. Lemma global_ext_constraints_trans Σ @@ -1033,7 +1014,7 @@ Proof. destruct a as [? []]; reflexivity. Qed. -Lemma trans_cumul (Σ : Ast.global_env_ext) Γ T U : +Lemma trans_cumul {cf} (Σ : Ast.global_env_ext) Γ T U : TTy.on_global_env (fun Σ => wf_decl_pred) Σ -> List.Forall wf_decl Γ -> T.wf T -> T.wf U -> TTy.cumul Σ Γ T U -> @@ -1057,7 +1038,7 @@ Definition Tlift_typing (P : Template.Ast.global_env_ext -> Tcontext -> Tterm -> | None => { s : Universe.t & P Σ Γ t (T.tSort s) } end. -Lemma trans_wf_local: +Lemma trans_wf_local {cf}: forall (Σ : Template.Ast.global_env_ext) (Γ : Tcontext) (wfΓ : TTy.wf_local Σ Γ), let P := (fun Σ0 (Γ0 : Tcontext) _ (t T : Tterm) _ => @@ -1075,7 +1056,7 @@ Proof. - simpl. constructor; auto. red. destruct tu. exists x. auto. Qed. -Lemma trans_wf_local_env Σ Γ : +Lemma trans_wf_local_env {cf} Σ Γ : TTy.All_local_env (TTy.lift_typing (fun (Σ : Ast.global_env_ext) (Γ : Tcontext) (b ty : Tterm) => @@ -1093,7 +1074,7 @@ Proof. red. red in t1. destruct t1. eapply t2. Qed. -Lemma typing_wf_wf: +Lemma typing_wf_wf {cf}: forall (Σ : Template.Ast.global_env_ext), TTy.wf Σ -> TTy.Forall_decls_typing @@ -1124,12 +1105,17 @@ Admitted. Hint Resolve trans_wf_local : trans. +Lemma context_assumptions_map ctx : context_assumptions (map trans_decl ctx) = Ast.context_assumptions ctx. +Proof. + induction ctx as [|[na [b|] ty] ctx]; simpl; auto. +Qed. + Axiom fix_guard_trans : forall Σ Γ mfix, TTy.fix_guard mfix -> fix_guard Σ Γ (map (map_def trans trans) mfix). -Lemma isWFArity_wf (Σ : Ast.global_env_ext) Γ T : Typing.wf Σ -> TTy.isWfArity TTy.typing Σ Γ T -> T.wf T. +Lemma isWFArity_wf {cf} (Σ : Ast.global_env_ext) Γ T : Typing.wf Σ -> TTy.isWfArity TTy.typing Σ Γ T -> T.wf T. Proof. intros wfΣ []. destruct s as [s [eq wf]]. @@ -1145,14 +1131,10 @@ Proof. eapply typing_wf; eauto. constructor. Qed. -Theorem template_to_pcuic (Σ : T.global_env_ext) Γ t T : - TTy.wf Σ -> - TTy.typing Σ Γ t T -> - typing (trans_global Σ) (trans_local Γ) (trans t) (trans T). +Theorem template_to_pcuic {cf} : + TTy.env_prop (fun Σ Γ t T => + typing (trans_global Σ) (trans_local Γ) (trans t) (trans T)). Proof. - intros X X0. - pose proof (TTy.typing_wf_local X0). - revert Σ X Γ X1 t T X0. apply (TTy.typing_ind_env (fun Σ Γ t T => typing (trans_global Σ) (trans_local Γ) (trans t) (trans T) )%type). @@ -1195,7 +1177,7 @@ Proof. eapply Forall_impl. eapply TypingWf.typing_all_wf_decl; eauto. intros. auto. eapply typing_wf in ty; eauto. destruct ty as [wfhd _]. - rewrite trans_subst in IHX1; eauto with wf. now inv wfAB. + rewrite trans_subst in IHX1; eauto with wf. eapply IHX1. apply Template.LiftSubst.wf_subst; try constructor; auto. now inv wfAB. - rewrite trans_subst_instance_constr. @@ -1213,21 +1195,14 @@ Proof. - pose proof (forall_decls_declared_constructor _ _ _ _ _ isdecl). unfold TTy.type_of_constructor in *. rewrite trans_subst. - -- apply Forall_All. apply wf_inds. - -- apply wf_subst_instance_constr. - eapply declared_constructor_wf in isdecl; eauto with wf. - eauto with wf trans. - apply typing_wf_wf; auto. - -- rewrite trans_subst_instance_constr. - rewrite trans_inds. simpl. - eapply refine_type. econstructor; eauto with trans. admit. - unfold type_of_constructor. simpl. f_equal. f_equal. - destruct cdecl as [[id t] p]; simpl; auto. + rewrite trans_subst_instance_constr. + rewrite trans_inds. simpl. + eapply refine_type. econstructor; eauto with trans. admit. + unfold type_of_constructor. simpl. f_equal. f_equal. + destruct cdecl as [[id t] p]; simpl; auto. - rewrite trans_mkApps; auto with wf trans. apply typing_wf in X1; intuition auto. solve_all. apply typing_wf in X3; auto. intuition auto. - apply wf_mkApps_inv in H4. - apply All_app_inv. apply All_skipn. solve_all. constructor; auto. rewrite map_app map_skipn. eapply type_Case. apply forall_decls_declared_inductive; eauto. destruct mdecl; auto. @@ -1236,7 +1211,6 @@ Proof. -- eapply X2. -- rewrite global_ext_constraints_trans; exact H1. -- rewrite trans_mkApps in X4; auto with wf. - eapply typing_wf in X3; auto. intuition. eapply wf_mkApps_inv in H4; auto. -- admit. -- apply trans_build_branches_type in H2. rewrite firstn_map. exact H2. @@ -1248,12 +1222,10 @@ Proof. eapply forall_decls_declared_projection in isdecl. destruct (typing_wf _ wfΣ _ _ _ X1) as [wfc wfind]. eapply wf_mkApps_inv in wfind; auto. - rewrite trans_subst; auto with wf. constructor; solve_all. - apply wf_subst_instance_constr, H0. - eapply typing_wf_wf; auto. + rewrite trans_subst; auto with wf. simpl. rewrite map_rev. rewrite trans_subst_instance_constr. eapply (type_Proj _ _ _ _ _ _ _ (arity, trans ty)). eauto. - rewrite trans_mkApps in X2; auto. constructor. rewrite map_length. + rewrite trans_mkApps in X2; auto. rewrite map_length. destruct mdecl; auto. - eapply refine_type. @@ -1324,3 +1296,198 @@ Proof. clear X. apply typing_all_wf_decl in wfΓ; auto. eapply typing_wf in X0; eauto. destruct X0. auto. Admitted. + +Theorem template_to_pcuic_typing {cf} Σ Γ t T : + TTy.wf Σ.1 -> + TTy.typing Σ Γ t T -> + typing (trans_global Σ) (trans_local Γ) (trans t) (trans T). +Proof. + intros wf ty. + apply (TTy.env_prop_typing _ template_to_pcuic _ wf); auto. + now eapply TTy.typing_wf_local. +Qed. + +Lemma Alli_map {A B} (P : nat -> B -> Type) n (f : A -> B) l : + Alli (fun n x => P n (f x)) n l -> + Alli P n (map f l). +Proof. + induction 1; constructor; auto. +Qed. + +Definition trans_constructor_shape (t : TTy.constructor_shape) : constructor_shape := + {| cshape_args := trans_local t.(TTy.cshape_args); + cshape_indices := map trans t.(TTy.cshape_indices); + cshape_sorts := t.(TTy.cshape_sorts) |}. + +Lemma trans_reln l p Γ : map trans (TemplateEnvironment.reln l p Γ) = + PCUICEnvironment.reln (map trans l) p (trans_local Γ). +Proof. + induction Γ as [|[na [b|] ty] Γ] in l, p |- *; simpl; auto. + now rewrite IHΓ. +Qed. + +Lemma trans_arities_context m : trans_local (Ast.arities_context (Ast.ind_bodies m)) = + arities_context (map trans_one_ind_body (Ast.ind_bodies m)). +Proof. + rewrite /trans_local /Ast.arities_context rev_map_spec map_rev map_map_compose + /PCUICEnvironment.arities_context rev_map_spec map_map_compose /= //. +Qed. + +Lemma trans_lift_context n k Γ : lift_context n k (trans_local Γ) = + trans_local (LiftSubst.lift_context n k Γ). +Proof. + rewrite /lift_context /LiftSubst.lift_context /fold_context /Ast.fold_context. + rewrite /trans_local map_rev map_mapi -List.map_rev mapi_map. + f_equal. apply mapi_ext. intros ? [na [b|] ty]; simpl; rewrite /trans_decl /= /map_decl; simpl; + f_equal; now rewrite trans_lift. +Qed. + +Lemma trans_subst_telescope s k Γ : + map trans_decl (LiftSubst.subst_telescope s k Γ) = + subst_telescope (map trans s) k (map trans_decl Γ). +Proof. + rewrite /subst_telescope /LiftSubst.subst_telescope. + rewrite map_mapi mapi_map. + apply mapi_ext => n [na [b|] ty] /=; + rewrite /map_decl /=; f_equal; + now rewrite trans_subst. +Qed. + +Lemma trans_on_global_env `{checker_flags} Σ P Q : + (forall Σ Γ t T, TTy.on_global_env P Σ.1 -> P Σ Γ t T -> Q (trans_global Σ) (trans_local Γ) (trans t) (option_map trans T)) -> + TTy.on_global_env P Σ -> on_global_env Q (trans_global_decls Σ). +Proof. + intros X X0. + simpl in *. induction X0; simpl; constructor; auto. + - red in f |- *. apply Forall_map. + solve_all. + - simpl. subst udecl. + clear -o. destruct d; simpl in *; + destruct o as [? [? [? ?]]]. + * split; rewrite global_levels_trans //. + repeat split => //. + red in H3 |- *. + rewrite -global_ext_constraints_trans in H3. + apply H3. + * split; rewrite global_levels_trans //. + repeat split => //. + red in H3 |- *. + rewrite -global_ext_constraints_trans in H3. + apply H3. + - simpl. + destruct d; simpl in *. + * destruct c; simpl. destruct cst_body; simpl in *. + red in o |- *. simpl in *. + apply (X (Σ, cst_universes) [] t (Some cst_type)); auto. + red in o0 |- *. simpl in *. + now apply (X (Σ, cst_universes) [] cst_type None). + * destruct o0 as [onI onP onNP]. + constructor; auto. + -- eapply Alli_map. eapply Alli_impl. exact onI. eauto. intros. + unshelve refine {| ind_indices := trans_local X1.(TTy.ind_indices); + ind_sort := X1.(TTy.ind_sort); + ind_cshapes := map trans_constructor_shape X1.(TTy.ind_cshapes) |}. + --- simpl; rewrite X1.(TTy.ind_arity_eq). + now rewrite !trans_it_mkProd_or_LetIn. + --- apply TTy.onArity in X1. unfold on_type in *; simpl in *. + now apply (X (Σ, Ast.ind_universes m) [] (Ast.ind_type x) None). + --- pose proof X1.(TTy.onConstructors) as X11. red in X11. + red. eapply All2_map. + eapply All2_impl; eauto. + simpl. intros [[? ?] ?] cs onc. destruct onc; unshelve econstructor; eauto. + + simpl. unfold trans_local. rewrite context_assumptions_map. + now rewrite cstr_args_length. + + simpl; unfold cdecl_type, TTy.cdecl_type in cstr_eq |- *; simpl in *. + rewrite cstr_eq. rewrite !trans_it_mkProd_or_LetIn. + autorewrite with len. f_equal. f_equal. + rewrite !trans_mkApps //. + f_equal; auto. simpl. + now rewrite /trans_local !map_length. + rewrite map_app /=. f_equal. + rewrite /trans_local !map_length. + unfold TemplateEnvironment.to_extended_list_k. + now rewrite trans_reln. + + unfold cdecl_type, TTy.cdecl_type in on_ctype |- *; simpl in *. + red. + move: (X (Σ, Ast.ind_universes m) (Ast.arities_context (Ast.ind_bodies m)) t None). + now rewrite trans_arities_context. + + clear -X0 X on_cargs. revert on_cargs. simpl. + generalize (TTy.cshape_args cs), (TTy.cshape_sorts cs). + have foo := (X (Σ, udecl) _ _ _ X0). + rewrite -trans_arities_context. + induction c; destruct l; simpl; auto; + destruct a as [na [b|] ty]; simpl in *; auto; + split; intuition eauto; + specialize (foo + (Ast.app_context (Ast.app_context (Ast.arities_context (Ast.ind_bodies m)) (Ast.ind_params m)) c)); + rewrite /trans_local !map_app in foo. + now apply (foo ty None). + now apply (foo b (Some ty)). + now apply (foo ty None). + now apply (foo b (Some ty)). + now apply (foo ty (Some (Ast.tSort _))). + + clear -X0 X on_cindices. + revert on_cindices. + rewrite trans_lift_context /trans_local -map_rev. + simpl. rewrite {2}/trans_local map_length. + generalize (List.rev (LiftSubst.lift_context #|TTy.cshape_args cs| 0 (TTy.ind_indices X1))). + generalize (TTy.cshape_indices cs). + rewrite -trans_arities_context. + induction 1; simpl; constructor; auto; + have foo := (X (Σ, Ast.ind_universes m) _ _ _ X0); + specialize (foo (Ast.app_context (Ast.app_context (Ast.arities_context (Ast.ind_bodies m)) + (Ast.ind_params m)) (TTy.cshape_args cs))). + rewrite /trans_local !map_app in foo. + now apply (foo i (Some t)). + now rewrite (trans_subst_telescope [i] 0) in IHon_cindices. + now rewrite (trans_subst_telescope [b] 0) in IHon_cindices. + + clear -on_ctype_positive. + unfold TTy.cdecl_type in *. unfold cdecl_type. simpl in *. + change [] with (map trans_decl []). revert on_ctype_positive. + generalize (@nil Ast.context_decl). induction 1; simpl. + rewrite trans_mkApps. simpl. + subst headrel. + assert (#|PCUICEnvironment.ind_bodies (trans_minductive_body m)| = #|TemplateEnvironment.ind_bodies m|) as <-. + now rewrite /trans_minductive_body /= map_length. + assert (#|ctx| = #|map trans_decl ctx|) as ->. now rewrite map_length. + eapply positive_cstr_concl. + rewrite map_length. + eapply All_map. eapply All_impl; eauto. + simpl; intros. admit. + constructor. now rewrite -(trans_subst [b]). + constructor. admit. + apply IHon_ctype_positive. + + clear -on_ctype_variance. + intros v indv. admit. + --- simpl; intros. have onp := X1.(TTy.onProjections). + admit. + --- have inds := X1.(TTy.ind_sorts). + admit. + --- have inds := X1.(TTy.onIndices). + admit. + -- red in onP. red. + admit. + -- admit. +Admitted. + +Lemma template_to_pcuic_env {cf} Σ : Template.Typing.wf_ext Σ -> wf_ext (trans_global Σ). +Proof. + intros [H Hu]. + split; auto. + eapply trans_on_global_env; eauto. simpl; intros. + epose proof (TTy.env_prop_typing _ template_to_pcuic _ X Γ). + forward X1. + red in X0. destruct T. + now eapply TTy.typing_wf_local. + destruct X0 as [s Hs]. eapply TTy.typing_wf_local; eauto. + destruct T; simpl in *. + - eapply X1; eauto. + - destruct X0 as [s Hs]. exists s. + eapply (X1 _ (Ast.tSort s)); eauto. + - destruct Hu as [? [? [? ?]]]. + split; rewrite global_levels_trans //. + repeat split => //. + red in H3 |- *. + rewrite -global_ext_constraints_trans in H3. + apply H3. +Qed. \ No newline at end of file From e79f5f1022c4b51e0b4b7f113a9188cb2a3a7a3e Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Wed, 2 Dec 2020 21:14:19 +0100 Subject: [PATCH 24/70] Fix erasure plugin build --- erasure/_PluginProject.in | 4 ++-- erasure/src/metacoq_erasure_plugin.mlpack | 2 -- erasure/theories/Erasure.v | 2 ++ test-suite/erasure_test.v | 3 ++- 4 files changed, 6 insertions(+), 5 deletions(-) diff --git a/erasure/_PluginProject.in b/erasure/_PluginProject.in index 4a9aa57a8..8515e3949 100644 --- a/erasure/_PluginProject.in +++ b/erasure/_PluginProject.in @@ -27,8 +27,8 @@ src/kernames.mli src/kernames.ml # src/reflect.mli # src/reflect.ml -src/typing0.mli -src/typing0.ml +# src/typing0.mli +# src/typing0.ml # From PCUIC src/pCUICAst.ml diff --git a/erasure/src/metacoq_erasure_plugin.mlpack b/erasure/src/metacoq_erasure_plugin.mlpack index 9b773b89d..ca6e73fdf 100644 --- a/erasure/src/metacoq_erasure_plugin.mlpack +++ b/erasure/src/metacoq_erasure_plugin.mlpack @@ -6,10 +6,8 @@ Utils WGraph UGraph0 -Typing0 OrderedTypeAlt Kernames -Reflect Init Classes0 diff --git a/erasure/theories/Erasure.v b/erasure/theories/Erasure.v index 4defe8095..e062b81d5 100644 --- a/erasure/theories/Erasure.v +++ b/erasure/theories/Erasure.v @@ -1,8 +1,10 @@ (* Distributed under the terms of the MIT license. *) From Coq Require Import Program. From MetaCoq.Template Require Import config utils uGraph Pretty Environment Typing. +Set Warnings "-notation-overridden". From MetaCoq.PCUIC Require Import PCUICAst PCUICAstUtils PCUICTyping TemplateToPCUIC TemplateToPCUICCorrectness. +Set Warnings "+notation-overridden". From MetaCoq.SafeChecker Require Import PCUICErrors. From MetaCoq.Erasure Require Import EAstUtils ErasureFunction EPretty. From MetaCoq.Erasure Require ErasureFunction EOptimizePropDiscr. diff --git a/test-suite/erasure_test.v b/test-suite/erasure_test.v index 6af5454da..4c74003d4 100644 --- a/test-suite/erasure_test.v +++ b/test-suite/erasure_test.v @@ -41,7 +41,8 @@ Require Import List. Import ListNotations. MetaCoq Erase (map negb [true; false]). -Definition bignat := 10000. +Set Warnings "-abstract-large-number". +Definition bignat := Eval compute in 10000. MetaCoq Erase bignat. Require Import vs. From 6d7e9898ceb6937313c3fe8092bb90d32c97505d Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Thu, 3 Dec 2020 00:22:50 +0100 Subject: [PATCH 25/70] Fix erasure plugin install --- erasure/_PluginProject.in | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/erasure/_PluginProject.in b/erasure/_PluginProject.in index 8515e3949..6edbd7d86 100644 --- a/erasure/_PluginProject.in +++ b/erasure/_PluginProject.in @@ -8,8 +8,8 @@ src/init.ml # src/classes0.ml # From Coq's stdlib -src/mSetWeakList.mli -src/mSetWeakList.ml +# src/mSetWeakList.mli +# src/mSetWeakList.ml # src/eqdepFacts.mli # src/eqdepFacts.ml src/orderedTypeAlt.mli From 66da11a377561ba1f7dc629e7ef996865f3c2355 Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Thu, 3 Dec 2020 00:57:17 +0100 Subject: [PATCH 26/70] MetaCoq tour --- dependency-graph/A tour of metacoq.png | Bin 0 -> 1151726 bytes dependency-graph/depgraph-2020-11-28.svg | 8138 ++++++++++++++++------ examples/_CoqProject | 3 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a/dependency-graph/depgraph-2020-11-28.svg +++ b/dependency-graph/depgraph-2020-11-28.svg @@ -1,2083 +1,6059 @@ - - - - - -dependencies - - - -safechecker/Extraction - -Extraction - - - -safechecker/PCUICSafeRetyping - -PCUICSafeRetyping - - - -erasure/ErasureFunction - -ErasureFunction - - - -safechecker/PCUICSafeRetyping->erasure/ErasureFunction - - - - - -safechecker/SafeTemplateChecker - -SafeTemplateChecker - - - -safechecker/SafeTemplateChecker->safechecker/Extraction - - - - - -safechecker/PCUICSafeChecker - -PCUICSafeChecker - - - -safechecker/PCUICSafeChecker->safechecker/SafeTemplateChecker - - - - - -safechecker/PCUICTypeChecker - -PCUICTypeChecker - - - -safechecker/PCUICTypeChecker->safechecker/PCUICSafeChecker - - - - - -safechecker/PCUICWfEnv - -PCUICWfEnv - - - -safechecker/PCUICWfEnv->safechecker/PCUICTypeChecker - - - - - -safechecker/PCUICWfReduction - -PCUICWfReduction - - - -safechecker/PCUICWfReduction->safechecker/PCUICTypeChecker - - - - - -safechecker/PCUICSafeConversion - -PCUICSafeConversion - - - -safechecker/PCUICSafeConversion->safechecker/PCUICWfReduction - - - - - -safechecker/PCUICEqualityDec - -PCUICEqualityDec - - - -safechecker/PCUICEqualityDec->safechecker/PCUICSafeConversion - - - - - -safechecker/PCUICSafeReduce - -PCUICSafeReduce - - - -safechecker/PCUICSafeReduce->safechecker/PCUICSafeRetyping - - - - - -safechecker/PCUICSafeReduce->safechecker/PCUICSafeConversion - - - - - -safechecker/PCUICErrors - -PCUICErrors - - - -safechecker/PCUICErrors->safechecker/PCUICSafeReduce - - - - - -erasure/Prelim - -Prelim - - - -safechecker/PCUICErrors->erasure/Prelim - - - - - -pcuic/PCUICValidity - -PCUICValidity - - - -pcuic/PCUICAlpha - -PCUICAlpha - - - -pcuic/PCUICValidity->pcuic/PCUICAlpha - - - - - -pcuic/PCUICInductiveInversion - -PCUICInductiveInversion - - - -pcuic/PCUICValidity->pcuic/PCUICInductiveInversion - - - - - -pcuic/PCUICSR - -PCUICSR - - - -pcuic/PCUICAlpha->pcuic/PCUICSR - - - - - -pcuic/PCUICWfUniverses - -PCUICWfUniverses - - - -pcuic/PCUICArities - -PCUICArities - - - -pcuic/PCUICWfUniverses->pcuic/PCUICArities - - - - - -pcuic/PCUICSpine - -PCUICSpine - - - -pcuic/PCUICArities->pcuic/PCUICSpine - - - - - -template-coq/EnvironmentTyping - -EnvironmentTyping - - - -pcuic/PCUICAst - -PCUICAst - - - -template-coq/EnvironmentTyping->pcuic/PCUICAst - - - - - -template-coq/Typing - -Typing - - - -template-coq/EnvironmentTyping->template-coq/Typing - - - - - -pcuic/PCUICSize - -PCUICSize - - - -pcuic/PCUICAst->pcuic/PCUICSize - - - - - -pcuic/TemplateToPCUIC - -TemplateToPCUIC - - - -pcuic/PCUICAst->pcuic/TemplateToPCUIC - - - - - -pcuic/PCUICAstUtils - -PCUICAstUtils - - - -pcuic/PCUICSize->pcuic/PCUICAstUtils - - - - - -pcuic/PCUICInduction - -PCUICInduction - - - -pcuic/PCUICAstUtils->pcuic/PCUICInduction - - - - - -pcuic/PCUICUtils - -PCUICUtils - - - -pcuic/PCUICAstUtils->pcuic/PCUICUtils - - - - - -pcuic/PCUICToTemplate - -PCUICToTemplate - - - -pcuic/PCUICAstUtils->pcuic/PCUICToTemplate - - - - - -template-coq/Reflect - -Reflect - - - -template-coq/Reflect->pcuic/PCUICAstUtils - - - - - -template-coq/Extraction - -Extraction - - - -template-coq/Reflect->template-coq/Extraction - - - - - -checker/WcbvEval - -WcbvEval - - - -template-coq/Reflect->checker/WcbvEval - - - - - -checker/Closed - -Closed - - - -template-coq/Reflect->checker/Closed - - - - - -checker/Generation - -Generation - - - -template-coq/Reflect->checker/Generation - - - - - -template-coq/common/uGraph - -uGraph - - - -template-coq/common/uGraph->pcuic/PCUICAstUtils - - - - - -template-coq/Constants - -Constants - - - -template-coq/common/uGraph->template-coq/Constants - - - - - -checker/Checker - -Checker - - - -template-coq/common/uGraph->checker/Checker - - - - - -pcuic/PCUICClosed - -PCUICClosed - - - -pcuic/PCUICCSubst - -PCUICCSubst - - - -pcuic/PCUICClosed->pcuic/PCUICCSubst - - - - - -pcuic/PCUICWeakening - -PCUICWeakening - - - -pcuic/PCUICClosed->pcuic/PCUICWeakening - - - - - -pcuic/PCUICWcbvEval - -PCUICWcbvEval - - - -pcuic/PCUICCSubst->pcuic/PCUICWcbvEval - - - - - -pcuic/PCUICElimination - -PCUICElimination - - - -pcuic/PCUICCanonicity - -PCUICCanonicity - - - -pcuic/PCUICElimination->pcuic/PCUICCanonicity - - - - - -erasure/Extract - -Extract - - - -pcuic/PCUICElimination->erasure/Extract - - - - - -pcuic/PCUICCanonicity->safechecker/PCUICSafeReduce - - - - - -erasure/EArities - -EArities - - - -pcuic/PCUICCanonicity->erasure/EArities - - - - - -pcuic/PCUICSN - -PCUICSN - - - -pcuic/PCUICSN->pcuic/PCUICCanonicity - - - - - -pcuic/PCUICWcbvEval->pcuic/PCUICCanonicity - - - - - -erasure/EWcbvEval - -EWcbvEval - - - -pcuic/PCUICWcbvEval->erasure/EWcbvEval - - - - - -pcuic/PCUICWeakeningEnv - -PCUICWeakeningEnv - - - -pcuic/PCUICWeakeningEnv->pcuic/PCUICClosed - - - - - -pcuic/PCUICParallelReductionConfluence - -PCUICParallelReductionConfluence - - - -pcuic/PCUICConfluence - -PCUICConfluence - - - -pcuic/PCUICParallelReductionConfluence->pcuic/PCUICConfluence - - - - - -pcuic/PCUICContextConversion - -PCUICContextConversion - - - -pcuic/PCUICConfluence->pcuic/PCUICContextConversion - - - - - -pcuic/PCUICConversion - -PCUICConversion - - - -pcuic/PCUICContextConversion->pcuic/PCUICConversion - - - - - -pcuic/PCUICContextRelation - -PCUICContextRelation - - - -pcuic/PCUICContextRelation->pcuic/PCUICContextConversion - - - - - -pcuic/PCUICNormal - -PCUICNormal - - - -pcuic/PCUICContextRelation->pcuic/PCUICNormal - - - - - -pcuic/PCUICTyping - -PCUICTyping - - - -pcuic/PCUICTyping->pcuic/PCUICWeakeningEnv - - - - - -pcuic/PCUICTyping->pcuic/PCUICContextRelation - - - - - -pcuic/PCUICNameless - -PCUICNameless - - - -pcuic/PCUICTyping->pcuic/PCUICNameless - - - - - -pcuic/PCUICGeneration - -PCUICGeneration - - - -pcuic/PCUICTyping->pcuic/PCUICGeneration - - - - - -pcuic/PCUICGlobalEnv - -PCUICGlobalEnv - - - -pcuic/PCUICTyping->pcuic/PCUICGlobalEnv - - - - - -pcuic/PCUICCtxShape - -PCUICCtxShape - - - -pcuic/PCUICContexts - -PCUICContexts - - - -pcuic/PCUICCtxShape->pcuic/PCUICContexts - - - - - -pcuic/PCUICContexts->pcuic/PCUICWfUniverses - - - - - -pcuic/PCUICCumulProp - -PCUICCumulProp - - - -pcuic/PCUICCumulProp->pcuic/PCUICElimination - - - - - -pcuic/PCUICConvCumInversion - -PCUICConvCumInversion - - - -pcuic/PCUICCumulProp->pcuic/PCUICConvCumInversion - - - - - -pcuic/PCUICPrincipality - -PCUICPrincipality - - - -pcuic/PCUICCumulProp->pcuic/PCUICPrincipality - - - - - -pcuic/PCUICConvCumInversion->safechecker/PCUICSafeConversion - - - - - -pcuic/PCUICInversion - -PCUICInversion - - - -pcuic/PCUICConversion->pcuic/PCUICInversion - - - - - -pcuic/PCUICInversion->pcuic/PCUICCtxShape - - - - - -pcuic/PCUICNameless->pcuic/PCUICCtxShape - - - - - -template-coq/UnivSubst - -UnivSubst - - - -template-coq/UnivSubst->pcuic/PCUICCtxShape - - - - - -template-coq/UnivSubst->pcuic/PCUICNormal - - - - - -template-coq/UnivSubst->template-coq/Typing - - - - - -template-coq/UnivSubst->template-coq/Extraction - - - - - -pcuic/PCUICSafeLemmata - -PCUICSafeLemmata - - - -pcuic/PCUICSafeLemmata->pcuic/PCUICSN - - - - - -pcuic/PCUICSafeLemmata->pcuic/PCUICCumulProp - - - - - -pcuic/PCUICReduction - -PCUICReduction - - - -pcuic/PCUICCumulativity - -PCUICCumulativity - - - -pcuic/PCUICReduction->pcuic/PCUICCumulativity - - - - - -pcuic/PCUICCumulativity->pcuic/PCUICTyping - - - - - -pcuic/PCUICLiftSubst - -PCUICLiftSubst - - - -pcuic/PCUICEquality - -PCUICEquality - - - -pcuic/PCUICLiftSubst->pcuic/PCUICEquality - - - - - -pcuic/PCUICPretty - -PCUICPretty - - - -pcuic/PCUICLiftSubst->pcuic/PCUICPretty - - - - - -pcuic/PCUICUnivSubst - -PCUICUnivSubst - - - -pcuic/PCUICLiftSubst->pcuic/PCUICUnivSubst - - - - - -pcuic/PCUICPosition - -PCUICPosition - - - -pcuic/PCUICEquality->pcuic/PCUICPosition - - - - - -pcuic/PCUICReflect - -PCUICReflect - - - -pcuic/PCUICReflect->pcuic/PCUICEquality - - - - - -erasure/EReflect - -EReflect - - - -pcuic/PCUICReflect->erasure/EReflect - - - - - -pcuic/PCUICGeneration->pcuic/PCUICWeakening - - - - - -pcuic/PCUICToTemplateCorrectness - -PCUICToTemplateCorrectness - - - -pcuic/PCUICGeneration->pcuic/PCUICToTemplateCorrectness - - - - - -pcuic/PCUICGlobalEnv->safechecker/PCUICWfEnv - - - - - -pcuic/PCUICGlobalEnv->safechecker/PCUICEqualityDec - - - - - -pcuic/PCUICInduction->pcuic/PCUICLiftSubst - - - - - -pcuic/PCUICInduction->pcuic/PCUICReflect - - - - - -pcuic/PCUICInductiveInversion->pcuic/PCUICSR - - - - - -pcuic/PCUICInductives - -PCUICInductives - - - -pcuic/PCUICSpine->pcuic/PCUICInductives - - - - - -pcuic/PCUICInductives->pcuic/PCUICValidity - - - - - -pcuic/PCUICNormal->pcuic/PCUICSafeLemmata - - - - - -pcuic/PCUICSubstitution - -PCUICSubstitution - - - -pcuic/PCUICParallelReduction - -PCUICParallelReduction - - - -pcuic/PCUICSubstitution->pcuic/PCUICParallelReduction - - - - - -pcuic/TemplateToPCUICCorrectness - -TemplateToPCUICCorrectness - - - -pcuic/PCUICSubstitution->pcuic/TemplateToPCUICCorrectness - - - - - -pcuic/PCUICParallelReduction->pcuic/PCUICParallelReductionConfluence - - - - - -pcuic/PCUICPosition->pcuic/PCUICReduction - - - - - -pcuic/PCUICPretty->safechecker/PCUICErrors - - - - - -pcuic/PCUICPrincipality->safechecker/PCUICSafeConversion - - - - - -pcuic/PCUICPrincipality->erasure/EArities - - - - - -pcuic/PCUICRelations - -PCUICRelations - - - -pcuic/PCUICRelations->pcuic/PCUICReduction - - - - - -pcuic/PCUICUnivSubst->pcuic/PCUICReduction - - - - - -pcuic/PCUICSR->pcuic/PCUICWcbvEval - - - - - -pcuic/PCUICSR->pcuic/PCUICSafeLemmata - - - - - -pcuic/PCUICSigmaCalculus - -PCUICSigmaCalculus - - - -pcuic/PCUICWeakening->pcuic/PCUICSigmaCalculus - - - - - -pcuic/PCUICUnivSubstitution - -PCUICUnivSubstitution - - - -pcuic/PCUICWeakening->pcuic/PCUICUnivSubstitution - - - - - -pcuic/PCUICSigmaCalculus->pcuic/PCUICSubstitution - - - - - -pcuic/PCUICUnivSubstitution->pcuic/PCUICSubstitution - - - - - -pcuic/PCUICUtils->pcuic/PCUICTyping - - - - - -template-coq/utils/LibHypsNaming - -LibHypsNaming - - - -template-coq/utils/LibHypsNaming->pcuic/PCUICTyping - - - - - -checker/WeakeningEnv - -WeakeningEnv - - - -template-coq/utils/LibHypsNaming->checker/WeakeningEnv - - - - - -pcuic/TemplateToPCUIC->safechecker/SafeTemplateChecker - - - - - -erasure/Erasure - -Erasure - - - -pcuic/TemplateToPCUIC->erasure/Erasure - - - - - -pcuic/TemplateToPCUIC->pcuic/TemplateToPCUICCorrectness - - - - - -template-coq/Environment - -Environment - - - -template-coq/Ast - -Ast - - - -template-coq/Environment->template-coq/Ast - - - - - -template-coq/AstUtils - -AstUtils - - - -template-coq/Ast->template-coq/AstUtils - - - - - -template-coq/TemplateMonad/Common - -Common - - - -template-coq/Ast->template-coq/TemplateMonad/Common - - - - - -template-coq/AstUtils->template-coq/EnvironmentTyping - - - - - -template-coq/Induction - -Induction - - - -template-coq/AstUtils->template-coq/Induction - - - - - -template-coq/TemplateMonad/Extractable - -Extractable - - - -template-coq/AstUtils->template-coq/TemplateMonad/Extractable - - - - - -template-coq/TemplateMonad/Core - -Core - - - -template-coq/AstUtils->template-coq/TemplateMonad/Core - - - - - -template-coq/WfInv - -WfInv - - - -template-coq/AstUtils->template-coq/WfInv - - - - - -template-coq/Kernames - -Kernames - - - -template-coq/AstUtils->template-coq/Kernames - - - - - -template-coq/utils - -utils - - - -template-coq/BasicAst - -BasicAst - - - -template-coq/utils->template-coq/BasicAst - - - - - -template-coq/Universes - -Universes - - - -template-coq/BasicAst->template-coq/Universes - - - - - -template-coq/Universes->template-coq/common/uGraph - - - - - -template-coq/Universes->template-coq/Environment - - - - - -erasure/EAst - -EAst - - - -template-coq/Universes->erasure/EAst - - - - - -template-coq/Induction->template-coq/Reflect - - - - - -template-coq/LiftSubst - -LiftSubst - - - -template-coq/Induction->template-coq/LiftSubst - - - - - -template-coq/LiftSubst->template-coq/UnivSubst - - - - - -template-coq/Pretty - -Pretty - - - -template-coq/LiftSubst->template-coq/Pretty - - - - - -template-coq/Typing->safechecker/SafeTemplateChecker - - - - - -template-coq/TypingWf - -TypingWf - - - -template-coq/Typing->template-coq/TypingWf - - - - - -checker/Normal - -Normal - - - -template-coq/Typing->checker/Normal - - - - - -template-coq/Typing->checker/WcbvEval - - - - - -template-coq/Typing->checker/Checker - - - - - -template-coq/Typing->checker/WeakeningEnv - - - - - -template-coq/Typing->checker/Generation - - - - - -template-coq/All - -template-coq/All - - - -template-coq/Typing->template-coq/All - - - - - -template-coq/config - -config - - - -template-coq/config->template-coq/Universes - - - - - -template-coq/utils/wGraph - -wGraph - - - -template-coq/utils/wGraph->template-coq/common/uGraph - - - - - -template-coq/utils/All_Forall - -All_Forall - - - -template-coq/monad_utils - -monad_utils - - - -template-coq/utils/All_Forall->template-coq/monad_utils - - - - - -template-coq/utils/MCUtils - -MCUtils - - - -template-coq/utils/All_Forall->template-coq/utils/MCUtils - - - - - -template-coq/monad_utils->template-coq/utils - - - - - -template-coq/utils/MCUtils->template-coq/utils - - - - - -template-coq/utils/MCUtils->template-coq/utils/wGraph - - - - - -template-coq/utils/MCOption - -MCOption - - - -template-coq/utils/MCOption->template-coq/utils/All_Forall - - - - - -template-coq/utils/MCSquash - -MCSquash - - - -template-coq/utils/MCSquash->template-coq/utils/All_Forall - - - - - -template-coq/utils/MCPrelude - -MCPrelude - - - -template-coq/utils/MCList - -MCList - - - -template-coq/utils/MCPrelude->template-coq/utils/MCList - - - - - -template-coq/utils/MCList->template-coq/utils/MCOption - - - - - -template-coq/utils/MCRelations - -MCRelations - - - -template-coq/utils/MCRelations->template-coq/utils/MCList - - - - - -template-coq/utils/MCProd - -MCProd - - - -template-coq/utils/MCProd->template-coq/utils/MCOption - - - - - -template-coq/utils/MCCompare - -MCCompare - - - -template-coq/utils/MCString - -MCString - - - -template-coq/utils/MCCompare->template-coq/utils/MCString - - - - - -template-coq/utils/MCString->template-coq/utils/MCUtils - - - - - -template-coq/utils/MCArith - -MCArith - - - -template-coq/utils/MCArith->template-coq/utils/MCUtils - - - - - -template-coq/utils/MCEquality - -MCEquality - - - -template-coq/utils/MCEquality->template-coq/utils/MCUtils - - - - - -template-coq/Loader - -template-coq/Loader - - - -template-coq/Constants->template-coq/Loader - - - - - -template-coq/TemplateMonad/Extractable->template-coq/Extraction - - - - - -template-coq/TemplateMonad/Extractable->template-coq/Constants - - - - - -template-coq/TemplateMonad - -TemplateMonad - - - -template-coq/TemplateMonad/Core->template-coq/TemplateMonad - - - - - -template-coq/TemplateMonad/Common->template-coq/TemplateMonad/Extractable - - - - - -template-coq/TemplateMonad/Common->template-coq/TemplateMonad/Core - - - - - -template-coq/TemplateMonad->template-coq/Constants - - - - - -template-coq/TypingWf->checker/Closed - - - - - -template-coq/TypingWf->pcuic/PCUICToTemplateCorrectness - - - - - -template-coq/TypingWf->pcuic/TemplateToPCUICCorrectness - - - - - -template-coq/WfInv->checker/WcbvEval - - - - - -template-coq/WfInv->pcuic/PCUICToTemplateCorrectness - - - - - -template-coq/WfInv->pcuic/TemplateToPCUICCorrectness - - - - - -template-coq/Pretty->template-coq/Extraction - - - - - -template-coq/Pretty->erasure/Erasure - - - - - -erasure/EAstUtils - -EAstUtils - - - -template-coq/Kernames->erasure/EAstUtils - - - - - -checker/All - -All - - - -checker/Retyping - -Retyping - - - -checker/Retyping->checker/All - - - - - -checker/Checker->checker/Retyping - - - - - -checker/Substitution - -Substitution - - - 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-erasure/ESubstitution->erasure/EDeps - - - - - -erasure/Prelim->erasure/EInversion - - - - - -erasure/Prelim->erasure/ESubstitution - - - - - -erasure/EAll - -EAll - - - -erasure/EDeps->erasure/ErasureCorrectness - - - - - -erasure/Extract->erasure/EArities - - - - - -erasure/Extract->erasure/EAll - - - - - -erasure/ETyping - -ETyping - - - -erasure/ETyping->erasure/Extract - - - - - -erasure/EWndEval - -EWndEval - - - -erasure/ETyping->erasure/EWndEval - - - - - -erasure/ETyping->erasure/EWcbvEval - - - - - -erasure/EPretty - -EPretty - - - -erasure/ETyping->erasure/EPretty - - - - - -erasure/EWndEval->erasure/EAll - - - - - -erasure/EWcbvEval->erasure/Prelim - - - - - -erasure/EWcbvEval->erasure/EAll - - - - - -erasure/ECSubst - -ECSubst - - - -erasure/ECSubst->erasure/EWcbvEval - - - - - -erasure/EPretty->erasure/Erasure - - - - - -erasure/EReflect->erasure/ETyping - - - - - -erasure/ELiftSubst - -ELiftSubst - - - -erasure/ELiftSubst->erasure/ETyping - - - - - -erasure/ELiftSubst->erasure/ECSubst - - - - - -erasure/EInduction - -EInduction - - - -erasure/EInduction->erasure/EReflect - - - - - -erasure/EInduction->erasure/ELiftSubst - - - - - -erasure/EAstUtils->erasure/ETyping - - - - - -erasure/EAst->erasure/EInduction - - - - - -erasure/EAst->erasure/EAstUtils - - - - - -pcuic/PCUICToTemplate->pcuic/PCUICToTemplateCorrectness - - - - + + + + + image/svg+xml + + + + + + + + + + dependencies + + + safechecker/Extraction + + Extraction + + + + safechecker/PCUICSafeRetyping + + PCUICSafeRetyping + + + + erasure/ErasureFunction + + ErasureFunction + + + + safechecker/PCUICSafeRetyping->erasure/ErasureFunction + + + + + + safechecker/SafeTemplateChecker + + SafeTemplateChecker + + + + safechecker/SafeTemplateChecker->safechecker/Extraction + + + + + + safechecker/PCUICSafeChecker + + PCUICSafeChecker + + + + safechecker/PCUICSafeChecker->safechecker/SafeTemplateChecker + + + + + + safechecker/PCUICTypeChecker + + PCUICTypeChecker + + + + safechecker/PCUICTypeChecker->safechecker/PCUICSafeChecker + + + + + + safechecker/PCUICWfEnv + + PCUICWfEnv + + + + safechecker/PCUICWfEnv->safechecker/PCUICTypeChecker + + + + + + safechecker/PCUICWfReduction + + PCUICWfReduction + + + + safechecker/PCUICWfReduction->safechecker/PCUICTypeChecker + + + + + + safechecker/PCUICSafeConversion + + PCUICSafeConversion + + + + safechecker/PCUICSafeConversion->safechecker/PCUICWfReduction + + + + + + safechecker/PCUICEqualityDec + + PCUICEqualityDec + + + + safechecker/PCUICEqualityDec->safechecker/PCUICSafeConversion + + + + + + safechecker/PCUICSafeReduce + + PCUICSafeReduce + + + + safechecker/PCUICSafeReduce->safechecker/PCUICSafeRetyping + + + + + + safechecker/PCUICSafeReduce->safechecker/PCUICSafeConversion + + + + + + safechecker/PCUICErrors + + PCUICErrors + + + + safechecker/PCUICErrors->safechecker/PCUICSafeReduce + + + + + + erasure/Prelim + + Prelim + + + + safechecker/PCUICErrors->erasure/Prelim + + + + + + pcuic/PCUICValidity + + PCUICValidity + + + + pcuic/PCUICAlpha + + PCUICAlpha + + + + pcuic/PCUICValidity->pcuic/PCUICAlpha + + + + + + pcuic/PCUICInductiveInversion + + PCUICInductiveInversion + + + + pcuic/PCUICValidity->pcuic/PCUICInductiveInversion + + + + + + pcuic/PCUICSR + + PCUICSR + + + + pcuic/PCUICAlpha->pcuic/PCUICSR + + + + + + pcuic/PCUICWfUniverses + + PCUICWfUniverses + + + + pcuic/PCUICArities + + PCUICArities + + + + pcuic/PCUICWfUniverses->pcuic/PCUICArities + + + + + + pcuic/PCUICSpine + + PCUICSpine + + + + pcuic/PCUICArities->pcuic/PCUICSpine + + + + + + template-coq/EnvironmentTyping + + EnvironmentTyping + + + + pcuic/PCUICAst + + PCUICAst + + + + template-coq/EnvironmentTyping->pcuic/PCUICAst + + + + + + template-coq/Typing + + Typing + + + + template-coq/EnvironmentTyping->template-coq/Typing + + + + + + pcuic/PCUICSize + + PCUICSize + + + + + pcuic/TemplateToPCUIC + + TemplateToPCUIC + + + + + pcuic/PCUICAstUtils + + PCUICAstUtils + + + + pcuic/PCUICSize->pcuic/PCUICAstUtils + + + + + pcuic/PCUICInduction + + PCUICInduction + + + + pcuic/PCUICAstUtils->pcuic/PCUICInduction + + + + + + pcuic/PCUICUtils + + PCUICUtils + + + + pcuic/PCUICAstUtils->pcuic/PCUICUtils + + + + + + pcuic/PCUICToTemplate + + PCUICToTemplate + + + + pcuic/PCUICAstUtils->pcuic/PCUICToTemplate + + + + + + template-coq/Reflect + + Reflect + + + + template-coq/Reflect->pcuic/PCUICAstUtils + + + + + template-coq/Extraction + + Extraction + + + + template-coq/Reflect->template-coq/Extraction + + + + + + + + + + + + template-coq/common/uGraph + + uGraph + + + + + template-coq/Constants + + Constants + + + + template-coq/common/uGraph->template-coq/Constants + + + + + + + + pcuic/PCUICClosed + + PCUICClosed + + + + pcuic/PCUICCSubst + + PCUICCSubst + + + + pcuic/PCUICClosed->pcuic/PCUICCSubst + + + + + + pcuic/PCUICWeakening + + PCUICWeakening + + + + pcuic/PCUICClosed->pcuic/PCUICWeakening + + + + + + pcuic/PCUICWcbvEval + + PCUICWcbvEval + + + + pcuic/PCUICCSubst->pcuic/PCUICWcbvEval + + + + + + pcuic/PCUICElimination + + PCUICElimination + + + + pcuic/PCUICCanonicity + + PCUICCanonicity + + + + pcuic/PCUICElimination->pcuic/PCUICCanonicity + + + + + + erasure/Extract + + Extract + + + + pcuic/PCUICElimination->erasure/Extract + + + + + + pcuic/PCUICCanonicity->safechecker/PCUICSafeReduce + + + + + + erasure/EArities + + EArities + + + + pcuic/PCUICCanonicity->erasure/EArities + + + + + + pcuic/PCUICSN + + PCUICSN + + + + pcuic/PCUICSN->pcuic/PCUICCanonicity + + + + + + pcuic/PCUICWcbvEval->pcuic/PCUICCanonicity + + + + + + erasure/EWcbvEval + + EWcbvEval + + + + pcuic/PCUICWcbvEval->erasure/EWcbvEval + + + + + + pcuic/PCUICWeakeningEnv + + PCUICWeakeningEnv + + + + pcuic/PCUICWeakeningEnv->pcuic/PCUICClosed + + + + + + pcuic/PCUICParallelReductionConfluence + + PCUICParallelReductionConfluence + + + + pcuic/PCUICConfluence + + PCUICConfluence + + + + pcuic/PCUICParallelReductionConfluence->pcuic/PCUICConfluence + + + + + + pcuic/PCUICContextConversion + + PCUICContextConversion + + + + pcuic/PCUICConfluence->pcuic/PCUICContextConversion + + + + + + pcuic/PCUICConversion + + PCUICConversion + + + + pcuic/PCUICContextConversion->pcuic/PCUICConversion + + + + + + pcuic/PCUICContextRelation + + PCUICContextRelation + + + + pcuic/PCUICContextRelation->pcuic/PCUICContextConversion + + + + + + pcuic/PCUICNormal + + PCUICNormal + + + + pcuic/PCUICContextRelation->pcuic/PCUICNormal + + + + + + pcuic/PCUICTyping + + PCUICTyping + + + + pcuic/PCUICTyping->pcuic/PCUICWeakeningEnv + + + + + + pcuic/PCUICTyping->pcuic/PCUICContextRelation + + + + + + pcuic/PCUICNameless + + PCUICNameless + + + + pcuic/PCUICTyping->pcuic/PCUICNameless + + + + + + pcuic/PCUICGeneration + + PCUICGeneration + + + + pcuic/PCUICTyping->pcuic/PCUICGeneration + + + + + + pcuic/PCUICGlobalEnv + + PCUICGlobalEnv + + + + pcuic/PCUICTyping->pcuic/PCUICGlobalEnv + + + + + + pcuic/PCUICCtxShape + + PCUICCtxShape + + + + pcuic/PCUICContexts + + PCUICContexts + + + + pcuic/PCUICCtxShape->pcuic/PCUICContexts + + + + + + pcuic/PCUICContexts->pcuic/PCUICWfUniverses + + + + + + pcuic/PCUICCumulProp + + PCUICCumulProp + + + + pcuic/PCUICCumulProp->pcuic/PCUICElimination + + + + + + pcuic/PCUICConvCumInversion + + PCUICConvCumInversion + + + + pcuic/PCUICCumulProp->pcuic/PCUICConvCumInversion + + + + + + pcuic/PCUICPrincipality + + PCUICPrincipality + + + + pcuic/PCUICCumulProp->pcuic/PCUICPrincipality + + + + + + pcuic/PCUICConvCumInversion->safechecker/PCUICSafeConversion + + + + + + pcuic/PCUICInversion + + PCUICInversion + + + + pcuic/PCUICConversion->pcuic/PCUICInversion + + + + + + pcuic/PCUICInversion->pcuic/PCUICCtxShape + + + + + + pcuic/PCUICNameless->pcuic/PCUICCtxShape + + + + + + template-coq/UnivSubst + + UnivSubst + + + + template-coq/UnivSubst->pcuic/PCUICCtxShape + + + + + + template-coq/UnivSubst->pcuic/PCUICNormal + + + + + + template-coq/UnivSubst->template-coq/Typing + + + + + + template-coq/UnivSubst->template-coq/Extraction + + + + + + pcuic/PCUICSafeLemmata + + PCUICSafeLemmata + + + + pcuic/PCUICSafeLemmata->pcuic/PCUICSN + + + + + + pcuic/PCUICSafeLemmata->pcuic/PCUICCumulProp + + + + + + pcuic/PCUICReduction + + PCUICReduction + + + + pcuic/PCUICCumulativity + + PCUICCumulativity + + + + pcuic/PCUICReduction->pcuic/PCUICCumulativity + + + + + + pcuic/PCUICCumulativity->pcuic/PCUICTyping + + + + + + pcuic/PCUICLiftSubst + + PCUICLiftSubst + + + + pcuic/PCUICEquality + + PCUICEquality + + + + pcuic/PCUICLiftSubst->pcuic/PCUICEquality + + + + + + pcuic/PCUICPretty + + PCUICPretty + + + + pcuic/PCUICLiftSubst->pcuic/PCUICPretty + + + + + + pcuic/PCUICUnivSubst + + PCUICUnivSubst + + + + pcuic/PCUICLiftSubst->pcuic/PCUICUnivSubst + + + + + + pcuic/PCUICPosition + + PCUICPosition + + + + pcuic/PCUICEquality->pcuic/PCUICPosition + + + + + + pcuic/PCUICReflect + + PCUICReflect + + + + pcuic/PCUICReflect->pcuic/PCUICEquality + + + + + + erasure/EReflect + + EReflect + + + + pcuic/PCUICReflect->erasure/EReflect + + + + + + pcuic/PCUICGeneration->pcuic/PCUICWeakening + + + + + + pcuic/PCUICToTemplateCorrectness + + PCUICToTemplateCorrectness + + + + pcuic/PCUICGeneration->pcuic/PCUICToTemplateCorrectness + + + + + + pcuic/PCUICGlobalEnv->safechecker/PCUICWfEnv + + + + + + pcuic/PCUICGlobalEnv->safechecker/PCUICEqualityDec + + + + + + pcuic/PCUICInduction->pcuic/PCUICLiftSubst + + + + + + pcuic/PCUICInduction->pcuic/PCUICReflect + + + + + + pcuic/PCUICInductiveInversion->pcuic/PCUICSR + + + + + + pcuic/PCUICInductives + + PCUICInductives + + + + pcuic/PCUICSpine->pcuic/PCUICInductives + + + + + + pcuic/PCUICInductives->pcuic/PCUICValidity + + + + + + pcuic/PCUICNormal->pcuic/PCUICSafeLemmata + + + + + + pcuic/PCUICSubstitution + + PCUICSubstitution + + + + pcuic/PCUICParallelReduction + + PCUICParallelReduction + + + + pcuic/PCUICSubstitution->pcuic/PCUICParallelReduction + + + + + + pcuic/TemplateToPCUICCorrectness + + TemplateToPCUICCorrectness + + + + pcuic/PCUICSubstitution->pcuic/TemplateToPCUICCorrectness + + + + + + pcuic/PCUICParallelReduction->pcuic/PCUICParallelReductionConfluence + + + + + + pcuic/PCUICPosition->pcuic/PCUICReduction + + + + + + pcuic/PCUICPretty->safechecker/PCUICErrors + + + + + + pcuic/PCUICPrincipality->safechecker/PCUICSafeConversion + + + + + + pcuic/PCUICPrincipality->erasure/EArities + + + + + + pcuic/PCUICRelations + + PCUICRelations + + + + pcuic/PCUICRelations->pcuic/PCUICReduction + + + + + + pcuic/PCUICUnivSubst->pcuic/PCUICReduction + + + + + + pcuic/PCUICSR->pcuic/PCUICWcbvEval + + + + + + pcuic/PCUICSR->pcuic/PCUICSafeLemmata + + + + + + pcuic/PCUICSigmaCalculus + + PCUICSigmaCalculus + + + + pcuic/PCUICWeakening->pcuic/PCUICSigmaCalculus + + + + + + pcuic/PCUICUnivSubstitution + + PCUICUnivSubstitution + + + + pcuic/PCUICWeakening->pcuic/PCUICUnivSubstitution + + + + + + pcuic/PCUICSigmaCalculus->pcuic/PCUICSubstitution + + + + + + pcuic/PCUICUnivSubstitution->pcuic/PCUICSubstitution + + + + + + pcuic/PCUICUtils->pcuic/PCUICTyping + + + + + + template-coq/utils/LibHypsNaming + + LibHypsNaming + + + + template-coq/utils/LibHypsNaming->pcuic/PCUICTyping + + + + + + + + pcuic/TemplateToPCUIC->safechecker/SafeTemplateChecker + + + + + + erasure/Erasure + + Erasure + + + + pcuic/TemplateToPCUIC->erasure/Erasure + + + + + + pcuic/TemplateToPCUIC->pcuic/TemplateToPCUICCorrectness + + + + + + template-coq/Environment + + Environment + + + + template-coq/Ast + + Ast + + + + template-coq/Environment->template-coq/Ast + + + + + + template-coq/AstUtils + + AstUtils + + + + template-coq/Ast->template-coq/AstUtils + + + + + + template-coq/TemplateMonad/Common + + Common + + + + template-coq/Ast->template-coq/TemplateMonad/Common + + + + + + template-coq/AstUtils->template-coq/EnvironmentTyping + + + + + + template-coq/Induction + + Induction + + + + template-coq/AstUtils->template-coq/Induction + + + + + + template-coq/TemplateMonad/Extractable + + Extractable + + + + template-coq/AstUtils->template-coq/TemplateMonad/Extractable + + + + + + template-coq/TemplateMonad/Core + + Core + + + + template-coq/AstUtils->template-coq/TemplateMonad/Core + + + + + + template-coq/WfInv + + WfInv + + + + template-coq/AstUtils->template-coq/WfInv + + + + + + template-coq/Kernames + + Kernames + + + + template-coq/AstUtils->template-coq/Kernames + + + + + + template-coq/utils + + utils + + + + template-coq/BasicAst + + BasicAst + + + + template-coq/utils->template-coq/BasicAst + + + + + + template-coq/Universes + + Universes + + + + template-coq/BasicAst->template-coq/Universes + + + + + + template-coq/Universes->template-coq/common/uGraph + + + + + + template-coq/Universes->template-coq/Environment + + + + + + erasure/EAst + + EAst + + + + template-coq/Universes->erasure/EAst + + + + + + template-coq/Induction->template-coq/Reflect + + + + + + template-coq/LiftSubst + + LiftSubst + + + + template-coq/Induction->template-coq/LiftSubst + + + + + + template-coq/LiftSubst->template-coq/UnivSubst + + + + + + template-coq/Pretty + + Pretty + + + + template-coq/LiftSubst->template-coq/Pretty + + + + + + template-coq/Typing->safechecker/SafeTemplateChecker + + + + + + template-coq/TypingWf + + TypingWf + + + + template-coq/Typing->template-coq/TypingWf + + + + + + + + + + + + template-coq/All + + template-coq/All + + + + template-coq/Typing->template-coq/All + + + + + + template-coq/config + + config + + + + template-coq/config->template-coq/Universes + + + + + + template-coq/utils/wGraph + + wGraph + + + + template-coq/utils/wGraph->template-coq/common/uGraph + + + + + + template-coq/utils/All_Forall + + All_Forall + + + + template-coq/monad_utils + + monad_utils + + + + template-coq/utils/All_Forall->template-coq/monad_utils + + + + + + template-coq/utils/MCUtils + + MCUtils + + + + template-coq/utils/All_Forall->template-coq/utils/MCUtils + + + + + + template-coq/monad_utils->template-coq/utils + + + + + + template-coq/utils/MCUtils->template-coq/utils + + + + + + template-coq/utils/MCUtils->template-coq/utils/wGraph + + + + + + template-coq/utils/MCOption + + MCOption + + + + template-coq/utils/MCOption->template-coq/utils/All_Forall + + + + + + template-coq/utils/MCSquash + + MCSquash + + + + template-coq/utils/MCSquash->template-coq/utils/All_Forall + + + + + + template-coq/utils/MCPrelude + + MCPrelude + + + + template-coq/utils/MCList + + MCList + + + + template-coq/utils/MCPrelude->template-coq/utils/MCList + + + + + + template-coq/utils/MCList->template-coq/utils/MCOption + + + + + + template-coq/utils/MCRelations + + MCRelations + + + + template-coq/utils/MCRelations->template-coq/utils/MCList + + + + + + template-coq/utils/MCProd + + MCProd + + + + template-coq/utils/MCProd->template-coq/utils/MCOption + + + + + + template-coq/utils/MCCompare + + MCCompare + + + + template-coq/utils/MCString + + MCString + + + + template-coq/utils/MCCompare->template-coq/utils/MCString + + + + + + template-coq/utils/MCString->template-coq/utils/MCUtils + + + + + + template-coq/utils/MCArith + + MCArith + + + + template-coq/utils/MCArith->template-coq/utils/MCUtils + + + + + + template-coq/utils/MCEquality + + MCEquality + + + + template-coq/utils/MCEquality->template-coq/utils/MCUtils + + + + + + template-coq/Loader + + template-coq/Loader + + + + template-coq/Constants->template-coq/Loader + + + + + + template-coq/TemplateMonad/Extractable->template-coq/Extraction + + + + + + template-coq/TemplateMonad/Extractable->template-coq/Constants + + + + + + template-coq/TemplateMonad + + TemplateMonad + + + + template-coq/TemplateMonad/Core->template-coq/TemplateMonad + + + + + + template-coq/TemplateMonad/Common->template-coq/TemplateMonad/Extractable + + + + + + template-coq/TemplateMonad/Common->template-coq/TemplateMonad/Core + + + + + + template-coq/TemplateMonad->template-coq/Constants + + + + + + + template-coq/TypingWf->pcuic/PCUICToTemplateCorrectness + + + + + + template-coq/TypingWf->pcuic/TemplateToPCUICCorrectness + + + + + + + template-coq/WfInv->pcuic/PCUICToTemplateCorrectness + + + + + + template-coq/WfInv->pcuic/TemplateToPCUICCorrectness + + + + + + template-coq/Pretty->template-coq/Extraction + + + + + + template-coq/Pretty->erasure/Erasure + + + + + + erasure/EAstUtils + + EAstUtils + + + + template-coq/Kernames->erasure/EAstUtils + + + + + + + + + + + + + + + + + template-coq/Loader->template-coq/All + + + + + + + erasure/Extraction + + Extraction + + + + erasure/Erasure->erasure/Extraction + + + + + + erasure/EOptimizePropDiscr + + EOptimizePropDiscr + + + + erasure/EOptimizePropDiscr->erasure/Erasure + + + + + + erasure/ErasureFunction->erasure/EOptimizePropDiscr + + + + + + erasure/ErasureCorrectness + + ErasureCorrectness + + + + erasure/ErasureCorrectness->erasure/ErasureFunction + + + + + + erasure/EArities->erasure/Prelim + + + + + + erasure/EInversion + + EInversion + + + + erasure/EInversion->erasure/ErasureCorrectness + + + + + + erasure/ESubstitution + + ESubstitution + + + + erasure/EDeps + + EDeps + + + + erasure/ESubstitution->erasure/EDeps + + + + + + erasure/Prelim->erasure/EInversion + + + + + + erasure/Prelim->erasure/ESubstitution + + + + + + erasure/EAll + + EAll + + + + erasure/EDeps->erasure/ErasureCorrectness + + + + + + erasure/Extract->erasure/EArities + + + + + + erasure/Extract->erasure/EAll + + + + + + erasure/ETyping + + ETyping + + + + erasure/ETyping->erasure/Extract + + + + + + erasure/EWndEval + + EWndEval + + + + erasure/ETyping->erasure/EWndEval + + + + + + erasure/ETyping->erasure/EWcbvEval + + + + + + erasure/EPretty + + EPretty + + + + erasure/ETyping->erasure/EPretty + + + + + + erasure/EWndEval->erasure/EAll + + + + + + erasure/EWcbvEval->erasure/Prelim + + + + + + erasure/EWcbvEval->erasure/EAll + + + + + + erasure/ECSubst + + ECSubst + + + + erasure/ECSubst->erasure/EWcbvEval + + + + + + erasure/EPretty->erasure/Erasure + + + + + + erasure/EReflect->erasure/ETyping + + + + + + erasure/ELiftSubst + + ELiftSubst + + + + erasure/ELiftSubst->erasure/ETyping + + + + + + erasure/ELiftSubst->erasure/ECSubst + + + + + + erasure/EInduction + + EInduction + + + + erasure/EInduction->erasure/EReflect + + + + + + erasure/EInduction->erasure/ELiftSubst + + + + + + erasure/EAstUtils->erasure/ETyping + + + + + + erasure/EAst->erasure/EInduction + + + + + + erasure/EAst->erasure/EAstUtils + + + + + + pcuic/PCUICToTemplate->pcuic/PCUICToTemplateCorrectness + + + + + diff --git a/examples/_CoqProject b/examples/_CoqProject index 1c889d23d..c3e5fd220 100644 --- a/examples/_CoqProject +++ b/examples/_CoqProject @@ -8,4 +8,5 @@ demo.v add_constructor.v tauto.v -typing_correctness.v \ No newline at end of file +typing_correctness.v +metacoq_tour_prelude.v \ No newline at end of file diff --git a/examples/metacoq_tour.v b/examples/metacoq_tour.v new file mode 100644 index 000000000..7231d35ed --- /dev/null +++ b/examples/metacoq_tour.v @@ -0,0 +1,149 @@ +From Coq Require Import String. +From MetaCoq.Template Require config utils All. +From MetaCoq.Template Require Import TemplateMonad. +From MetaCoq.PCUIC Require Import PCUICAst PCUICReduction PCUICCumulativity PCUICTyping PCUICSafeLemmata. + +Local Open Scope string_scope. + +(** MetaCoq is: + + - The "template-coq" monad, dealing with reification of terms + and environments. + - The PCUIC development of the syntactic metatheory of Coq. + - The SafeChecker package implementing reduction, conversion + and typechecking in a sound and complete way. + - The Erasure package implementing verified extraction to + untyped lambda-calculus +*) + +(* The Template monad *) + +Print Ast.term. + + +MetaCoq Quote Definition reifx := (fun x : nat => x). +Print reifx. +MetaCoq Unquote Definition x := + (Ast.tConstruct (mkInd (MPfile ["Datatypes"; "Init"; "Coq"], "nat") 0) 0 []). + +MetaCoq Run (tmBind (tmQuote (3 + 3)) tmPrint). + +MetaCoq Run (t <- tmLemma "foo44" nat ;; + qt <- tmQuote t ;; + t <- tmEval all t ;; + tmPrint qt ;; tmPrint t). +Next Obligation. + exact (3+2). +Defined. + +(* PCUIC: + + + Universes (with full algebraic universes supported everywhere) + + Universe polymorphism + + Standard type theory with dependent products and let-ins + + Inductive types and coinductive types + + Constant and axiom declarations in a global environment *) + +Print typing. + +Check type_Sort. +Check type_LetIn. +Check type_Const. + +From MetaCoq.PCUIC Require PCUICSR. + +Check PCUICSR.subject_reduction. + +(** Verified conversion and type-checking *) + +From MetaCoq.SafeChecker Require Import PCUICErrors PCUICTypeChecker PCUICSafeChecker PCUICSafeRetyping Loader. +From MetaCoq.Erasure Require Import Erasure Loader. + +Check PCUICSafeConversion.isconv_term_sound. +Check PCUICSafeConversion.isconv_term_complete. + +Check PCUICSafeChecker.infer_wf_env. +(** Proof of completeness is near completion. *) + +(** Verified retyping: from a term that is known to be well-typeable, + compute its principal type. Very common in tactics to avoid retypechecking + the whole term. *) +Check type_of. +Check type_of_subtype. + +(* Running the safe checker inside Coq *) +From MetaCoq.Examples Require Import metacoq_tour_prelude. + +Check check_inh. + +(** We construct a proof of typing entirely within Coq, calling the typechecker to produce the derivation *) +Lemma identity_typing (u := Universe.make univ): + inh gctx_wf_env [] (tProd (bNamed "s") (tSort u) (tImpl (tRel 0) (tRel 0))). +Proof. + (* We construct a term *) + set (impl := tLambda (bNamed "s") (tSort u) (tLambda bAnon (tRel 0) (tRel 0))). + (* Show that the empty context is well-formed *) + assert (wfΓ : ∥ wf_local gctx_wf_env [] ∥) by do 2 constructor. + fill_inh impl. +Qed. + +(** The extracted typechecker also runs in OCaml *) +MetaCoq SafeCheck (fun x : nat => x + 1). + +(** Erasure *) + +(** Running erasure live in Coq *) +Definition test (p : Ast.program) : string := + erase_and_print_template_program p. + +MetaCoq Quote Recursively Definition zero := 0. + +Definition zerocst := Eval lazy in test zero. +Print zerocst. + +MetaCoq Quote Recursively Definition singleton_elim := + ((fun (X : Set) (x : X) (e : x = x) => + match e in eq _ x' return bool with + | eq_refl => true + end)). +Eval lazy in (test singleton_elim). (* Optimized to remove match on Props *) + +MetaCoq Erase singleton_elim. + +(** Conclusion: Status of MetaCoq + + - 1.0 expected by Christmas with correctness and completeness of the typechecker. + + - All metatheory proofs are finished. Compared to Coq's implementation: + + - full (max (i + k, j + l)) universe support (including a naïve acyclicity checking + algorithm) + + - partial support for SProp (in programs but not yet formalized typing rules) + + - approximate cumulative inductive types checking (not yet up to reduction) + + - missing eta-conversion: the plan is to use contravariant subtyping and eta-reduction, + as in Coq CEP #47 + + - missing template-polymorphism: we're studying a sort polymorphism extension + (with G. Gilbert, K. Maillard and N. Tabareau) to subsume it completely. + + - missing modules and fast conversion machines. + + - Much work to come on the template-coq side to ease meta-programming. + + - Relation to CertiCoq: fast and verified correct erasure, not depending on type-checking + (only retyping). + + + CertiCoq needs to have all constructors eta-expanded, a proof of the + syntactic translation expanding constructors is in progress. + + + Otherwise the front-end part of CertiCoq is complete with proofs. + + + Future work: handling of primitive types (ints, floats, arrays, ...) + +*) + + + diff --git a/examples/metacoq_tour_prelude.v b/examples/metacoq_tour_prelude.v new file mode 100644 index 000000000..14a04e9b2 --- /dev/null +++ b/examples/metacoq_tour_prelude.v @@ -0,0 +1,77 @@ +(* Distributed under the terms of the MIT license. *) +From MetaCoq.Template Require Import config Universes All. +From MetaCoq.PCUIC Require Import PCUICAst PCUICAstUtils PCUICTyping PCUICLiftSubst. +From MetaCoq.SafeChecker Require Import PCUICErrors PCUICTypeChecker PCUICSafeChecker. +From Equations Require Import Equations. + +Existing Instance default_checker_flags. + +(* ********************************************************* *) +(* In this file we define a small plugin which proves *) +(* the identity theorem for any sort using the safe checker. *) +(* ********************************************************* *) + +Definition bAnon := {| binder_name := nAnon; binder_relevance := Relevant |}. +Definition bNamed s := {| binder_name := nNamed s; binder_relevance := Relevant |}. + +Definition tImpl X Y := tProd bAnon X (lift0 1 Y). + +Definition univ := Level.Level "s". + +(* TODO move to SafeChecker *) + +Definition gctx : global_env_ext := + ([], Monomorphic_ctx (LevelSet.singleton univ, ConstraintSet.empty)). + +(** We use the environment checker to produce the proof that gctx, which is a singleton with only + universe "s" declared is well-formed. *) + +Program Definition check_wf_env_ext {cf:checker_flags} (Σ : global_env) id (ext : universes_decl) : + EnvCheck ({ Σ' : wf_env_ext | Σ'.(wf_env_ext_env) = (Σ, ext)}) := + '(G; pf) <- check_wf_env Σ ;; + '(G'; pf') <- check_wf_env_ext Σ id _ G _ ext ;; + ret (exist {| wf_env_ext_env := (Σ, ext) ; + wf_env_ext_wf := _ ; + wf_env_ext_graph := G' ; + wf_env_ext_graph_wf := _ |} eq_refl). + +Definition kername_of_string (s : string) : kername := + (MPfile [], s). + +Definition make_wf_env_ext {cf:checker_flags} (Σ : global_env_ext) : EnvCheck wf_env_ext := + '(exist Σ' pf) <- check_wf_env_ext Σ.1 (kername_of_string "toplevel") Σ.2 ;; + ret Σ'. + +Definition gctx_wf_env : wf_env_ext. +Proof. + let wf_proof := eval hnf in (make_wf_env_ext gctx) in + match wf_proof with + | CorrectDecl ?x => exact x + | _ => fail "Couldn't prove the global environment is well-formed" + end. +Defined. + + + +(** There is always a proof of `forall x : Sort s, x -> x` *) + +Definition inh {cf:checker_flags} (Σ : wf_env_ext) Γ T := (∑ t, ∥ typing Σ Γ t T ∥). + +Definition check_inh {cf:checker_flags} (Σ : wf_env_ext) Γ (wfΓ : ∥ wf_local Σ Γ ∥) t {T} : typing_result (inh Σ Γ T) := + prf <- check_type_wf_env_fast Σ Γ wfΓ t (T := T) ;; + ret (t; prf). + +Ltac fill_inh t := + lazymatch goal with + [ wfΓ : ∥ wf_local _ ?Γ ∥ |- inh ?Σ ?Γ ?T ] => + let t := uconstr:(check_inh Σ Γ wfΓ t (T:=T)) in + let proof := eval lazy in t in + match proof with + | Checked ?d => exact_no_check d + | TypeError ?e => + let str := eval cbn in (string_of_type_error Σ e) in + fail "Failed to inhabit " T " : " str + | _ => fail "Anomaly: unexpected return value: " proof + end + | [ |- inh _ ?Γ _ ] => fail "Missing local wellformedness assumption for" Γ + end. From ed2de989b6d4484afb79190fe891b575bbd954bf Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Thu, 3 Dec 2020 00:58:17 +0100 Subject: [PATCH 27/70] Erasure live test shortening using the monad --- examples/_CoqProject | 5 ++++- test-suite/erasure_live_test.v | 39 +++++++++++++--------------------- 2 files changed, 19 insertions(+), 25 deletions(-) diff --git a/examples/_CoqProject b/examples/_CoqProject index c3e5fd220..4e09fd051 100644 --- a/examples/_CoqProject +++ b/examples/_CoqProject @@ -1,4 +1,6 @@ -I ../template-coq/build +-I ../safechecker/src +-I ../erasure/src -Q ../template-coq/theories MetaCoq.Template -Q ../checker/theories MetaCoq.Checker -Q ../pcuic/theories MetaCoq.PCUIC @@ -9,4 +11,5 @@ demo.v add_constructor.v tauto.v typing_correctness.v -metacoq_tour_prelude.v \ No newline at end of file +metacoq_tour_prelude.v +metacoq_tour.v \ No newline at end of file diff --git a/test-suite/erasure_live_test.v b/test-suite/erasure_live_test.v index 02b4cf88d..3a9d162bf 100644 --- a/test-suite/erasure_live_test.v +++ b/test-suite/erasure_live_test.v @@ -1,5 +1,5 @@ From Coq Require Import Recdef. -From MetaCoq.Template Require Import Loader. +From MetaCoq.Template Require Import TemplateMonad Loader. From MetaCoq.SafeChecker Require Import SafeTemplateChecker. From MetaCoq.PCUIC Require Import PCUICAstUtils. From MetaCoq.Erasure Require Import Erasure. @@ -21,21 +21,26 @@ Definition exprooftest := Eval lazy in test exproof. MetaCoq Quote Recursively Definition exintro := (@exist _ _ 0 (@eq_refl _ 0) : {x : nat | x = 0}). Definition exintrotest := Eval lazy in test exintro. -MetaCoq Quote Recursively Definition idnat := ((fun (X : Set) (x : X) => x) nat). -Definition test_idnat := Eval lazy in test idnat. +Definition idnat := ((fun (X : Set) (x : X) => x) nat). + +MetaCoq Quote Recursively Definition idnatc := idnat. +Definition test_idnat := Eval lazy in test idnatc. (** Check that optimization of singleton pattern-matchings work *) -MetaCoq Quote Recursively Definition singlelim := ((fun (X : Set) (x : X) (e : x = x) => +Definition singlelim := ((fun (X : Set) (x : X) (e : x = x) => match e in eq _ x' return bool with | eq_refl => true end)). -Time Definition singelim_test := Eval lazy in test singlelim. - -MetaCoq Quote Recursively Definition plusr := (plus 0 1). - -Time Definition plusrtest := Eval lazy in test plusr. +Definition erase {A} (a : A) : TemplateMonad unit := + aq <- tmQuoteRec a ;; + s <- tmEval lazy (erase_and_print_template_program aq) ;; + tmMsg s. +MetaCoq Run (erase 0). +MetaCoq Run (tmEval hnf idnat >>= erase). +MetaCoq Run (tmEval hnf singlelim >>= erase). +MetaCoq Run (erase (plus 0 1)). (** vector addition **) Require Coq.Vectors.Vector. @@ -47,21 +52,7 @@ Definition v01 : Vector.t nat 2 := Definition v23 : Vector.t nat 2 := (Vector.cons nat 2 1 (Vector.cons nat 3 0 (Vector.nil nat))). Definition vplus0123 := (vplus v01 v23). -MetaCoq Quote Recursively Definition cbv_vplus0123 := (* [program] of Coq's answer *) - ltac:(let t:=(eval cbv in (vplus0123)) in exact t). - -(* [Term] of Coq's answer *) -Definition ans_vplus0123 := Eval lazy in test cbv_vplus0123. - -(* [program] of the program *) -MetaCoq Quote Recursively Definition p_vplus0123 := vplus0123. -Time Definition test_p_vplus0123 := Eval lazy in test p_vplus0123. (* 5s *) -(* - Time Eval vm_compute in test p_vplus0123. (* 3.54s *) -Time Eval native_compute in test p_vplus0123. (* 23.54s on first run *) - -Time Eval native_compute in test p_vplus0123. (* 2.8s on second run *) -*) +MetaCoq Run (tmEval hnf vplus0123 >>= erase). (** Ackermann **) Fixpoint ack (n m:nat) {struct n} : nat := From faa62acc01e3a357fbfdc4fb6a26123708895fe6 Mon Sep 17 00:00:00 2001 From: Jakob Botsch Nielsen Date: Thu, 3 Dec 2020 11:23:48 +0100 Subject: [PATCH 28/70] Add missing reduction for predicate types The safe checker was destructing the inferred type of predicates directly as an arity, which was not complete. It meant that the following example was not accepted by the safe checker: Definition WrappedType := Type. Definition WrappedNat : WrappedType := nat. Definition foo : nat := match 0 return WrappedNat with | 0 => 0 | S n => 0 end. To fix we now use reduction for the predicate type. --- pcuic/theories/PCUICAstUtils.v | 14 ++ safechecker/theories/PCUICSafeReduce.v | 140 +++++++++++++++++- safechecker/theories/PCUICTypeChecker.v | 186 ++++++++++++------------ safechecker/theories/PCUICWfReduction.v | 3 +- 4 files changed, 250 insertions(+), 93 deletions(-) diff --git a/pcuic/theories/PCUICAstUtils.v b/pcuic/theories/PCUICAstUtils.v index aa8e5ea87..005ebeac5 100644 --- a/pcuic/theories/PCUICAstUtils.v +++ b/pcuic/theories/PCUICAstUtils.v @@ -886,3 +886,17 @@ Inductive view_ind : term -> Type := Equations view_indc (t : term) : view_ind t := view_indc (tInd ind u) => view_ind_tInd ind u; view_indc t => view_ind_other t _. + +Inductive view_prod_sort : term -> Type := +| view_prod_sort_prod na A B : view_prod_sort (tProd na A B) +| view_prod_sort_sort u : view_prod_sort (tSort u) +| view_prod_sort_other t : + ~isProd t -> + ~isSort t -> + view_prod_sort t. + +Equations view_prod_sortc (t : term) : view_prod_sort t := { + | tProd na A B => view_prod_sort_prod na A B; + | tSort u => view_prod_sort_sort u; + | t => view_prod_sort_other t _ _ + }. diff --git a/safechecker/theories/PCUICSafeReduce.v b/safechecker/theories/PCUICSafeReduce.v index 12226aa5a..df4493b96 100644 --- a/safechecker/theories/PCUICSafeReduce.v +++ b/safechecker/theories/PCUICSafeReduce.v @@ -6,6 +6,7 @@ From MetaCoq.PCUIC Require Import PCUICAst PCUICAstUtils PCUICUnivSubst PCUICTyping PCUICPosition PCUICNormal PCUICInversion PCUICSafeLemmata PCUICSR PCUICSN PCUICUtils PCUICReduction PCUICValidity. +From MetaCoq.SafeChecker Require Import PCUICWfReduction. Require Import Equations.Prop.DepElim. From Equations Require Import Equations. @@ -1880,5 +1881,142 @@ Section ReduceFns. noconf e0. discriminate i0. Qed. + + (* Definition of assumption-only arities (without lets) *) + Definition arity_ass := aname * term. -End ReduceFns. \ No newline at end of file + Fixpoint mkAssumArity (l : list arity_ass) (s : Universe.t) : term := + match l with + | [] => tSort s + | (na, A) :: l => tProd na A (mkAssumArity l s) + end. + + Definition arity_ass_context := rev_map (fun '(na, A) => vass na A). + + Lemma assumption_context_arity_ass_context l : + assumption_context (arity_ass_context l). + Proof. + unfold arity_ass_context. + rewrite rev_map_spec. + induction l using MCList.rev_ind; cbn. + - constructor. + - rewrite map_app, rev_app_distr. + cbn. + destruct x. + constructor; auto. + Qed. + + Lemma mkAssumArity_it_mkProd_or_LetIn (l : list arity_ass) (s : Universe.t) : + mkAssumArity l s = it_mkProd_or_LetIn (arity_ass_context l) (tSort s). + Proof. + unfold arity_ass_context. + rewrite rev_map_spec. + induction l; auto. + cbn. + destruct a. + rewrite IHl, it_mkProd_or_LetIn_app; auto. + Qed. + + Lemma isArity_mkAssumArity l s : + isArity (mkAssumArity l s). + Proof. + induction l as [|(na & A) l IH]; cbn; auto. + Qed. + + Record conv_arity {Γ T} : Type := + build_conv_arity { + conv_ar_context : list arity_ass; + conv_ar_univ : Universe.t; + conv_ar_red : ∥red Σ Γ T (mkAssumArity conv_ar_context conv_ar_univ)∥ + }. + + Global Arguments conv_arity : clear implicits. + + Lemma conv_arity_Is_conv_to_Arity {Γ T} : + conv_arity Γ T -> + Is_conv_to_Arity Σ Γ T. + Proof. + intros [asses univ r]. + eexists. + split; [eassumption|]. + apply isArity_mkAssumArity. + Qed. + + Lemma isArity_red Γ u v : + isArity u -> + red Σ Γ u v -> + isArity v. + Proof. + intros arity_u r. + induction r using red_rect_n1; [easy|]. + eapply isArity_red1; eassumption. + Qed. + + Lemma Is_conv_to_Arity_red Γ T T' : + Is_conv_to_Arity Σ Γ T -> + red Σ Γ T T' -> + Is_conv_to_Arity Σ Γ T'. + Proof. + unfold Is_conv_to_Arity. + intros [T'' (redT'' & is_arity)] red. + sq. + destruct (red_confluence HΣ red redT'') as (a & reda' & reda''). + exists a. + split; [easy|]. + clear -is_arity reda''. + eapply isArity_red; eauto. + Qed. + + Local Instance wellfounded : WellFounded (@hnf_subterm_rel _ Σ) := + @wf_hnf_subterm _ _ HΣ. + + Equations? (noeqns) reduce_to_arity (Γ : context) (T : term) (wt : welltyped Σ Γ T) + : (conv_arity Γ T) + {~Is_conv_to_Arity Σ Γ T} + by wf ((Γ;T; wt) : (∑ Γ t, welltyped Σ Γ t)) hnf_subterm_rel := + reduce_to_arity Γ T wt with inspect (hnf Γ T wt) := + | exist Thnf eqhnf with view_prod_sortc Thnf := { + | view_prod_sort_prod na A B with reduce_to_arity (Γ,, vass na A) B _ := { + | inleft car => inleft {| conv_ar_context := (na, A) :: conv_ar_context car; + conv_ar_univ := conv_ar_univ car |}; + | inright nocar => inright _ + }; + | view_prod_sort_sort u => inleft {| conv_ar_context := []; + conv_ar_univ := u |}; + | view_prod_sort_other nonar notprod notsort => inright _ + }. + Proof. + all: pose proof (@hnf_sound Γ T wt) as [r]. + all: rewrite <- ?eqhnf in r. + all: destruct HΣ as [wf]. + - destruct wt as (?&typ). + eapply subject_reduction in r; eauto. + apply inversion_Prod in r as (?&?&?&?&?); auto. + econstructor; eauto. + - constructor. + eexists _; split; eauto. + unshelve eexists _; [constructor; constructor|]; auto. + - destruct car as [c_ar c_univ [c_red]]; cbn. + constructor. + etransitivity; eauto. + eapply red_prod; eauto. + - eapply Is_conv_to_Arity_red in H as (?&[r']&isar); eauto. + apply invert_red_prod in r' as (?&?&(->&?)&?); auto. + contradiction nocar. + eexists; eauto using sq. + - constructor; auto. + - pose proof (@hnf_complete Γ T wt) as [w]. + destruct HΣ. + apply Is_conv_to_Arity_inv in H as [(na&A&B&[r'])|(u&[r'])]; auto. + + eapply red_confluence in r' as (?&r1&r2); eauto. + apply invert_red_prod in r2 as (?&?&(->&?)&?); auto. + eapply whnf_red_inv in r1; eauto. + depelim r1. + rewrite H in notprod; auto. + + eapply red_confluence in r' as (?&r1&r2); eauto. + apply invert_red_sort in r2 as ->. + eapply whnf_red_inv in r1; eauto. + depelim r1. + rewrite H in notsort; cbn in *; auto. + Qed. + +End ReduceFns. diff --git a/safechecker/theories/PCUICTypeChecker.v b/safechecker/theories/PCUICTypeChecker.v index 315cd9e0d..bb97f5824 100644 --- a/safechecker/theories/PCUICTypeChecker.v +++ b/safechecker/theories/PCUICTypeChecker.v @@ -119,9 +119,28 @@ Section Typecheck. Next Obligation. destruct HΣ, HΓ, hA, X, X0. constructor. eapply type_Cumul'; eassumption. Qed. + + Program Definition infer_scheme Γ HΓ t : + typing_result (∑ ctx u, ∥ Σ ;;; Γ |- t : mkAssumArity ctx u ∥) := + '(T; p) <- infer Γ HΓ t;; + match reduce_to_arity HΣ Γ T _ with + | inleft car => ret (conv_ar_context car; conv_ar_univ car; _) + | inright _ => TypeError (NotAnArity T) + end. + Next Obligation. + intros; subst. + cbn in *. + eapply validity_wf; eauto. + Qed. + Next Obligation. + destruct car as [? ? [r]]. + cbn. + clear Heq_anonymous. + sq. + eapply type_reduction; eauto. + Qed. End InferAux. - Program Definition lookup_ind_decl ind : typing_result ({decl & {body & declared_inductive (fst Σ) decl ind body}}) := @@ -314,41 +333,39 @@ Section Typecheck. (Msg "Case on coinductives disallowed") ;; check_eq_true (ind_npars decl =? par) (Msg "not the right number of parameters") ;; - pty <- infer Γ HΓ p ;; - match destArity [] pty.π1 with - | None => raise (Msg "the type of the return predicate of a Case is not an arity") - | Some (pctx, ps) => - check_is_allowed_elimination ps (ind_kelim body);; - let params := firstn par args in - match build_case_predicate_type ind decl body params u ps with - | None => raise (Msg "failure in build_case_predicate_type") - | Some pty' => - (* We could avoid one useless sort comparison by only comparing *) - (* the contexts [pctx] and [indctx] (what is done in Coq). *) - match iscumul Γ pty.π1 _ pty' _ with - | ConvError e => raise (NotCumulSmaller G Γ pty.π1 pty' pty.π1 pty' e) - | ConvSuccess => - match map_option_out (build_branches_type ind decl body params u p) with - | None => raise (Msg "failure in build_branches_type") - | Some btys => - let btyswf : ∥ All (isType Σ Γ ∘ snd) btys ∥ := _ in - (fix check_branches (brs btys : list (nat * term)) - (HH : ∥ All (isType Σ Γ ∘ snd) btys ∥) {struct brs} - : typing_result - (All2 (fun br bty => br.1 = bty.1 /\ ∥ Σ ;;; Γ |- br.2 : bty.2 ∥) brs btys) - := match brs, btys with - | [], [] => ret All2_nil - | (n, t) :: brs , (m, A) :: btys => - W <- check_dec (Msg "not nat eq") - (EqDecInstances.nat_eqdec n m) ;; - Z <- infer_cumul infer Γ HΓ t A _ ;; - X <- check_branches brs btys _ ;; - ret (All2_cons (conj _ _) X) - | [], _ :: _ - | _ :: _, [] => raise (Msg "wrong number of branches") - end) brs btys btyswf ;; - ret (mkApps p (List.skipn par args ++ [c]); _) - end + IS <- infer_scheme infer Γ HΓ p ;; + let '(pctx; IS') := IS in let '(ps; typ_p) := IS' in + check_is_allowed_elimination ps (ind_kelim body);; + let pty := mkAssumArity pctx ps in + let params := firstn par args in + match build_case_predicate_type ind decl body params u ps with + | None => raise (Msg "failure in build_case_predicate_type") + | Some pty' => + (* We could avoid one useless sort comparison by only comparing *) + (* the contexts [pctx] and [indctx] (what is done in Coq). *) + match iscumul Γ pty _ pty' _ with + | ConvError e => raise (NotCumulSmaller G Γ pty pty' pty pty' e) + | ConvSuccess => + match map_option_out (build_branches_type ind decl body params u p) with + | None => raise (Msg "failure in build_branches_type") + | Some btys => + let btyswf : ∥ All (isType Σ Γ ∘ snd) btys ∥ := _ in + (fix check_branches (brs btys : list (nat * term)) + (HH : ∥ All (isType Σ Γ ∘ snd) btys ∥) {struct brs} + : typing_result + (All2 (fun br bty => br.1 = bty.1 /\ ∥ Σ ;;; Γ |- br.2 : bty.2 ∥) brs btys) + := match brs, btys with + | [], [] => ret All2_nil + | (n, t) :: brs , (m, A) :: btys => + W <- check_dec (Msg "not nat eq") + (EqDecInstances.nat_eqdec n m) ;; + Z <- infer_cumul infer Γ HΓ t A _ ;; + X <- check_branches brs btys _ ;; + ret (All2_cons (conj _ _) X) + | [], _ :: _ + | _ :: _, [] => raise (Msg "wrong number of branches") + end) brs btys btyswf ;; + ret (mkApps p (List.skipn par args ++ [c]); _) end end end @@ -516,82 +533,77 @@ Section Typecheck. Next Obligation. simpl; eauto using validity_wf. Qed. Next Obligation. simpl; eauto using validity_wf. Qed. Next Obligation. - destruct X, X9. sq. + destruct X1, X11. sq. change (eqb ind I = true) in H0. destruct (eqb_spec ind I) as [e|e]; [destruct e|discriminate]. change (eqb (ind_npars d) par = true) in H1. destruct (eqb_spec (ind_npars d) par) as [e|e]; [|discriminate]. rename Heq_anonymous into HH. symmetry in HH. simpl in *. - eapply type_reduction in t0; eauto. eapply validity in t0; eauto. rewrite <- e in HH. eapply PCUICInductiveInversion.WfArity_build_case_predicate_type in HH; eauto. destruct HH as [[s Hs] ?]. eexists; eauto. - eapply validity in t; eauto. - generalize (PCUICClosed.destArity_spec [] pty). - rewrite -Heq_anonymous0 /=. intros ->. - eapply PCUICInductives.isType_it_mkProd_or_LetIn_inv in t; eauto. - eapply isType_wf_universes in t. simpl in t. - now exact (elimT wf_universe_reflect t). auto. + eapply isType_red; [|eassumption]. + eapply validity; eauto. + rewrite mkAssumArity_it_mkProd_or_LetIn in X. + eapply validity in X; auto. + eapply PCUICInductives.isType_it_mkProd_or_LetIn_inv in X; eauto. + eapply isType_wf_universes in X; auto. + now exact (elimT wf_universe_reflect X). Qed. Next Obligation. - symmetry in Heq_anonymous2. - unfold iscumul in Heq_anonymous2. simpl in Heq_anonymous2. - apply isconv_term_sound in Heq_anonymous2. - red in Heq_anonymous2. + symmetry in Heq_anonymous1. + unfold iscumul in Heq_anonymous1. simpl in Heq_anonymous1. + apply isconv_term_sound in Heq_anonymous1. + red in Heq_anonymous1. noconf Heq_I''. noconf Heq_I'. noconf Heq_I. noconf Heq_d. noconf Heq_d'. + noconf Heq_IS. noconf Heq_IS'. simpl in *; sq. change (eqb ind I = true) in H0. destruct (eqb_spec ind I) as [e|e]; [destruct e|discriminate H0]. change (eqb (ind_npars d) par = true) in H1. destruct (eqb_spec (ind_npars d) par) as [e|e]; [|discriminate]; subst. assert (wfΣ : wf_ext Σ) by (split; auto). - eapply type_reduction in X9; eauto. - have val:= validity_term wfΣ X9. - eapply type_Cumul' in X; [| |eassumption]. + eapply type_reduction in X11; eauto. + have val:= validity_term wfΣ X11. + eapply type_Cumul' in typ_p; [| |eassumption]. 2:{ eapply PCUICInductiveInversion.WfArity_build_case_predicate_type; eauto. - eapply validity in X; eauto. - generalize (PCUICClosed.destArity_spec [] pty). - rewrite -Heq_anonymous0 /=. intros ->. - eapply PCUICInductives.isType_it_mkProd_or_LetIn_inv in X; eauto. - eapply isType_wf_universes in X. simpl in X. - now exact (elimT wf_universe_reflect X). auto. } - have [pctx' da] : (∑ pctx', destArity [] pty' = Some (pctx', ps)). - { symmetry in Heq_anonymous1. - unshelve eapply (PCUICInductives.build_case_predicate_type_spec (Σ.1, ind_universes d)) in Heq_anonymous1 as [parsubst [_ ->]]. + eapply validity in typ_p; eauto. + rewrite mkAssumArity_it_mkProd_or_LetIn in typ_p. + eapply PCUICInductives.isType_it_mkProd_or_LetIn_inv in typ_p; eauto. + apply isType_wf_universes in typ_p; auto. + now exact (elimT wf_universe_reflect typ_p). } + have [pctx' da] : (∑ pctx', destArity [] pty' = Some (pctx', X0)). + { symmetry in Heq_anonymous0. + unshelve eapply (PCUICInductives.build_case_predicate_type_spec (Σ.1, ind_universes d)) in Heq_anonymous0 as [parsubst [_ ->]]. eauto. eapply (PCUICWeakeningEnv.on_declared_inductive wfΣ) in HH as [? ?]. eauto. eexists. rewrite !destArity_it_mkProd_or_LetIn; simpl. reflexivity. } - eapply PCUICInductiveInversion.build_branches_type_wt. 6:eapply X. all:eauto. + eapply PCUICInductiveInversion.build_branches_type_wt. 6:eapply typ_p. all:eauto. Defined. - Obligation Tactic := simpl; intros. - Next Obligation. - rename Heq_anonymous2 into XX2. - symmetry in XX2. simpl in *. eapply isconv_sound in XX2. - change (eqb ind ind' = true) in H0. - destruct (eqb_spec ind ind') as [e|e]; [destruct e|discriminate H0]. - change (eqb (ind_npars decl) par = true) in H1. - destruct (eqb_spec (ind_npars decl) par) as [e|e]; [|discriminate]; subst. - depelim HH. - sq. auto. now depelim X. + sq. + depelim HH; auto. Defined. Next Obligation. - sq. now depelim HH. + sq. + depelim HH; auto. Defined. (* The obligation tactic removes a useful let here. *) Obligation Tactic := idtac. Next Obligation. intros. clearbody btyswf. idtac; Program.Tactics.program_simplify. - symmetry in Heq_anonymous2. - unfold iscumul in Heq_anonymous2. simpl in Heq_anonymous2. - apply isconv_term_sound in Heq_anonymous2. + symmetry in Heq_anonymous1. + unfold iscumul in Heq_anonymous1. simpl in Heq_anonymous1. + apply isconv_term_sound in Heq_anonymous1. noconf Heq_I''. noconf Heq_I'. noconf Heq_I. - noconf Heq_d. noconf Heq_d'. simpl in *. + noconf Heq_d. noconf Heq_d'. + noconf Heq_IS. noconf Heq_IS'. + simpl in *. assert (∥ All2 (fun x y => ((fst x = fst y) * (Σ;;; Γ |- snd x : snd y) * isType Σ Γ y.2)%type) brs btys ∥). { solve_all. simpl in *. @@ -602,21 +614,15 @@ Section Typecheck. change (eqb (ind_npars d) par = true) in H1. destruct (eqb_spec (ind_npars d) par) as [e|e]; [|discriminate]; subst. assert (wfΣ : wf_ext Σ) by (split; auto). - eapply type_reduction in X9; eauto. - eapply type_Cumul' in X; eauto. + eapply type_reduction in X11; eauto. + eapply type_Cumul' in typ_p; eauto. 2:{ eapply PCUICInductiveInversion.WfArity_build_case_predicate_type; eauto. - now eapply validity in X9. - eapply validity in X; eauto. - generalize (PCUICClosed.destArity_spec [] pty). - rewrite -Heq_anonymous0 /=. intros ->. - eapply PCUICInductives.isType_it_mkProd_or_LetIn_inv in X; eauto. - eapply isType_wf_universes in X. simpl in X. - now exact (elimT wf_universe_reflect X). auto. } - have [pctx' da] : (∑ pctx', destArity [] pty' = Some (pctx', ps)). - { symmetry in Heq_anonymous1. - unshelve eapply (PCUICInductives.build_case_predicate_type_spec (Σ.1, ind_universes d)) in Heq_anonymous1 as [parsubst [_ ->]]. - eauto. eapply (PCUICWeakeningEnv.on_declared_inductive wfΣ) in HH as [? ?]. eauto. - eexists. rewrite !destArity_it_mkProd_or_LetIn; simpl. reflexivity. } + eapply validity in X11; eauto. + eapply validity in typ_p; auto. + rewrite mkAssumArity_it_mkProd_or_LetIn in typ_p. + eapply PCUICInductives.isType_it_mkProd_or_LetIn_inv in typ_p; eauto. + apply isType_wf_universes in typ_p; auto. + now exact (elimT wf_universe_reflect typ_p). } eapply type_Case with (pty0:=pty'); tea. - reflexivity. - symmetry; eassumption. diff --git a/safechecker/theories/PCUICWfReduction.v b/safechecker/theories/PCUICWfReduction.v index 91ae67eb6..befb3a7a8 100644 --- a/safechecker/theories/PCUICWfReduction.v +++ b/safechecker/theories/PCUICWfReduction.v @@ -6,7 +6,6 @@ From MetaCoq.PCUIC Require Import PCUICAst PCUICAstUtils PCUICWeakening PCUICPosition PCUICCumulativity PCUICSafeLemmata PCUICSN PCUICPretty PCUICArities PCUICConfluence PCUICSize PCUICContextConversion PCUICConversion PCUICWfUniverses. -From MetaCoq.SafeChecker Require Import PCUICSafeReduce PCUICSafeConversion. From Equations Require Import Equations. Require Import ssreflect ssrbool. @@ -268,4 +267,4 @@ Section fix_sigma. | H : ∥ _ ∥ |- _ => destruct H end; try eapply sq. -End fix_sigma. \ No newline at end of file +End fix_sigma. From 006b4abfc67216d9aa710ab69fd0a0f7c6316793 Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Thu, 3 Dec 2020 11:49:53 +0100 Subject: [PATCH 29/70] Dependency on erasure missing --- Makefile | 2 +- examples/_CoqProject | 1 + 2 files changed, 2 insertions(+), 1 deletion(-) diff --git a/Makefile b/Makefile index 89b059dd3..f69fca98e 100644 --- a/Makefile +++ b/Makefile @@ -72,7 +72,7 @@ erasure: template-coq safechecker pcuic checker: template-coq $(MAKE) -C checker -examples: checker safechecker +examples: checker safechecker erasure $(MAKE) -C examples test-suite: template-coq checker safechecker erasure diff --git a/examples/_CoqProject b/examples/_CoqProject index 4e09fd051..a84ae72c0 100644 --- a/examples/_CoqProject +++ b/examples/_CoqProject @@ -5,6 +5,7 @@ -Q ../checker/theories MetaCoq.Checker -Q ../pcuic/theories MetaCoq.PCUIC -Q ../safechecker/theories MetaCoq.SafeChecker +-Q ../erasure/theories MetaCoq.Erasure -R . MetaCoq.Examples demo.v From c7f8694af94bbec24de1314a9e1f5315dd65a433 Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Thu, 3 Dec 2020 22:12:50 +0100 Subject: [PATCH 30/70] Implement denotation of evars, with special case for "fresh_evar_id" --- template-coq/src/ast_denoter.ml | 4 ++ template-coq/src/constr_denoter.ml | 14 ++++ template-coq/src/constr_reification.ml | 3 +- template-coq/src/denoter.ml | 90 +++++++++++++++----------- template-coq/src/g_template_coq.mlg | 3 +- template-coq/src/run_extractable.ml | 8 ++- template-coq/src/run_template_monad.ml | 45 ++++++------- template-coq/theories/Ast.v | 6 ++ template-coq/theories/BasicAst.v | 4 ++ template-coq/theories/Constants.v | 1 + test-suite/evars.v | 35 +++++++++- 11 files changed, 145 insertions(+), 68 deletions(-) diff --git a/template-coq/src/ast_denoter.ml b/template-coq/src/ast_denoter.ml index 5d1c541bd..5ff4e52df 100644 --- a/template-coq/src/ast_denoter.ml +++ b/template-coq/src/ast_denoter.ml @@ -119,6 +119,10 @@ struct match q with | Datatypes.O -> 0 | Datatypes.S x -> succ (unquote_int x) + + let unquote_evar env evm n l = + let id = Evar.unsafe_of_int (unquote_int n) in + evm, mkEvar (id, Array.of_list l) let unquote_bool (q : quoted_bool) : bool = q diff --git a/template-coq/src/constr_denoter.ml b/template-coq/src/constr_denoter.ml index e0f95a4b5..9e1ae3c27 100644 --- a/template-coq/src/constr_denoter.ml +++ b/template-coq/src/constr_denoter.ml @@ -129,6 +129,16 @@ struct else not_supported_verb trm "unquote_name" + let unquote_evar env evm id args = + if constr_equall id tfresh_evar_id then + let evm, (tyev, s) = Evarutil.new_type_evar env evm Evd.univ_flexible_alg in + let evm, ev = Evarutil.new_evar env evm tyev in + evm, EConstr.Unsafe.to_constr ev + else + let id = unquote_nat id in + let ev = Evar.unsafe_of_int id in + evm, Constr.mkEvar (ev, Array.of_list args) + let unquote_relevance trm = if Constr.equal trm (Lazy.force tRelevant) then Sorts.Relevant @@ -336,6 +346,10 @@ struct match args with x :: _ -> ACoq_tVar x | _ -> CErrors.user_err (print_term t ++ Pp.str ("has bad structure")) + else if constr_equall h tEvar then + match args with + | [x; y] -> ACoq_tEvar (x, unquote_list y) + | _ -> CErrors.user_err (print_term t ++ Pp.str ("has bad structure")) else if constr_equall h tSort then match args with x :: _ -> ACoq_tSort x diff --git a/template-coq/src/constr_reification.ml b/template-coq/src/constr_reification.ml index ceb39fe67..65fd3bcbe 100644 --- a/template-coq/src/constr_reification.ml +++ b/template-coq/src/constr_reification.ml @@ -148,7 +148,8 @@ struct let tMPfile = ast "MPfile" let tMPbound = ast "MPbound" let tMPdot = ast "MPdot" - + let tfresh_evar_id = ast "fresh_evar_id" + let tproplevel = ast "level.prop_level_type" let tlevelSProp = ast "level.lsprop" let tlevelProp = ast "level.lprop" diff --git a/template-coq/src/denoter.ml b/template-coq/src/denoter.ml index 938d2c45d..d7ab41fc7 100644 --- a/template-coq/src/denoter.ml +++ b/template-coq/src/denoter.ml @@ -10,7 +10,8 @@ sig val unquote_name : quoted_name -> Name.t val unquote_aname : quoted_aname -> Name.t Context.binder_annot val unquote_relevance : quoted_relevance -> Sorts.relevance - val unquote_int : quoted_int -> int + val unquote_evar : Environ.env -> Evd.evar_map -> quoted_int -> Constr.t list -> Evd.evar_map * Constr.t + val unquote_int : quoted_int -> int val unquote_bool : quoted_bool -> bool (* val unquote_sort : quoted_sort -> Sorts.t *) (* val unquote_sort_family : quoted_sort_family -> Sorts.family *) @@ -36,6 +37,9 @@ let map_evm (f : 'a -> 'b -> 'a * 'c) (evm : 'a) (l : 'b list) : 'a * ('c list) let evm, res = List.fold_left (fun (evm, l) b -> let evm, c = f evm b in evm, c :: l) (evm, []) l in evm, List.rev res +let fold_env_evm_right (f : 'a -> 'b -> 'c -> 'a * 'b * 'd) (env : 'a) (evm : 'b) (l : 'c list) : 'a * 'b * ('d list) = + List.fold_right (fun b (env, evm, l) -> let env, evm, c = f env evm b in env, evm, c :: l) l (env, evm, []) + module Denoter (D : BaseDenoter) = struct @@ -45,28 +49,42 @@ struct ACoq_tApp (f, xs) -> app_full_abs f (xs @ acc) | _ -> (trm, acc) - let denote_term (evm : Evd.evar_map) (trm: D.t) : Evd.evar_map * Constr.t = - let rec aux evm (trm: D.t) : _ * Constr.t = + let push_rec_types (lna,typarray) env = + let open Context.Rel.Declaration in + let ctxt = CArray.map2_i (fun i na t -> LocalAssum (na, Vars.lift i t)) lna typarray in + Array.fold_left (fun e assum -> Environ.push_rel assum e) env ctxt + + let denote_term (env : Environ.env) (evm : Evd.evar_map) (trm: D.t) : Evd.evar_map * Constr.t = + let open Context.Rel.Declaration in + let rec aux env evm (trm: D.t) : _ * Constr.t = (* debug (fun () -> Pp.(str "denote_term" ++ spc () ++ pr_constr trm)) ; *) match D.inspect_term trm with | ACoq_tRel x -> evm, Constr.mkRel (D.unquote_int x + 1) | ACoq_tVar x -> evm, Constr.mkVar (D.unquote_ident x) + | ACoq_tEvar (n, l) -> + let evm, l' = map_evm (aux env) evm l in + D.unquote_evar env evm n l' | ACoq_tSort x -> let evm, u = D.unquote_universe evm x in evm, Constr.mkType u - | ACoq_tCast (t,c,ty) -> let evm, t = aux evm t in - let evm, ty = aux evm ty in + | ACoq_tCast (t,c,ty) -> let evm, t = aux env evm t in + let evm, ty = aux env evm ty in evm, Constr.mkCast (t, D.unquote_cast_kind c, ty) - | ACoq_tProd (n,t,b) -> let evm, t = aux evm t in - let evm, b = aux evm b in - evm, Constr.mkProd (D.unquote_aname n, t, b) - | ACoq_tLambda (n,t,b) -> let evm, t = aux evm t in - let evm, b = aux evm b in - evm, Constr.mkLambda (D.unquote_aname n, t, b) - | ACoq_tLetIn (n,e,t,b) -> let evm, e = aux evm e in - let evm, t = aux evm t in - let evm, b = aux evm b in - evm, Constr.mkLetIn (D.unquote_aname n, e, t, b) - | ACoq_tApp (f,xs) -> let evm, f = aux evm f in - let evm, xs = map_evm aux evm xs in + | ACoq_tProd (n,t,b) -> let evm, t = aux env evm t in + let n = D.unquote_aname n in + let evm, b = aux (Environ.push_rel (LocalAssum (n, t)) env) evm b in + evm, Constr.mkProd (n, t, b) + | ACoq_tLambda (n,t,b) -> + let n = D.unquote_aname n in + let evm, t = aux env evm t in + let evm, b = aux (Environ.push_rel (LocalAssum (n, t)) env) evm b in + evm, Constr.mkLambda (n, t, b) + | ACoq_tLetIn (n,e,t,b) -> + let n = D.unquote_aname n in + let evm, e = aux env evm e in + let evm, t = aux env evm t in + let evm, b = aux (Environ.push_rel (LocalDef (n, e, t)) env) evm b in + evm, Constr.mkLetIn (n, e, t, b) + | ACoq_tApp (f,xs) -> let evm, f = aux env evm f in + let evm, xs = map_evm (aux env) evm xs in evm, Constr.mkApp (f, Array.of_list xs) | ACoq_tConst (s,u) -> let s = D.unquote_kn s in @@ -83,28 +101,32 @@ struct | ACoq_tCase (((i, _), r), ty, d, brs) -> let ind = D.unquote_inductive i in let relevance = D.unquote_relevance r in - let evm, ty = aux evm ty in - let evm, d = aux evm d in - let evm, brs = map_evm aux evm (List.map snd brs) in + let evm, ty = aux env evm ty in + let evm, d = aux env evm d in + let evm, brs = map_evm (aux env) evm (List.map snd brs) in (* todo: reify better case_info *) let ci = Inductiveops.make_case_info (Global.env ()) ind relevance Constr.RegularStyle in evm, Constr.mkCase (ci, ty, d, Array.of_list brs) | ACoq_tFix (lbd, i) -> let (names,types,bodies,rargs) = (List.map (fun p->p.adname) lbd, List.map (fun p->p.adtype) lbd, List.map (fun p->p.adbody) lbd, List.map (fun p->p.rarg) lbd) in - let evm, types = map_evm aux evm types in - let evm, bodies = map_evm aux evm bodies in + let evm, types = map_evm (aux env) evm types in let (names,rargs) = (List.map D.unquote_aname names, List.map D.unquote_int rargs) in let la = Array.of_list in - evm, Constr.mkFix ((la rargs, D.unquote_int i), (la names, la types, la bodies)) + let lnames = la names and ltypes = la types in + let env = push_rec_types (lnames, ltypes) env in + let evm, bodies = map_evm (aux env) evm bodies in + evm, Constr.mkFix ((la rargs, D.unquote_int i), (lnames, ltypes, la bodies)) | ACoq_tCoFix (lbd, i) -> let (names,types,bodies,rargs) = (List.map (fun p->p.adname) lbd, List.map (fun p->p.adtype) lbd, List.map (fun p->p.adbody) lbd, List.map (fun p->p.rarg) lbd) in - let evm, types = map_evm aux evm types in - let evm, bodies = map_evm aux evm bodies in + let evm, types = map_evm (aux env) evm types in let (names,rargs) = (List.map D.unquote_aname names, List.map D.unquote_int rargs) in let la = Array.of_list in - evm, Constr.mkCoFix (D.unquote_int i, (la names, la types, la bodies)) + let lnames = la names and ltypes = la types in + let env = push_rec_types (lnames, ltypes) env in + let evm, bodies = map_evm (aux env) evm bodies in + evm, Constr.mkCoFix (D.unquote_int i, (lnames, ltypes, la bodies)) | ACoq_tProj (proj,t) -> let (ind, npars, arg) = D.unquote_proj proj in @@ -115,19 +137,9 @@ struct | Some p -> Names.Constant.label p | None -> failwith "tproj case of denote_term") in let p' = Names.Projection.make (Projection.Repr.make ind' ~proj_npars ~proj_arg l) false in - let evm, t' = aux evm t in + let evm, t' = aux env evm t in evm, Constr.mkProj (p', t') - (* | _ -> not_supported_verb trm "big_case" - * - * | ACoq_tProj (proj,t) -> - * let (ind, _, narg) = D.unquote_proj proj in (\* todo: is narg the correct projection? *\) - * let ind' = D.unquote_inductive ind in - * let projs = Recordops.lookup_projections ind' in - * let evm, t = aux evm t in - * (match List.nth projs (D.unquote_int narg) with - * | Some p -> evm, Constr.mkProj (Names.Projection.make p false, t) - * | None -> (\*bad_term trm *\) ) *) - | _ -> failwith "big case of denote_term" - in aux evm trm + + in aux env evm trm end diff --git a/template-coq/src/g_template_coq.mlg b/template-coq/src/g_template_coq.mlg index 1be9112d1..be66af2c2 100644 --- a/template-coq/src/g_template_coq.mlg +++ b/template-coq/src/g_template_coq.mlg @@ -180,8 +180,9 @@ END TACTIC EXTEND TemplateCoq_denote_term | [ "denote_term" constr(c) tactic(tac) ] -> { Proofview.Goal.enter (begin fun gl -> + let env = Proofview.Goal.env gl in let evm = Proofview.Goal.sigma gl in - let evm, c = Constr_denoter.denote_term evm (to_constr_evars evm c) in + let evm, c = Constr_denoter.denote_term env evm (to_constr_evars evm c) in Proofview.tclTHEN (Proofview.Unsafe.tclEVARS evm) (ltac_apply tac (List.map to_ltac_val [EConstr.of_constr c])) end) } diff --git a/template-coq/src/run_extractable.ml b/template-coq/src/run_extractable.ml index 47e581b07..6910d6364 100644 --- a/template-coq/src/run_extractable.ml +++ b/template-coq/src/run_extractable.ml @@ -137,11 +137,13 @@ let of_cast_kind (ck: BasicAst.cast_kind) : Constr.cast_kind = | RevertCast -> Constr.REVERTcast (* todo(gmm): determine what of these already exist. *) -let rec to_constr_ev (evm : Evd.evar_map) (t : Ast0.term) : Evd.evar_map * Constr.t = - denote_term evm t +let rec to_constr_ev env (evm : Evd.evar_map) (t : Ast0.term) : Evd.evar_map * Constr.t = + denote_term env evm t let to_constr (t : Ast0.term) : Constr.t = - snd (to_constr_ev Evd.empty t) + let env = Global.env () in + let evm = Evd.from_env env in + snd (to_constr_ev env evm t) let tmOfConstr (t : Constr.t) : Ast0.term tm = Plugin_core.with_env_evm (fun env _ -> tmReturn (quote_term env t)) diff --git a/template-coq/src/run_template_monad.ml b/template-coq/src/run_template_monad.ml index 4e9b557b0..e9f5e6992 100644 --- a/template-coq/src/run_template_monad.ml +++ b/template-coq/src/run_template_monad.ml @@ -220,16 +220,16 @@ let denote_universes_entry evm trm (* of type universes_entry *) : _ * Entries.u | _ -> bad_term_verb trm "denote_universes_entry" -let unquote_one_inductive_entry evm trm (* of type one_inductive_entry *) : _ * Entries.one_inductive_entry = +let unquote_one_inductive_entry env evm trm (* of type one_inductive_entry *) : _ * Entries.one_inductive_entry = let (h,args) = app_full trm [] in if constr_equall h tBuild_one_inductive_entry then match args with | id::ar::template::cnames::ctms::[] -> let id = unquote_ident id in - let evm, ar = denote_term evm ar in + let evm, ar = denote_term env evm ar in let template = unquote_bool template in let cnames = List.map unquote_ident (unquote_list cnames) in - let evm, ctms = map_evm denote_term evm (unquote_list ctms) in + let evm, ctms = map_evm (denote_term env) evm (unquote_list ctms) in evm, { mind_entry_typename = id ; mind_entry_arity = ar; mind_entry_template = template; @@ -244,32 +244,33 @@ let map_option f o = | Some x -> Some (f x) | None -> None -let denote_decl evm d = +let denote_decl env evm d = let (h, args) = app_full d [] in if constr_equall h tmkdecl then match args with | name :: body :: typ :: [] -> let name = unquote_aname name in - let evm, ty = denote_term evm typ in - (match unquote_option body with + let evm, ty = denote_term env evm typ in + let evm, decl = (match unquote_option body with | None -> evm, Context.Rel.Declaration.LocalAssum (name, ty) - | Some body -> let evm, body = denote_term evm body in + | Some body -> let evm, body = denote_term env evm body in evm, Context.Rel.Declaration.LocalDef (name, body, ty)) + in Environ.push_rel decl env, evm, decl | _ -> bad_term_verb d "denote_decl" else bad_term_verb d "denote_decl" -let denote_context evm ctx = - map_evm denote_decl evm (unquote_list ctx) +let denote_context env evm ctx = + fold_env_evm_right denote_decl env evm (unquote_list ctx) -let unquote_mutual_inductive_entry evm trm (* of type mutual_inductive_entry *) : _ * Entries.mutual_inductive_entry = +let unquote_mutual_inductive_entry env evm trm (* of type mutual_inductive_entry *) : _ * Entries.mutual_inductive_entry = let (h,args) = app_full trm [] in if constr_equall h tBuild_mutual_inductive_entry then match args with | record::finite::params::inds::univs::variance::priv::[] -> let record = map_option (map_option (fun x -> [|x|])) (unquote_map_option (unquote_map_option unquote_ident) record) in let finite = denote_mind_entry_finite finite in - let evm, params = denote_context evm params in - let evm, inds = map_evm unquote_one_inductive_entry evm (unquote_list inds) in + let envpars, evm, params = denote_context env evm params in + let evm, inds = map_evm (unquote_one_inductive_entry env) evm (unquote_list inds) in let evm, univs = denote_universes_entry evm univs in let evm, variance = denote_variances evm variance in let priv = unquote_map_option unquote_bool priv in @@ -287,7 +288,7 @@ let unquote_mutual_inductive_entry evm trm (* of type mutual_inductive_entry *) let declare_inductive (env: Environ.env) (evm: Evd.evar_map) (mind: Constr.t) : unit = let mind = reduce_all env evm mind in - let evm, mind = unquote_mutual_inductive_entry evm mind in + let evm, mind = unquote_mutual_inductive_entry env evm mind in ignore (DeclareInd.declare_mutual_inductive_with_eliminations mind Names.Id.Map.empty []) let not_in_tactic s = @@ -332,19 +333,19 @@ let rec run_template_program_rec ~poly ?(intactic=false) (k : Environ.env * Evd. else let name = unquote_ident (reduce_all env evm name) in let opaque = unquote_bool (reduce_all env evm opaque) in - let evm,body = denote_term evm (reduce_all env evm body) in + let evm,body = denote_term env evm (reduce_all env evm body) in let evm,typ = match unquote_option typ with | None -> (evm, None) | Some t -> - let (evm, t) = denote_term evm (reduce_all env evm t) in + let (evm, t) = denote_term env evm (reduce_all env evm t) in (evm, Some t) in Plugin_core.run (Plugin_core.tmDefinition name ~poly ~opaque typ body) env evm (fun env evm res -> k (env, evm, quote_kn res)) | TmLemmaTerm (name, typ) -> let ident = unquote_ident (reduce_all env evm name) in - let evm,typ = denote_term evm (reduce_all env evm typ) in + let evm,typ = denote_term env evm (reduce_all env evm typ) in Plugin_core.run (Plugin_core.tmLemma ident ~poly typ) env evm (fun env evm kn -> k (env, evm, quote_kn kn)) @@ -364,7 +365,7 @@ let rec run_template_program_rec ~poly ?(intactic=false) (k : Environ.env * Evd. then not_in_tactic "tmAxiom" else let name = unquote_ident (reduce_all env evm name) in - let evm,typ = denote_term evm (reduce_all env evm typ) in + let evm,typ = denote_term env evm (reduce_all env evm typ) in Plugin_core.run (Plugin_core.tmAxiom name ~poly typ) env evm (fun a b c -> k (a,b,quote_kn c)) @@ -437,7 +438,7 @@ let rec run_template_program_rec ~poly ?(intactic=false) (k : Environ.env * Evd. in k (env, evm, trm) | TmEvalTerm (s,trm) -> let red = unquote_reduction_strategy env evm (reduce_all env evm s) in - let evm,trm = denote_term evm (reduce_all env evm trm) in + let evm,trm = denote_term env evm (reduce_all env evm trm) in Plugin_core.run (Plugin_core.tmEval red trm) env evm (fun env evm trm -> k (env, evm, quote_term env trm)) | TmMkInductive mind -> @@ -448,7 +449,7 @@ let rec run_template_program_rec ~poly ?(intactic=false) (k : Environ.env * Evd. begin try let t = reduce_all env evm t in - let evm, t' = denote_term evm t in + let evm, t' = denote_term env evm t in let typ = Retyping.get_type_of env evm (EConstr.of_constr t') in let evm, typ = Evarsolve.refresh_universes (Some false) env evm typ in let make_typed_term typ term evm = @@ -465,7 +466,7 @@ let rec run_template_program_rec ~poly ?(intactic=false) (k : Environ.env * Evd. with Reduction.NotArity -> CErrors.user_err (str "unquoting ill-typed term") end | TmUnquoteTyped (typ, t) -> - let evm, t' = denote_term evm (reduce_all env evm t) in + let evm, t' = denote_term env evm (reduce_all env evm t) in (* let t' = Typing.e_solve_evars env evdref (EConstr.of_constr t') in *) let evm = Typing.check env evm (EConstr.of_constr t') (EConstr.of_constr typ) in k (env, evm, t') @@ -494,7 +495,7 @@ let rec run_template_program_rec ~poly ?(intactic=false) (k : Environ.env * Evd. Not_found -> k (env, evm, constr_mkApp (cNone_instance, [|typ|])) end | TmInferInstanceTerm typ -> - let evm,typ = denote_term evm (reduce_all env evm typ) in + let evm,typ = denote_term env evm (reduce_all env evm typ) in Plugin_core.run (Plugin_core.tmInferInstance typ) env evm (fun env evm -> function None -> k (env, evm, constr_mkAppl (cNone, [| tTerm|])) @@ -502,6 +503,6 @@ let rec run_template_program_rec ~poly ?(intactic=false) (k : Environ.env * Evd. let qtrm = quote_term env trm in k (env, evm, constr_mkApp (cSome, [| Lazy.force tTerm; qtrm |]))) | TmPrintTerm trm -> - let evm,trm = denote_term evm (reduce_all env evm trm) in + let evm,trm = denote_term env evm (reduce_all env evm trm) in Plugin_core.run (Plugin_core.tmPrint trm) env evm (fun env evm _ -> k (env, evm, Lazy.force unit_tt)) diff --git a/template-coq/theories/Ast.v b/template-coq/theories/Ast.v index e053947ec..2f7a2d1fd 100644 --- a/template-coq/theories/Ast.v +++ b/template-coq/theories/Ast.v @@ -52,6 +52,12 @@ Inductive term : Type := | tFix (mfix : mfixpoint term) (idx : nat) | tCoFix (mfix : mfixpoint term) (idx : nat). +(** This can be used to represent holes, that, when unquoted, turn into fresh existential variables. + The fresh evar will depend on the whole context at this point in the term, despite the empty instance. + Denotation will call Coq's Typing.solve_evars to try and fill these holes using typing information. +*) +Definition hole := tEvar fresh_evar_id []. + Definition mkApps t us := match us with | nil => t diff --git a/template-coq/theories/BasicAst.v b/template-coq/theories/BasicAst.v index 6fc49a384..01e715b0a 100644 --- a/template-coq/theories/BasicAst.v +++ b/template-coq/theories/BasicAst.v @@ -218,6 +218,10 @@ Inductive conv_pb := | Cumul. Derive NoConfusion EqDec for conv_pb. +(* This opaque natural number is a hack to inform unquoting to generate + a fresh evar when encountering it. *) +Definition fresh_evar_id : nat. exact 0. Qed. + (* Parametrized by term because term is not yet defined *) Record def term := mkdef { dname : aname; (* the name, annotated with relevance **) diff --git a/template-coq/theories/Constants.v b/template-coq/theories/Constants.v index def487a2c..46dbb195a 100644 --- a/template-coq/theories/Constants.v +++ b/template-coq/theories/Constants.v @@ -87,6 +87,7 @@ Register MetaCoq.Template.BasicAst.VarRef as metacoq.ast.VarRef. Register MetaCoq.Template.BasicAst.ConstRef as metacoq.ast.ConstRef. Register MetaCoq.Template.BasicAst.IndRef as metacoq.ast.IndRef. Register MetaCoq.Template.BasicAst.ConstructRef as metacoq.ast.ConstructRef. +Register MetaCoq.Template.BasicAst.fresh_evar_id as metacoq.ast.fresh_evar_id. (* Universes *) diff --git a/test-suite/evars.v b/test-suite/evars.v index 3e76b17d4..7ac22f79f 100644 --- a/test-suite/evars.v +++ b/test-suite/evars.v @@ -1,4 +1,8 @@ -Require Import MetaCoq.Template.Loader. +From Coq Require Import String List. +From MetaCoq.Template Require Import Ast Loader. +Import ListNotations. +Definition bAnon := {| binder_name := nAnon; binder_relevance := Relevant |}. +Definition bNamed s := {| binder_name := nNamed s; binder_relevance := Relevant |}. Goal True. evar (n : nat). @@ -10,4 +14,31 @@ Goal True. end. exact I. Unshelve. exact 0. -Qed. \ No newline at end of file +Qed. + +(** Evars *) +MetaCoq Quote Definition lnil := @nil. +MetaCoq Quote Definition listnat := (list nat). +MetaCoq Unquote Definition foo := (tCast (tApp lnil [hole]) Cast listnat). + +Local Open Scope string_scope. + +Goal list nat. + (* Back and forth *) + let x := open_constr:(nil) in quote_term x (fun qt => + ltac:(denote_term qt (fun unqt => set (e := eq_refl : unqt = x :> list bool)))). + (* Creation of evars by denotation of 'hole' *) + let x := eval cbv in (tApp lnil [hole]) in + denote_term x (fun k => exact k). +Defined. + +Goal True. + let x := eval cbv in (tLambda bAnon listnat hole) in + (* We check that created evars are in the right context *) + denote_term x (fun k => set (ev := k); revert ev). + instantiate (1 := list nat). + instantiate (1 := l). + exact I. +Qed. + + From 879ef1d23c47bc1f4b15ecd88c1790b4acddd781 Mon Sep 17 00:00:00 2001 From: Fabian Kunze Date: Fri, 4 Dec 2020 09:40:09 +0100 Subject: [PATCH 31/70] extraction in template-coq compiles --- template-coq/_CoqProject | 1 + template-coq/_PluginProject | 2 + .../gen-src/metacoq_template_plugin.mlpack | 1 + template-coq/src/ast_denoter.ml | 6 +- template-coq/src/ast_quoter.ml | 18 +++--- template-coq/src/constr_denoter.ml | 5 +- template-coq/src/constr_reification.ml | 9 +-- template-coq/src/denoter.ml | 8 ++- template-coq/src/reification.ml | 1 + template-coq/src/tm_util.ml | 5 +- template-coq/theories/Ast.v | 8 ++- template-coq/theories/AstUtils.v | 1 + template-coq/theories/Constants.v | 1 + template-coq/theories/Extraction.v | 8 ++- template-coq/theories/Induction.v | 9 ++- template-coq/theories/Pretty.v | 2 + template-coq/theories/Reflect.v | 2 + template-coq/theories/Typing.v | 23 ++++---- template-coq/theories/UnivSubst.v | 2 +- template-coq/theories/WfInv.v | 4 +- template-coq/theories/utils/MCString.v | 18 ++++++ .../theories/utils/MC_ExtrOCamlInt63.v | 56 +++++++++++++++++++ 22 files changed, 150 insertions(+), 40 deletions(-) create mode 100644 template-coq/theories/utils/MC_ExtrOCamlInt63.v diff --git a/template-coq/_CoqProject b/template-coq/_CoqProject index 91e041d1e..7e0f6be60 100644 --- a/template-coq/_CoqProject +++ b/template-coq/_CoqProject @@ -16,6 +16,7 @@ theories/utils/MCSquash.v theories/utils/MCString.v theories/utils/wGraph.v theories/utils/MCUtils.v +theories/utils/MC_ExtrOCamlInt63.v # common theories/common/uGraph.v diff --git a/template-coq/_PluginProject b/template-coq/_PluginProject index 97bcd978c..68af75daf 100644 --- a/template-coq/_PluginProject +++ b/template-coq/_PluginProject @@ -56,6 +56,8 @@ gen-src/extractable.ml gen-src/extractable.mli #gen-src/induction.ml #gen-src/induction.mli +gen-src/int63.ml +gen-src/int63.mli gen-src/liftSubst.ml gen-src/liftSubst.mli gen-src/list0.ml diff --git a/template-coq/gen-src/metacoq_template_plugin.mlpack b/template-coq/gen-src/metacoq_template_plugin.mlpack index 6bbb09b00..e541ccdb1 100644 --- a/template-coq/gen-src/metacoq_template_plugin.mlpack +++ b/template-coq/gen-src/metacoq_template_plugin.mlpack @@ -11,6 +11,7 @@ BinPosDef BinPos BinNat BinInt +Int63 Ascii String0 Orders diff --git a/template-coq/src/ast_denoter.ml b/template-coq/src/ast_denoter.ml index 5ff4e52df..ea06d0a22 100644 --- a/template-coq/src/ast_denoter.ml +++ b/template-coq/src/ast_denoter.ml @@ -9,6 +9,7 @@ struct type t = Ast0.term type quoted_ident = char list type quoted_int = Datatypes.nat + type quoted_int63 = Uint63.t type quoted_bool = bool type quoted_name = name type quoted_aname = name binder_annot @@ -77,7 +78,7 @@ struct rarg=rarg x } - let inspect_term (tt: t):(t, quoted_int, quoted_ident, quoted_aname, quoted_sort, quoted_cast_kind, quoted_kernel_name, quoted_inductive, quoted_relevance, quoted_univ_instance, quoted_proj) structure_of_term= + let inspect_term (tt: t):(t, quoted_int, quoted_ident, quoted_aname, quoted_sort, quoted_cast_kind, quoted_kernel_name, quoted_inductive, quoted_relevance, quoted_univ_instance, quoted_proj, quoted_int63) structure_of_term= match tt with | Coq_tRel n -> ACoq_tRel n | Coq_tVar v -> ACoq_tVar v @@ -95,6 +96,7 @@ struct | Coq_tProj (a,b) -> ACoq_tProj (a,b) | Coq_tFix (a,b) -> ACoq_tFix (List.map unquote_def a,b) | Coq_tCoFix (a,b) -> ACoq_tCoFix (List.map unquote_def a,b) + | Coq_tInt i -> ACoq_tInt i let unquote_ident (qi: quoted_ident) : Id.t = @@ -125,6 +127,8 @@ struct evm, mkEvar (id, Array.of_list l) let unquote_bool (q : quoted_bool) : bool = q + + let unquote_int63 i = i (* val unquote_sort : quoted_sort -> Sorts.t *) (* val unquote_sort_family : quoted_sort_family -> Sorts.family *) diff --git a/template-coq/src/ast_quoter.ml b/template-coq/src/ast_quoter.ml index aec798a60..425182d49 100644 --- a/template-coq/src/ast_quoter.ml +++ b/template-coq/src/ast_quoter.ml @@ -9,6 +9,7 @@ struct type t = Ast0.term type quoted_ident = char list type quoted_int = Datatypes.nat + type quoted_int63 = Uint63.t type quoted_bool = bool type quoted_name = BasicAst.name type quoted_aname = BasicAst.aname @@ -55,7 +56,7 @@ struct let quote_relevance = function | Sorts.Relevant -> BasicAst.Relevant | Sorts.Irrelevant -> BasicAst.Irrelevant - + let quote_name = function | Anonymous -> Coq_nAnon | Name i -> Coq_nNamed (quote_ident i) @@ -150,7 +151,7 @@ struct let is_Eq = function | Univ.Eq -> true | _ -> false - + let quote_univ_constraint ((l, ct, l') : Univ.univ_constraint) : quoted_univ_constraint = ((quote_nonprop_level l, quote_constraint_type ct), quote_nonprop_level l') @@ -232,6 +233,7 @@ struct let mkInd i u = Coq_tInd (i, u) let mkConstruct (ind, i) u = Coq_tConstruct (ind, i, u) let mkLetIn na b t t' = Coq_tLetIn (na,b,t,t') + let mkInt i = Coq_tInt i let rec seq f t = if f < t then @@ -278,7 +280,7 @@ struct let mk_mutual_inductive_body finite npars params inds uctx variance = {ind_finite = finite; - ind_npars = npars; ind_params = params; ind_bodies = inds; + ind_npars = npars; ind_params = params; ind_bodies = inds; ind_universes = uctx; ind_variance = variance} let mk_constant_body ty tm uctx = @@ -315,7 +317,7 @@ struct mind_entry_variance = variance; mind_entry_private = None } - let quote_definition_entry ty body ctx = + let quote_definition_entry ty body ctx = { definition_entry_type = ty; definition_entry_body = body; definition_entry_universes = ctx; @@ -324,11 +326,11 @@ struct let quote_parameter_entry ty ctx = { parameter_entry_type = ty; parameter_entry_universes = ctx } - + let quote_constant_entry = function | Left ce -> DefinitionEntry ce | Right pe -> ParameterEntry pe -(* +(* let quote_entry e = match e with | Some (Left (ty, body, ctx)) -> @@ -337,7 +339,7 @@ struct Some (Right mind_entry) | None -> None *) - let inspectTerm (t : term) : (term, quoted_int, quoted_ident, quoted_name, quoted_sort, quoted_cast_kind, quoted_kernel_name, quoted_inductive, quoted_relevance, quoted_univ_instance, quoted_proj) structure_of_term = + let inspectTerm (t : term) : (term, quoted_int, quoted_ident, quoted_name, quoted_sort, quoted_cast_kind, quoted_kernel_name, quoted_inductive, quoted_relevance, quoted_univ_instance, quoted_proj, quoted_int63) structure_of_term = match t with | Coq_tRel n -> ACoq_tRel n (* so on *) @@ -364,7 +366,7 @@ struct let mkPolymorphic_entry names c = Universes0.Polymorphic_entry (names, c) let mkMonomorphic_entry c = Universes0.Monomorphic_entry c - + end module ExtractedASTQuoter = Quoter.Quoter(ExtractedASTBaseQuoter) diff --git a/template-coq/src/constr_denoter.ml b/template-coq/src/constr_denoter.ml index 9e1ae3c27..64763652c 100644 --- a/template-coq/src/constr_denoter.ml +++ b/template-coq/src/constr_denoter.ml @@ -73,6 +73,9 @@ struct false else not_supported_verb trm "from_bool" + let unquote_int63 i = i + + let unquote_char trm = let (h,args) = app_full trm [] in if constr_equall h tAscii then @@ -336,7 +339,7 @@ struct let inspect_term (t:Constr.t) - : (Constr.t, quoted_int, quoted_ident, quoted_name, quoted_sort, quoted_cast_kind, quoted_kernel_name, quoted_inductive, quoted_relevance, quoted_univ_instance, quoted_proj) structure_of_term = + : (Constr.t, quoted_int, quoted_ident, quoted_name, quoted_sort, quoted_cast_kind, quoted_kernel_name, quoted_inductive, quoted_relevance, quoted_univ_instance, quoted_proj, quoted_int63) structure_of_term = let (h,args) = app_full t [] in if constr_equall h tRel then match args with diff --git a/template-coq/src/constr_reification.ml b/template-coq/src/constr_reification.ml index 65fd3bcbe..56fd67546 100644 --- a/template-coq/src/constr_reification.ml +++ b/template-coq/src/constr_reification.ml @@ -6,6 +6,7 @@ struct type quoted_ident = Constr.t (* of type Ast.ident *) type quoted_int = Constr.t (* of type nat *) + type quoted_int63 = Uint63.t (* of type nat *) type quoted_bool = Constr.t (* of type bool *) type quoted_name = Constr.t (* of type BasicAst.name *) type quoted_aname = Constr.t (* of type BasicAst.aname (names with relevance) *) @@ -77,17 +78,17 @@ struct let cZ0 = resolve "metacoq.Z.zero" let cZpos = resolve "metacoq.Z.pos" let cZneg = resolve "metacoq.Z.neg" - + let tpos = resolve "metacoq.pos.type" let cposzero = resolve "metacoq.pos.xH" let cposI = resolve "metacoq.pos.xI" let cposO = resolve "metacoq.pos.xO" - + let cSome_instance = resolve "metacoq.option_instance.some" let cNone_instance = resolve "metacoq.option_instance.none" let unit_tt = resolve "metacoq.unit.intro" - + let tAscii = resolve "metacoq.ascii.intro" let tlist = resolve "metacoq.list.type" let c_nil = resolve "metacoq.list.nil" @@ -223,7 +224,7 @@ struct let cMonomorphic_entry = ast "Monomorphic_entry" let cPolymorphic_entry = ast "Polymorphic_entry" - let (tcbv, tcbn, thnf, tall, tlazy, tunfold) = + let (tcbv, tcbn, thnf, tall, tlazy, tunfold) = (template "cbv", template "cbn", template "hnf", template "all", template "lazy", template "unfold") diff --git a/template-coq/src/denoter.ml b/template-coq/src/denoter.ml index d7ab41fc7..a71909a48 100644 --- a/template-coq/src/denoter.ml +++ b/template-coq/src/denoter.ml @@ -13,6 +13,8 @@ sig val unquote_evar : Environ.env -> Evd.evar_map -> quoted_int -> Constr.t list -> Evd.evar_map * Constr.t val unquote_int : quoted_int -> int val unquote_bool : quoted_bool -> bool + val unquote_int63 : quoted_prim_int -> Uint63.t + val unquote_int63 : quoted_prim_float -> Float64.t (* val unquote_sort : quoted_sort -> Sorts.t *) (* val unquote_sort_family : quoted_sort_family -> Sorts.family *) val unquote_cast_kind : quoted_cast_kind -> Constr.cast_kind @@ -23,7 +25,7 @@ sig val unquote_universe : Evd.evar_map -> quoted_sort -> Evd.evar_map * Univ.Universe.t val unquote_universe_instance: Evd.evar_map -> quoted_univ_instance -> Evd.evar_map * Univ.Instance.t (* val representsIndConstuctor : quoted_inductive -> Term.constr -> bool *) - val inspect_term : t -> (t, quoted_int, quoted_ident, quoted_aname, quoted_sort, quoted_cast_kind, quoted_kernel_name, quoted_inductive, quoted_relevance, quoted_univ_instance, quoted_proj) structure_of_term + val inspect_term : t -> (t, quoted_int, quoted_ident, quoted_aname, quoted_sort, quoted_cast_kind, quoted_kernel_name, quoted_inductive, quoted_relevance, quoted_univ_instance, quoted_proj, quoted_int63) structure_of_term end @@ -139,7 +141,9 @@ struct let p' = Names.Projection.make (Projection.Repr.make ind' ~proj_npars ~proj_arg l) false in let evm, t' = aux env evm t in evm, Constr.mkProj (p', t') - + | ACoq_tInt x -> evm, Constr.mkInt (D.unquote_int63 x) + | ACoq_tFloat x -> evm, Constr.mkFloat (D.unquote_float64 x) + in aux env evm trm end diff --git a/template-coq/src/reification.ml b/template-coq/src/reification.ml index ef9b2d8e7..8791b7853 100644 --- a/template-coq/src/reification.ml +++ b/template-coq/src/reification.ml @@ -5,6 +5,7 @@ sig type quoted_ident type quoted_int + type quoted_int63 type quoted_bool type quoted_name type quoted_aname diff --git a/template-coq/src/tm_util.ml b/template-coq/src/tm_util.ml index 676361a3f..c0fe9b8f7 100644 --- a/template-coq/src/tm_util.ml +++ b/template-coq/src/tm_util.ml @@ -51,7 +51,7 @@ let not_supported trm = let not_supported_verb trm rs = let env = Global.env () in - CErrors.user_err (str "Not Supported raised at " ++ str rs ++ str ":" ++ spc () ++ + CErrors.user_err (str "Not Supported raised at " ++ str rs ++ str ":" ++ spc () ++ Printer.pr_constr_env env (Evd.from_env env) trm) let bad_term trm = @@ -68,7 +68,7 @@ type ('term, 'name, 'nat) adef = { adname : 'name; adtype : 'term; adbody : 'ter type ('term, 'name, 'nat) amfixpoint = ('term, 'name, 'nat) adef list -type ('term, 'nat, 'ident, 'name, 'quoted_sort, 'cast_kind, 'kername, 'inductive, 'relevance, 'universe_instance, 'projection) structure_of_term = +type ('term, 'nat, 'ident, 'name, 'quoted_sort, 'cast_kind, 'kername, 'inductive, 'relevance, 'universe_instance, 'projection, 'int63) structure_of_term = | ACoq_tRel of 'nat | ACoq_tVar of 'ident | ACoq_tEvar of 'nat * 'term list @@ -85,4 +85,5 @@ type ('term, 'nat, 'ident, 'name, 'quoted_sort, 'cast_kind, 'kername, 'inductive | ACoq_tProj of 'projection * 'term | ACoq_tFix of ('term, 'name, 'nat) amfixpoint * 'nat | ACoq_tCoFix of ('term, 'name, 'nat) amfixpoint * 'nat + | ACoq_tInt of 'int63 diff --git a/template-coq/theories/Ast.v b/template-coq/theories/Ast.v index 2f7a2d1fd..06cf4e6d3 100644 --- a/template-coq/theories/Ast.v +++ b/template-coq/theories/Ast.v @@ -1,7 +1,7 @@ (* Distributed under the terms of the MIT license. *) From MetaCoq.Template Require Import utils Environment. From MetaCoq.Template Require Export Universes. - +From Coq Require Int63. (** * AST of Coq kernel terms and kernel data structures @@ -50,7 +50,8 @@ Inductive term : Type := (discr:term) (branches : list (nat * term)) | tProj (proj : projection) (t : term) | tFix (mfix : mfixpoint term) (idx : nat) -| tCoFix (mfix : mfixpoint term) (idx : nat). +| tCoFix (mfix : mfixpoint term) (idx : nat) +| tInt (i : Int63.int). (** This can be used to represent holes, that, when unquoted, turn into fresh existential variables. The fresh evar will depend on the whole context at this point in the term, despite the empty instance. @@ -124,7 +125,8 @@ Inductive wf : term -> Prop := | wf_tProj p t : wf t -> wf (tProj p t) | wf_tFix mfix k : Forall (fun def => wf def.(dtype) /\ wf def.(dbody) /\ isLambda def.(dbody) = true) mfix -> wf (tFix mfix k) -| wf_tCoFix mfix k : Forall (fun def => wf def.(dtype) /\ wf def.(dbody)) mfix -> wf (tCoFix mfix k). +| wf_tCoFix mfix k : Forall (fun def => wf def.(dtype) /\ wf def.(dbody)) mfix -> wf (tCoFix mfix k) +| wf_tInt i : wf (tInt i). (** ** Entries diff --git a/template-coq/theories/AstUtils.v b/template-coq/theories/AstUtils.v index f270290e0..6cfc0d80a 100644 --- a/template-coq/theories/AstUtils.v +++ b/template-coq/theories/AstUtils.v @@ -42,6 +42,7 @@ Fixpoint string_of_term (t : term) := ^ string_of_term c ^ ")" | tFix l n => "Fix(" ^ (string_of_list (string_of_def string_of_term) l) ^ "," ^ string_of_nat n ^ ")" | tCoFix l n => "CoFix(" ^ (string_of_list (string_of_def string_of_term) l) ^ "," ^ string_of_nat n ^ ")" + | tInt i => "Int(" ^ string_of_int i ^ ")" end. Definition decompose_app (t : term) := diff --git a/template-coq/theories/Constants.v b/template-coq/theories/Constants.v index 46dbb195a..5b24b33c8 100644 --- a/template-coq/theories/Constants.v +++ b/template-coq/theories/Constants.v @@ -167,6 +167,7 @@ Register MetaCoq.Template.Ast.tCase as metacoq.ast.tCase. Register MetaCoq.Template.Ast.tProj as metacoq.ast.tProj. Register MetaCoq.Template.Ast.tFix as metacoq.ast.tFix. Register MetaCoq.Template.Ast.tCoFix as metacoq.ast.tCoFix. +Register MetaCoq.Template.Ast.tCoFix as metacoq.ast.tInt. (* Local and global declarations *) Register MetaCoq.Template.Ast.parameter_entry as metacoq.ast.parameter_entry. diff --git a/template-coq/theories/Extraction.v b/template-coq/theories/Extraction.v index f7a6482e3..a97444fee 100644 --- a/template-coq/theories/Extraction.v +++ b/template-coq/theories/Extraction.v @@ -1,7 +1,7 @@ (* Distributed under the terms of the MIT license. *) From MetaCoq.Template Require Import utils Ast Reflect Induction. -Require Import FSets ExtrOcamlBasic ExtrOcamlString ExtrOcamlZInt. - +Require Import FSets ExtrOcamlBasic ExtrOcamlString ExtrOcamlZInt MC_ExtrOCamlInt63 (*b/c nameclash with `comparion` *). +From Coq Require Extraction. (** * Extraction setup for template-coq. Any extracted code planning to link with the plugin's OCaml reifier @@ -20,7 +20,7 @@ Extract Inductive Equations.Init.sigma => "( * )" ["(,)"]. Extract Constant Equations.Init.pr1 => "fst". Extract Constant Equations.Init.pr2 => "snd". Extraction Inline Equations.Init.pr1 Equations.Init.pr2. - + Extraction Blacklist Classes config uGraph Universes Ast String List Nat Int UnivSubst Typing Checker Retyping OrderedType Logic Common Equality UnivSubst. Set Warnings "-extraction-opaque-accessed". @@ -30,6 +30,8 @@ Cd "gen-src". From MetaCoq.Template Require Import TemplateMonad.Extractable config Induction LiftSubst UnivSubst Pretty. +Import Init.Nat. +Locate Nat. Recursive Extraction Library Extractable. Extraction Library MCPrelude. diff --git a/template-coq/theories/Induction.v b/template-coq/theories/Induction.v index 6b9cecb42..5c76dd3f1 100644 --- a/template-coq/theories/Induction.v +++ b/template-coq/theories/Induction.v @@ -30,6 +30,7 @@ Lemma term_forall_list_ind : (forall (s : projection) (t : term), P t -> P (tProj s t)) -> (forall (m : mfixpoint term) (n : nat), tFixProp P P m -> P (tFix m n)) -> (forall (m : mfixpoint term) (n : nat), tFixProp P P m -> P (tCoFix m n)) -> + (forall (i : Int63.int), P (tInt i)) -> forall t : term, P t. Proof. intros until t. revert t. @@ -87,16 +88,17 @@ Lemma term_wf_forall_list_ind : (forall (s : projection) (t : term), P t -> P (tProj s t)) -> (forall (m : mfixpoint term) (n : nat), tFixProp P P m -> Forall (fun def => isLambda (dbody def) = true) m -> P (tFix m n)) -> (forall (m : mfixpoint term) (n : nat), tFixProp P P m -> P (tCoFix m n)) -> + (forall (i : Int63.int), P (tInt i)) -> forall t : term, wf t -> P t. Proof. - pose proof I as H1. (* can go away, to avoid renaming everything... *) - intros until t. revert t. + pose proof I as H1. (* can go away, to avoid renaming everything... *) + intros until t. revert t. rename H16 into H16'. apply (term_forall_list_ind (fun t => wf t -> P t)); intros; try solve [match goal with H : _ |- _ => apply H end; auto]. apply H2. inv H17. - auto using lift_to_wf_list. + { auto using lift_to_wf_list. } - inv H18; auto. - inv H18; auto. @@ -155,6 +157,7 @@ Lemma term_forall_list_rect : (forall (s : projection) (t : term), P t -> P (tProj s t)) -> (forall (m : mfixpoint term) (n : nat), tFixType P P m -> P (tFix m n)) -> (forall (m : mfixpoint term) (n : nat), tFixType P P m -> P (tCoFix m n)) -> + (forall (i : Int63.int), P (tInt i)) -> forall t : term, P t. Proof. intros until t. revert t. diff --git a/template-coq/theories/Pretty.v b/template-coq/theories/Pretty.v index 5a50a483a..15099ea86 100644 --- a/template-coq/theories/Pretty.v +++ b/template-coq/theories/Pretty.v @@ -67,6 +67,7 @@ Section print_term. | Some body => substring 0 1 (body.(ind_name)) | None => "X" end + | tInt _ => "i" | _ => "U" end. @@ -201,6 +202,7 @@ Section print_term. | tCoFix l n => parens top ("let cofix " ^ print_defs print_term Γ l ^ nl ^ " in " ^ List.nth_default (string_of_nat n) (map (string_of_name ∘ binder_name ∘ dname) l) n) + | tInt i => "Int(" ^ string_of_int i ^ ")" end. End print_term. diff --git a/template-coq/theories/Reflect.v b/template-coq/theories/Reflect.v index 4b0ad19ee..c2844b9c4 100644 --- a/template-coq/theories/Reflect.v +++ b/template-coq/theories/Reflect.v @@ -496,6 +496,8 @@ Proof. subst. inversion e1. subst. destruct (eq_dec rarg rarg0) ; nodec. subst. left. reflexivity. + - destruct (Int63.eqs i i0) ; nodec. + subst. left. reflexivity. Defined. Instance reflect_term : ReflectEq term := diff --git a/template-coq/theories/Typing.v b/template-coq/theories/Typing.v index a91534b64..0e371e949 100644 --- a/template-coq/theories/Typing.v +++ b/template-coq/theories/Typing.v @@ -9,7 +9,7 @@ From MetaCoq.Template Require Import config utils Ast AstUtils LiftSubst UnivSub *) - + Definition isSort T := match T with | tSort u => True @@ -506,7 +506,10 @@ Inductive eq_term_upto_univ (Re Rle : Universe.t -> Universe.t -> Prop) : term - eq_term_upto_univ Re Re x.(dbody) y.(dbody) × x.(rarg) = y.(rarg) ) mfix mfix' -> - eq_term_upto_univ Re Rle (tCoFix mfix idx) (tCoFix mfix' idx). + eq_term_upto_univ Re Rle (tCoFix mfix idx) (tCoFix mfix' idx) + +| eq_Int i : + eq_term_upto_univ Re Rle (tInt i) (tInt i). Definition eq_term `{checker_flags} φ := eq_term_upto_univ (eq_universe φ) (eq_universe φ). @@ -536,7 +539,7 @@ Fixpoint strip_casts t := | tCoFix mfix idx => let mfix' := List.map (map_def strip_casts strip_casts) mfix in tCoFix mfix' idx - | tRel _ | tVar _ | tSort _ | tConst _ _ | tInd _ _ | tConstruct _ _ _ => t + | tRel _ | tVar _ | tSort _ | tConst _ _ | tInd _ _ | tConstruct _ _ _ | tInt _ => t end. Definition eq_term_nocast `{checker_flags} (φ : ConstraintSet.t) (t u : term) := @@ -758,14 +761,14 @@ Definition build_case_predicate_type ind mdecl idecl params u ps : option term : decl_type := mkApps (tInd ind u) (map (lift0 #|X.1|) params ++ to_extended_list X.1) |} in ret (it_mkProd_or_LetIn (X.1 ,, inddecl) (tSort ps)). -Definition wf_universe Σ s := +Definition wf_universe Σ s := match s with - | Universe.lProp + | Universe.lProp | Universe.lSProp => True - | Universe.lType u => + | Universe.lType u => forall l, UnivExprSet.In l u -> LevelSet.In (UnivExpr.get_level l) (global_ext_levels Σ) end. - + Inductive typing `{checker_flags} (Σ : global_env_ext) (Γ : context) : term -> term -> Type := | type_Rel n decl : @@ -1475,7 +1478,7 @@ Proof. remember (fix_context mfix) as mfixcontext. clear Heqmfixcontext. induction a1; econstructor; eauto. - ++ split; auto. + ++ split; auto. eapply (X _ (typing_wf_local (fst p)) _ _ (fst p)). simpl. lia. ++ eapply IHa1. intros. eapply (X _ X0 _ _ Hty). simpl; lia. @@ -1511,9 +1514,9 @@ Proof. clear X14 X13. clear e decl a0. remember (fix_context mfix) as mfixcontext. clear Heqmfixcontext. - + induction a1; econstructor; eauto. - ++ split; auto. + ++ split; auto. eapply (X _ (typing_wf_local p) _ _ p). simpl. lia. ++ eapply IHa1. intros. eapply (X _ X0 _ _ Hty). simpl; lia. diff --git a/template-coq/theories/UnivSubst.v b/template-coq/theories/UnivSubst.v index b46ece465..5231b9966 100644 --- a/template-coq/theories/UnivSubst.v +++ b/template-coq/theories/UnivSubst.v @@ -10,7 +10,7 @@ From MetaCoq Require Import utils Ast AstUtils Induction LiftSubst. Instance subst_instance_constr : UnivSubst term := fix subst_instance_constr u c {struct c} : term := match c with - | tRel _ | tVar _ => c + | tRel _ | tVar _ | tInt _ => c | tEvar ev args => tEvar ev (List.map (subst_instance_constr u) args) | tSort s => tSort (subst_instance_univ u s) | tConst c u' => tConst c (subst_instance_instance u u') diff --git a/template-coq/theories/WfInv.v b/template-coq/theories/WfInv.v index 7b1921c7e..01626483f 100644 --- a/template-coq/theories/WfInv.v +++ b/template-coq/theories/WfInv.v @@ -14,7 +14,7 @@ Fixpoint wf_Inv (t : term) := | tLambda na t b => wf t /\ wf b | tLetIn na t b b' => wf t /\ wf b /\ wf b' | tApp t u => isApp t = false /\ u <> nil /\ wf t /\ Forall wf u - | tConst _ _ | tInd _ _ | tConstruct _ _ _ => True + | tConst _ _ | tInd _ _ | tConstruct _ _ _ | tInt _ => True | tCase ci p c brs => wf p /\ wf c /\ Forall (wf ∘ snd) brs | tProj p t => wf t | tFix mfix k => Forall (fun def => wf def.(dtype) /\ wf def.(dbody) /\ isLambda def.(dbody) = true) mfix @@ -69,7 +69,7 @@ Fixpoint wf_term (t : term) : bool := | tLambda na t b => wf_term t && wf_term b | tLetIn na t b b' => wf_term t && wf_term b && wf_term b' | tApp t u => ~~ isApp t && ~~ is_empty u && wf_term t && forallb wf_term u - | tConst _ _ | tInd _ _ | tConstruct _ _ _ => true + | tConst _ _ | tInd _ _ | tConstruct _ _ _ | tInt _ => true | tCase ci p c brs => wf_term p && wf_term c && forallb (wf_term ∘ snd) brs | tProj p t => wf_term t | tFix mfix k => diff --git a/template-coq/theories/utils/MCString.v b/template-coq/theories/utils/MCString.v index 2784e436f..70b7d30c7 100644 --- a/template-coq/theories/utils/MCString.v +++ b/template-coq/theories/utils/MCString.v @@ -1,4 +1,5 @@ From Coq Require Import String. +From Coq.Numbers Require Import (* DecimalString *) Int63. From MetaCoq.Template Require Import MCCompare. Local Open Scope string_scope. @@ -80,6 +81,23 @@ Definition string_of_nat n : string := | _ => "todo string_of_nat" end. + +(* Definition string_of_nat n : string := DecimalString.NilZero.string_of_uint (Nat.to_uint n). *) +(* Definition string_of_int (i:Int63.int) : string := BinNat.N.to_uint (BinInt.Z.to_N (Int63.to_Z i))). *) +Definition string_of_int (i:Int63.int) : string := + (if Int63.ltb i 8 + then + if Int63.ltb i 4 + then + if Int63.ltb i 2 + then if Int63.ltb i 1 then "0" else "1" + else if Int63.ltb i 3 then "2" else "3" + else + if Int63.ltb i 6 + then if Int63.ltb i 5 then "4" else "5" + else if Int63.ltb i 7 then "6" else "7" + else if Int63.eqb i 42 then "42" else "todo string_of_int")%int63. + Hint Resolve String.string_dec : eq_dec. diff --git a/template-coq/theories/utils/MC_ExtrOCamlInt63.v b/template-coq/theories/utils/MC_ExtrOCamlInt63.v new file mode 100644 index 000000000..a82fb2502 --- /dev/null +++ b/template-coq/theories/utils/MC_ExtrOCamlInt63.v @@ -0,0 +1,56 @@ +(************************************************************************) +(* * The Coq Proof Assistant / The Coq Development Team *) +(* v * INRIA, CNRS and contributors - Copyright 1999-2019 *) +(* bool [ true false ]. +Extract Inductive prod => "( * )" [ "" ]. +(* Extract Inductive comparison => int [ "0" "(-1)" "1" ]. *) +Extract Inductive DoubleType.carry => "Uint63.carry" [ "Uint63.C0" "Uint63.C1" ]. + +(** Primitive types and operators. *) +Extract Constant Int63.int => "Uint63.t". +Extraction Inline Int63.int. +(* Otherwise, the name conflicts with the primitive OCaml type [int] *) + +Extract Constant Int63.lsl => "Uint63.l_sl". +Extract Constant Int63.lsr => "Uint63.l_sr". +Extract Constant Int63.land => "Uint63.l_and". +Extract Constant Int63.lor => "Uint63.l_or". +Extract Constant Int63.lxor => "Uint63.l_xor". + +Extract Constant Int63.add => "Uint63.add". +Extract Constant Int63.sub => "Uint63.sub". +Extract Constant Int63.mul => "Uint63.mul". +Extract Constant Int63.mulc => "Uint63.mulc". +Extract Constant Int63.div => "Uint63.div". +Extract Constant Int63.mod => "Uint63.rem". + +Extract Constant Int63.eqb => "Uint63.equal". +Extract Constant Int63.ltb => "Uint63.lt". +Extract Constant Int63.leb => "Uint63.le". + +Extract Constant Int63.addc => "Uint63.addc". +Extract Constant Int63.addcarryc => "Uint63.addcarryc". +Extract Constant Int63.subc => "Uint63.subc". +Extract Constant Int63.subcarryc => "Uint63.subcarryc". + +Extract Constant Int63.diveucl => "Uint63.diveucl". +Extract Constant Int63.diveucl_21 => "Uint63.div21". +Extract Constant Int63.addmuldiv => "Uint63.addmuldiv". + +Extract Constant Int63.compare => "fun _x _y -> failwith ""not yet implemented""". + +Extract Constant Int63.head0 => "Uint63.head0". +Extract Constant Int63.tail0 => "Uint63.tail0". From 453dc7d5d26c140e78d3615508f29717d59e2760 Mon Sep 17 00:00:00 2001 From: Fabian Kunze Date: Fri, 4 Dec 2020 12:29:17 +0100 Subject: [PATCH 32/70] wip --- template-coq/src/ast_quoter.ml | 2 ++ template-coq/src/constr_denoter.ml | 6 +++++- template-coq/src/constr_quoter.ml | 3 +++ template-coq/src/constr_reification.ml | 6 +++--- template-coq/src/quoter.ml | 4 +++- template-coq/theories/Constants.v | 2 +- test-suite/int.v | 14 ++++++++++++++ 7 files changed, 31 insertions(+), 6 deletions(-) create mode 100644 test-suite/int.v diff --git a/template-coq/src/ast_quoter.ml b/template-coq/src/ast_quoter.ml index 425182d49..b38544e0f 100644 --- a/template-coq/src/ast_quoter.ml +++ b/template-coq/src/ast_quoter.ml @@ -73,6 +73,8 @@ struct let quote_bool x = x + let quote_int63 x = x + (* NOTE: fails if it hits Prop or SProp *) let quote_nonprop_level (l : Univ.Level.t) : Universes0.Level.t = if Univ.Level.is_prop l || Univ.Level.is_sprop l then diff --git a/template-coq/src/constr_denoter.ml b/template-coq/src/constr_denoter.ml index 64763652c..31fdc4dcf 100644 --- a/template-coq/src/constr_denoter.ml +++ b/template-coq/src/constr_denoter.ml @@ -73,7 +73,11 @@ struct false else not_supported_verb trm "from_bool" - let unquote_int63 i = i + let unquote_int63 trm = + match Constr.kind trm with + | Constr.Int i -> i + | _ -> not_supported_verb trm "unquote_int63" + let unquote_char trm = diff --git a/template-coq/src/constr_quoter.ml b/template-coq/src/constr_quoter.ml index f0f148a6d..a2071a87c 100644 --- a/template-coq/src/constr_quoter.ml +++ b/template-coq/src/constr_quoter.ml @@ -33,6 +33,7 @@ struct let mkRel i = constr_mkApp (tRel, [| i |]) let mkVar id = constr_mkApp (tVar, [| id |]) + let mkInt i = constr_mkApp (tInt, [| i |]) let mkEvar n args = constr_mkApp (tEvar, [| n; to_coq_listl tTerm (Array.to_list args) |]) let mkSort s = constr_mkApp (tSort, [| s |]) let mkCast c k t = constr_mkApp (tCast, [| c ; k ; t |]) @@ -109,6 +110,8 @@ struct let quote_bool b = if b then Lazy.force ttrue else Lazy.force tfalse + let quote_int63 i = Lazy.force tInt + let quote_char i = constr_mkApp (tAscii, Array.of_list (List.map (fun m -> quote_bool ((i land m) = m)) (List.rev [128;64;32;16;8;4;2;1]))) diff --git a/template-coq/src/constr_reification.ml b/template-coq/src/constr_reification.ml index 56fd67546..2d1253a26 100644 --- a/template-coq/src/constr_reification.ml +++ b/template-coq/src/constr_reification.ml @@ -6,7 +6,7 @@ struct type quoted_ident = Constr.t (* of type Ast.ident *) type quoted_int = Constr.t (* of type nat *) - type quoted_int63 = Uint63.t (* of type nat *) + type quoted_int63 = Constr.t (* of type int63 *) type quoted_bool = Constr.t (* of type bool *) type quoted_name = Constr.t (* of type BasicAst.name *) type quoted_aname = Constr.t (* of type BasicAst.aname (names with relevance) *) @@ -139,11 +139,11 @@ struct let tmkInd = ast "mkInd" let tmkdecl = ast "mkdecl" let (tTerm,tRel,tVar,tEvar,tSort,tCast,tProd, - tLambda,tLetIn,tApp,tCase,tFix,tConstructor,tConst,tInd,tCoFix,tProj) = + tLambda,tLetIn,tApp,tCase,tFix,tConstructor,tConst,tInd,tCoFix,tProj,tInt) = (ast "term", ast "tRel", ast "tVar", ast "tEvar", ast "tSort", ast "tCast", ast "tProd", ast "tLambda", ast "tLetIn", ast "tApp", ast "tCase", ast "tFix", - ast "tConstruct", ast "tConst", ast "tInd", ast "tCoFix", ast "tProj") + ast "tConstruct", ast "tConst", ast "tInd", ast "tCoFix", ast "tProj", ast "tInt") let tkername = ast "kername" let tmodpath = ast "modpath" let tMPfile = ast "MPfile" diff --git a/template-coq/src/quoter.ml b/template-coq/src/quoter.ml index 414bd9dc4..72282be8e 100644 --- a/template-coq/src/quoter.ml +++ b/template-coq/src/quoter.ml @@ -58,6 +58,7 @@ sig val mkProj : quoted_proj -> t -> t val mkFix : (quoted_int array * quoted_int) * (quoted_aname array * t array * t array) -> t val mkCoFix : quoted_int * (quoted_aname array * t array * t array) -> t + val mkInt : quoted_int63 -> t val mkBindAnn : quoted_name -> quoted_relevance -> quoted_aname val mkName : quoted_ident -> quoted_name @@ -68,6 +69,7 @@ sig val quote_aname : Name.t Context.binder_annot -> quoted_aname val quote_relevance : Sorts.relevance -> quoted_relevance val quote_int : int -> quoted_int + val quote_int63 : Uint63.t -> quoted_int63 val quote_bool : bool -> quoted_bool val quote_sort : Sorts.t -> quoted_sort val quote_sort_family : Sorts.family -> quoted_sort_family @@ -262,7 +264,7 @@ struct let t', acc = quote_term acc env c in (Q.mkProj p' t', add_inductive (Projection.inductive p) acc) | Constr.Meta _ -> failwith "Meta not supported by TemplateCoq" - | Constr.Int _ -> failwith "Native integers not supported by TemplateCoq" + | Constr.Int i -> (Q.mkInt (Q.quote_int63 i), acc) | Constr.Float _ -> failwith "Native floating point numbers not supported by TemplateCoq" in let in_prop, env' = env in diff --git a/template-coq/theories/Constants.v b/template-coq/theories/Constants.v index 5b24b33c8..27291717c 100644 --- a/template-coq/theories/Constants.v +++ b/template-coq/theories/Constants.v @@ -167,7 +167,7 @@ Register MetaCoq.Template.Ast.tCase as metacoq.ast.tCase. Register MetaCoq.Template.Ast.tProj as metacoq.ast.tProj. Register MetaCoq.Template.Ast.tFix as metacoq.ast.tFix. Register MetaCoq.Template.Ast.tCoFix as metacoq.ast.tCoFix. -Register MetaCoq.Template.Ast.tCoFix as metacoq.ast.tInt. +Register MetaCoq.Template.Ast.tInt as metacoq.ast.tInt. (* Local and global declarations *) Register MetaCoq.Template.Ast.parameter_entry as metacoq.ast.parameter_entry. diff --git a/test-suite/int.v b/test-suite/int.v new file mode 100644 index 000000000..9288926c1 --- /dev/null +++ b/test-suite/int.v @@ -0,0 +1,14 @@ +Require Import MetaCoq.Template.Loader. +Require Import Int63. + +Definition n : Int63.int := 42. +Import List.ListNotations. +Definition ns : list Int63.int := [n]%list. + + +MetaCoq Quote Recursively Definition q_n := n. +MetaCoq Unquote Definition n' := (snd q_n). + +MetaCoq Quote Recursively Definition q_ns := ns. +MetaCoq Unquote Definition ns' := (snd q_ns). + From f713e106e5e87b2048c483024601e72deb1867f2 Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Fri, 4 Dec 2020 12:31:06 +0100 Subject: [PATCH 33/70] ML reification of primitive int/floats --- template-coq/src/constr_reification.ml | 2 ++ template-coq/src/quoter.ml | 10 +++++++--- template-coq/src/reification.ml | 3 +++ 3 files changed, 12 insertions(+), 3 deletions(-) diff --git a/template-coq/src/constr_reification.ml b/template-coq/src/constr_reification.ml index 2d1253a26..41356063c 100644 --- a/template-coq/src/constr_reification.ml +++ b/template-coq/src/constr_reification.ml @@ -16,6 +16,8 @@ struct type quoted_kernel_name = Constr.t (* of type Ast.kername *) type quoted_inductive = Constr.t (* of type Ast.inductive *) type quoted_proj = Constr.t (* of type Ast.projection *) + type quoted_prim_int = Constr.t (* of type UInt63.t *) + type quoted_prim_float = Constr.t (* of type Float64.t *) type quoted_global_reference = Constr.t (* of type Ast.global_reference *) type quoted_sort_family = Constr.t (* of type Ast.sort_family *) diff --git a/template-coq/src/quoter.ml b/template-coq/src/quoter.ml index 72282be8e..1bc838cd8 100644 --- a/template-coq/src/quoter.ml +++ b/template-coq/src/quoter.ml @@ -78,6 +78,10 @@ sig val quote_inductive : quoted_kernel_name * quoted_int -> quoted_inductive val quote_proj : quoted_inductive -> quoted_int -> quoted_int -> quoted_proj + (* Primitive objects *) + val quote_prim_int : Uint63.t -> quoted_prim_int + val quote_prim_float : Float64.t -> quoted_prim_float + val quote_constraint_type : Univ.constraint_type -> quoted_constraint_type val quote_univ_constraint : Univ.univ_constraint -> quoted_univ_constraint val quote_univ_instance : Univ.Instance.t -> quoted_univ_instance @@ -229,7 +233,7 @@ struct | Constr.Const (c,pu) -> let kn = Constant.canonical c in - (Q.mkConst (Q.quote_kn kn) (Q.quote_univ_instance pu), add_constant kn acc) + (Q.mkConst (Q.quote_kn kn) (Q.quote_univ_instance pu), add_constant kn acc) | Constr.Construct ((mind,c),pu) -> (Q.mkConstruct (quote_inductive' mind, Q.quote_int (c - 1)) (Q.quote_univ_instance pu), @@ -263,9 +267,9 @@ struct let p' = Q.quote_proj ind pars arg in let t', acc = quote_term acc env c in (Q.mkProj p' t', add_inductive (Projection.inductive p) acc) + | Constr.Int i -> (Q.quote_prim_int i, acc) + | Constr.Float f -> (Q.quote_prim_float f, acc) | Constr.Meta _ -> failwith "Meta not supported by TemplateCoq" - | Constr.Int i -> (Q.mkInt (Q.quote_int63 i), acc) - | Constr.Float _ -> failwith "Native floating point numbers not supported by TemplateCoq" in let in_prop, env' = env in if is_cast_prop () && not in_prop then diff --git a/template-coq/src/reification.ml b/template-coq/src/reification.ml index 8791b7853..b8b6397b1 100644 --- a/template-coq/src/reification.ml +++ b/template-coq/src/reification.ml @@ -15,6 +15,9 @@ sig type quoted_kernel_name type quoted_inductive type quoted_proj + type quoted_prim_int + type quoted_prim_float + type quoted_global_reference type quoted_sort_family From a44cad1e6baa848e082c453354c047c84570940f Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Fri, 4 Dec 2020 12:31:17 +0100 Subject: [PATCH 34/70] Support for primitive types --- template-coq/theories/Ast.v | 16 +++++++--- template-coq/theories/AstUtils.v | 12 ++++++- template-coq/theories/Induction.v | 43 ++++++++++++++------------ template-coq/theories/Reflect.v | 25 +++++++++++++++ template-coq/theories/WfInv.v | 4 +-- template-coq/theories/utils/MCString.v | 24 ++++++++++---- 6 files changed, 91 insertions(+), 33 deletions(-) diff --git a/template-coq/theories/Ast.v b/template-coq/theories/Ast.v index 06cf4e6d3..2fb2ab019 100644 --- a/template-coq/theories/Ast.v +++ b/template-coq/theories/Ast.v @@ -1,7 +1,8 @@ (* Distributed under the terms of the MIT license. *) From MetaCoq.Template Require Import utils Environment. From MetaCoq.Template Require Export Universes. -From Coq Require Int63. +(* For primitive integers and floats *) +From Coq Require Int63 Floats.PrimFloat. (** * AST of Coq kernel terms and kernel data structures @@ -51,7 +52,14 @@ Inductive term : Type := | tProj (proj : projection) (t : term) | tFix (mfix : mfixpoint term) (idx : nat) | tCoFix (mfix : mfixpoint term) (idx : nat) -| tInt (i : Int63.int). +| tInt (i : Int63.int) +| tFloat (f : PrimFloat.float). + +(** This can be used to represent holes, that, when unquoted, turn into fresh existential variables. + The fresh evar will depend on the whole context at this point in the term, despite the empty instance. + Denotation will call Coq's Typing.solve_evars to try and fill these holes using typing information. +*) +Definition hole := tEvar fresh_evar_id []. (** This can be used to represent holes, that, when unquoted, turn into fresh existential variables. The fresh evar will depend on the whole context at this point in the term, despite the empty instance. @@ -68,7 +76,6 @@ Definition mkApps t us := end end. - Module TemplateTerm <: Term. Definition term := term. @@ -126,7 +133,8 @@ Inductive wf : term -> Prop := | wf_tFix mfix k : Forall (fun def => wf def.(dtype) /\ wf def.(dbody) /\ isLambda def.(dbody) = true) mfix -> wf (tFix mfix k) | wf_tCoFix mfix k : Forall (fun def => wf def.(dtype) /\ wf def.(dbody)) mfix -> wf (tCoFix mfix k) -| wf_tInt i : wf (tInt i). +| wf_tInt i : wf (tInt i) +| wf_tFloat f : wf (tFloat f). (** ** Entries diff --git a/template-coq/theories/AstUtils.v b/template-coq/theories/AstUtils.v index 6cfc0d80a..9cd14353f 100644 --- a/template-coq/theories/AstUtils.v +++ b/template-coq/theories/AstUtils.v @@ -1,9 +1,18 @@ +(* For primitive integers and floats *) +From Coq Require Numbers.Cyclic.Int63.Int63 Floats.PrimFloat. (* Distributed under the terms of the MIT license. *) From MetaCoq.Template Require Import utils BasicAst Ast. Require Import ssreflect. +Require Import ZArith. (** Raw term printing *) +Definition string_of_prim_int n := + string_of_Z (Numbers.Cyclic.Int63.Int63.to_Z n). + +Definition string_of_float (f : PrimFloat.float) := + "". + Fixpoint string_of_term (t : term) := match t with | tRel n => "Rel(" ^ string_of_nat n ^ ")" @@ -42,7 +51,8 @@ Fixpoint string_of_term (t : term) := ^ string_of_term c ^ ")" | tFix l n => "Fix(" ^ (string_of_list (string_of_def string_of_term) l) ^ "," ^ string_of_nat n ^ ")" | tCoFix l n => "CoFix(" ^ (string_of_list (string_of_def string_of_term) l) ^ "," ^ string_of_nat n ^ ")" - | tInt i => "Int(" ^ string_of_int i ^ ")" + | tInt i => "Int(" ^ string_of_prim_int i ^ ")" + | tFloat f => "Float(" ^ string_of_float f ^ ")" end. Definition decompose_app (t : term) := diff --git a/template-coq/theories/Induction.v b/template-coq/theories/Induction.v index 5c76dd3f1..0332b235c 100644 --- a/template-coq/theories/Induction.v +++ b/template-coq/theories/Induction.v @@ -30,7 +30,8 @@ Lemma term_forall_list_ind : (forall (s : projection) (t : term), P t -> P (tProj s t)) -> (forall (m : mfixpoint term) (n : nat), tFixProp P P m -> P (tFix m n)) -> (forall (m : mfixpoint term) (n : nat), tFixProp P P m -> P (tCoFix m n)) -> - (forall (i : Int63.int), P (tInt i)) -> + (forall i, P (tInt i)) -> + (forall f, P (tFloat f)) -> forall t : term, P t. Proof. intros until t. revert t. @@ -88,7 +89,8 @@ Lemma term_wf_forall_list_ind : (forall (s : projection) (t : term), P t -> P (tProj s t)) -> (forall (m : mfixpoint term) (n : nat), tFixProp P P m -> Forall (fun def => isLambda (dbody def) = true) m -> P (tFix m n)) -> (forall (m : mfixpoint term) (n : nat), tFixProp P P m -> P (tCoFix m n)) -> - (forall (i : Int63.int), P (tInt i)) -> + (forall i, P (tInt i)) -> + (forall f, P (tFloat f)) -> forall t : term, wf t -> P t. Proof. pose proof I as H1. (* can go away, to avoid renaming everything... *) @@ -97,37 +99,37 @@ Proof. intros; try solve [match goal with H : _ |- _ => apply H end; auto]. - apply H2. inv H17. - { auto using lift_to_wf_list. } - - - inv H18; auto. - - inv H18; auto. - - inv H18; auto. - - inv H19; auto. - - inv H18; auto. + apply H2. inv H19. + auto using lift_to_wf_list. + + - inv H20; auto. + - inv H20; auto. + - inv H20; auto. + - inv H21; auto. + - inv H20; auto. apply H8; auto. auto using lift_to_wf_list. - - inv H18; apply H12; auto. + - inv H20; apply H12; auto. red. red in X. induction X. + constructor. - + constructor. inv H21; auto. apply IHX. inv H21; auto. + + constructor. inv H23; auto. apply IHX. inv H23; auto. - - inv H17; auto. + - inv H19; auto. - - inv H16; auto. + - inv H18; auto. apply H14. red. red in X. induction X; constructor. - + split; inv H17; intuition. - + apply IHX. now inv H17. + + split; inv H19; intuition. + + apply IHX. now inv H19. + eapply Forall_impl; tea. clear; intros; cbn in *; intuition. - - inv H16; auto. + - inv H18; auto. apply H15. red. red in X. induction X; constructor. - + split; inv H17; intuition. - + apply IHX. now inv H17. + + split; inv H19; intuition. + + apply IHX. now inv H19. Qed. Definition tCaseBrsType {A} (P : A -> Type) (l : list (nat * A)) := @@ -157,7 +159,8 @@ Lemma term_forall_list_rect : (forall (s : projection) (t : term), P t -> P (tProj s t)) -> (forall (m : mfixpoint term) (n : nat), tFixType P P m -> P (tFix m n)) -> (forall (m : mfixpoint term) (n : nat), tFixType P P m -> P (tCoFix m n)) -> - (forall (i : Int63.int), P (tInt i)) -> + (forall i, P (tInt i)) -> + (forall f, P (tFloat f)) -> forall t : term, P t. Proof. intros until t. revert t. diff --git a/template-coq/theories/Reflect.v b/template-coq/theories/Reflect.v index c2844b9c4..1ca917444 100644 --- a/template-coq/theories/Reflect.v +++ b/template-coq/theories/Reflect.v @@ -1,4 +1,6 @@ (* Distributed under the terms of the MIT license. *) +(* For primitive integers and floats *) +From Coq Require Numbers.Cyclic.Int63.Int63 Floats.PrimFloat Floats.FloatAxioms. From MetaCoq.Template Require Import utils AstUtils BasicAst Ast Induction. Require Import ssreflect. From Equations Require Import Equations. @@ -135,6 +137,29 @@ Instance reflect_nat : ReflectEq nat := { eqb_spec := Nat.eqb_spec }. +#[program] +Instance reflect_prim_int : ReflectEq Numbers.Cyclic.Int63.Int63.int := + { eqb := Numbers.Cyclic.Int63.Int63.eqb +}. +Next Obligation. + destruct (Int63.eqb x y) eqn:eq; constructor. + now apply (Numbers.Cyclic.Int63.Int63.eqb_spec x y) in eq. + now apply (Numbers.Cyclic.Int63.Int63.eqb_false_spec x y) in eq. +Qed. + +Derive NoConfusion EqDec for SpecFloat.spec_float. + +Arguments eqb : simpl never. +#[program] +Instance reflect_prim_float : ReflectEq PrimFloat.float := + { eqb x y := eqb (ReflectEq := EqDec_ReflectEq SpecFloat.spec_float) (FloatOps.Prim2SF x) (FloatOps.Prim2SF y) }. +Next Obligation. + destruct (eqb_spec (ReflectEq := EqDec_ReflectEq SpecFloat.spec_float) (FloatOps.Prim2SF x) (FloatOps.Prim2SF y)); constructor. + now apply FloatAxioms.Prim2SF_inj. + intros e; apply n. rewrite e. + reflexivity. +Qed. + Definition eq_level l1 l2 := match l1, l2 with | Level.lSet, Level.lSet => true diff --git a/template-coq/theories/WfInv.v b/template-coq/theories/WfInv.v index 01626483f..55f00d098 100644 --- a/template-coq/theories/WfInv.v +++ b/template-coq/theories/WfInv.v @@ -7,7 +7,7 @@ From MetaCoq.Template Require Import config utils Ast AstUtils. Fixpoint wf_Inv (t : term) := match t with - | tRel _ | tVar _ | tSort _ => True + | tRel _ | tVar _ | tSort _ | tInt _ | tFloat _ => True | tEvar n l => Forall wf l | tCast t k t' => wf t /\ wf t' | tProd na t b => wf t /\ wf b @@ -61,7 +61,7 @@ Qed. Fixpoint wf_term (t : term) : bool := match t with - | tRel _ | tVar _ => true + | tRel _ | tVar _ | tInt _ | tFloat _ => true | tEvar n l => forallb wf_term l | tSort u => true | tCast t k t' => wf_term t && wf_term t' diff --git a/template-coq/theories/utils/MCString.v b/template-coq/theories/utils/MCString.v index 70b7d30c7..72c7cf3d1 100644 --- a/template-coq/theories/utils/MCString.v +++ b/template-coq/theories/utils/MCString.v @@ -1,5 +1,4 @@ -From Coq Require Import String. -From Coq.Numbers Require Import (* DecimalString *) Int63. +From Coq Require Import String Decimal DecimalString ZArith. From MetaCoq.Template Require Import MCCompare. Local Open Scope string_scope. @@ -26,8 +25,10 @@ Definition print_list {A} (f : A -> string) (sep : string) (l : list A) : string Definition parens (top : bool) (s : string) := if top then s else "(" ++ s ++ ")". +(* TODO: reuse the Decimal support for parsing and printing numbers in Coq *) Definition string_of_nat n : string := - match n with + DecimalString.NilEmpty.string_of_uint (Nat.to_uint n). +(* match n with | 0 => "0" | 1 => "1" | 2 => "2" @@ -79,12 +80,12 @@ Definition string_of_nat n : string := | 48 => "48" | 49 => "49" | _ => "todo string_of_nat" - end. + end. *) (* Definition string_of_nat n : string := DecimalString.NilZero.string_of_uint (Nat.to_uint n). *) (* Definition string_of_int (i:Int63.int) : string := BinNat.N.to_uint (BinInt.Z.to_N (Int63.to_Z i))). *) -Definition string_of_int (i:Int63.int) : string := +(* Definition string_of_int (i:Int63.int) : string := (if Int63.ltb i 8 then if Int63.ltb i 4 @@ -96,11 +97,22 @@ Definition string_of_int (i:Int63.int) : string := if Int63.ltb i 6 then if Int63.ltb i 5 then "4" else "5" else if Int63.ltb i 7 then "6" else "7" - else if Int63.eqb i 42 then "42" else "todo string_of_int")%int63. + else if Int63.eqb i 42 then "42" else "todo string_of_int")%int63. *) Hint Resolve String.string_dec : eq_dec. + +Definition string_of_positive p := + string_of_nat (Pos.to_nat p). + +Definition string_of_Z (z : Z) : string := + match z with + | Z0 => "0" + | Zpos p => string_of_positive p + | Zneg p => "-" ++ string_of_positive p + end. + Definition eq_string s s' := match string_compare s s' with | Eq => true From f36c75d5efd4d2a0a91d96dfb937558f6f5e1fd1 Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Fri, 4 Dec 2020 13:18:37 +0100 Subject: [PATCH 35/70] Extract float64 as well --- template-coq/_PluginProject | 19 +++++++++++++ .../gen-src/metacoq_template_plugin.mlpack | 4 +++ template-coq/src/ast_denoter.ml | 11 ++++++-- template-coq/src/ast_quoter.ml | 9 +++++- template-coq/src/constr_denoter.ml | 18 ++++++++++-- template-coq/src/constr_quoter.ml | 8 ++++-- template-coq/src/constr_reification.ml | 9 +++--- template-coq/src/denoter.ml | 8 ++++-- template-coq/src/quoter.ml | 10 +++---- template-coq/src/reification.ml | 5 ++-- template-coq/src/tm_util.ml | 3 +- template-coq/theories/Ast.v | 6 ---- template-coq/theories/Constants.v | 1 + template-coq/theories/Extraction.v | 13 ++++++++- template-coq/theories/Induction.v | 28 +++++++++---------- template-coq/theories/Pretty.v | 3 +- template-coq/theories/Reflect.v | 2 ++ template-coq/theories/Typing.v | 3 +- template-coq/theories/UnivSubst.v | 2 +- template-coq/theories/WfInv.v | 4 +-- 20 files changed, 115 insertions(+), 51 deletions(-) diff --git a/template-coq/_PluginProject b/template-coq/_PluginProject index 68af75daf..e777b2e71 100644 --- a/template-coq/_PluginProject +++ b/template-coq/_PluginProject @@ -58,6 +58,21 @@ gen-src/extractable.mli #gen-src/induction.mli gen-src/int63.ml gen-src/int63.mli + +# gen-src/sumbool.mli +# gen-src/sumbool.ml +# gen-src/zeven.mli +# gen-src/zeven.ml +# gen-src/zArith_dec.mli +# gen-src/zArith_dec.ml +# gen-src/zbool.mli +# gen-src/zbool.ml +gen-src/specFloat.mli +gen-src/specFloat.ml +gen-src/floatOps.mli +gen-src/floatOps.ml +# gen-src/float64.mli +# gen-src/float64.ml gen-src/liftSubst.ml gen-src/liftSubst.mli gen-src/list0.ml @@ -76,6 +91,10 @@ gen-src/mCProd.ml gen-src/mCProd.mli gen-src/mCRelations.ml gen-src/mCRelations.mli +gen-src/primFloat.mli +gen-src/primFloat.ml +gen-src/decimalString.mli +gen-src/decimalString.ml gen-src/mCString.ml gen-src/mCString.mli gen-src/mCUtils.ml diff --git a/template-coq/gen-src/metacoq_template_plugin.mlpack b/template-coq/gen-src/metacoq_template_plugin.mlpack index e541ccdb1..1c13613e2 100644 --- a/template-coq/gen-src/metacoq_template_plugin.mlpack +++ b/template-coq/gen-src/metacoq_template_plugin.mlpack @@ -36,6 +36,10 @@ MCRelations MCOption MCProd MCCompare +SpecFloat +PrimFloat +FloatOps +DecimalString MCString MCUtils Signature diff --git a/template-coq/src/ast_denoter.ml b/template-coq/src/ast_denoter.ml index ea06d0a22..99fcb8b26 100644 --- a/template-coq/src/ast_denoter.ml +++ b/template-coq/src/ast_denoter.ml @@ -10,6 +10,7 @@ struct type quoted_ident = char list type quoted_int = Datatypes.nat type quoted_int63 = Uint63.t + type quoted_float64 = Float64.t type quoted_bool = bool type quoted_name = name type quoted_aname = name binder_annot @@ -69,6 +70,8 @@ struct let mkInd = mkInd let mkCase = mkCase let mkProj = mkProj + let mkInt = mkInt + let mkFloat = mkFloat let unquote_def (x: 't BasicAst.def) : ('t, name binder_annot, quoted_int) adef = { @@ -78,7 +81,9 @@ struct rarg=rarg x } - let inspect_term (tt: t):(t, quoted_int, quoted_ident, quoted_aname, quoted_sort, quoted_cast_kind, quoted_kernel_name, quoted_inductive, quoted_relevance, quoted_univ_instance, quoted_proj, quoted_int63) structure_of_term= + let inspect_term (tt: t):(t, quoted_int, quoted_ident, quoted_aname, quoted_sort, quoted_cast_kind, + quoted_kernel_name, quoted_inductive, quoted_relevance, quoted_univ_instance, quoted_proj, + quoted_int63, quoted_float64) structure_of_term= match tt with | Coq_tRel n -> ACoq_tRel n | Coq_tVar v -> ACoq_tVar v @@ -97,7 +102,7 @@ struct | Coq_tFix (a,b) -> ACoq_tFix (List.map unquote_def a,b) | Coq_tCoFix (a,b) -> ACoq_tCoFix (List.map unquote_def a,b) | Coq_tInt i -> ACoq_tInt i - + | Coq_tFloat f -> ACoq_tFloat f let unquote_ident (qi: quoted_ident) : Id.t = let s = list_to_string qi in @@ -130,6 +135,8 @@ struct let unquote_int63 i = i + let unquote_float64 i = i + (* val unquote_sort : quoted_sort -> Sorts.t *) (* val unquote_sort_family : quoted_sort_family -> Sorts.family *) let unquote_cast_kind (q : quoted_cast_kind) : Constr.cast_kind = diff --git a/template-coq/src/ast_quoter.ml b/template-coq/src/ast_quoter.ml index b38544e0f..a0abb64ad 100644 --- a/template-coq/src/ast_quoter.ml +++ b/template-coq/src/ast_quoter.ml @@ -10,6 +10,7 @@ struct type quoted_ident = char list type quoted_int = Datatypes.nat type quoted_int63 = Uint63.t + type quoted_float64 = Float64.t type quoted_bool = bool type quoted_name = BasicAst.name type quoted_aname = BasicAst.aname @@ -75,6 +76,8 @@ struct let quote_int63 x = x + let quote_float64 x = x + (* NOTE: fails if it hits Prop or SProp *) let quote_nonprop_level (l : Univ.Level.t) : Universes0.Level.t = if Univ.Level.is_prop l || Univ.Level.is_sprop l then @@ -236,6 +239,7 @@ struct let mkConstruct (ind, i) u = Coq_tConstruct (ind, i, u) let mkLetIn na b t t' = Coq_tLetIn (na,b,t,t') let mkInt i = Coq_tInt i + let mkFloat f = Coq_tFloat f let rec seq f t = if f < t then @@ -341,9 +345,12 @@ struct Some (Right mind_entry) | None -> None *) - let inspectTerm (t : term) : (term, quoted_int, quoted_ident, quoted_name, quoted_sort, quoted_cast_kind, quoted_kernel_name, quoted_inductive, quoted_relevance, quoted_univ_instance, quoted_proj, quoted_int63) structure_of_term = + let inspectTerm (t : term) : (term, quoted_int, quoted_ident, quoted_name, quoted_sort, quoted_cast_kind, + quoted_kernel_name, quoted_inductive, quoted_relevance, quoted_univ_instance, quoted_proj, + quoted_int63, quoted_float64) structure_of_term = match t with | Coq_tRel n -> ACoq_tRel n + (* todo ! *) (* so on *) | _ -> failwith "not yet implemented" diff --git a/template-coq/src/constr_denoter.ml b/template-coq/src/constr_denoter.ml index 31fdc4dcf..2bc45bfbb 100644 --- a/template-coq/src/constr_denoter.ml +++ b/template-coq/src/constr_denoter.ml @@ -78,7 +78,10 @@ struct | Constr.Int i -> i | _ -> not_supported_verb trm "unquote_int63" - + let unquote_float64 trm = + match Constr.kind trm with + | Constr.Float f -> f + | _ -> not_supported_verb trm "unquote_float64" let unquote_char trm = let (h,args) = app_full trm [] in @@ -343,7 +346,9 @@ struct let inspect_term (t:Constr.t) - : (Constr.t, quoted_int, quoted_ident, quoted_name, quoted_sort, quoted_cast_kind, quoted_kernel_name, quoted_inductive, quoted_relevance, quoted_univ_instance, quoted_proj, quoted_int63) structure_of_term = + : (Constr.t, quoted_int, quoted_ident, quoted_name, quoted_sort, quoted_cast_kind, quoted_kernel_name, + quoted_inductive, quoted_relevance, quoted_univ_instance, quoted_proj, + quoted_int63, quoted_float64) structure_of_term = let (h,args) = app_full t [] in if constr_equall h tRel then match args with @@ -435,7 +440,14 @@ struct match args with proj::t::_ -> ACoq_tProj (proj, t) | _ -> CErrors.user_err (print_term t ++ Pp.str ("has bad structure")) - + else if constr_equall h tInt then + match args with + t::_ -> ACoq_tInt t + | _ -> CErrors.user_err (print_term t ++ Pp.str ("has bad structure")) + else if constr_equall h tFloat then + match args with + t::_ -> ACoq_tFloat t + | _ -> CErrors.user_err (print_term t ++ Pp.str ("has bad structure")) else CErrors.user_err (str"inspect_term: cannot recognize " ++ print_term t ++ str" (maybe you forgot to reduce it?)") diff --git a/template-coq/src/constr_quoter.ml b/template-coq/src/constr_quoter.ml index a2071a87c..1fdb41263 100644 --- a/template-coq/src/constr_quoter.ml +++ b/template-coq/src/constr_quoter.ml @@ -33,7 +33,6 @@ struct let mkRel i = constr_mkApp (tRel, [| i |]) let mkVar id = constr_mkApp (tVar, [| id |]) - let mkInt i = constr_mkApp (tInt, [| i |]) let mkEvar n args = constr_mkApp (tEvar, [| n; to_coq_listl tTerm (Array.to_list args) |]) let mkSort s = constr_mkApp (tSort, [| s |]) let mkCast c k t = constr_mkApp (tCast, [| c ; k ; t |]) @@ -81,6 +80,9 @@ struct let mkProj kn t = constr_mkApp (tProj, [| kn; t |]) + let mkInt i = constr_mkApp (tInt, [| i |]) + let mkFloat f = constr_mkApp (tFloat, [| f |]) + let quote_option ty = function | Some tm -> constr_mkApp (cSome, [|ty; tm|]) | None -> constr_mkApp (cNone, [|ty|]) @@ -110,7 +112,9 @@ struct let quote_bool b = if b then Lazy.force ttrue else Lazy.force tfalse - let quote_int63 i = Lazy.force tInt + let quote_int63 i = constr_mkApp (tInt, [| Constr.mkInt i |]) + + let quote_float64 f = constr_mkApp (tFloat, [| Constr.mkFloat f |]) let quote_char i = constr_mkApp (tAscii, Array.of_list (List.map (fun m -> quote_bool ((i land m) = m)) diff --git a/template-coq/src/constr_reification.ml b/template-coq/src/constr_reification.ml index 41356063c..e78f965e4 100644 --- a/template-coq/src/constr_reification.ml +++ b/template-coq/src/constr_reification.ml @@ -6,7 +6,6 @@ struct type quoted_ident = Constr.t (* of type Ast.ident *) type quoted_int = Constr.t (* of type nat *) - type quoted_int63 = Constr.t (* of type int63 *) type quoted_bool = Constr.t (* of type bool *) type quoted_name = Constr.t (* of type BasicAst.name *) type quoted_aname = Constr.t (* of type BasicAst.aname (names with relevance) *) @@ -16,8 +15,8 @@ struct type quoted_kernel_name = Constr.t (* of type Ast.kername *) type quoted_inductive = Constr.t (* of type Ast.inductive *) type quoted_proj = Constr.t (* of type Ast.projection *) - type quoted_prim_int = Constr.t (* of type UInt63.t *) - type quoted_prim_float = Constr.t (* of type Float64.t *) + type quoted_int63 = Constr.t (* of type UInt63.t *) + type quoted_float64 = Constr.t (* of type Float64.t *) type quoted_global_reference = Constr.t (* of type Ast.global_reference *) type quoted_sort_family = Constr.t (* of type Ast.sort_family *) @@ -141,11 +140,11 @@ struct let tmkInd = ast "mkInd" let tmkdecl = ast "mkdecl" let (tTerm,tRel,tVar,tEvar,tSort,tCast,tProd, - tLambda,tLetIn,tApp,tCase,tFix,tConstructor,tConst,tInd,tCoFix,tProj,tInt) = + tLambda,tLetIn,tApp,tCase,tFix,tConstructor,tConst,tInd,tCoFix,tProj,tInt,tFloat) = (ast "term", ast "tRel", ast "tVar", ast "tEvar", ast "tSort", ast "tCast", ast "tProd", ast "tLambda", ast "tLetIn", ast "tApp", ast "tCase", ast "tFix", - ast "tConstruct", ast "tConst", ast "tInd", ast "tCoFix", ast "tProj", ast "tInt") + ast "tConstruct", ast "tConst", ast "tInd", ast "tCoFix", ast "tProj", ast "tInt", ast "tFloat") let tkername = ast "kername" let tmodpath = ast "modpath" let tMPfile = ast "MPfile" diff --git a/template-coq/src/denoter.ml b/template-coq/src/denoter.ml index a71909a48..1c673c757 100644 --- a/template-coq/src/denoter.ml +++ b/template-coq/src/denoter.ml @@ -13,8 +13,8 @@ sig val unquote_evar : Environ.env -> Evd.evar_map -> quoted_int -> Constr.t list -> Evd.evar_map * Constr.t val unquote_int : quoted_int -> int val unquote_bool : quoted_bool -> bool - val unquote_int63 : quoted_prim_int -> Uint63.t - val unquote_int63 : quoted_prim_float -> Float64.t + val unquote_int63 : quoted_int63 -> Uint63.t + val unquote_float64 : quoted_float64 -> Float64.t (* val unquote_sort : quoted_sort -> Sorts.t *) (* val unquote_sort_family : quoted_sort_family -> Sorts.family *) val unquote_cast_kind : quoted_cast_kind -> Constr.cast_kind @@ -25,7 +25,9 @@ sig val unquote_universe : Evd.evar_map -> quoted_sort -> Evd.evar_map * Univ.Universe.t val unquote_universe_instance: Evd.evar_map -> quoted_univ_instance -> Evd.evar_map * Univ.Instance.t (* val representsIndConstuctor : quoted_inductive -> Term.constr -> bool *) - val inspect_term : t -> (t, quoted_int, quoted_ident, quoted_aname, quoted_sort, quoted_cast_kind, quoted_kernel_name, quoted_inductive, quoted_relevance, quoted_univ_instance, quoted_proj, quoted_int63) structure_of_term + val inspect_term : t -> (t, quoted_int, quoted_ident, quoted_aname, quoted_sort, quoted_cast_kind, + quoted_kernel_name, quoted_inductive, quoted_relevance, quoted_univ_instance, quoted_proj, + quoted_int63, quoted_float64) structure_of_term end diff --git a/template-coq/src/quoter.ml b/template-coq/src/quoter.ml index 1bc838cd8..43442c697 100644 --- a/template-coq/src/quoter.ml +++ b/template-coq/src/quoter.ml @@ -59,6 +59,7 @@ sig val mkFix : (quoted_int array * quoted_int) * (quoted_aname array * t array * t array) -> t val mkCoFix : quoted_int * (quoted_aname array * t array * t array) -> t val mkInt : quoted_int63 -> t + val mkFloat : quoted_float64 -> t val mkBindAnn : quoted_name -> quoted_relevance -> quoted_aname val mkName : quoted_ident -> quoted_name @@ -69,7 +70,6 @@ sig val quote_aname : Name.t Context.binder_annot -> quoted_aname val quote_relevance : Sorts.relevance -> quoted_relevance val quote_int : int -> quoted_int - val quote_int63 : Uint63.t -> quoted_int63 val quote_bool : bool -> quoted_bool val quote_sort : Sorts.t -> quoted_sort val quote_sort_family : Sorts.family -> quoted_sort_family @@ -79,8 +79,8 @@ sig val quote_proj : quoted_inductive -> quoted_int -> quoted_int -> quoted_proj (* Primitive objects *) - val quote_prim_int : Uint63.t -> quoted_prim_int - val quote_prim_float : Float64.t -> quoted_prim_float + val quote_int63 : Uint63.t -> quoted_int63 + val quote_float64 : Float64.t -> quoted_float64 val quote_constraint_type : Univ.constraint_type -> quoted_constraint_type val quote_univ_constraint : Univ.univ_constraint -> quoted_univ_constraint @@ -267,8 +267,8 @@ struct let p' = Q.quote_proj ind pars arg in let t', acc = quote_term acc env c in (Q.mkProj p' t', add_inductive (Projection.inductive p) acc) - | Constr.Int i -> (Q.quote_prim_int i, acc) - | Constr.Float f -> (Q.quote_prim_float f, acc) + | Constr.Int i -> (Q.mkInt (Q.quote_int63 i), acc) + | Constr.Float f -> (Q.mkFloat (Q.quote_float64 f), acc) | Constr.Meta _ -> failwith "Meta not supported by TemplateCoq" in let in_prop, env' = env in diff --git a/template-coq/src/reification.ml b/template-coq/src/reification.ml index b8b6397b1..120a833ae 100644 --- a/template-coq/src/reification.ml +++ b/template-coq/src/reification.ml @@ -5,7 +5,6 @@ sig type quoted_ident type quoted_int - type quoted_int63 type quoted_bool type quoted_name type quoted_aname @@ -15,8 +14,8 @@ sig type quoted_kernel_name type quoted_inductive type quoted_proj - type quoted_prim_int - type quoted_prim_float + type quoted_int63 + type quoted_float64 type quoted_global_reference diff --git a/template-coq/src/tm_util.ml b/template-coq/src/tm_util.ml index c0fe9b8f7..b2cf92ef8 100644 --- a/template-coq/src/tm_util.ml +++ b/template-coq/src/tm_util.ml @@ -68,7 +68,7 @@ type ('term, 'name, 'nat) adef = { adname : 'name; adtype : 'term; adbody : 'ter type ('term, 'name, 'nat) amfixpoint = ('term, 'name, 'nat) adef list -type ('term, 'nat, 'ident, 'name, 'quoted_sort, 'cast_kind, 'kername, 'inductive, 'relevance, 'universe_instance, 'projection, 'int63) structure_of_term = +type ('term, 'nat, 'ident, 'name, 'quoted_sort, 'cast_kind, 'kername, 'inductive, 'relevance, 'universe_instance, 'projection, 'int63, 'float64) structure_of_term = | ACoq_tRel of 'nat | ACoq_tVar of 'ident | ACoq_tEvar of 'nat * 'term list @@ -86,4 +86,5 @@ type ('term, 'nat, 'ident, 'name, 'quoted_sort, 'cast_kind, 'kername, 'inductive | ACoq_tFix of ('term, 'name, 'nat) amfixpoint * 'nat | ACoq_tCoFix of ('term, 'name, 'nat) amfixpoint * 'nat | ACoq_tInt of 'int63 + | ACoq_tFloat of 'float64 diff --git a/template-coq/theories/Ast.v b/template-coq/theories/Ast.v index 2fb2ab019..a7d03bd8a 100644 --- a/template-coq/theories/Ast.v +++ b/template-coq/theories/Ast.v @@ -61,12 +61,6 @@ Inductive term : Type := *) Definition hole := tEvar fresh_evar_id []. -(** This can be used to represent holes, that, when unquoted, turn into fresh existential variables. - The fresh evar will depend on the whole context at this point in the term, despite the empty instance. - Denotation will call Coq's Typing.solve_evars to try and fill these holes using typing information. -*) -Definition hole := tEvar fresh_evar_id []. - Definition mkApps t us := match us with | nil => t diff --git a/template-coq/theories/Constants.v b/template-coq/theories/Constants.v index 27291717c..989b102cf 100644 --- a/template-coq/theories/Constants.v +++ b/template-coq/theories/Constants.v @@ -168,6 +168,7 @@ Register MetaCoq.Template.Ast.tProj as metacoq.ast.tProj. Register MetaCoq.Template.Ast.tFix as metacoq.ast.tFix. Register MetaCoq.Template.Ast.tCoFix as metacoq.ast.tCoFix. Register MetaCoq.Template.Ast.tInt as metacoq.ast.tInt. +Register MetaCoq.Template.Ast.tFloat as metacoq.ast.tFloat. (* Local and global declarations *) Register MetaCoq.Template.Ast.parameter_entry as metacoq.ast.parameter_entry. diff --git a/template-coq/theories/Extraction.v b/template-coq/theories/Extraction.v index a97444fee..c5184ef36 100644 --- a/template-coq/theories/Extraction.v +++ b/template-coq/theories/Extraction.v @@ -1,6 +1,7 @@ (* Distributed under the terms of the MIT license. *) From MetaCoq.Template Require Import utils Ast Reflect Induction. -Require Import FSets ExtrOcamlBasic ExtrOcamlString ExtrOcamlZInt MC_ExtrOCamlInt63 (*b/c nameclash with `comparion` *). +Require Import FSets ExtrOcamlBasic ExtrOcamlString ExtrOcamlZInt MC_ExtrOCamlInt63 (*b/c nameclash with `comparion` *) + ExtrOCamlFloats. From Coq Require Extraction. (** * Extraction setup for template-coq. @@ -33,6 +34,15 @@ From MetaCoq.Template Require Import TemplateMonad.Extractable config Induction Import Init.Nat. Locate Nat. +(* Floats *) +(* Extraction Library Zeven. +Extraction Library Zeven. +Extraction Library ZArith_dec. +Extraction Library Sumbool. +Extraction Library Zbool. +Extraction Library SpecFloat. *) +Separate Extraction FloatOps.Prim2SF. + Recursive Extraction Library Extractable. Extraction Library MCPrelude. Extraction Library MCOption. @@ -43,6 +53,7 @@ Extraction Library Induction. Extraction Library LiftSubst. Extraction Library UnivSubst. Extraction Library BasicAst. + Extraction Library Reflect. Extraction Library Pretty. Extraction Library config. diff --git a/template-coq/theories/Induction.v b/template-coq/theories/Induction.v index 0332b235c..6d8f12934 100644 --- a/template-coq/theories/Induction.v +++ b/template-coq/theories/Induction.v @@ -99,37 +99,37 @@ Proof. intros; try solve [match goal with H : _ |- _ => apply H end; auto]. - apply H2. inv H19. + apply H2. inv H18. auto using lift_to_wf_list. + - inv H19; auto. + - inv H19; auto. + - inv H19; auto. - inv H20; auto. - - inv H20; auto. - - inv H20; auto. - - inv H21; auto. - - inv H20; auto. + - inv H19; auto. apply H8; auto. auto using lift_to_wf_list. - - inv H20; apply H12; auto. + - inv H19; apply H12; auto. red. red in X. induction X. + constructor. - + constructor. inv H23; auto. apply IHX. inv H23; auto. - - - inv H19; auto. + + constructor. inv H22; auto. apply IHX. inv H22; auto. - inv H18; auto. + + - inv H16; auto. apply H14. red. red in X. induction X; constructor. - + split; inv H19; intuition. - + apply IHX. now inv H19. + + split; inv H18; intuition. + + apply IHX. now inv H18. + eapply Forall_impl; tea. clear; intros; cbn in *; intuition. - - inv H18; auto. + - inv H16; auto. apply H15. red. red in X. induction X; constructor. - + split; inv H19; intuition. - + apply IHX. now inv H19. + + split; inv H18; intuition. + + apply IHX. now inv H18. Qed. Definition tCaseBrsType {A} (P : A -> Type) (l : list (nat * A)) := diff --git a/template-coq/theories/Pretty.v b/template-coq/theories/Pretty.v index 15099ea86..893d593cb 100644 --- a/template-coq/theories/Pretty.v +++ b/template-coq/theories/Pretty.v @@ -202,7 +202,8 @@ Section print_term. | tCoFix l n => parens top ("let cofix " ^ print_defs print_term Γ l ^ nl ^ " in " ^ List.nth_default (string_of_nat n) (map (string_of_name ∘ binder_name ∘ dname) l) n) - | tInt i => "Int(" ^ string_of_int i ^ ")" + | tInt i => "Int(" ^ string_of_prim_int i ^ ")" + | tFloat f => "Float(" ^ string_of_float f ^ ")" end. End print_term. diff --git a/template-coq/theories/Reflect.v b/template-coq/theories/Reflect.v index 1ca917444..f7c22c6f2 100644 --- a/template-coq/theories/Reflect.v +++ b/template-coq/theories/Reflect.v @@ -523,6 +523,8 @@ Proof. subst. left. reflexivity. - destruct (Int63.eqs i i0) ; nodec. subst. left. reflexivity. + - destruct (eq_dec f f0) ; nodec. + subst. left. reflexivity. Defined. Instance reflect_term : ReflectEq term := diff --git a/template-coq/theories/Typing.v b/template-coq/theories/Typing.v index 0e371e949..5104daec6 100644 --- a/template-coq/theories/Typing.v +++ b/template-coq/theories/Typing.v @@ -539,7 +539,8 @@ Fixpoint strip_casts t := | tCoFix mfix idx => let mfix' := List.map (map_def strip_casts strip_casts) mfix in tCoFix mfix' idx - | tRel _ | tVar _ | tSort _ | tConst _ _ | tInd _ _ | tConstruct _ _ _ | tInt _ => t + | tRel _ | tVar _ | tSort _ | tConst _ _ | tInd _ _ | tConstruct _ _ _ + | tInt _ | tFloat _ => t end. Definition eq_term_nocast `{checker_flags} (φ : ConstraintSet.t) (t u : term) := diff --git a/template-coq/theories/UnivSubst.v b/template-coq/theories/UnivSubst.v index 5231b9966..19838d06e 100644 --- a/template-coq/theories/UnivSubst.v +++ b/template-coq/theories/UnivSubst.v @@ -10,7 +10,7 @@ From MetaCoq Require Import utils Ast AstUtils Induction LiftSubst. Instance subst_instance_constr : UnivSubst term := fix subst_instance_constr u c {struct c} : term := match c with - | tRel _ | tVar _ | tInt _ => c + | tRel _ | tVar _ | tInt _ | tFloat _ => c | tEvar ev args => tEvar ev (List.map (subst_instance_constr u) args) | tSort s => tSort (subst_instance_univ u s) | tConst c u' => tConst c (subst_instance_instance u u') diff --git a/template-coq/theories/WfInv.v b/template-coq/theories/WfInv.v index 55f00d098..8e982e7aa 100644 --- a/template-coq/theories/WfInv.v +++ b/template-coq/theories/WfInv.v @@ -14,7 +14,7 @@ Fixpoint wf_Inv (t : term) := | tLambda na t b => wf t /\ wf b | tLetIn na t b b' => wf t /\ wf b /\ wf b' | tApp t u => isApp t = false /\ u <> nil /\ wf t /\ Forall wf u - | tConst _ _ | tInd _ _ | tConstruct _ _ _ | tInt _ => True + | tConst _ _ | tInd _ _ | tConstruct _ _ _ => True | tCase ci p c brs => wf p /\ wf c /\ Forall (wf ∘ snd) brs | tProj p t => wf t | tFix mfix k => Forall (fun def => wf def.(dtype) /\ wf def.(dbody) /\ isLambda def.(dbody) = true) mfix @@ -69,7 +69,7 @@ Fixpoint wf_term (t : term) : bool := | tLambda na t b => wf_term t && wf_term b | tLetIn na t b b' => wf_term t && wf_term b && wf_term b' | tApp t u => ~~ isApp t && ~~ is_empty u && wf_term t && forallb wf_term u - | tConst _ _ | tInd _ _ | tConstruct _ _ _ | tInt _ => true + | tConst _ _ | tInd _ _ | tConstruct _ _ _ => true | tCase ci p c brs => wf_term p && wf_term c && forallb (wf_term ∘ snd) brs | tProj p t => wf_term t | tFix mfix k => From d71b2a0a7c61d4e8594a40fc9bceab51442fcff7 Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Fri, 4 Dec 2020 14:15:27 +0100 Subject: [PATCH 36/70] Fix Typing and cleanup --- template-coq/theories/AstUtils.v | 5 +- template-coq/theories/Typing.v | 5 +- template-coq/theories/utils/MCString.v | 73 -------------------------- 3 files changed, 7 insertions(+), 76 deletions(-) diff --git a/template-coq/theories/AstUtils.v b/template-coq/theories/AstUtils.v index 9cd14353f..5200f8ff7 100644 --- a/template-coq/theories/AstUtils.v +++ b/template-coq/theories/AstUtils.v @@ -7,8 +7,9 @@ Require Import ZArith. (** Raw term printing *) -Definition string_of_prim_int n := - string_of_Z (Numbers.Cyclic.Int63.Int63.to_Z n). +Definition string_of_prim_int (i:Int63.int) : string := + (* Better? DecimalString.NilZero.string_of_uint (BinNat.N.to_uint (BinInt.Z.to_N (Int63.to_Z i))). ? *) + string_of_Z (Numbers.Cyclic.Int63.Int63.to_Z i). Definition string_of_float (f : PrimFloat.float) := "". diff --git a/template-coq/theories/Typing.v b/template-coq/theories/Typing.v index 5104daec6..b123bbc4e 100644 --- a/template-coq/theories/Typing.v +++ b/template-coq/theories/Typing.v @@ -509,7 +509,10 @@ Inductive eq_term_upto_univ (Re Rle : Universe.t -> Universe.t -> Prop) : term - eq_term_upto_univ Re Rle (tCoFix mfix idx) (tCoFix mfix' idx) | eq_Int i : - eq_term_upto_univ Re Rle (tInt i) (tInt i). + eq_term_upto_univ Re Rle (tInt i) (tInt i) + + | eq_Float f : + eq_term_upto_univ Re Rle (tFloat f) (tFloat f). Definition eq_term `{checker_flags} φ := eq_term_upto_univ (eq_universe φ) (eq_universe φ). diff --git a/template-coq/theories/utils/MCString.v b/template-coq/theories/utils/MCString.v index 72c7cf3d1..c395a6941 100644 --- a/template-coq/theories/utils/MCString.v +++ b/template-coq/theories/utils/MCString.v @@ -25,84 +25,11 @@ Definition print_list {A} (f : A -> string) (sep : string) (l : list A) : string Definition parens (top : bool) (s : string) := if top then s else "(" ++ s ++ ")". -(* TODO: reuse the Decimal support for parsing and printing numbers in Coq *) Definition string_of_nat n : string := DecimalString.NilEmpty.string_of_uint (Nat.to_uint n). -(* match n with - | 0 => "0" - | 1 => "1" - | 2 => "2" - | 3 => "3" - | 4 => "4" - | 5 => "5" - | 6 => "6" - | 7 => "7" - | 8 => "8" - | 9 => "9" - | 10 => "10" - | 11 => "11" - | 12 => "12" - | 13 => "13" - | 14 => "14" - | 15 => "15" - | 16 => "16" - | 17 => "17" - | 18 => "18" - | 19 => "19" - | 20 => "20" - | 21 => "21" - | 22 => "22" - | 23 => "23" - | 24 => "24" - | 25 => "25" - | 26 => "26" - | 27 => "27" - | 28 => "28" - | 29 => "29" - | 30 => "30" - | 31 => "31" - | 32 => "32" - | 33 => "33" - | 34 => "34" - | 35 => "35" - | 36 => "36" - | 37 => "37" - | 38 => "38" - | 39 => "39" - | 40 => "40" - | 41 => "41" - | 42 => "42" - | 43 => "43" - | 44 => "44" - | 45 => "45" - | 46 => "46" - | 47 => "47" - | 48 => "48" - | 49 => "49" - | _ => "todo string_of_nat" - end. *) - - -(* Definition string_of_nat n : string := DecimalString.NilZero.string_of_uint (Nat.to_uint n). *) -(* Definition string_of_int (i:Int63.int) : string := BinNat.N.to_uint (BinInt.Z.to_N (Int63.to_Z i))). *) -(* Definition string_of_int (i:Int63.int) : string := - (if Int63.ltb i 8 - then - if Int63.ltb i 4 - then - if Int63.ltb i 2 - then if Int63.ltb i 1 then "0" else "1" - else if Int63.ltb i 3 then "2" else "3" - else - if Int63.ltb i 6 - then if Int63.ltb i 5 then "4" else "5" - else if Int63.ltb i 7 then "6" else "7" - else if Int63.eqb i 42 then "42" else "todo string_of_int")%int63. *) Hint Resolve String.string_dec : eq_dec. - - Definition string_of_positive p := string_of_nat (Pos.to_nat p). From ffce38708415a61fd7425b0590eabdfec39b7827 Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Fri, 4 Dec 2020 16:51:23 +0100 Subject: [PATCH 37/70] Add (modeled) ints and floats to PCUIC --- checker/theories/Checker.v | 6 +- checker/theories/Retyping.v | 2 + pcuic/theories/PCUICArities.v | 2 +- pcuic/theories/PCUICAst.v | 25 +++++++- pcuic/theories/PCUICAstUtils.v | 5 ++ pcuic/theories/PCUICCSubst.v | 1 - pcuic/theories/PCUICCanonicity.v | 4 +- pcuic/theories/PCUICClosed.v | 11 ++-- pcuic/theories/PCUICConfluence.v | 18 +++--- pcuic/theories/PCUICContexts.v | 10 ++-- pcuic/theories/PCUICConvCumInversion.v | 3 +- pcuic/theories/PCUICElimination.v | 14 ++--- pcuic/theories/PCUICEquality.v | 23 +++++++- pcuic/theories/PCUICInduction.v | 5 ++ pcuic/theories/PCUICInductiveInversion.v | 7 ++- pcuic/theories/PCUICInductives.v | 7 ++- pcuic/theories/PCUICInversion.v | 15 +++++ pcuic/theories/PCUICLiftSubst.v | 2 + pcuic/theories/PCUICNameless.v | 3 + pcuic/theories/PCUICNormal.v | 58 ++++++++++++++----- pcuic/theories/PCUICParallelReduction.v | 7 ++- .../PCUICParallelReductionConfluence.v | 4 +- pcuic/theories/PCUICPretty.v | 4 ++ pcuic/theories/PCUICPrincipality.v | 17 ++++-- pcuic/theories/PCUICReflect.v | 35 +++++++++++ pcuic/theories/PCUICSR.v | 3 +- pcuic/theories/PCUICSigmaCalculus.v | 3 +- pcuic/theories/PCUICSpine.v | 4 +- pcuic/theories/PCUICSubstitution.v | 8 +-- pcuic/theories/PCUICToTemplate.v | 9 +++ pcuic/theories/PCUICToTemplateCorrectness.v | 6 +- pcuic/theories/PCUICUnivSubst.v | 3 +- pcuic/theories/PCUICUnivSubstitution.v | 8 ++- pcuic/theories/PCUICValidity.v | 7 +-- pcuic/theories/PCUICWcbvEval.v | 2 +- pcuic/theories/PCUICWeakening.v | 2 +- pcuic/theories/TemplateToPCUIC.v | 15 +++++ template-coq/theories/Reflect.v | 3 +- 38 files changed, 276 insertions(+), 85 deletions(-) diff --git a/checker/theories/Checker.v b/checker/theories/Checker.v index 984cffa87..a1acfb784 100644 --- a/checker/theories/Checker.v +++ b/checker/theories/Checker.v @@ -447,7 +447,8 @@ Inductive type_error := | IllFormedFix (m : mfixpoint term) (i : nat) | UnsatisfiedConstraints (c : ConstraintSet.t) | UnsatisfiableConstraints (c : ConstraintSet.t) -| NotEnoughFuel (n : nat). +| NotEnoughFuel (n : nat) +| NotSupported (s : string). Definition string_of_type_error (e : type_error) : string := match e with @@ -468,6 +469,7 @@ Definition string_of_type_error (e : type_error) : string := | UnsatisfiedConstraints c => "Unsatisfied constraints" | UnsatisfiableConstraints c => "Unsatisfiable constraints" | NotEnoughFuel n => "Not enough fuel" + | NotSupported s => s ^ " are not supported" end. Inductive typing_result (A : Type) := @@ -769,6 +771,8 @@ Section Typecheck2. | Some f => ret f.(dtype) | None => raise (IllFormedFix mfix n) end + + | tInt _ | tFloat _ => raise (NotSupported "primitive types") end. Definition check (Γ : context) (t : term) (ty : term) : typing_result unit := diff --git a/checker/theories/Retyping.v b/checker/theories/Retyping.v index b91fcc9e6..0a0db7b9d 100644 --- a/checker/theories/Retyping.v +++ b/checker/theories/Retyping.v @@ -99,6 +99,8 @@ Section TypeOf. | Some f => ret f.(dtype) | None => raise (IllFormedFix mfix n) end + + | tInt _ | tFloat _ => raise (NotSupported "primitive types") end. Definition sort_of (Γ : context) (t : term) : typing_result Universe.t := diff --git a/pcuic/theories/PCUICArities.v b/pcuic/theories/PCUICArities.v index a998f28c3..7b029062e 100644 --- a/pcuic/theories/PCUICArities.v +++ b/pcuic/theories/PCUICArities.v @@ -87,7 +87,7 @@ Proof. constructor; pcuic. eapply context_relation_app in convctx as [_ convctx]. unshelve eapply (context_relation_impl convctx). - simpl; firstorder. destruct X. constructor; auto. + simpl; pcuicfo. destruct X. constructor; auto. eapply conv_conv_ctx; eauto. eapply context_relation_app_inv. constructor; pcuic. constructor; pcuic. constructor; pcuic. now symmetry. diff --git a/pcuic/theories/PCUICAst.v b/pcuic/theories/PCUICAst.v index 5d7f4d5a9..bfd510844 100644 --- a/pcuic/theories/PCUICAst.v +++ b/pcuic/theories/PCUICAst.v @@ -1,4 +1,5 @@ (* Distributed under the terms of the MIT license. *) +From Coq Require Import Floats.SpecFloat. From MetaCoq.Template Require Export utils Universes BasicAst Environment EnvironmentTyping. From Equations Require Import Equations. @@ -9,11 +10,28 @@ From Equations Require Import Equations. In particular, it has binary applications and all terms are well-formed. Casts are absent as well. *) - Declare Scope pcuic. Delimit Scope pcuic with pcuic. Open Scope pcuic. +(** DO NOT USE firstorder, since the introduction of Ints and Floats, it became unusuable. *) +Ltac pcuicfo_gen tac := + simpl in *; intuition (simpl; intuition tac). + +Tactic Notation "pcuicfo" := pcuicfo_gen auto. +Tactic Notation "pcuicfo" tactic(tac) := pcuicfo_gen tac. + +(** Model of unsigned integers *) +Definition uint_size := 63. +Definition uint_wB := (2 ^ (Z.of_nat uint_size))%Z. +Definition uint63_model := { z : Z | ((0 <=? z) && (z ". + Fixpoint string_of_term (t : term) := match t with | tRel n => "Rel(" ^ string_of_nat n ^ ")" @@ -36,6 +39,8 @@ Fixpoint string_of_term (t : term) := ^ string_of_term c ^ ")" | tFix l n => "Fix(" ^ (string_of_list (string_of_def string_of_term) l) ^ "," ^ string_of_nat n ^ ")" | tCoFix l n => "CoFix(" ^ (string_of_list (string_of_def string_of_term) l) ^ "," ^ string_of_nat n ^ ")" + | tInt n => "Int(" ^ string_of_Z (proj1_sig n) ^ ")" + | tFloat f => "Float(" ^ string_of_float64_model f ^ ")" end. Lemma lookup_env_nil c s : lookup_env [] c = Some s -> False. diff --git a/pcuic/theories/PCUICCSubst.v b/pcuic/theories/PCUICCSubst.v index 46e5e19ff..42f4781f6 100644 --- a/pcuic/theories/PCUICCSubst.v +++ b/pcuic/theories/PCUICCSubst.v @@ -11,7 +11,6 @@ From Equations Require Import Equations. no lifting involved and one term at a time. *) - Local Ltac inv H := inversion H; subst. Fixpoint csubst t k u := diff --git a/pcuic/theories/PCUICCanonicity.v b/pcuic/theories/PCUICCanonicity.v index d0db7188f..da25c7bf0 100644 --- a/pcuic/theories/PCUICCanonicity.v +++ b/pcuic/theories/PCUICCanonicity.v @@ -738,8 +738,8 @@ Section Normalization. - simpl in cl; move/andP: cl => [clf cla]. eapply inversion_App in typed as [na [A [B [Hf _]]]]; eauto. - simpl in cl; move/andP: cl => [/andP[_ clc] _]. - eapply inversion_Case in typed; firstorder eauto. - - eapply inversion_Proj in typed; firstorder auto. + eapply inversion_Case in typed; pcuicfo eauto. + - eapply inversion_Proj in typed; pcuicfo auto. Qed. Lemma ind_normal_constructor t i u args : diff --git a/pcuic/theories/PCUICClosed.v b/pcuic/theories/PCUICClosed.v index 52273ee77..979270033 100644 --- a/pcuic/theories/PCUICClosed.v +++ b/pcuic/theories/PCUICClosed.v @@ -331,8 +331,6 @@ Proof. now rewrite closedn_subst_instance_constr IHl. Qed. -Arguments skipn : simpl never. - Lemma destArity_spec ctx T : match destArity ctx T with | Some (ctx', s) => it_mkProd_or_LetIn ctx T = it_mkProd_or_LetIn ctx' (tSort s) @@ -940,8 +938,7 @@ Proof. now move/andP: oib => []. - pose proof (onConstructors oib). red in X. eapply All_forallb. eapply All2_All_left; eauto. - firstorder auto. - eapply on_ctype in X0. + intros cdecl cs X0; eapply on_ctype in X0. now move/andP: X0 => []. - eapply All_forallb. pose proof (onProjections oib). @@ -1130,8 +1127,8 @@ Proof. erewrite hidecl in clbodies. simpl in clbodies. unfold closed_inductive_body in clbodies. move/andP: clbodies => [/andP [_ cl] _]. - eapply forallb_All in cl. apply (All_impl cl). - intros [[? ?] ?]; simpl; firstorder. + eapply forallb_All in cl. apply (All_impl cl). + now intros [[? ?] ?]; simpl. Qed. Lemma declared_minductive_closed_inds {cf:checker_flags} : @@ -1215,6 +1212,8 @@ Lemma term_closedn_list_ind : (forall k (s : projection) (t : term), P k t -> P k (tProj s t)) -> (forall k (m : mfixpoint term) (n : nat), tFixProp (P k) (P (#|fix_context m| + k)) m -> P k (tFix m n)) -> (forall k (m : mfixpoint term) (n : nat), tFixProp (P k) (P (#|fix_context m| + k)) m -> P k (tCoFix m n)) -> + (forall k i, P k (tInt i)) -> + (forall k f, P k (tFloat f)) -> forall k (t : term), closedn k t -> P k t. Proof. intros until t. revert k t. diff --git a/pcuic/theories/PCUICConfluence.v b/pcuic/theories/PCUICConfluence.v index ecd7cb18b..2c70b6d6d 100644 --- a/pcuic/theories/PCUICConfluence.v +++ b/pcuic/theories/PCUICConfluence.v @@ -2047,15 +2047,15 @@ Section RedConfluence. intros x y H. induction H; firstorder. - red in p. - induction p. repeat constructor. firstorder. + induction p. repeat constructor. pcuicfo. constructor 2. econstructor 3 with (Γ ,, vass na y); auto. - subst. - induction a. repeat constructor. firstorder. + induction a. repeat constructor. pcuicfo. constructor 2. econstructor 3 with (Γ ,, vdef na y t'); auto. - subst. - induction a. constructor. constructor. red. right. firstorder. + induction a. constructor. constructor. red. right. pcuicfo. constructor 2. econstructor 3 with (Γ ,, vdef na b' y); auto. - clear H. induction IHOnOne2_local_env. constructor. now constructor 3. @@ -2257,7 +2257,7 @@ Section RedConfluence. Lemma clos_refl_trans_out Γ x y : clos_refl_trans (red1 Σ Γ) x y -> clos_refl_trans red1_rel (Γ, x) (Γ, y). Proof. - induction 1. constructor. red. left. firstorder. + induction 1. constructor. red. left. pcuicfo. constructor 2. econstructor 3; eauto. Qed. @@ -2317,8 +2317,8 @@ Section RedConfluence. clear - Hctx. induction (fix_context mfix0). + assumption. + simpl. destruct a as [na [b|] ty]. - * constructor ; firstorder (hnf ; auto). - * constructor ; firstorder (hnf ; auto). + * constructor ; pcuicfo (hnf ; auto). + * constructor ; pcuicfo (hnf ; auto). - eapply red_cofix_one_ty. eapply OnOne2_impl ; eauto. intros [? ? ? ?] [? ? ? ?] [[r ih] e]. simpl in *. @@ -2333,8 +2333,8 @@ Section RedConfluence. clear - Hctx. induction (fix_context mfix0). + assumption. + simpl. destruct a as [na [b|] ty]. - * constructor ; firstorder (hnf ; auto). - * constructor ; firstorder (hnf ; auto). + * constructor ; pcuicfo (hnf ; auto). + * constructor ; pcuicfo (hnf ; auto). - auto. - eapply red_trans; eauto. Qed. @@ -2632,7 +2632,7 @@ Section RedConfluence. Lemma clos_rt_red1_red1_rel_alpha Γ x y : clos_refl_trans (red1 Σ Γ) x y -> clos_refl_trans red1_rel_alpha (Γ, x) (Γ, y). Proof. - induction 1. constructor. red. left. firstorder. + induction 1. constructor. red. left. pcuicfo. constructor 2. econstructor 3; eauto. Qed. diff --git a/pcuic/theories/PCUICContexts.v b/pcuic/theories/PCUICContexts.v index 97fa3f68b..1a5a648e9 100644 --- a/pcuic/theories/PCUICContexts.v +++ b/pcuic/theories/PCUICContexts.v @@ -520,13 +520,13 @@ Proof. unfold lift_typing in X |- *. now rewrite app_context_assoc. - apply IHΓ. auto. eapply All_local_env_subst; eauto. simpl; intros. - destruct T; unfold lift_typing in X |- *; simpl in *; firstorder auto. + destruct T; unfold lift_typing in X |- *; simpl in *; pcuicfo auto. rewrite Nat.add_0_r. eapply (substitution _ (Δ' ,,, Γ) [vdef na b t] [b] Γ0) in X; eauto. rewrite -{1}(subst_empty 0 b). repeat constructor. now rewrite !subst_empty. - exists x. + destruct X as [s Hs]; exists s. rewrite Nat.add_0_r. - eapply (substitution _ _ [vdef na b t] [b] Γ0) in p; eauto. + eapply (substitution _ _ [vdef na b t] [b] Γ0) in Hs; eauto. rewrite -{1}(subst_empty 0 b). repeat constructor. now rewrite !subst_empty. Qed. @@ -551,9 +551,9 @@ Qed. Lemma wf_local_rel_empty {cf:checker_flags} Σ Γ : wf_local_rel Σ [] Γ <~> wf_local Σ Γ. Proof. split. - - intros h. eapply (All_local_env_impl _ _ _ h). firstorder. + - intros h. eapply (All_local_env_impl _ _ _ h). pcuicfo. red in X |- *. now rewrite app_context_nil_l in X. - - intros h. eapply (All_local_env_impl _ _ _ h). firstorder. + - intros h. eapply (All_local_env_impl _ _ _ h). pcuicfo. red in X |- *. now rewrite app_context_nil_l. Qed. diff --git a/pcuic/theories/PCUICConvCumInversion.v b/pcuic/theories/PCUICConvCumInversion.v index b90b3755b..1710f1d55 100644 --- a/pcuic/theories/PCUICConvCumInversion.v +++ b/pcuic/theories/PCUICConvCumInversion.v @@ -108,7 +108,8 @@ Section fixed. all: depelim e. all: depelim w0. all: apply All2_length in a. - all: constructor; constructor; rewrite a; auto. + all: try (constructor; constructor; rewrite a; auto). + all: destruct leq; cbn; repeat constructor. - clear -a1 a a0. induction a1 in args, args', x2, a, x3, a0, a1 |- *; depelim a; depelim a0; [now constructor|]. constructor. diff --git a/pcuic/theories/PCUICElimination.v b/pcuic/theories/PCUICElimination.v index d1b1d605c..73b33e6df 100644 --- a/pcuic/theories/PCUICElimination.v +++ b/pcuic/theories/PCUICElimination.v @@ -292,7 +292,7 @@ Proof. eapply All_local_assum_subst; eauto. simpl. intros. destruct X as [s [Ht2 isp]]. - exists s; firstorder. + exists s; pcuicfo. rewrite Nat.add_0_r. eapply (substitution _ Γ [vdef na b ty] [b] Γ1 _ (tSort s)); auto. rewrite -{1}(subst_empty 0 b). repeat (constructor; auto). rewrite !subst_empty. @@ -342,7 +342,7 @@ Proof. eapply All_local_assum_subst; eauto. simpl. intros. destruct X as [s [Ht2 isp]]. - exists s; firstorder auto. + exists s; pcuicfo auto. rewrite Nat.add_0_r. eapply (substitution _ Γ [vass na ty] [t] Γ1 _ (tSort s)); auto. repeat (constructor; auto). now rewrite subst_empty. now rewrite app_context_assoc in Ht2. } @@ -619,7 +619,7 @@ Proof. eapply build_branches_type_lookup in e2. eauto. 2:eauto. 3:destruct declc; eauto. - 2:{ eapply (All2_impl a); firstorder. } + 2:{ eapply (All2_impl a); pcuicfo eauto. } destruct e2 as [nargs [br [brty [[[Hnth Hnth'] brtyped]]]]]. epose proof (All2_nth_error _ _ _ a H). specialize (X0 Hnth'). @@ -885,7 +885,7 @@ Lemma cumul_prop1 (Σ : global_env_ext) Γ A B u : Proof. intros. destruct X0 as [s Hs]. - eapply cumul_prop_inv in H. 4:eauto. firstorder. auto. + eapply cumul_prop_inv in H. 4:eauto. pcuicfo. auto. right; eauto. Qed. @@ -899,7 +899,7 @@ Lemma cumul_prop2 (Σ : global_env_ext) Γ A B u : Proof. intros. destruct X0 as [s Hs]. - eapply cumul_prop_inv in H. 4:eauto. firstorder. auto. + eapply cumul_prop_inv in H. 4:eauto. pcuicfo. auto. left; eauto. Qed. @@ -913,7 +913,7 @@ Lemma cumul_sprop1 (Σ : global_env_ext) Γ A B u : Proof. intros. destruct X0 as [s Hs]. - eapply cumul_sprop_inv in H. 4:eauto. firstorder. auto. + eapply cumul_sprop_inv in H. 4:eauto. pcuicfo. auto. right; eauto. Qed. @@ -927,7 +927,7 @@ Lemma cumul_sprop2 (Σ : global_env_ext) Γ A B u : Proof. intros. destruct X0 as [s Hs]. - eapply cumul_sprop_inv in H. 4:eauto. firstorder. auto. + eapply cumul_sprop_inv in H. 4:eauto. pcuicfo. auto. left; eauto. Qed. diff --git a/pcuic/theories/PCUICEquality.v b/pcuic/theories/PCUICEquality.v index ab95796d1..5d953c008 100644 --- a/pcuic/theories/PCUICEquality.v +++ b/pcuic/theories/PCUICEquality.v @@ -201,7 +201,10 @@ Inductive eq_term_upto_univ_napp Σ (Re Rle : Universe.t -> Universe.t -> Prop) (x.(rarg) = y.(rarg)) * eq_binder_annot x.(dname) y.(dname) ) mfix mfix' -> - eq_term_upto_univ_napp Σ Re Rle napp (tCoFix mfix idx) (tCoFix mfix' idx). + eq_term_upto_univ_napp Σ Re Rle napp (tCoFix mfix idx) (tCoFix mfix' idx) + +| eq_Int i : eq_term_upto_univ_napp Σ Re Rle napp (tInt i) (tInt i) +| eq_Float f : eq_term_upto_univ_napp Σ Re Rle napp (tFloat f) (tFloat f). Notation eq_term_upto_univ Σ Re Rle := (eq_term_upto_univ_napp Σ Re Rle 0). @@ -890,6 +893,9 @@ Fixpoint eqb_term_upto_univ_napp Σ (equ lequ : Universe.t -> Universe.t -> bool eqb_annot x.(dname) y.(dname) ) mfix mfix' + | tInt i, tInt i' => eqb i i' + | tFloat f, tFloat f' => eqb f f' + | _, _ => false end. @@ -1030,6 +1036,8 @@ Proof. cbn -[eqb]. intros x X0 y. eqspec; [|rewrite andb_false_r; discriminate]. intro. rtoProp. split; tas. split;tas. split; eapply X0; tea. now apply eqb_annot_spec. + - eqspec; [|discriminate]. constructor. + - eqspec; [|discriminate]. constructor. Qed. Lemma reflect_eq_term_upto_univ Σ equ lequ (Re Rle : Universe.t -> Universe.t -> Prop) napp : @@ -1222,6 +1230,8 @@ Proof. apply X2. -- constructor. intro bot. apply f. inversion bot. subst. inversion X0. subst. apply X2. + - cbn - [eqb]. eqspecs. do 2 constructor. + - cbn - [eqb]. eqspecs. do 2 constructor. Qed. Lemma compare_global_instance_refl : @@ -1239,6 +1249,15 @@ Proof. eapply forallb2_map, forallb2_refl; intro; apply eqb_refl. Qed. +Lemma eq_dec_to_bool_refl {A} {ea : Classes.EqDec A} (x : A) : + eq_dec_to_bool x x. +Proof. + unfold eq_dec_to_bool. + destruct (Classes.eq_dec x x). + constructor. + congruence. +Qed. + Lemma eqb_term_upto_univ_refl : forall Σ (eqb leqb : Universe.t -> Universe.t -> bool) napp t, (forall u, eqb u u) -> @@ -1281,6 +1300,8 @@ Proof. destruct p as [e1 e2]. rewrite -> e1 by assumption. rewrite -> e2 by assumption. rewrite eqb_annot_refl; assumption. + - apply eq_dec_to_bool_refl. + - apply eq_dec_to_bool_refl. Qed. (** ** Behavior on mkApps and it_mkLambda_or_LetIn ** *) diff --git a/pcuic/theories/PCUICInduction.v b/pcuic/theories/PCUICInduction.v index d0b2a0d99..d1c90e6e2 100644 --- a/pcuic/theories/PCUICInduction.v +++ b/pcuic/theories/PCUICInduction.v @@ -35,6 +35,8 @@ Lemma term_forall_list_ind : (forall (s : projection) (t : term), P t -> P (tProj s t)) -> (forall (m : mfixpoint term) (n : nat), tFixProp P P m -> P (tFix m n)) -> (forall (m : mfixpoint term) (n : nat), tFixProp P P m -> P (tCoFix m n)) -> + (forall i, P (tInt i)) -> + (forall f, P (tFloat f)) -> forall t : term, P t. Proof. intros until t. revert t. @@ -231,9 +233,12 @@ Lemma term_forall_mkApps_ind : (forall (s : projection) (t : term), P t -> P (tProj s t)) -> (forall (m : mfixpoint term) (n : nat), tFixProp P P m -> P (tFix m n)) -> (forall (m : mfixpoint term) (n : nat), tFixProp P P m -> P (tCoFix m n)) -> + (forall i, P (tInt i)) -> + (forall f, P (tFloat f)) -> forall t : term, P t. Proof. intros until t. + rename X14 into Pint. rename X15 into Pfloat. assert (Acc (MR lt size) t) by eapply measure_wf, Wf_nat.lt_wf. induction H. rename X14 into auxt. clear H. rename x into t. move auxt at top. diff --git a/pcuic/theories/PCUICInductiveInversion.v b/pcuic/theories/PCUICInductiveInversion.v index 005b3b80a..34b790797 100644 --- a/pcuic/theories/PCUICInductiveInversion.v +++ b/pcuic/theories/PCUICInductiveInversion.v @@ -2592,7 +2592,7 @@ Proof. - subst c. exists (lift_constraint #|u| x). rewrite -> In_lift_constraints. - firstorder eauto. + pcuicfo eauto. specialize (clcstra _ H0). simpl in *. destruct x as [[l c] r]; rewrite /subst_instance_cstr; simpl. @@ -2615,8 +2615,9 @@ Proof. subst. exists x; intuition eauto. now rewrite ConstraintSetFact.add_iff. - firstorder eauto. - subst. exists x0; firstorder. + destruct H0 as [c' [-> ?]]. + eexists c'; split; firstorder eauto. + now rewrite ConstraintSetFact.add_iff. Qed. Lemma subst_instance_variance_cstrs l u i i' : diff --git a/pcuic/theories/PCUICInductives.v b/pcuic/theories/PCUICInductives.v index 57cd19d59..c3c9983a8 100644 --- a/pcuic/theories/PCUICInductives.v +++ b/pcuic/theories/PCUICInductives.v @@ -1300,7 +1300,10 @@ Lemma invert_red1_letin {cf:checker_flags} (Σ : global_env_ext) Γ C na d ty b red1 Σ.1 (Γ ,, vdef na d ty) b b') + (C = subst10 d b)%type. Proof. - intros H; depelim H; try solve_discr; firstorder auto. + intros H; depelim H; try solve_discr; pcuicfo auto. + - left. left. left. eexists; eauto. + - left. left. right. eexists; eauto. + - left. right. eexists; eauto. Qed. Lemma decompose_prod_assum_it_mkProd_or_LetIn' ctx Γ t : @@ -1360,7 +1363,7 @@ Lemma destInd_head_subst s k t f : destInd (head (subst s k t)) = Some f -> (destInd (head t) = Some f) + (∑ n u, (head t = tRel n) /\ k <= n /\ (nth_error s (n - k) = Some u /\ destInd (head (lift0 k u)) = Some f)). Proof. - induction t in s, k, f |- *; simpl; try solve [firstorder auto]. + induction t in s, k, f |- *; simpl; try solve [pcuicfo auto]. elim: leb_spec_Set => le; intros destI. right. destruct nth_error eqn:Heq. diff --git a/pcuic/theories/PCUICInversion.v b/pcuic/theories/PCUICInversion.v index 48e3a037a..04565ada9 100644 --- a/pcuic/theories/PCUICInversion.v +++ b/pcuic/theories/PCUICInversion.v @@ -239,6 +239,21 @@ Section Inversion. intros Γ mfix idx T h. invtac h. Qed. + (** At this stage we don't typecheck primitive types *) + Lemma inversion_Int : + forall {Γ i T}, + Σ ;;; Γ |- tInt i : T -> False. + Proof. + intros Γ i T h. now depind h. + Qed. + + Lemma inversion_Float : + forall {Γ f T}, + Σ ;;; Γ |- tFloat f : T -> False. + Proof. + intros Γ i T h. now depind h. + Qed. + Lemma inversion_it_mkLambda_or_LetIn : forall {Γ Δ t T}, Σ ;;; Γ |- it_mkLambda_or_LetIn Δ t : T -> diff --git a/pcuic/theories/PCUICLiftSubst.v b/pcuic/theories/PCUICLiftSubst.v index e6ff1f1bc..3ad96ba01 100644 --- a/pcuic/theories/PCUICLiftSubst.v +++ b/pcuic/theories/PCUICLiftSubst.v @@ -1813,6 +1813,8 @@ Lemma term_forall_ctx_list_ind : (forall Γ (s : projection) (t : term), P Γ t -> P Γ (tProj s t)) -> (forall Γ (m : mfixpoint term) (n : nat), tFixProp (P Γ) (P (Γ ,,, fix_context m)) m -> P Γ (tFix m n)) -> (forall Γ (m : mfixpoint term) (n : nat), tFixProp (P Γ) (P (Γ ,,, fix_context m)) m -> P Γ (tCoFix m n)) -> + (forall Γ i, P Γ (tInt i)) -> + (forall Γ f, P Γ (tFloat f)) -> forall Γ (t : term), P Γ t. Proof. intros. revert Γ t0. diff --git a/pcuic/theories/PCUICNameless.v b/pcuic/theories/PCUICNameless.v index 8bd0d071f..e4df6614c 100644 --- a/pcuic/theories/PCUICNameless.v +++ b/pcuic/theories/PCUICNameless.v @@ -47,6 +47,7 @@ Fixpoint nameless (t : term) : bool := | tCoFix mfix idx => forallb (fun d => banon d.(dname)) mfix && forallb (test_def nameless nameless) mfix + | tInt _ | tFloat _ => true end. Definition anonymize (b : binder_annot name) : binder_annot name := @@ -76,6 +77,8 @@ Fixpoint nl (t : term) : term := | tProj p c => tProj p (nl c) | tFix mfix idx => tFix (map (map_def_anon nl nl) mfix) idx | tCoFix mfix idx => tCoFix (map (map_def_anon nl nl) mfix) idx + | tInt n => tInt n + | tFloat f => tFloat f end. Definition map_decl_anon f (d : context_decl) := {| diff --git a/pcuic/theories/PCUICNormal.v b/pcuic/theories/PCUICNormal.v index c4dfa2dc2..bec0519be 100644 --- a/pcuic/theories/PCUICNormal.v +++ b/pcuic/theories/PCUICNormal.v @@ -52,6 +52,8 @@ Section Normal. end -> whnf Γ (mkApps (tFix mfix idx) v) | whnf_cofixapp mfix idx v : whnf Γ (mkApps (tCoFix mfix idx) v) + | whnf_int i : whnf Γ (tInt i) + | whnf_float f : whnf Γ (tFloat f) with whne (Γ : context) : term -> Type := | whne_rel i : @@ -155,7 +157,7 @@ Section Normal. right. exists x0, x1, x2, x3, x4. repeat split; eauto. now eapply nth_error_app_left. + rewrite <- mkApps_snoc in x. eapply (f_equal decompose_app) in x; - rewrite !decompose_app_mkApps in x; cbn in *; try firstorder congruence. + rewrite !decompose_app_mkApps in x; cbn in *; try intuition congruence. inversion x. subst. right. exists mfix, idx, rarg, body, arg. repeat split; eauto. Qed. @@ -173,7 +175,7 @@ Local Ltac inv H := inversion H; subst; clear H. Ltac help' := try repeat match goal with | [ H0 : _ = mkApps _ _ |- _ ] => eapply (f_equal decompose_app) in H0; - rewrite !decompose_app_mkApps in H0; cbn in *; firstorder congruence + rewrite !decompose_app_mkApps in H0; cbn in *; intuition congruence | [ H1 : tApp _ _ = mkApps _ ?args |- _ ] => destruct args using rev_ind; cbn in *; [ inv H1 | rewrite <- mkApps_nested in H1; cbn in *; inv H1 @@ -198,7 +200,7 @@ Defined. Lemma negb_is_true b : ~ is_true b -> is_true (negb b). Proof. - destruct b; firstorder. + destruct b; pcuicfo. Qed. Hint Resolve negb_is_true : core. @@ -249,6 +251,10 @@ Proof. lia. - destruct (mkApps_elim t l). apply mkApps_eq_inj in eq as (<-&<-); auto. + - destruct l using MCList.rev_ind; [|now rewrite <- mkApps_nested in eq]. + cbn in *; subst; auto. + - destruct l using MCList.rev_ind; [|now rewrite <- mkApps_nested in eq]. + cbn in *; subst; auto. Qed. Lemma whnf_fixapp' {flags} Σ Γ mfix idx narg body v : @@ -307,6 +313,8 @@ Proof. - inv whn; solve_discr; easy. Qed. +Set Firstorder Solver auto with core. + Definition whnf_whne_dec flags Σ Γ t : ({∥whnf flags Σ Γ t∥} + {~∥whnf flags Σ Γ t∥}) * ({∥whne flags Σ Γ t∥} + {~∥whne flags Σ Γ t∥}). @@ -335,18 +343,18 @@ Proof with eauto using sq with pcuic. right. intros [w]. depelim w. depelim w. all:help. clear IHt. eapply whne_mkApps_inv in w as []... -- depelim w. help. - -- firstorder congruence. + -- destruct s0 as [? [? [? [? [? [? ?]]]]]]. congruence. * destruct v as [ | ? v]... right. intros [w]. depelim w. depelim w. all:help. clear IHt. eapply whne_mkApps_inv in w as []... -- depelim w. help. - -- firstorder congruence. + -- destruct s0 as (?&?&?&?&?&?&?); congruence. * destruct v as [ | ? v]... destruct (RedFlags.beta flags) eqn:?. -- right. intros [w]. depelim w. depelim w. all:help. clear IHl. eapply whne_mkApps_inv in w as []... ++ depelim w. congruence. help. - ++ firstorder congruence. + ++ destruct s0 as (?&?&?&?&?&?&?); congruence. -- left; constructor. apply whnf_mkApps. constructor. @@ -360,23 +368,34 @@ Proof with eauto using sq with pcuic. eapply whne_mkApps_inv in w as []; eauto. --- depelim w; [|congruence]. help. eapply (f_equal decompose_app) in x; - rewrite !decompose_app_mkApps in x; cbn in *; try firstorder congruence. + rewrite !decompose_app_mkApps in x; cbn in *; try intuition congruence. inv x. destruct rarg; inv e0. --- destruct s0 as (? & ? & ? & ? & ? & ? & ? & ? & ?). inv e. rewrite E1 in e0. inv e0. eapply (nth_error_app_left v [x0]) in e1. rewrite E2 in e1. inv e1... - --- help. - eapply (f_equal decompose_app) in x; - rewrite !decompose_app_mkApps in x; - cbn in *; try firstorder congruence. - inv x. rewrite E1 in y. congruence. + --- solve_discr. + rewrite E1 in e. injection e as -> ->. + rewrite E2 in e0. injection e0 as ->. + apply n; sq; auto. + --- solve_discr. + rewrite E1 in y. congruence. ** left. constructor. apply whnf_mkApps. constructor. assumption. -- left. constructor. eapply whnf_fixapp. rewrite E1. eauto. + * destruct v as [ | ? v]... + right. intros [w]. depelim w. depelim w. all:help. clear IHt. + eapply whne_mkApps_inv in w as []... + -- depelim w. help. + -- destruct s0 as [? [? [? [? [? [? ?]]]]]]. congruence. + * destruct v as [ | ? v]... + right. intros [w]. depelim w. depelim w. all:help. clear IHt. + eapply whne_mkApps_inv in w as []... + -- depelim w. help. + -- destruct s0 as [? [? [? [? [? [? ?]]]]]]. congruence. + right. intros [w]. eapply n. constructor. now eapply whnf_mkApps_inv. - destruct (IHt Γ) as [_ []]. + left. destruct s as [w]. constructor. now eapply whne_mkApps. @@ -392,7 +411,10 @@ Proof with eauto using sq with pcuic. destruct s as (? & ? & ? & ? & ? & ? & ? & ? & ?). inv e. rewrite E1 in e0. inv e0. eapply (nth_error_app_left v [x0]) in e1. - rewrite E2 in e1. inv e1... + rewrite E2 in e1. inv e1... solve_discr. + rewrite E1 in e. injection e as -> ->. + rewrite E2 in e0. injection e0 as ->. + apply n0; sq; auto. --- left. constructor. apply whne_mkApps. constructor. assumption. ++ right. intros [[ | (mfix' & idx' & narg' & body' & a' & [=] & ? & ? & ?) ] % whne_mkApps_inv]; subst; cbn... congruence. @@ -914,6 +936,8 @@ Proof. destruct s as [->|(?&?)]; [easy|]. now inv e. - eapply red1_mkApps_tCoFix_inv in r as [[(?&->&?)|(?&->&?)]|(?&->&?)]; eauto. + - depelim r. solve_discr. + - depelim r; solve_discr. Qed. Lemma whnf_pres Σ Γ t t' : @@ -977,7 +1001,9 @@ Inductive whnf_red Σ Γ : term -> term -> Type := red Σ Γ (dtype d) (dtype d') × red Σ (Γ,,, fix_context mfix) (dbody d) (dbody d')) mfix mfix' -> - whnf_red Σ Γ (tCoFix mfix idx) (tCoFix mfix' idx). + whnf_red Σ Γ (tCoFix mfix idx) (tCoFix mfix' idx) +| whnf_red_tInt i : whnf_red Σ Γ (tInt i) (tInt i) +| whnf_red_tFloat f : whnf_red Σ Γ (tFloat f) (tFloat f). Derive Signature for whnf_red. @@ -1263,6 +1289,8 @@ Proof. cbn. intros ? ? (?&[= -> -> ->]). auto. + - depelim r; solve_discr. + - depelim r; solve_discr. Qed. Lemma whnf_red_inv Σ Γ t t' : @@ -1352,6 +1380,8 @@ Proof. - apply eq_term_upto_univ_napp_mkApps_l_inv in eq as (?&?&(?&?)&->). depelim e. apply whnf_cofixapp. + - depelim eq; auto. + - depelim eq; auto. Qed. Lemma whnf_eq_term {cf:checker_flags} f Σ φ Γ t t' : diff --git a/pcuic/theories/PCUICParallelReduction.v b/pcuic/theories/PCUICParallelReduction.v index c8f24298b..518578733 100644 --- a/pcuic/theories/PCUICParallelReduction.v +++ b/pcuic/theories/PCUICParallelReduction.v @@ -96,6 +96,8 @@ Lemma term_forall_ctx_list_ind : (forall Γ (m : mfixpoint term) (n : nat), All_local_env (on_local_decl (fun Γ' t => P (Γ ,,, Γ') t)) (fix_context m) -> tFixProp (P Γ) (P (Γ ,,, fix_context m)) m -> P Γ (tCoFix m n)) -> + (forall Γ i, P Γ (tInt i)) -> + (forall Γ f, P Γ (tFloat f)) -> forall Γ (t : term), P Γ t. Proof. intros. @@ -148,6 +150,7 @@ Proof. eapply X13; try (apply aux; red; simpl; lia). apply auxl'. simpl. lia. red. apply All_pair. split; apply auxl; simpl; auto. + Defined. (** All2 lemmas *) @@ -385,7 +388,9 @@ Section ParallelReduction. | tVar _ | tSort _ | tInd _ _ - | tConstruct _ _ _ => true + | tConstruct _ _ _ + | tInt _ + | tFloat _ => true | _ => false end. diff --git a/pcuic/theories/PCUICParallelReductionConfluence.v b/pcuic/theories/PCUICParallelReductionConfluence.v index 5bf961238..2f34692da 100644 --- a/pcuic/theories/PCUICParallelReductionConfluence.v +++ b/pcuic/theories/PCUICParallelReductionConfluence.v @@ -244,6 +244,8 @@ Lemma term_ind_size_app : tFixProp P P m -> P (tFix m n)) -> (forall (m : mfixpoint term) (n : nat), tFixProp (P) P m -> P (tCoFix m n)) -> + (forall i, P (tInt i)) -> + (forall f, P (tFloat f)) -> forall (t : term), P t. Proof. intros. @@ -1520,7 +1522,7 @@ Section Rho. rename r (rho Γ t) = rho Δ (rename r t). Proof. revert t Γ Δ r. - refine (term_ind_size_app _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _); + refine (term_ind_size_app _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _); intros; try subst Γ; try rename Γ0 into Γ(* ; rename_all_hyps *). all:auto 2. diff --git a/pcuic/theories/PCUICPretty.v b/pcuic/theories/PCUICPretty.v index eb834ed63..0d9e238f1 100644 --- a/pcuic/theories/PCUICPretty.v +++ b/pcuic/theories/PCUICPretty.v @@ -190,6 +190,10 @@ Section print_term. | tCoFix l n => parens top ("let cofix " ^ print_defs print_term Γ l ^ nl ^ " in " ^ List.nth_default (string_of_nat n) (map (string_of_aname ∘ dname) l) n) + | tInt i => + parens top (string_of_Z (proj1_sig i)) + | tFloat f => + parens top (string_of_float64_model f) end. End print_term. diff --git a/pcuic/theories/PCUICPrincipality.v b/pcuic/theories/PCUICPrincipality.v index 50151457a..08bd0e832 100644 --- a/pcuic/theories/PCUICPrincipality.v +++ b/pcuic/theories/PCUICPrincipality.v @@ -343,6 +343,8 @@ Section Principality. rewrite nthe' in nthe; noconf nthe. repeat split; eauto. eapply type_CoFix; eauto. + - now apply inversion_Int in hA. + - now apply inversion_Float in hA. Qed. (** A weaker version that is often convenient to use. *) @@ -594,7 +596,8 @@ Proof. eapply PCUICValidity.validity; eauto. eapply (type_Case _ _ (ind, npar)). eapply isdecl. all:eauto. - eapply (All2_impl X5); firstorder. + eapply (All2_impl X5); pcuicfo. + destruct b1 as [s [? ?]]. now exists s. eapply conv_cumul. eapply mkApps_conv_args; pcuic. eapply All2_app. simpl in *. @@ -637,8 +640,9 @@ Proof. econstructor; eauto. eapply PCUICValidity.validity; eauto. econstructor. 2:eapply H0. all:eauto. - eapply (All_impl X0); firstorder. - eapply (All_impl X1); firstorder. + eapply (All_impl X0); pcuicfo. + destruct X2 as [s [Hs ?]]; now exists s. + eapply (All_impl X1); pcuicfo. eapply All2_nth_error in a; eauto. destruct a as [[[eqty _] _] _]. constructor. eapply eq_term_empty_leq_term in eqty. @@ -649,12 +653,13 @@ Proof. econstructor; eauto. eapply PCUICValidity.validity; eauto. eapply type_CoFix. 2:eapply H0. all:eauto. - eapply (All_impl X0); firstorder. - eapply (All_impl X1); firstorder. + eapply (All_impl X0); pcuicfo. + destruct X2 as [s [? ?]]; now exists s. + eapply (All_impl X1); pcuicfo. eapply All2_nth_error in a; eauto. destruct a as [[[eqty _] _] _]. constructor. apply eq_term_empty_leq_term in eqty. - now eapply leq_term_empty_leq_term. Show Existentials. + now eapply leq_term_empty_leq_term. Qed. Lemma typing_eq_term {cf:checker_flags} (Σ : global_env_ext) Γ t t' T T' : diff --git a/pcuic/theories/PCUICReflect.v b/pcuic/theories/PCUICReflect.v index 39e5b23de..3d73d76e6 100644 --- a/pcuic/theories/PCUICReflect.v +++ b/pcuic/theories/PCUICReflect.v @@ -20,6 +20,39 @@ Local Ltac fcase c := let e := fresh "e" in case c ; intro e ; [ subst ; try (left ; reflexivity) | finish ]. +Instance reflect_eq_Z : ReflectEq Z := EqDec_ReflectEq _. + +Lemma exist_irrel_eq {A} (P : A -> bool) (x y : sig P) : proj1_sig x = proj1_sig y -> x = y. +Proof. + destruct x as [x p], y as [y q]; simpl; intros ->. + now destruct (uip p q). +Qed. + +Local Obligation Tactic := idtac. +#[program] +Instance reflect_eq_uint63 : ReflectEq uint63_model := + { eqb x y := eqb (proj1_sig x) (proj1_sig y) }. +Next Obligation. + cbn -[eqb]. + intros x y. + elim: eqb_spec. constructor. + now apply exist_irrel_eq. + intros neq; constructor => H'; apply neq; now subst x. +Qed. + +Instance reflect_eq_spec_float : ReflectEq SpecFloat.spec_float := EqDec_ReflectEq _. + +#[program] +Instance reflect_eq_float64 : ReflectEq float64_model := + { eqb x y := eqb (proj1_sig x) (proj1_sig y) }. +Next Obligation. + cbn -[eqb]. + intros x y. + elim: eqb_spec. constructor. + now apply exist_irrel_eq. + intros neq; constructor => H'; apply neq; now subst x. +Qed. + Local Ltac term_dec_tac term_dec := repeat match goal with | t : term, u : term |- _ => fcase (term_dec t u) @@ -34,6 +67,8 @@ Local Ltac term_dec_tac term_dec := | i : string, i' : kername |- _ => fcase (string_dec i i') | n : name, n' : name |- _ => fcase (eq_dec n n') | n : aname, n' : aname |- _ => fcase (eq_dec n n') + | i : uint63_model, j : uint63_model |- _ => fcase (eq_dec i j) + | i : float64_model, j : float64_model |- _ => fcase (eq_dec i j) | i : inductive, i' : inductive |- _ => fcase (eq_dec i i') | x : inductive * nat, y : inductive * nat |- _ => fcase (eq_dec x y) diff --git a/pcuic/theories/PCUICSR.v b/pcuic/theories/PCUICSR.v index c9d8fcc80..b9d288b5f 100644 --- a/pcuic/theories/PCUICSR.v +++ b/pcuic/theories/PCUICSR.v @@ -716,8 +716,7 @@ Proof. - (* Case congruence on discriminee *) eapply type_Cumul. eapply type_Case; eauto. - * solve_all. - firstorder auto. + * solve_all. destruct b0 as [s Hs]; exists s; pcuic. * pose proof typec as typec'. eapply (env_prop_typing _ _ validity) in typec' as wat; auto. unshelve eapply isType_mkApps_Ind in wat as [parsubst [argsubst wat]]; eauto. diff --git a/pcuic/theories/PCUICSigmaCalculus.v b/pcuic/theories/PCUICSigmaCalculus.v index 5a36ab61a..352f95e68 100644 --- a/pcuic/theories/PCUICSigmaCalculus.v +++ b/pcuic/theories/PCUICSigmaCalculus.v @@ -366,7 +366,8 @@ Proof. - move/andb_and: clt => [] ? ?. f_equal; eauto. - move/andb_and: clt => [] /andb_and[] ? ? b1. red in X. solve_all. f_equal; eauto. - eapply All_map_eq. eapply (All_impl b1). firstorder. + eapply All_map_eq. eapply (All_impl b1). pcuicfo. + unfold on_snd. f_equal. now eapply a0. - f_equal; eauto. red in X. solve_all. move/andb_and: b => []. eauto. intros. apply map_def_eq_spec; eauto. diff --git a/pcuic/theories/PCUICSpine.v b/pcuic/theories/PCUICSpine.v index 4fd78d885..c412a2dd1 100644 --- a/pcuic/theories/PCUICSpine.v +++ b/pcuic/theories/PCUICSpine.v @@ -130,8 +130,8 @@ Proof. rewrite H [firstn _ [u]]firstn_0 // app_nil_r in Hr |- *. specialize (IHctx Hr). rewrite app_assoc. now econstructor. - * destruct a as [na' [b'|] ty']; simpl in *; noconf H. - rewrite skipn_S in Hl, Hr, H. subst b. + * rewrite skipn_S in Hl, Hr, H. + destruct a as [na' [b'|] ty']; simpl in *; noconf H. pose proof (context_subst_length Hl). rewrite subst_context_length in H. rewrite {3}H -subst_app_simpl [firstn #|ctx| _ ++ _]firstn_skipn. constructor. apply IHctx => //. diff --git a/pcuic/theories/PCUICSubstitution.v b/pcuic/theories/PCUICSubstitution.v index 0f66fc5ee..caeff121c 100644 --- a/pcuic/theories/PCUICSubstitution.v +++ b/pcuic/theories/PCUICSubstitution.v @@ -372,7 +372,7 @@ Proof. eapply closed_upwards; eauto; lia. + simpl in X. rewrite -X in cp. eapply forallb_All in cp. eapply All_map_id; eauto. - eapply (All_impl cp); firstorder auto. + eapply (All_impl cp); pcuicfo. destruct x; unfold on_snd; simpl; f_equal. apply subst_closedn. rewrite context_assumptions_fold. eapply closed_upwards; eauto; lia. @@ -1004,14 +1004,14 @@ Lemma subst_decompose_prod_assum_rec ctx t s k : (decompose_prod_assum (subst_context s k ctx) (subst s (length ctx + k) t) = (subst_context s k ctx' ,,, ctx'', t'')). Proof. - induction t in ctx, k |- *; simpl; try solve [ eexists _, _; firstorder eauto ]. + induction t in ctx, k |- *; simpl; try solve [ eexists _, _; pcuicfo ]. - elim: leb_spec_Set => comp. + destruct (nth_error s (n - (#|ctx| + k))) eqn:Heq. * destruct decompose_prod_assum eqn:Heq'. eexists _, _; intuition eauto. now rewrite decompose_prod_assum_ctx Heq'. - * eexists _,_; firstorder eauto. - + eexists _,_; firstorder eauto. + * eexists _,_; pcuicfo. + + eexists _,_; pcuicfo. - destruct decompose_prod_assum eqn:Heq. rewrite decompose_prod_assum_ctx in Heq. destruct (decompose_prod_assum [] t2) eqn:Heq'. diff --git a/pcuic/theories/PCUICToTemplate.v b/pcuic/theories/PCUICToTemplate.v index 424a06e58..5512e1950 100644 --- a/pcuic/theories/PCUICToTemplate.v +++ b/pcuic/theories/PCUICToTemplate.v @@ -1,9 +1,16 @@ (* Distributed under the terms of the MIT license. *) +From Coq Require Import Int63 FloatOps FloatAxioms. From MetaCoq.PCUIC Require Import PCUICAst PCUICAstUtils. Set Warnings "-notation-overridden". From MetaCoq.Template Require Import config utils AstUtils BasicAst Ast. Set Warnings "+notation-overridden". +Definition uint63_from_model (i : uint63_model) : Int63.int := + Int63.of_Z (proj1_sig i). + +Definition float64_from_model (f : float64_model) : PrimFloat.float := + FloatOps.SF2Prim (proj1_sig f). + Fixpoint trans (t : PCUICAst.term) : Ast.term := match t with | PCUICAst.tRel n => tRel n @@ -27,6 +34,8 @@ Fixpoint trans (t : PCUICAst.term) : Ast.term := | PCUICAst.tCoFix mfix idx => let mfix' := List.map (map_def trans trans) mfix in tCoFix mfix' idx + | PCUICAst.tInt i => tInt (uint63_from_model i) + | PCUICAst.tFloat f => tFloat (float64_from_model f) end. Definition trans_decl (d : PCUICAst.context_decl) := diff --git a/pcuic/theories/PCUICToTemplateCorrectness.v b/pcuic/theories/PCUICToTemplateCorrectness.v index b5921b369..fb83909cf 100644 --- a/pcuic/theories/PCUICToTemplateCorrectness.v +++ b/pcuic/theories/PCUICToTemplateCorrectness.v @@ -966,7 +966,8 @@ in All (for wf_local assumptions) unfold map_def. reflexivity. + eapply All_map, (All_impl X0). - firstorder. + intuition auto. destruct X2 as [s [? ?]]. + exists s; intuition auto. + fold trans. subst types. eapply trans_mfix_All2;eassumption. @@ -978,7 +979,8 @@ in All (for wf_local assumptions) unfold map_def. reflexivity. + fold trans. - eapply All_map, (All_impl X0); firstorder. + eapply All_map, (All_impl X0). + intros x [s ?]; exists s; intuition auto. + fold trans;subst types. (* like trans_mfix_All2 without isLambda *) admit. diff --git a/pcuic/theories/PCUICUnivSubst.v b/pcuic/theories/PCUICUnivSubst.v index 77d68a0c9..2e79b4583 100644 --- a/pcuic/theories/PCUICUnivSubst.v +++ b/pcuic/theories/PCUICUnivSubst.v @@ -11,7 +11,7 @@ From MetaCoq.PCUIC Require Import PCUICAst PCUICInduction PCUICLiftSubst. Instance subst_instance_constr : UnivSubst term := fix subst_instance_constr u c {struct c} : term := match c with - | tRel _ | tVar _ => c + | tRel _ | tVar _ => c | tEvar ev args => tEvar ev (List.map (subst_instance_constr u) args) | tSort s => tSort (subst_instance_univ u s) | tConst c u' => tConst c (subst_instance_instance u u') @@ -32,6 +32,7 @@ Instance subst_instance_constr : UnivSubst term := | tCoFix mfix idx => let mfix' := List.map (map_def (subst_instance_constr u) (subst_instance_constr u)) mfix in tCoFix mfix' idx + | tInt _ | tFloat _ => c end. Instance subst_instance_decl : UnivSubst context_decl diff --git a/pcuic/theories/PCUICUnivSubstitution.v b/pcuic/theories/PCUICUnivSubstitution.v index 2c58be262..aed89cfc8 100644 --- a/pcuic/theories/PCUICUnivSubstitution.v +++ b/pcuic/theories/PCUICUnivSubstitution.v @@ -347,7 +347,7 @@ Proof. /\ In c' (CS.elements ctrs)). - generalize (CS.elements ctrs), CS.empty. induction l; cbn. - + firstorder. + + pcuicfo. now destruct H0 as [? ?]. + intros t. etransitivity. 1: eapply IHl. split; intros [HH|HH]. * destruct a as [[l1 a] l2]. apply CS.add_spec in HH. @@ -1085,9 +1085,11 @@ Proof. econstructor. now rewrite nth_error_map, H. - cbn. econstructor; eauto. eapply OnOne2_map. eapply OnOne2_impl. 1: eassumption. - firstorder. + (* Used to be pcuicfo *) + simpl in *; intuition; simpl in *. unfold on_Trel. + simpl. split; auto. - cbn; econstructor; - eapply OnOne2_map; eapply OnOne2_impl; [ eassumption | firstorder]. + eapply OnOne2_map; eapply OnOne2_impl; [ eassumption | pcuicfo]. - cbn; econstructor; eapply OnOne2_map; eapply OnOne2_impl; [ eassumption | ]. intros. destruct X1. destruct p. inversion e. destruct x, y; cbn in *; subst. diff --git a/pcuic/theories/PCUICValidity.v b/pcuic/theories/PCUICValidity.v index 859eea3ac..a68266978 100644 --- a/pcuic/theories/PCUICValidity.v +++ b/pcuic/theories/PCUICValidity.v @@ -267,12 +267,11 @@ Section Validity. assumption. - (* Fix *) - eapply nth_error_all in X0; eauto. - firstorder auto. + eapply nth_error_all in X0 as [s Hs]; eauto. + pcuic. - (* CoFix *) - eapply nth_error_all in X0; eauto. - firstorder auto. + eapply nth_error_all in X0 as [s Hs]; pcuic. - (* Conv *) now exists s. diff --git a/pcuic/theories/PCUICWcbvEval.v b/pcuic/theories/PCUICWcbvEval.v index 2fcb83e2f..d5b17f105 100644 --- a/pcuic/theories/PCUICWcbvEval.v +++ b/pcuic/theories/PCUICWcbvEval.v @@ -644,7 +644,7 @@ Section Wcbv. (* intros H; depind H; try solve_discr. *) (* - depelim H. *) (* - depelim H. *) - (* - eexists _, _; firstorder eauto. *) + (* - eexists _, _; pcuicfo eauto. *) (* - now depelim H. *) (* - discriminate. *) (* Qed. *) diff --git a/pcuic/theories/PCUICWeakening.v b/pcuic/theories/PCUICWeakening.v index 4019419da..253d04b27 100644 --- a/pcuic/theories/PCUICWeakening.v +++ b/pcuic/theories/PCUICWeakening.v @@ -293,7 +293,7 @@ Proof. eapply closed_upwards; eauto; lia. + simpl in X. rewrite -X in cp. eapply forallb_All in cp. eapply All_map_id; eauto. - eapply (All_impl cp); firstorder auto. + eapply (All_impl cp); intuition auto. destruct x; unfold on_snd; simpl; f_equal. apply lift_closed. rewrite context_assumptions_fold. eapply closed_upwards; eauto; lia. diff --git a/pcuic/theories/TemplateToPCUIC.v b/pcuic/theories/TemplateToPCUIC.v index 1214cb324..2846a4223 100644 --- a/pcuic/theories/TemplateToPCUIC.v +++ b/pcuic/theories/TemplateToPCUIC.v @@ -1,7 +1,20 @@ (* Distributed under the terms of the MIT license. *) +From Coq Require Import Int63 FloatOps FloatAxioms. From MetaCoq.Template Require Import config utils AstUtils. From MetaCoq.PCUIC Require Import PCUICAst. +Lemma to_Z_bounded_bool (i : Int63.int) : + ((0 <=? φ (i)%int63) && (φ (i)%int63 %Z.leb_le ->%Z.ltb_lt]. +Qed. + +Definition uint63_to_model (i : Int63.int) : uint63_model := + exist _ (Int63.to_Z i) (to_Z_bounded_bool i). + +Definition float64_to_model (f : PrimFloat.float) : float64_model := + exist _ (FloatOps.Prim2SF f) (FloatAxioms.Prim2SF_valid f). Fixpoint trans (t : Ast.term) : term := match t with @@ -27,6 +40,8 @@ Fixpoint trans (t : Ast.term) : term := | Ast.tCoFix mfix idx => let mfix' := List.map (map_def trans trans) mfix in tCoFix mfix' idx + | Ast.tInt n => tInt (uint63_to_model n) + | Ast.tFloat n => tFloat (float64_to_model n) end. Definition trans_decl (d : Ast.context_decl) := diff --git a/template-coq/theories/Reflect.v b/template-coq/theories/Reflect.v index f7c22c6f2..d87c4ccf3 100644 --- a/template-coq/theories/Reflect.v +++ b/template-coq/theories/Reflect.v @@ -149,11 +149,12 @@ Qed. Derive NoConfusion EqDec for SpecFloat.spec_float. -Arguments eqb : simpl never. +Local Obligation Tactic := idtac. #[program] Instance reflect_prim_float : ReflectEq PrimFloat.float := { eqb x y := eqb (ReflectEq := EqDec_ReflectEq SpecFloat.spec_float) (FloatOps.Prim2SF x) (FloatOps.Prim2SF y) }. Next Obligation. + intros. cbn -[eqb]. destruct (eqb_spec (ReflectEq := EqDec_ReflectEq SpecFloat.spec_float) (FloatOps.Prim2SF x) (FloatOps.Prim2SF y)); constructor. now apply FloatAxioms.Prim2SF_inj. intros e; apply n. rewrite e. From 0858b8a12d8d5d713d79d7764fc824e76f92847b Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Fri, 4 Dec 2020 21:50:22 +0100 Subject: [PATCH 38/70] Move erasure to new ast as well (using model still) --- erasure/theories/EAst.v | 5 +- erasure/theories/EAstUtils.v | 2 + erasure/theories/EInduction.v | 2 + erasure/theories/ELiftSubst.v | 3 +- erasure/theories/EOptimizePropDiscr.v | 2 + erasure/theories/EPretty.v | 5 +- erasure/theories/EReflect.v | 2 + erasure/theories/ESubstitution.v | 10 +- erasure/theories/ErasureCorrectness.v | 9 +- erasure/theories/ErasureFunction.v | 4 +- erasure/theories/Extraction.v | 3 +- pcuic/theories/PCUICAst.v | 12 - pcuic/theories/PCUICCanonicity.v | 2 + pcuic/theories/PCUICPretty.v | 2 +- safechecker/theories/Extraction.v | 4 +- safechecker/theories/PCUICSafeConversion.v | 43 ++ safechecker/theories/PCUICSafeReduce.v | 9 + safechecker/theories/PCUICSafeRetyping.v | 8 +- safechecker/theories/PCUICTypeChecker.v | 2 + template-coq/_PluginProject | 18 +- .../gen-src/metacoq_template_plugin.mlpack | 5 + template-coq/gen-src/specFloat.ml.orig | 553 ++++++++++++++++++ template-coq/gen-src/specFloat.ml.rej | 16 + template-coq/specFloat.patch | 10 + template-coq/theories/BasicAst.v | 21 + template-coq/update_plugin.sh | 5 +- 26 files changed, 719 insertions(+), 38 deletions(-) create mode 100644 template-coq/gen-src/specFloat.ml.orig create mode 100644 template-coq/gen-src/specFloat.ml.rej create mode 100644 template-coq/specFloat.patch diff --git a/erasure/theories/EAst.v b/erasure/theories/EAst.v index 01d7ac4c9..e90eacb4e 100644 --- a/erasure/theories/EAst.v +++ b/erasure/theories/EAst.v @@ -1,6 +1,5 @@ (* Distributed under the terms of the MIT license. *) From MetaCoq.Template Require Export utils BasicAst Universes. - (** * Extracted terms These are the terms produced by extraction: compared to kernel terms, @@ -37,7 +36,9 @@ Inductive term : Set := term (* discriminee *) -> list (nat * term) (* branches *) -> term | tProj : projection -> term -> term | tFix : mfixpoint term -> nat -> term -| tCoFix : mfixpoint term -> nat -> term. +| tCoFix : mfixpoint term -> nat -> term +| tInt : uint63_model -> term +| tFloat : float64_model -> term. Fixpoint mkApps t us := match us with diff --git a/erasure/theories/EAstUtils.v b/erasure/theories/EAstUtils.v index a3b246653..d680a533a 100644 --- a/erasure/theories/EAstUtils.v +++ b/erasure/theories/EAstUtils.v @@ -267,6 +267,8 @@ Fixpoint string_of_term (t : term) : string := ^ string_of_term c ^ ")" | tFix l n => "Fix(" ^ (string_of_list (string_of_def string_of_term) l) ^ "," ^ string_of_nat n ^ ")" | tCoFix l n => "CoFix(" ^ (string_of_list (string_of_def string_of_term) l) ^ "," ^ string_of_nat n ^ ")" + | tInt i => "Int(" ^ string_of_Z (proj1_sig i) ^ ")" + | tFloat f => "Float(" ^ "" ^ ")" end. (** Compute all the global environment dependencies of the term *) diff --git a/erasure/theories/EInduction.v b/erasure/theories/EInduction.v index 192b9a05c..1d4789fe8 100644 --- a/erasure/theories/EInduction.v +++ b/erasure/theories/EInduction.v @@ -28,6 +28,8 @@ Lemma term_forall_list_ind : (forall (s : projection) (t : term), P t -> P (tProj s t)) -> (forall (m : mfixpoint term) (n : nat), All (fun x => P (dbody x)) m -> P (tFix m n)) -> (forall (m : mfixpoint term) (n : nat), All (fun x => P (dbody x)) m -> P (tCoFix m n)) -> + (forall i, P (tInt i)) -> + (forall f, P (tFloat f)) -> forall t : term, P t. Proof. intros until t. revert t. diff --git a/erasure/theories/ELiftSubst.v b/erasure/theories/ELiftSubst.v index 940d650e4..cedeace38 100644 --- a/erasure/theories/ELiftSubst.v +++ b/erasure/theories/ELiftSubst.v @@ -32,9 +32,10 @@ Fixpoint lift n k t : term := | tVar _ => t | tConst _ => t | tConstruct _ _ => t + | tInt _ => t + | tFloat _ => t end. - Notation lift0 n := (lift n 0). Definition up := lift 1 0. diff --git a/erasure/theories/EOptimizePropDiscr.v b/erasure/theories/EOptimizePropDiscr.v index a507445a8..310dc0535 100644 --- a/erasure/theories/EOptimizePropDiscr.v +++ b/erasure/theories/EOptimizePropDiscr.v @@ -66,6 +66,8 @@ Section optimize. | tVar _ => t | tConst _ => t | tConstruct _ _ => t + | tInt _ => t + | tFloat _ => t end. Lemma optimize_mkApps f l : optimize (mkApps f l) = mkApps (optimize f) (map optimize l). diff --git a/erasure/theories/EPretty.v b/erasure/theories/EPretty.v index 3dd6f2161..4ae00c2f5 100644 --- a/erasure/theories/EPretty.v +++ b/erasure/theories/EPretty.v @@ -5,7 +5,6 @@ From MetaCoq.Erasure Require Import EAst EAstUtils ETyping. (** * Pretty printing *) - Section print_term. Context (Σ : global_context). @@ -160,6 +159,10 @@ Section print_term. | tCoFix l n => parens top ("let cofix " ^ print_defs print_term Γ l ^ nl ^ " in " ^ List.nth_default (string_of_nat n) (map (string_of_name ∘ dname) l) n) + | tInt i => + parens top (string_of_uint63_model i) + | tFloat f => + parens top (string_of_float64_model f) end. End print_term. diff --git a/erasure/theories/EReflect.v b/erasure/theories/EReflect.v index 73f0398d8..d2a139bb2 100644 --- a/erasure/theories/EReflect.v +++ b/erasure/theories/EReflect.v @@ -23,6 +23,8 @@ Local Ltac term_dec_tac term_dec := | i : kername, i' : kername |- _ => fcase (kername_eq_dec i i') | i : string, i' : kername |- _ => fcase (string_dec i i') | n : name, n' : name |- _ => fcase (eq_dec n n') + | i : uint63_model, i' : uint63_model |- _ => fcase (eq_dec i i') + | i : float64_model, i' : float64_model |- _ => fcase (eq_dec i i') | i : inductive, i' : inductive |- _ => fcase (eq_dec i i') | x : inductive * nat, y : inductive * nat |- _ => fcase (eq_dec x y) diff --git a/erasure/theories/ESubstitution.v b/erasure/theories/ESubstitution.v index fac131d22..941f35bee 100644 --- a/erasure/theories/ESubstitution.v +++ b/erasure/theories/ESubstitution.v @@ -206,8 +206,9 @@ Proof. split; eauto. - assert (HT : Σ;;; Γ ,,, Γ' |- PCUICAst.tFix mfix n : (decl.(dtype))). econstructor; eauto. eapply All_impl. eassumption. intros. - destruct X4; cbn in *; firstorder. - eapply (All_impl X1). firstorder. + destruct X4; cbn in *; pcuicfo. + exists x0; auto. + eapply (All_impl X1). pcuicfo. eapply weakening_typing in HT; auto. 2:{ apply All_local_env_app_inv in X2 as [X2 _]. eapply X2. } @@ -238,8 +239,9 @@ Proof. - assert (HT : Σ;;; Γ ,,, Γ' |- PCUICAst.tCoFix mfix n : (decl.(dtype))). econstructor; eauto. eapply All_impl. eassumption. intros. - destruct X4; cbn in *; firstorder. - eapply (All_impl X1). firstorder. + destruct X4; cbn in *; pcuicfo. + now exists x0. + eapply (All_impl X1). pcuicfo. eapply weakening_typing in HT; auto. 2:{ apply All_local_env_app_inv in X2 as [X2 _]. eapply X2. } diff --git a/erasure/theories/ErasureCorrectness.v b/erasure/theories/ErasureCorrectness.v index c207da5b2..d5f531381 100644 --- a/erasure/theories/ErasureCorrectness.v +++ b/erasure/theories/ErasureCorrectness.v @@ -131,7 +131,8 @@ Proof. eapply All2_All_left in X3. 2:{ idtac. intros ? ? [[? e] ?]. exact e. } eapply All2_impl. eapply All2_All_mix_left. - all: firstorder. + eauto. eauto. + all: pcuicfo. - econstructor. eapply All2_impl. eapply All2_All_mix_left. eassumption. eassumption. @@ -258,7 +259,8 @@ Proof. - assert (Hw : wf_local (Σ.1, univs) (subst_instance_context u (Γ ,,, types))). { (* rewrite subst_instance_context_app. *) assert(All (fun d => isType Σ Γ (dtype d)) mfix). - eapply (All_impl X0); firstorder. + eapply (All_impl X0); pcuicfo. + now destruct X5 as [s [Hs ?]]; exists s. eapply All_mfix_wf in X5; auto. subst types. revert X5. clear - wfΣ wfΓ H2 H3 X2 X3. @@ -292,7 +294,8 @@ Proof. - assert (Hw : wf_local (Σ.1, univs) (subst_instance_context u (Γ ,,, types))). { (* rewrite subst_instance_context_app. *) assert(All (fun d => isType Σ Γ (dtype d)) mfix). - eapply (All_impl X0); firstorder. + eapply (All_impl X0); pcuicfo. + destruct X5 as [s [Hs ?]]; now exists s. eapply All_mfix_wf in X5; auto. subst types. revert X5. clear - wfΣ wfΓ H2 H3 X2 X3. diff --git a/erasure/theories/ErasureFunction.v b/erasure/theories/ErasureFunction.v index 410c5e4e8..449ad6a01 100644 --- a/erasure/theories/ErasureFunction.v +++ b/erasure/theories/ErasureFunction.v @@ -403,7 +403,9 @@ Section Erase. E.tFix mfix' n; erase Γ (tCoFix mfix n) Ht _ := let mfix' := erase_mfix (erase) Γ mfix _ in - E.tCoFix mfix' n + E.tCoFix mfix' n; + erase Γ (tInt i) Ht _ := E.tInt i; + erase Γ (tFloat f) Ht _ := E.tFloat f }. Proof. all:try clear b'; try clear f'; try clear brs'; try clear erase. diff --git a/erasure/theories/Extraction.v b/erasure/theories/Extraction.v index 57b9bfd0a..99f66ef0c 100644 --- a/erasure/theories/Extraction.v +++ b/erasure/theories/Extraction.v @@ -1,5 +1,6 @@ (* Distributed under the terms of the MIT license. *) -Require Import FSets ExtrOcamlBasic ExtrOcamlString ExtrOcamlZInt. +Require Import FSets ExtrOcamlBasic ExtrOcamlString ExtrOcamlZInt + MC_ExtrOCamlInt63 (*b/c nameclash with `comparion` *) ExtrOCamlFloats. (** * Extraction setup for the erasure phase of template-coq. diff --git a/pcuic/theories/PCUICAst.v b/pcuic/theories/PCUICAst.v index bfd510844..56c5da61b 100644 --- a/pcuic/theories/PCUICAst.v +++ b/pcuic/theories/PCUICAst.v @@ -1,5 +1,4 @@ (* Distributed under the terms of the MIT license. *) -From Coq Require Import Floats.SpecFloat. From MetaCoq.Template Require Export utils Universes BasicAst Environment EnvironmentTyping. From Equations Require Import Equations. @@ -21,17 +20,6 @@ Ltac pcuicfo_gen tac := Tactic Notation "pcuicfo" := pcuicfo_gen auto. Tactic Notation "pcuicfo" tactic(tac) := pcuicfo_gen tac. -(** Model of unsigned integers *) -Definition uint_size := 63. -Definition uint_wB := (2 ^ (Z.of_nat uint_size))%Z. -Definition uint63_model := { z : Z | ((0 <=? z) && (z diff --git a/pcuic/theories/PCUICPretty.v b/pcuic/theories/PCUICPretty.v index 0d9e238f1..df6dc897f 100644 --- a/pcuic/theories/PCUICPretty.v +++ b/pcuic/theories/PCUICPretty.v @@ -191,7 +191,7 @@ Section print_term. parens top ("let cofix " ^ print_defs print_term Γ l ^ nl ^ " in " ^ List.nth_default (string_of_nat n) (map (string_of_aname ∘ dname) l) n) | tInt i => - parens top (string_of_Z (proj1_sig i)) + parens top (string_of_uint63_model i) | tFloat f => parens top (string_of_float64_model f) end. diff --git a/safechecker/theories/Extraction.v b/safechecker/theories/Extraction.v index abfa71959..8984b445e 100644 --- a/safechecker/theories/Extraction.v +++ b/safechecker/theories/Extraction.v @@ -1,5 +1,6 @@ (* Distributed under the terms of the MIT license. *) -Require Import OrdersTac ExtrOcamlBasic ExtrOcamlString ExtrOcamlZInt. +Require Import OrdersTac ExtrOcamlBasic ExtrOcamlString ExtrOcamlZInt + MC_ExtrOCamlInt63 (*b/c nameclash with `comparion` *) ExtrOCamlFloats. Require Import MetaCoq.Template.utils. From MetaCoq.SafeChecker Require Import PCUICSafeChecker PCUICSafeConversion SafeTemplateChecker. @@ -10,6 +11,7 @@ From MetaCoq.SafeChecker Require Import PCUICSafeChecker PCUICSafeConversion should use these same directives for consistency. *) +(** Here we could extract uint63_from/to_model to the identity *) (* Ignore [Decimal.int] before the extraction issue is solved: https://github.com/coq/coq/issues/7017. *) diff --git a/safechecker/theories/PCUICSafeConversion.v b/safechecker/theories/PCUICSafeConversion.v index 21b758aa8..8992b5272 100644 --- a/safechecker/theories/PCUICSafeConversion.v +++ b/safechecker/theories/PCUICSafeConversion.v @@ -4056,7 +4056,42 @@ Section Conversion. - reflexivity. - reflexivity. Qed. + + (* TODO move to PCUICNormal *) + Lemma whnf_mkApps_tInt_inv : + forall (f : RedFlags.t) (Σ : global_env) (Γ : context) i (args : list term), + whnf f Σ Γ (mkApps (tInt i) args) -> args = []. + Proof. + intros * wh. + inversion wh; solve_discr. + clear -X. + remember (mkApps (tInt i) args) eqn:teq. + exfalso. + revert teq. + induction X in args |- *; intros; solve_discr. + destruct args as [|? ? _] using MCList.rev_ind; [easy|]. + rewrite <- mkApps_nested in teq. + cbn in teq. noconf teq. + eauto. + Qed. + Lemma whnf_mkApps_tFloat_inv : + forall (rf : RedFlags.t) (Σ : global_env) (Γ : context) f (args : list term), + whnf rf Σ Γ (mkApps (tFloat f) args) -> args = []. + Proof. + intros * wh. + inversion wh; solve_discr. + clear -X. + remember (mkApps (tFloat f) args) eqn:teq. + exfalso. + revert teq. + induction X in args |- *; intros; solve_discr. + destruct args as [|? ? _] using MCList.rev_ind; [easy|]. + rewrite <- mkApps_nested in teq. + cbn in teq. noconf teq. + eauto. + Qed. + Lemma reducible_head_None Γ t π h : isApp t = false -> whnf RedFlags.nodelta Σ (Γ,,, stack_context π) (mkApps t (decompose_stack π).1) -> @@ -4115,6 +4150,12 @@ Section Conversion. - constructor; eexists _, (decompose_stack π).1. split; [constructor; eauto with pcuic|]. eauto with pcuic. + - apply whnf_mkApps_tInt_inv in wh as ->. + constructor; eexists _, []. + eauto using whnf_red with pcuic. + - apply whnf_mkApps_tFloat_inv in wh as ->. + constructor; eexists _, []. + eauto using whnf_red with pcuic. - constructor; eexists _, (decompose_stack π).1. split; [econstructor|]; eauto. split; [eauto with pcuic|]. @@ -4498,6 +4539,8 @@ Section Conversion. apply inversion_Sort in h2 as (_&h2&_); auto. apply inversion_Sort in h1 as (_&h1&_); auto. eapply conv_pb_relb_complete in H0; eauto. + - now rewrite eq_dec_to_bool_refl in noteq. + - now rewrite eq_dec_to_bool_refl in noteq. Qed. Equations _isconv (s : state) (Γ : context) diff --git a/safechecker/theories/PCUICSafeReduce.v b/safechecker/theories/PCUICSafeReduce.v index df4493b96..f4c14f156 100644 --- a/safechecker/theories/PCUICSafeReduce.v +++ b/safechecker/theories/PCUICSafeReduce.v @@ -1256,6 +1256,8 @@ Section Reduce. unfold is_true in typ. unfold PCUICAst.fst_ctx in *. congruence. + - now eapply inversion_Int in typ. + - now eapply inversion_Float in typ. Qed. Definition isCoFix_app t := @@ -1287,6 +1289,8 @@ Section Reduce. - exfalso; eapply invert_fix_ind; eauto. - unfold isCoFix_app in cof. now rewrite decompose_app_mkApps in cof. + - now eapply inversion_Int in typ. + - now eapply inversion_Float in typ. Qed. Lemma whnf_fix_arg_whne mfix idx body Γ t before args aftr ty : @@ -1435,6 +1439,11 @@ Section Reduce. apply inversion_App in h as (?&?&?&?&?); auto. apply inversion_Prod in t0 as (?&?&?&?&?); auto. eapply PCUICConversion.cumul_Sort_Prod_inv; eauto. + + exfalso. + eapply welltyped_context in h as [s Hs]; tas. + now eapply inversion_Int in Hs. + + exfalso; eapply welltyped_context in h as [s Hs]; tas. + now eapply inversion_Float in Hs. - unfold zipp. case_eq (decompose_stack π0). intros l ρ e. constructor. constructor. eapply whne_mkApps. eapply whne_rel_nozeta. assumption. diff --git a/safechecker/theories/PCUICSafeRetyping.v b/safechecker/theories/PCUICSafeRetyping.v index ee891f44f..02b003fdc 100644 --- a/safechecker/theories/PCUICSafeRetyping.v +++ b/safechecker/theories/PCUICSafeRetyping.v @@ -261,7 +261,10 @@ Section TypeOf. infer Γ (tCoFix mfix n) wt with inspect (nth_error mfix n) := { | ret (Some f) => ret f.(dtype); - | ret None => ! } + | ret None => ! }; + + infer Γ (tInt i) wt := ! ; + infer Γ (tFloat f) wt := ! }. Proof. all:try clear infer. @@ -655,6 +658,9 @@ Section TypeOf. congruence. - now eapply inversion_CoFix in HT as [decl [fg [hnth [htys [hbods [wf cum]]]]]]; auto. + + - now eapply inversion_Int in HT. + - now eapply inversion_Float in HT. Defined. Definition type_of Γ t wt : term := (infer Γ t wt). diff --git a/safechecker/theories/PCUICTypeChecker.v b/safechecker/theories/PCUICTypeChecker.v index bb97f5824..344470aac 100644 --- a/safechecker/theories/PCUICTypeChecker.v +++ b/safechecker/theories/PCUICTypeChecker.v @@ -455,6 +455,8 @@ Section Typecheck. wfcofix <- check_eq_true (wf_cofixpoint Σ.1 mfix) (Msg "Ill-formed cofixpoint: not producing values in a mutually coinductive family") ;; ret (dtype decl; _) end + + | tInt _ | tFloat _ => raise (Msg "Primitive types are not supported") end. (* tRel *) diff --git a/template-coq/_PluginProject b/template-coq/_PluginProject index e777b2e71..13baec6c9 100644 --- a/template-coq/_PluginProject +++ b/template-coq/_PluginProject @@ -59,14 +59,16 @@ gen-src/extractable.mli gen-src/int63.ml gen-src/int63.mli -# gen-src/sumbool.mli -# gen-src/sumbool.ml -# gen-src/zeven.mli -# gen-src/zeven.ml -# gen-src/zArith_dec.mli -# gen-src/zArith_dec.ml -# gen-src/zbool.mli -# gen-src/zbool.ml +gen-src/sumbool.mli +gen-src/sumbool.ml +gen-src/zeven.mli +gen-src/zeven.ml +gen-src/zArith_dec.mli +gen-src/zArith_dec.ml +gen-src/zbool.mli +gen-src/zbool.ml +gen-src/zpower.mli +gen-src/zpower.ml gen-src/specFloat.mli gen-src/specFloat.ml gen-src/floatOps.mli diff --git a/template-coq/gen-src/metacoq_template_plugin.mlpack b/template-coq/gen-src/metacoq_template_plugin.mlpack index 1c13613e2..2eb7057d0 100644 --- a/template-coq/gen-src/metacoq_template_plugin.mlpack +++ b/template-coq/gen-src/metacoq_template_plugin.mlpack @@ -36,6 +36,11 @@ MCRelations MCOption MCProd MCCompare +Sumbool +Zeven +ZArith_dec +Zbool +Zpower SpecFloat PrimFloat FloatOps diff --git a/template-coq/gen-src/specFloat.ml.orig b/template-coq/gen-src/specFloat.ml.orig new file mode 100644 index 000000000..48bad30a5 --- /dev/null +++ b/template-coq/gen-src/specFloat.ml.orig @@ -0,0 +1,553 @@ +open BinInt +open BinPos +open Bool +open Datatypes +open Zbool +open Zpower + +type spec_float = +| S754_zero of bool +| S754_infinity of bool +| S754_nan +| S754_finite of bool * int * int + +(** val emin : int -> int -> int **) + +let emin prec emax = + Z.sub (Z.sub ((fun p->1+2*p) 1) emax) prec + +(** val fexp : int -> int -> int -> int **) + +let fexp prec emax e = + Z.max (Z.sub e prec) (emin prec emax) + +(** val digits2_pos : int -> int **) + +let rec digits2_pos n = + (fun f2p1 f2p f1 p -> + if p<=1 then f1 () else if p mod 2 = 0 then f2p (p/2) else f2p1 (p/2)) + (fun p -> Pos.succ (digits2_pos p)) + (fun p -> Pos.succ (digits2_pos p)) + (fun _ -> 1) + n + +(** val coq_Zdigits2 : int -> int **) + +let coq_Zdigits2 n = + (fun f0 fp fn z -> if z=0 then f0 () else if z>0 then fp z else fn (-z)) + (fun _ -> n) + (fun p -> (digits2_pos p)) + (fun p -> (digits2_pos p)) + n + +(** val canonical_mantissa : int -> int -> int -> int -> bool **) + +let canonical_mantissa prec emax m e = + coq_Zeq_bool (fexp prec emax (Z.add (digits2_pos m) e)) e + +(** val bounded : int -> int -> int -> int -> bool **) + +let bounded prec emax m e = + (&&) (canonical_mantissa prec emax m e) (Z.leb e (Z.sub emax prec)) + +(** val valid_binary : int -> int -> spec_float -> bool **) + +let valid_binary prec emax = function +| S754_finite (_, m, e) -> bounded prec emax m e +| _ -> true + +(** val iter_pos : ('a1 -> 'a1) -> int -> 'a1 -> 'a1 **) + +let rec iter_pos f n x = + (fun f2p1 f2p f1 p -> + if p<=1 then f1 () else if p mod 2 = 0 then f2p (p/2) else f2p1 (p/2)) + (fun n' -> iter_pos f n' (iter_pos f n' (f x))) + (fun n' -> iter_pos f n' (iter_pos f n' x)) + (fun _ -> f x) + n + +type location = +| Coq_loc_Exact +| Coq_loc_Inexact of comparison + +(** val location_rect : 'a1 -> (comparison -> 'a1) -> location -> 'a1 **) + +let location_rect f f0 = function +| Coq_loc_Exact -> f +| Coq_loc_Inexact x -> f0 x + +(** val location_rec : 'a1 -> (comparison -> 'a1) -> location -> 'a1 **) + +let location_rec f f0 = function +| Coq_loc_Exact -> f +| Coq_loc_Inexact x -> f0 x + +type shr_record = { shr_m : int; shr_r : bool; shr_s : bool } + +(** val shr_m : shr_record -> int **) + +let shr_m s = + s.shr_m + +(** val shr_r : shr_record -> bool **) + +let shr_r s = + s.shr_r + +(** val shr_s : shr_record -> bool **) + +let shr_s s = + s.shr_s + +(** val shr_1 : shr_record -> shr_record **) + +let shr_1 mrs = + let { shr_m = m; shr_r = r; shr_s = s } = mrs in + let s0 = (||) r s in + ((fun f0 fp fn z -> if z=0 then f0 () else if z>0 then fp z else fn (-z)) + (fun _ -> { shr_m = 0; shr_r = false; shr_s = s0 }) + (fun p0 -> + (fun f2p1 f2p f1 p -> + if p<=1 then f1 () else if p mod 2 = 0 then f2p (p/2) else f2p1 (p/2)) + (fun p -> { shr_m = p; shr_r = true; shr_s = s0 }) + (fun p -> { shr_m = p; shr_r = false; shr_s = s0 }) + (fun _ -> { shr_m = 0; shr_r = true; shr_s = s0 }) + p0) + (fun p0 -> + (fun f2p1 f2p f1 p -> + if p<=1 then f1 () else if p mod 2 = 0 then f2p (p/2) else f2p1 (p/2)) + (fun p -> { shr_m = ((~-) p); shr_r = true; shr_s = s0 }) + (fun p -> { shr_m = ((~-) p); shr_r = false; shr_s = s0 }) + (fun _ -> { shr_m = 0; shr_r = true; shr_s = s0 }) + p0) + m) + +(** val loc_of_shr_record : shr_record -> location **) + +let loc_of_shr_record mrs = + let { shr_m = _; shr_r = shr_r0; shr_s = shr_s0 } = mrs in + if shr_r0 + then if shr_s0 then Coq_loc_Inexact Gt else Coq_loc_Inexact Eq + else if shr_s0 then Coq_loc_Inexact Lt else Coq_loc_Exact + +(** val shr_record_of_loc : int -> location -> shr_record **) + +let shr_record_of_loc m = function +| Coq_loc_Exact -> { shr_m = m; shr_r = false; shr_s = false } +| Coq_loc_Inexact c -> + (match c with + | Eq -> { shr_m = m; shr_r = true; shr_s = false } + | Lt -> { shr_m = m; shr_r = false; shr_s = true } + | Gt -> { shr_m = m; shr_r = true; shr_s = true }) + +(** val shr : shr_record -> int -> int -> shr_record * int **) + +let shr mrs e n = + (fun f0 fp fn z -> if z=0 then f0 () else if z>0 then fp z else fn (-z)) + (fun _ -> (mrs, e)) + (fun p -> ((iter_pos shr_1 p mrs), (Z.add e n))) + (fun _ -> (mrs, e)) + n + +(** val shr_fexp : + int -> int -> int -> int -> location -> shr_record * int **) + +let shr_fexp prec emax m e l = + shr (shr_record_of_loc m l) e + (Z.sub (fexp prec emax (Z.add (coq_Zdigits2 m) e)) e) + +(** val round_nearest_even : int -> location -> int **) + +let round_nearest_even mx = function +| Coq_loc_Exact -> mx +| Coq_loc_Inexact c -> + (match c with + | Eq -> if Z.even mx then mx else Z.add mx 1 + | Lt -> mx + | Gt -> Z.add mx 1) + +(** val binary_round_aux : + int -> int -> bool -> int -> int -> location -> spec_float **) + +let binary_round_aux prec emax sx mx ex lx = + let (mrs', e') = shr_fexp prec emax mx ex lx in + let (mrs'', e'') = + shr_fexp prec emax + (round_nearest_even mrs'.shr_m (loc_of_shr_record mrs')) e' + Coq_loc_Exact + in + ((fun f0 fp fn z -> if z=0 then f0 () else if z>0 then fp z else fn (-z)) + (fun _ -> S754_zero sx) + (fun m -> + if Z.leb e'' (Z.sub emax prec) + then S754_finite (sx, m, e'') + else S754_infinity sx) + (fun _ -> S754_nan) + mrs''.shr_m) + +(** val shl_align : int -> int -> int -> int * int **) + +let shl_align mx ex ex' = + (fun f0 fp fn z -> if z=0 then f0 () else if z>0 then fp z else fn (-z)) + (fun _ -> (mx, ex)) + (fun _ -> (mx, ex)) + (fun d -> ((shift_pos d mx), ex')) + (Z.sub ex' ex) + +(** val binary_round : int -> int -> bool -> int -> int -> spec_float **) + +let binary_round prec emax sx mx ex = + let (mz, ez) = shl_align mx ex (fexp prec emax (Z.add (digits2_pos mx) ex)) + in + binary_round_aux prec emax sx mz ez Coq_loc_Exact + +(** val binary_normalize : int -> int -> int -> int -> bool -> spec_float **) + +let binary_normalize prec emax m e szero = + (fun f0 fp fn z -> if z=0 then f0 () else if z>0 then fp z else fn (-z)) + (fun _ -> S754_zero szero) + (fun m0 -> binary_round prec emax false m0 e) + (fun m0 -> binary_round prec emax true m0 e) + m + +(** val coq_SFopp : spec_float -> spec_float **) + +let coq_SFopp = function +| S754_zero sx -> S754_zero (negb sx) +| S754_infinity sx -> S754_infinity (negb sx) +| S754_nan -> S754_nan +| S754_finite (sx, mx, ex) -> S754_finite ((negb sx), mx, ex) + +(** val coq_SFabs : spec_float -> spec_float **) + +let coq_SFabs = function +| S754_zero _ -> S754_zero false +| S754_infinity _ -> S754_infinity false +| S754_nan -> S754_nan +| S754_finite (_, mx, ex) -> S754_finite (false, mx, ex) + +(** val coq_SFcompare : spec_float -> spec_float -> comparison option **) + +let coq_SFcompare f1 f2 = + match f1 with + | S754_zero _ -> + (match f2 with + | S754_zero _ -> Some Eq + | S754_infinity s -> Some (if s then Gt else Lt) + | S754_nan -> None + | S754_finite (s, _, _) -> Some (if s then Gt else Lt)) + | S754_infinity s -> + (match f2 with + | S754_infinity s0 -> + Some (if s then if s0 then Eq else Lt else if s0 then Gt else Eq) + | S754_nan -> None + | _ -> Some (if s then Lt else Gt)) + | S754_nan -> None + | S754_finite (s1, m1, e1) -> + (match f2 with + | S754_zero _ -> Some (if s1 then Lt else Gt) + | S754_infinity s -> Some (if s then Gt else Lt) + | S754_nan -> None + | S754_finite (s2, m2, e2) -> + Some + (if s1 + then if s2 + then (match Z.compare e1 e2 with + | Eq -> coq_CompOpp (Pos.compare_cont Eq m1 m2) + | Lt -> Gt + | Gt -> Lt) + else Lt + else if s2 + then Gt + else (match Z.compare e1 e2 with + | Eq -> Pos.compare_cont Eq m1 m2 + | x -> x))) + +(** val coq_SFeqb : spec_float -> spec_float -> bool **) + +let coq_SFeqb f1 f2 = + match coq_SFcompare f1 f2 with + | Some c -> (match c with + | Eq -> true + | _ -> false) + | None -> false + +(** val coq_SFltb : spec_float -> spec_float -> bool **) + +let coq_SFltb f1 f2 = + match coq_SFcompare f1 f2 with + | Some c -> (match c with + | Lt -> true + | _ -> false) + | None -> false + +(** val coq_SFleb : spec_float -> spec_float -> bool **) + +let coq_SFleb f1 f2 = + match coq_SFcompare f1 f2 with + | Some _ -> true + | None -> false + +(** val coq_SFclassify : int -> spec_float -> Float64.float_class **) + +let coq_SFclassify prec = function +| S754_zero s -> if s then PZero else NZero +| S754_infinity s -> if s then NInf else PInf +| S754_nan -> NaN +| S754_finite (s, m, _) -> + if s + then if Pos.eqb (digits2_pos m) (Z.to_pos prec) then NNormal else NSubn + else if Pos.eqb (digits2_pos m) (Z.to_pos prec) then PNormal else PSubn + +(** val coq_SFmul : int -> int -> spec_float -> spec_float -> spec_float **) + +let coq_SFmul prec emax x y = + match x with + | S754_zero sx -> + (match y with + | S754_zero sy -> S754_zero (xorb sx sy) + | S754_finite (sy, _, _) -> S754_zero (xorb sx sy) + | _ -> S754_nan) + | S754_infinity sx -> + (match y with + | S754_infinity sy -> S754_infinity (xorb sx sy) + | S754_finite (sy, _, _) -> S754_infinity (xorb sx sy) + | _ -> S754_nan) + | S754_nan -> S754_nan + | S754_finite (sx, mx, ex) -> + (match y with + | S754_zero sy -> S754_zero (xorb sx sy) + | S754_infinity sy -> S754_infinity (xorb sx sy) + | S754_nan -> S754_nan + | S754_finite (sy, my, ey) -> + binary_round_aux prec emax (xorb sx sy) (Pos.mul mx my) (Z.add ex ey) + Coq_loc_Exact) + +(** val cond_Zopp : bool -> int -> int **) + +let cond_Zopp b m = + if b then Z.opp m else m + +(** val coq_SFadd : int -> int -> spec_float -> spec_float -> spec_float **) + +let coq_SFadd prec emax x y = + match x with + | S754_zero sx -> + (match y with + | S754_zero sy -> if eqb sx sy then x else S754_zero false + | S754_nan -> S754_nan + | _ -> y) + | S754_infinity sx -> + (match y with + | S754_infinity sy -> if eqb sx sy then x else S754_nan + | S754_nan -> S754_nan + | _ -> x) + | S754_nan -> S754_nan + | S754_finite (sx, mx, ex) -> + (match y with + | S754_zero _ -> x + | S754_infinity _ -> y + | S754_nan -> S754_nan + | S754_finite (sy, my, ey) -> + let ez = Z.min ex ey in + binary_normalize prec emax + (Z.add (cond_Zopp sx (fst (shl_align mx ex ez))) + (cond_Zopp sy (fst (shl_align my ey ez)))) ez false) + +(** val coq_SFsub : int -> int -> spec_float -> spec_float -> spec_float **) + +let coq_SFsub prec emax x y = + match x with + | S754_zero sx -> + (match y with + | S754_zero sy -> if eqb sx (negb sy) then x else S754_zero false + | S754_infinity sy -> S754_infinity (negb sy) + | S754_nan -> S754_nan + | S754_finite (sy, my, ey) -> S754_finite ((negb sy), my, ey)) + | S754_infinity sx -> + (match y with + | S754_infinity sy -> if eqb sx (negb sy) then x else S754_nan + | S754_nan -> S754_nan + | _ -> x) + | S754_nan -> S754_nan + | S754_finite (sx, mx, ex) -> + (match y with + | S754_zero _ -> x + | S754_infinity sy -> S754_infinity (negb sy) + | S754_nan -> S754_nan + | S754_finite (sy, my, ey) -> + let ez = Z.min ex ey in + binary_normalize prec emax + (Z.sub (cond_Zopp sx (fst (shl_align mx ex ez))) + (cond_Zopp sy (fst (shl_align my ey ez)))) ez false) + +(** val new_location_even : int -> int -> location **) + +let new_location_even nb_steps k = + if coq_Zeq_bool k 0 + then Coq_loc_Exact + else Coq_loc_Inexact (Z.compare (Z.mul ((fun p->2*p) 1) k) nb_steps) + +(** val new_location_odd : int -> int -> location **) + +let new_location_odd nb_steps k = + if coq_Zeq_bool k 0 + then Coq_loc_Exact + else Coq_loc_Inexact + (match Z.compare (Z.add (Z.mul ((fun p->2*p) 1) k) 1) nb_steps with + | Eq -> Lt + | x -> x) + +(** val new_location : int -> int -> location **) + +let new_location nb_steps = + if Z.even nb_steps + then new_location_even nb_steps + else new_location_odd nb_steps + +(** val coq_SFdiv_core_binary : + int -> int -> int -> int -> int -> int -> (int * int) * location **) + +let coq_SFdiv_core_binary prec emax m1 e1 m2 e2 = + let d1 = coq_Zdigits2 m1 in + let d2 = coq_Zdigits2 m2 in + let e' = + Z.min (fexp prec emax (Z.sub (Z.add d1 e1) (Z.add d2 e2))) (Z.sub e1 e2) + in + let s = Z.sub (Z.sub e1 e2) e' in + let m' = + (fun f0 fp fn z -> if z=0 then f0 () else if z>0 then fp z else fn (-z)) + (fun _ -> m1) + (fun _ -> Z.shiftl m1 s) + (fun _ -> 0) + s + in + let (q, r) = Z.div_eucl m' m2 in ((q, e'), (new_location m2 r)) + +(** val coq_SFdiv : int -> int -> spec_float -> spec_float -> spec_float **) + +let coq_SFdiv prec emax x y = + match x with + | S754_zero sx -> + (match y with + | S754_infinity sy -> S754_zero (xorb sx sy) + | S754_finite (sy, _, _) -> S754_zero (xorb sx sy) + | _ -> S754_nan) + | S754_infinity sx -> + (match y with + | S754_zero sy -> S754_infinity (xorb sx sy) + | S754_finite (sy, _, _) -> S754_infinity (xorb sx sy) + | _ -> S754_nan) + | S754_nan -> S754_nan + | S754_finite (sx, mx, ex) -> + (match y with + | S754_zero sy -> S754_infinity (xorb sx sy) + | S754_infinity sy -> S754_zero (xorb sx sy) + | S754_nan -> S754_nan + | S754_finite (sy, my, ey) -> + let (p, lz) = coq_SFdiv_core_binary prec emax mx ex my ey in + let (mz, ez) = p in binary_round_aux prec emax (xorb sx sy) mz ez lz) + +(** val coq_SFsqrt_core_binary : + int -> int -> int -> int -> (int * int) * location **) + +let coq_SFsqrt_core_binary prec emax m e = + let d = coq_Zdigits2 m in + let e' = Z.min (fexp prec emax (Z.div2 (Z.add (Z.add d e) 1))) (Z.div2 e) in + let s = Z.sub e (Z.mul ((fun p->2*p) 1) e') in + let m' = + (fun f0 fp fn z -> if z=0 then f0 () else if z>0 then fp z else fn (-z)) + (fun _ -> m) + (fun _ -> Z.shiftl m s) + (fun _ -> 0) + s + in + let (q, r) = Z.sqrtrem m' in + let l = + if coq_Zeq_bool r 0 + then Coq_loc_Exact + else Coq_loc_Inexact (if Z.leb r q then Lt else Gt) + in + ((q, e'), l) + +(** val coq_SFsqrt : int -> int -> spec_float -> spec_float **) + +let coq_SFsqrt prec emax x = match x with +| S754_zero _ -> x +| S754_infinity s -> if s then S754_nan else x +| S754_nan -> S754_nan +| S754_finite (sx, mx, ex) -> + if sx + then S754_nan + else let (p, lz) = coq_SFsqrt_core_binary prec emax mx ex in + let (mz, ez) = p in binary_round_aux prec emax false mz ez lz + +(** val coq_SFnormfr_mantissa : int -> spec_float -> int **) + +let coq_SFnormfr_mantissa prec = function +| S754_finite (_, mx, ex) -> if Z.eqb ex (Z.opp prec) then mx else 0 +| _ -> 0 + +(** val coq_SFldexp : int -> int -> spec_float -> int -> spec_float **) + +let coq_SFldexp prec emax f e = + match f with + | S754_finite (sx, mx, ex) -> binary_round prec emax sx mx (Z.add ex e) + | _ -> f + +(** val coq_SFfrexp : int -> int -> spec_float -> spec_float * int **) + +let coq_SFfrexp prec emax f = match f with +| S754_finite (sx, mx, ex) -> + if Pos.leb (Z.to_pos prec) (digits2_pos mx) + then ((S754_finite (sx, mx, (Z.opp prec))), (Z.add ex prec)) + else let d = Z.sub prec (digits2_pos mx) in + ((S754_finite (sx, (shift_pos (Z.to_pos d) mx), (Z.opp prec))), + (Z.sub (Z.add ex prec) d)) +| _ -> (f, (Z.sub (Z.mul ((~-) ((fun p->2*p) 1)) emax) prec)) + +(** val coq_SFone : int -> int -> spec_float **) + +let coq_SFone prec emax = + binary_round prec emax false 1 0 + +(** val coq_SFulp : int -> int -> spec_float -> spec_float **) + +let coq_SFulp prec emax x = + coq_SFldexp prec emax (coq_SFone prec emax) + (fexp prec emax (snd (coq_SFfrexp prec emax x))) + +(** val coq_SFpred_pos : int -> int -> spec_float -> spec_float **) + +let coq_SFpred_pos prec emax x = match x with +| S754_finite (_, mx, _) -> + let d = + if Pos.eqb ((fun p->2*p) mx) (shift_pos (Z.to_pos prec) 1) + then coq_SFldexp prec emax (coq_SFone prec emax) + (fexp prec emax (Z.sub (snd (coq_SFfrexp prec emax x)) 1)) + else coq_SFulp prec emax x + in + coq_SFsub prec emax x d +| _ -> x + +(** val coq_SFmax_float : int -> int -> spec_float **) + +let coq_SFmax_float prec emax = + S754_finite (false, (Pos.sub (shift_pos (Z.to_pos prec) 1) 1), + (Z.sub emax prec)) + +(** val coq_SFsucc : int -> int -> spec_float -> spec_float **) + +let coq_SFsucc prec emax x = match x with +| S754_zero _ -> coq_SFldexp prec emax (coq_SFone prec emax) (emin prec emax) +| S754_infinity s -> if s then coq_SFopp (coq_SFmax_float prec emax) else x +| S754_nan -> x +| S754_finite (s, _, _) -> + if s + then coq_SFopp (coq_SFpred_pos prec emax (coq_SFopp x)) + else coq_SFadd prec emax x (coq_SFulp prec emax x) + +(** val coq_SFpred : int -> int -> spec_float -> spec_float **) + +let coq_SFpred prec emax f = + coq_SFopp (coq_SFsucc prec emax (coq_SFopp f)) diff --git a/template-coq/gen-src/specFloat.ml.rej b/template-coq/gen-src/specFloat.ml.rej new file mode 100644 index 000000000..04dcccf83 --- /dev/null +++ b/template-coq/gen-src/specFloat.ml.rej @@ -0,0 +1,16 @@ +*************** +*** 4,9 **** + open Datatypes + open Zbool + open Zpower + + type spec_float = + | S754_zero of bool +--- 4,10 ---- + open Datatypes + open Zbool + open Zpower ++ open Float64 + + type spec_float = + | S754_zero of bool diff --git a/template-coq/specFloat.patch b/template-coq/specFloat.patch new file mode 100644 index 000000000..294627074 --- /dev/null +++ b/template-coq/specFloat.patch @@ -0,0 +1,10 @@ +--- gen-src/specFloat.ml.orig 2020-12-04 21:48:20.000000000 +0100 ++++ gen-src/specFloat.ml 2020-12-04 21:48:33.000000000 +0100 +@@ -4,6 +4,7 @@ + open Datatypes + open Zbool + open Zpower ++open Float64 + + type spec_float = + | S754_zero of bool diff --git a/template-coq/theories/BasicAst.v b/template-coq/theories/BasicAst.v index 01e715b0a..e521dec0b 100644 --- a/template-coq/theories/BasicAst.v +++ b/template-coq/theories/BasicAst.v @@ -1,5 +1,6 @@ (* Distributed under the terms of the MIT license. *) From MetaCoq.Template Require Import utils. +From Coq Require Import Floats.SpecFloat. (** ** Reification of names ** *) @@ -27,6 +28,8 @@ From MetaCoq.Template Require Import utils. - constructor => [inductive * nat] - Projection.t => [projection] - GlobRef.t => global_reference + + Finally, we define the models of primitive types (uint63 and floats64). *) Definition ident := string. (* e.g. nat *) @@ -382,3 +385,21 @@ Ltac close_All := | H : All2 _ _ _ |- All _ _ => (apply (All2_All_left H) || apply (All2_All_right H)); clear H; simpl end. + +(** Primitive types models (axiom free) *) + +(** Model of unsigned integers *) +Definition uint_size := 63. +Definition uint_wB := (2 ^ (Z.of_nat uint_size))%Z. +Definition uint63_model := { z : Z | ((0 <=? z) && (z ". diff --git a/template-coq/update_plugin.sh b/template-coq/update_plugin.sh index 2821b1fa0..b9a5ecaf4 100755 --- a/template-coq/update_plugin.sh +++ b/template-coq/update_plugin.sh @@ -4,7 +4,7 @@ TOCOPY="ast_denoter.ml ast_quoter.ml denoter.ml plugin_core.ml plugin_core.mli r # Test is gen-src is older than src if [[ "gen-src" -ot "src" || ! -f "gen-src/denoter.ml" || ! -f "gen-src/metacoq_template_plugin.cmxs" || - "gen-src/extractable.ml" -nt "gen-src/metacoq_template_plugin.cmxs" ]] + "gen-src/extractable.ml" -nt "gen-src/metacoq_template_plugin.cmxs" || "$1" = "force" ]] then echo "Updating gen-src from src" mkdir -p build @@ -12,9 +12,10 @@ then for x in ${TOCOPY}; do rm -f gen-src/$x; cp src/$x gen-src/$x; done echo "Renaming files to camelCase" (cd gen-src; ./to-lower.sh) - rm -f gen-src/*.d + rm -f gen-src/*.d gen-src/*.cm* # Fix an extraction bug: wrong type annotation on eq_equivalence patch -N -p0 < extraction.patch + patch -N -p0 < specFloat.patch exit 0 else echo "Extracted code is up-to-date" From 6a13d5564d5a6e0090af72de2d385649f6037bc3 Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Sat, 5 Dec 2020 12:02:27 +0100 Subject: [PATCH 39/70] Fix Imports for opam installation --- erasure/theories/Extraction.v | 4 ++-- safechecker/theories/Extraction.v | 5 ++--- template-coq/theories/Extraction.v | 5 ++--- 3 files changed, 6 insertions(+), 8 deletions(-) diff --git a/erasure/theories/Extraction.v b/erasure/theories/Extraction.v index 99f66ef0c..a145b71b6 100644 --- a/erasure/theories/Extraction.v +++ b/erasure/theories/Extraction.v @@ -1,6 +1,6 @@ (* Distributed under the terms of the MIT license. *) -Require Import FSets ExtrOcamlBasic ExtrOcamlString ExtrOcamlZInt - MC_ExtrOCamlInt63 (*b/c nameclash with `comparion` *) ExtrOCamlFloats. +From Coq Require Import FSets ExtrOcamlBasic ExtrOcamlString ExtrOcamlZInt ExtrOCamlFloats. +From MetaCoq.Template Require Import MC_ExtrOCamlInt63 (*b/c nameclash with `comparion` *). (** * Extraction setup for the erasure phase of template-coq. diff --git a/safechecker/theories/Extraction.v b/safechecker/theories/Extraction.v index 8984b445e..a5e51d625 100644 --- a/safechecker/theories/Extraction.v +++ b/safechecker/theories/Extraction.v @@ -1,7 +1,6 @@ (* Distributed under the terms of the MIT license. *) -Require Import OrdersTac ExtrOcamlBasic ExtrOcamlString ExtrOcamlZInt - MC_ExtrOCamlInt63 (*b/c nameclash with `comparion` *) ExtrOCamlFloats. -Require Import MetaCoq.Template.utils. +From Coq Require Import OrdersTac ExtrOcamlBasic ExtrOcamlString ExtrOcamlZInt ExtrOCamlFloats. +From MetaCoq.Template Require Import utils MC_ExtrOCamlInt63 (*b/c nameclash with `comparion` *). From MetaCoq.SafeChecker Require Import PCUICSafeChecker PCUICSafeConversion SafeTemplateChecker. diff --git a/template-coq/theories/Extraction.v b/template-coq/theories/Extraction.v index c5184ef36..b938e219a 100644 --- a/template-coq/theories/Extraction.v +++ b/template-coq/theories/Extraction.v @@ -1,7 +1,6 @@ (* Distributed under the terms of the MIT license. *) -From MetaCoq.Template Require Import utils Ast Reflect Induction. -Require Import FSets ExtrOcamlBasic ExtrOcamlString ExtrOcamlZInt MC_ExtrOCamlInt63 (*b/c nameclash with `comparion` *) - ExtrOCamlFloats. +From MetaCoq.Template Require Import utils Ast Reflect Induction MC_ExtrOCamlInt63 (*b/c nameclash with `comparion` *). +From Coq Require Import FSets ExtrOcamlBasic ExtrOcamlString ExtrOcamlZInt ExtrOCamlFloats. From Coq Require Extraction. (** * Extraction setup for template-coq. From aaf56aaf87e13769d0d40e8b4203b67f15760822 Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Sat, 5 Dec 2020 13:01:15 +0100 Subject: [PATCH 40/70] Fix translations --- translations/param_binary.v | 1 + translations/param_original.v | 1 + 2 files changed, 2 insertions(+) diff --git a/translations/param_binary.v b/translations/param_binary.v index 54228deec..05e5ae322 100644 --- a/translations/param_binary.v +++ b/translations/param_binary.v @@ -141,6 +141,7 @@ Fixpoint tsl_rec1_app (app : list term) (E : tsl_table) (t : term) : term := | tFix _ _ | tCoFix _ _ => todo "tsl" | tVar _ | tEvar _ _ => todo "tsl" | tLambda _ _ _ => tVar "impossible" + | tInt _ | tFloat _ => todo "impossible" end in apply app t1 end. diff --git a/translations/param_original.v b/translations/param_original.v index ead473d68..8a07f3bc1 100644 --- a/translations/param_original.v +++ b/translations/param_original.v @@ -103,6 +103,7 @@ Fixpoint tsl_rec1_app (app : option term) (E : tsl_table) (t : term) : term := | tFix _ _ | tCoFix _ _ => todo "tsl" | tVar _ | tEvar _ _ => todo "tsl" | tLambda _ _ _ => tVar "impossible" + | tInt _ | tFloat _ => todo "impossible" end in match app with Some t' => mkApp t1 (t' {3 := tRel 1} {2 := tRel 0}) | None => t1 end From b60716a92a517ba6940ab29a901406a677c72a16 Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Sat, 5 Dec 2020 13:38:46 +0100 Subject: [PATCH 41/70] Fix configure.sg conditional? --- configure.sh | 3 +-- 1 file changed, 1 insertion(+), 2 deletions(-) diff --git a/configure.sh b/configure.sh index 54be2c123..efe799abe 100755 --- a/configure.sh +++ b/configure.sh @@ -16,8 +16,7 @@ if command -v coqc >/dev/null 2>&1 then COQLIB=`coqc -where` - if [ "$1" == "local" ] - then + if [ "$1" = "local" ]; then echo "Building MetaCoq locally" CHECKER_DEPS="-R ../template-coq/theories MetaCoq.Template -I ../template-coq/build" PCUIC_MLDEPS="-I ../checker/src" From 2f93367365ba37b4b65f18100b1e825055690226 Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Sat, 5 Dec 2020 17:56:51 +0100 Subject: [PATCH 42/70] Fix constr_quoter and add test-suite file for primitives --- template-coq/src/constr_quoter.ml | 4 ++-- test-suite/_CoqProject | 1 + test-suite/primitive.v | 37 +++++++++++++++++++++++++++++++ 3 files changed, 40 insertions(+), 2 deletions(-) create mode 100644 test-suite/primitive.v diff --git a/template-coq/src/constr_quoter.ml b/template-coq/src/constr_quoter.ml index 1fdb41263..423187e43 100644 --- a/template-coq/src/constr_quoter.ml +++ b/template-coq/src/constr_quoter.ml @@ -80,8 +80,8 @@ struct let mkProj kn t = constr_mkApp (tProj, [| kn; t |]) - let mkInt i = constr_mkApp (tInt, [| i |]) - let mkFloat f = constr_mkApp (tFloat, [| f |]) + let mkInt i = i + let mkFloat f = f let quote_option ty = function | Some tm -> constr_mkApp (cSome, [|ty; tm|]) diff --git a/test-suite/_CoqProject b/test-suite/_CoqProject index 86f9eaa69..4163b0a62 100644 --- a/test-suite/_CoqProject +++ b/test-suite/_CoqProject @@ -46,3 +46,4 @@ univ.v vs.v tmVariable.v order_rec.v +primitive.v \ No newline at end of file diff --git a/test-suite/primitive.v b/test-suite/primitive.v new file mode 100644 index 000000000..6a085b9e6 --- /dev/null +++ b/test-suite/primitive.v @@ -0,0 +1,37 @@ +From Coq Require Import String. +From MetaCoq.Template Require Import monad_utils All. +From Coq.Numbers.Cyclic Require Import Int63. + +Local Open Scope string_scope. +Import MonadNotation. + +Definition bigint : Int63.int := 542985047%int63. + +Notation eval_hnf := (tmEval hnf). +Notation eval := (tmEval all). + +MetaCoq Run (eval_hnf bigint >>= + (fun x => tmQuote (x + 1)%int63) >>= + tmMkDefinition "foo"). + +Print foo. + +MetaCoq Run (eval_hnf bigint >>= + (fun x => tmQuote (x + 1)%int63 >>= fun q => + tmUnquoteTyped int q >>= fun unq => + tmPrint unq >>= fun _ => + tmLemma "foo'" (bigint + 1 = unq)%int63 >>= + fun x => tmPrint x)). + +From Coq Require Import Int63 PrimFloat. + +Definition f := (of_int63 bigint / 3)%float. +Eval lazy in f. +MetaCoq Run (tmEval lazy f >>= + (fun x => tmQuote (x + 1)%float) >>= + tmMkDefinition "fplus1"). + +MetaCoq Run (tmUnquoteTyped float (tFloat f) >>= + (fun x : float => tmPrint x >>= + fun _ => tmQuote x >>= tmMkDefinition "somefloat")). + Print somefloat. \ No newline at end of file From 52ee5dec36403fbccda1986dac60fb101804d109 Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Tue, 8 Dec 2020 14:00:09 +0100 Subject: [PATCH 43/70] WIP on primitive types --- pcuic/_CoqProject.in | 1 + pcuic/theories/PCUICAst.v | 6 +- pcuic/theories/PCUICAstUtils.v | 6 +- pcuic/theories/PCUICInduction.v | 3 +- pcuic/theories/PCUICPrimitive.v | 103 +++++++++++++++++++++++++++++++ pcuic/theories/PCUICReflect.v | 33 ---------- pcuic/theories/PCUICToTemplate.v | 10 ++- pcuic/theories/TemplateToPCUIC.v | 4 +- 8 files changed, 119 insertions(+), 47 deletions(-) create mode 100644 pcuic/theories/PCUICPrimitive.v diff --git a/pcuic/_CoqProject.in b/pcuic/_CoqProject.in index 1a946ce6d..38dd47169 100644 --- a/pcuic/_CoqProject.in +++ b/pcuic/_CoqProject.in @@ -2,6 +2,7 @@ theories/PCUICUtils.v theories/PCUICRelations.v +theories/PCUICPrimitive.v theories/PCUICAst.v theories/PCUICSize.v theories/PCUICAstUtils.v diff --git a/pcuic/theories/PCUICAst.v b/pcuic/theories/PCUICAst.v index 56c5da61b..21e587a85 100644 --- a/pcuic/theories/PCUICAst.v +++ b/pcuic/theories/PCUICAst.v @@ -1,6 +1,7 @@ (* Distributed under the terms of the MIT license. *) From MetaCoq.Template Require Export utils Universes BasicAst Environment EnvironmentTyping. +From MetaCoq.PCUIC Require Export PCUICPrimitive. From Equations Require Import Equations. (** * AST of the Polymorphic Cumulative Calculus of Inductive Constructions @@ -36,9 +37,8 @@ Inductive term := | tProj (p : projection) (c : term) | tFix (mfix : mfixpoint term) (idx : nat) | tCoFix (mfix : mfixpoint term) (idx : nat) -(** We use faithful models of primitive types in PCUIC *) -| tInt (z : uint63_model) -| tFloat (f : float64_model). +(** We use faithful models of primitive type values in PCUIC *) +| tPrim (prim : prim_val term). Derive NoConfusion for term. diff --git a/pcuic/theories/PCUICAstUtils.v b/pcuic/theories/PCUICAstUtils.v index 84e714eb5..4d2889a20 100644 --- a/pcuic/theories/PCUICAstUtils.v +++ b/pcuic/theories/PCUICAstUtils.v @@ -11,9 +11,6 @@ Derive Signature for All All2. Definition string_of_aname (b : binder_annot name) := string_of_name b.(binder_name). -Definition string_of_float64_model (f : float64_model) := - "". - Fixpoint string_of_term (t : term) := match t with | tRel n => "Rel(" ^ string_of_nat n ^ ")" @@ -39,8 +36,7 @@ Fixpoint string_of_term (t : term) := ^ string_of_term c ^ ")" | tFix l n => "Fix(" ^ (string_of_list (string_of_def string_of_term) l) ^ "," ^ string_of_nat n ^ ")" | tCoFix l n => "CoFix(" ^ (string_of_list (string_of_def string_of_term) l) ^ "," ^ string_of_nat n ^ ")" - | tInt n => "Int(" ^ string_of_Z (proj1_sig n) ^ ")" - | tFloat f => "Float(" ^ string_of_float64_model f ^ ")" + | tPrim i => "Int(" ^ string_of_prim string_of_term i ^ ")" end. Lemma lookup_env_nil c s : lookup_env [] c = Some s -> False. diff --git a/pcuic/theories/PCUICInduction.v b/pcuic/theories/PCUICInduction.v index d1c90e6e2..b9f097965 100644 --- a/pcuic/theories/PCUICInduction.v +++ b/pcuic/theories/PCUICInduction.v @@ -35,8 +35,7 @@ Lemma term_forall_list_ind : (forall (s : projection) (t : term), P t -> P (tProj s t)) -> (forall (m : mfixpoint term) (n : nat), tFixProp P P m -> P (tFix m n)) -> (forall (m : mfixpoint term) (n : nat), tFixProp P P m -> P (tCoFix m n)) -> - (forall i, P (tInt i)) -> - (forall f, P (tFloat f)) -> + (forall p, P (tPrim p)) -> forall t : term, P t. Proof. intros until t. revert t. diff --git a/pcuic/theories/PCUICPrimitive.v b/pcuic/theories/PCUICPrimitive.v new file mode 100644 index 000000000..9edd16344 --- /dev/null +++ b/pcuic/theories/PCUICPrimitive.v @@ -0,0 +1,103 @@ +(* Distributed under the terms of the MIT license. *) +From MetaCoq.Template Require Export utils Universes BasicAst Reflect + Environment EnvironmentTyping. +From Equations Require Import Equations. +From Coq Require Import ssreflect. + +Variant prim_tag := + | primInt + | primFloat + | primArray. +Derive NoConfusion EqDec for prim_tag. + +(** We don't enforce the type of the array here*) +Record array_model (term : Type) := + { array_instance : Instance.t; + array_type : term; + array_default : term; + array_value : list term }. +Derive NoConfusion for array_model. +Instance array_model_eqdec {term} (e : EqDec term) : EqDec (array_model term). +Proof. eqdec_proof. Qed. + +Inductive prim_model (term : Type) : prim_tag -> Type := +| primIntModel (i : uint63_model) : prim_model term primInt +| primFloatModel (f : float64_model) : prim_model term primFloat. +(* | primArrayModel (a : array_model term) : prim_model term primArray. *) +Arguments primIntModel {term}. +Arguments primFloatModel {term}. +Arguments primArrayModel {term}. + +Derive Signature NoConfusion for prim_model. + +Definition prim_model_of term (p : prim_tag) : Type := + match p with + | primInt => uint63_model + | primFloat => float64_model + | primArray => array_model term + end. + +Definition prim_val term := ∑ t : prim_tag, prim_model term t. +Definition prim_val_tag {term} (s : prim_val term) := s.π1. +Definition prim_val_model {term} (s : prim_val term) : prim_model term (prim_val_tag s) := s.π2. + +Definition prim_model_val {term} (p : prim_val term) : prim_model_of term (prim_val_tag p) := + match prim_val_model p in prim_model _ t return prim_model_of term t with + | primIntModel i => i + | primFloatModel f => f + | primArrayModel a => a + end. + +Lemma exist_irrel_eq {A} (P : A -> bool) (x y : sig P) : proj1_sig x = proj1_sig y -> x = y. +Proof. + destruct x as [x p], y as [y q]; simpl; intros ->. + now destruct (uip p q). +Qed. + +Instance reflect_eq_Z : ReflectEq Z := EqDec_ReflectEq _. + +Local Obligation Tactic := idtac. +#[program] +Instance reflect_eq_uint63 : ReflectEq uint63_model := + { eqb x y := eqb (proj1_sig x) (proj1_sig y) }. +Next Obligation. + cbn -[eqb]. + intros x y. + elim: eqb_spec. constructor. + now apply exist_irrel_eq. + intros neq; constructor => H'; apply neq; now subst x. +Qed. + +Instance reflect_eq_spec_float : ReflectEq SpecFloat.spec_float := EqDec_ReflectEq _. + +#[program] +Instance reflect_eq_float64 : ReflectEq float64_model := + { eqb x y := eqb (proj1_sig x) (proj1_sig y) }. +Next Obligation. + cbn -[eqb]. + intros x y. + elim: eqb_spec. constructor. + now apply exist_irrel_eq. + intros neq; constructor => H'; apply neq; now subst x. +Qed. + +(** Propositional UIP is needed below *) +Set Equations With UIP. + +Instance prim_model_eqdec {term} (e : EqDec term) : forall p : prim_tag, EqDec (prim_model term p). +Proof. eqdec_proof. Qed. + +Instance prim_tag_model_eqdec {term} (e : EqDec term) : EqDec (prim_val term). +Proof. eqdec_proof. Defined. + +(** Printing *) + +Definition string_of_float64_model (f : float64_model) := + "<>". + +Definition string_of_prim {term} (soft : term -> string) (p : prim_val term) : string := + match p.π2 return string with + | primIntModel f => "(int: " ^ string_of_Z (proj1_sig f) ^ ")" + | primFloatModel f => "(float: " ^ string_of_float64_model f ^ ")" + | primArrayModel a => "(array:" ^ ")" + end. diff --git a/pcuic/theories/PCUICReflect.v b/pcuic/theories/PCUICReflect.v index 3d73d76e6..b92ea01e5 100644 --- a/pcuic/theories/PCUICReflect.v +++ b/pcuic/theories/PCUICReflect.v @@ -20,39 +20,6 @@ Local Ltac fcase c := let e := fresh "e" in case c ; intro e ; [ subst ; try (left ; reflexivity) | finish ]. -Instance reflect_eq_Z : ReflectEq Z := EqDec_ReflectEq _. - -Lemma exist_irrel_eq {A} (P : A -> bool) (x y : sig P) : proj1_sig x = proj1_sig y -> x = y. -Proof. - destruct x as [x p], y as [y q]; simpl; intros ->. - now destruct (uip p q). -Qed. - -Local Obligation Tactic := idtac. -#[program] -Instance reflect_eq_uint63 : ReflectEq uint63_model := - { eqb x y := eqb (proj1_sig x) (proj1_sig y) }. -Next Obligation. - cbn -[eqb]. - intros x y. - elim: eqb_spec. constructor. - now apply exist_irrel_eq. - intros neq; constructor => H'; apply neq; now subst x. -Qed. - -Instance reflect_eq_spec_float : ReflectEq SpecFloat.spec_float := EqDec_ReflectEq _. - -#[program] -Instance reflect_eq_float64 : ReflectEq float64_model := - { eqb x y := eqb (proj1_sig x) (proj1_sig y) }. -Next Obligation. - cbn -[eqb]. - intros x y. - elim: eqb_spec. constructor. - now apply exist_irrel_eq. - intros neq; constructor => H'; apply neq; now subst x. -Qed. - Local Ltac term_dec_tac term_dec := repeat match goal with | t : term, u : term |- _ => fcase (term_dec t u) diff --git a/pcuic/theories/PCUICToTemplate.v b/pcuic/theories/PCUICToTemplate.v index 5512e1950..fefc5a675 100644 --- a/pcuic/theories/PCUICToTemplate.v +++ b/pcuic/theories/PCUICToTemplate.v @@ -11,6 +11,13 @@ Definition uint63_from_model (i : uint63_model) : Int63.int := Definition float64_from_model (f : float64_model) : PrimFloat.float := FloatOps.SF2Prim (proj1_sig f). +Definition trans_prim {term} (t : prim_val term) : Ast.term := + match t.π2 with + | primIntModel i => Ast.tInt (uint63_from_model i) + | primFloatModel f => Ast.tFloat (float64_from_model f) + | primArrayModel a => Ast.tRel 0 (* todo *) + end. + Fixpoint trans (t : PCUICAst.term) : Ast.term := match t with | PCUICAst.tRel n => tRel n @@ -34,8 +41,7 @@ Fixpoint trans (t : PCUICAst.term) : Ast.term := | PCUICAst.tCoFix mfix idx => let mfix' := List.map (map_def trans trans) mfix in tCoFix mfix' idx - | PCUICAst.tInt i => tInt (uint63_from_model i) - | PCUICAst.tFloat f => tFloat (float64_from_model f) + | PCUICAst.tPrim i => trans_prim i end. Definition trans_decl (d : PCUICAst.context_decl) := diff --git a/pcuic/theories/TemplateToPCUIC.v b/pcuic/theories/TemplateToPCUIC.v index 2846a4223..a707b82c4 100644 --- a/pcuic/theories/TemplateToPCUIC.v +++ b/pcuic/theories/TemplateToPCUIC.v @@ -40,8 +40,8 @@ Fixpoint trans (t : Ast.term) : term := | Ast.tCoFix mfix idx => let mfix' := List.map (map_def trans trans) mfix in tCoFix mfix' idx - | Ast.tInt n => tInt (uint63_to_model n) - | Ast.tFloat n => tFloat (float64_to_model n) + | Ast.tInt n => tPrim (primInt; primIntModel (uint63_to_model n)) + | Ast.tFloat n => tPrim (primFloat; primFloatModel (float64_to_model n)) end. Definition trans_decl (d : Ast.context_decl) := From 0649aedee96c78607623036af8deae3df06a89c8 Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Tue, 8 Dec 2020 16:46:40 +0100 Subject: [PATCH 44/70] Slight refinement: in PCUIC, use a common tagged sum for all primitive types --- .gitignore | 2 ++ erasure/_PluginProject.in | 2 ++ erasure/src/metacoq_erasure_plugin.mlpack | 1 + erasure/theories/EAst.v | 4 +-- erasure/theories/EAstUtils.v | 4 +-- erasure/theories/EInduction.v | 3 +- erasure/theories/ELiftSubst.v | 3 +- erasure/theories/EOptimizePropDiscr.v | 3 +- erasure/theories/EPretty.v | 7 ++--- erasure/theories/EReflect.v | 5 ++- erasure/theories/ErasureFunction.v | 10 ++++-- pcuic/theories/PCUICAst.v | 2 ++ pcuic/theories/PCUICCanonicity.v | 3 +- pcuic/theories/PCUICClosed.v | 3 +- pcuic/theories/PCUICEquality.v | 9 ++---- pcuic/theories/PCUICInduction.v | 8 ++--- pcuic/theories/PCUICInversion.v | 13 ++------ pcuic/theories/PCUICLiftSubst.v | 5 +-- pcuic/theories/PCUICNameless.v | 5 ++- pcuic/theories/PCUICNormal.v | 16 ++-------- pcuic/theories/PCUICParallelReduction.v | 6 ++-- .../PCUICParallelReductionConfluence.v | 24 ++------------ pcuic/theories/PCUICPretty.v | 5 +-- pcuic/theories/PCUICPrimitive.v | 22 +++++++------ pcuic/theories/PCUICPrincipality.v | 3 +- pcuic/theories/PCUICReflect.v | 3 +- pcuic/theories/PCUICToTemplate.v | 3 +- pcuic/theories/PCUICToTemplateCorrectness.v | 6 ++++ pcuic/theories/PCUICUnivSubst.v | 2 +- safechecker/_PluginProject.in | 2 ++ .../src/metacoq_safechecker_plugin.mlpack | 1 + safechecker/theories/Extraction.v | 1 + safechecker/theories/PCUICSafeConversion.v | 31 +++---------------- safechecker/theories/PCUICSafeReduce.v | 10 ++---- safechecker/theories/PCUICSafeRetyping.v | 6 ++-- safechecker/theories/PCUICTypeChecker.v | 2 +- 36 files changed, 86 insertions(+), 149 deletions(-) diff --git a/.gitignore b/.gitignore index 7f8e6dcb8..67dab47bd 100644 --- a/.gitignore +++ b/.gitignore @@ -416,3 +416,5 @@ erasure/src/pCUICErrors.ml erasure/src/pCUICErrors.mli erasure/src/pCUICTypeChecker.ml erasure/src/pCUICTypeChecker.mli +erasure/src/pCUICPrimitive.ml +erasure/src/pCUICPrimitive.mli diff --git a/erasure/_PluginProject.in b/erasure/_PluginProject.in index 6edbd7d86..f46d585c2 100644 --- a/erasure/_PluginProject.in +++ b/erasure/_PluginProject.in @@ -31,6 +31,8 @@ src/kernames.ml # src/typing0.ml # From PCUIC +src/pCUICPrimitive.mli +src/pCUICPrimitive.ml src/pCUICAst.ml src/pCUICAst.mli src/pCUICAstUtils.ml diff --git a/erasure/src/metacoq_erasure_plugin.mlpack b/erasure/src/metacoq_erasure_plugin.mlpack index ca6e73fdf..986078d2b 100644 --- a/erasure/src/metacoq_erasure_plugin.mlpack +++ b/erasure/src/metacoq_erasure_plugin.mlpack @@ -14,6 +14,7 @@ Classes0 Logic1 Relation Relation_Properties +PCUICPrimitive PCUICAst PCUICAstUtils PCUICUnivSubst diff --git a/erasure/theories/EAst.v b/erasure/theories/EAst.v index e90eacb4e..164fb08c4 100644 --- a/erasure/theories/EAst.v +++ b/erasure/theories/EAst.v @@ -1,5 +1,6 @@ (* Distributed under the terms of the MIT license. *) From MetaCoq.Template Require Export utils BasicAst Universes. +From MetaCoq.PCUIC Require Import PCUICPrimitive. (** * Extracted terms These are the terms produced by extraction: compared to kernel terms, @@ -37,8 +38,7 @@ Inductive term : Set := | tProj : projection -> term -> term | tFix : mfixpoint term -> nat -> term | tCoFix : mfixpoint term -> nat -> term -| tInt : uint63_model -> term -| tFloat : float64_model -> term. +| tPrim : prim_val term -> term. Fixpoint mkApps t us := match us with diff --git a/erasure/theories/EAstUtils.v b/erasure/theories/EAstUtils.v index d680a533a..d3e5f2acf 100644 --- a/erasure/theories/EAstUtils.v +++ b/erasure/theories/EAstUtils.v @@ -1,6 +1,7 @@ (* Distributed under the terms of the MIT license. *) From MetaCoq.Template Require Import utils Kernames. From MetaCoq.Erasure Require Import EAst. +From MetaCoq.PCUIC Require PCUICPrimitive. Require Import ssreflect ssrbool. @@ -267,8 +268,7 @@ Fixpoint string_of_term (t : term) : string := ^ string_of_term c ^ ")" | tFix l n => "Fix(" ^ (string_of_list (string_of_def string_of_term) l) ^ "," ^ string_of_nat n ^ ")" | tCoFix l n => "CoFix(" ^ (string_of_list (string_of_def string_of_term) l) ^ "," ^ string_of_nat n ^ ")" - | tInt i => "Int(" ^ string_of_Z (proj1_sig i) ^ ")" - | tFloat f => "Float(" ^ "" ^ ")" + | tPrim p => "Prim(" ^ PCUICPrimitive.string_of_prim string_of_term p ^ ")" end. (** Compute all the global environment dependencies of the term *) diff --git a/erasure/theories/EInduction.v b/erasure/theories/EInduction.v index 1d4789fe8..1312dbdf1 100644 --- a/erasure/theories/EInduction.v +++ b/erasure/theories/EInduction.v @@ -28,8 +28,7 @@ Lemma term_forall_list_ind : (forall (s : projection) (t : term), P t -> P (tProj s t)) -> (forall (m : mfixpoint term) (n : nat), All (fun x => P (dbody x)) m -> P (tFix m n)) -> (forall (m : mfixpoint term) (n : nat), All (fun x => P (dbody x)) m -> P (tCoFix m n)) -> - (forall i, P (tInt i)) -> - (forall f, P (tFloat f)) -> + (forall p, P (tPrim p)) -> forall t : term, P t. Proof. intros until t. revert t. diff --git a/erasure/theories/ELiftSubst.v b/erasure/theories/ELiftSubst.v index cedeace38..14147e571 100644 --- a/erasure/theories/ELiftSubst.v +++ b/erasure/theories/ELiftSubst.v @@ -32,8 +32,7 @@ Fixpoint lift n k t : term := | tVar _ => t | tConst _ => t | tConstruct _ _ => t - | tInt _ => t - | tFloat _ => t + | tPrim _ => t end. Notation lift0 n := (lift n 0). diff --git a/erasure/theories/EOptimizePropDiscr.v b/erasure/theories/EOptimizePropDiscr.v index 310dc0535..d995ae094 100644 --- a/erasure/theories/EOptimizePropDiscr.v +++ b/erasure/theories/EOptimizePropDiscr.v @@ -66,8 +66,7 @@ Section optimize. | tVar _ => t | tConst _ => t | tConstruct _ _ => t - | tInt _ => t - | tFloat _ => t + | tPrim _ => t end. Lemma optimize_mkApps f l : optimize (mkApps f l) = mkApps (optimize f) (map optimize l). diff --git a/erasure/theories/EPretty.v b/erasure/theories/EPretty.v index 4ae00c2f5..e14febe0f 100644 --- a/erasure/theories/EPretty.v +++ b/erasure/theories/EPretty.v @@ -2,6 +2,7 @@ From Coq Require Import Program. From MetaCoq.Template Require Import utils. From MetaCoq.Erasure Require Import EAst EAstUtils ETyping. +From MetaCoq.PCUIC Require Import PCUICPrimitive. (** * Pretty printing *) @@ -159,10 +160,8 @@ Section print_term. | tCoFix l n => parens top ("let cofix " ^ print_defs print_term Γ l ^ nl ^ " in " ^ List.nth_default (string_of_nat n) (map (string_of_name ∘ dname) l) n) - | tInt i => - parens top (string_of_uint63_model i) - | tFloat f => - parens top (string_of_float64_model f) + | tPrim p => + parens top (string_of_prim (print_term Γ false false) p) end. End print_term. diff --git a/erasure/theories/EReflect.v b/erasure/theories/EReflect.v index d2a139bb2..e0faac76e 100644 --- a/erasure/theories/EReflect.v +++ b/erasure/theories/EReflect.v @@ -1,6 +1,6 @@ From MetaCoq.Template Require Import Reflect. From MetaCoq.Erasure Require Import EAst EInduction. -From MetaCoq.PCUIC Require Import PCUICReflect. +From MetaCoq.PCUIC Require Import PCUICReflect PCUICPrimitive. From Equations Require Import Equations. Local Ltac finish := @@ -23,8 +23,7 @@ Local Ltac term_dec_tac term_dec := | i : kername, i' : kername |- _ => fcase (kername_eq_dec i i') | i : string, i' : kername |- _ => fcase (string_dec i i') | n : name, n' : name |- _ => fcase (eq_dec n n') - | i : uint63_model, i' : uint63_model |- _ => fcase (eq_dec i i') - | i : float64_model, i' : float64_model |- _ => fcase (eq_dec i i') + | i : prim_val _, i' : prim_val _ |- _ => fcase (eq_dec i i') | i : inductive, i' : inductive |- _ => fcase (eq_dec i i') | x : inductive * nat, y : inductive * nat |- _ => fcase (eq_dec x y) diff --git a/erasure/theories/ErasureFunction.v b/erasure/theories/ErasureFunction.v index 449ad6a01..006ec8c63 100644 --- a/erasure/theories/ErasureFunction.v +++ b/erasure/theories/ErasureFunction.v @@ -1,7 +1,7 @@ (* Distributed under the terms of the MIT license. *) From Coq Require Import Program. From MetaCoq.Template Require Import config utils Kernames. -From MetaCoq.PCUIC Require Import PCUICAst PCUICAstUtils +From MetaCoq.PCUIC Require Import PCUICAst PCUICAstUtils PCUICPrimitive PCUICReflect PCUICWeakeningEnv PCUICTyping PCUICInversion PCUICGeneration PCUICConfluence PCUICConversion @@ -366,6 +366,11 @@ Section Erase. End EraseMfix. + Equations erase_prim (ep : prim_val term) : PCUICPrimitive.prim_val E.term := + erase_prim (_; primIntModel i) := (_; primIntModel i); + erase_prim (_; primFloatModel f) := (_; primFloatModel f). + + Equations? (noeqns noind) erase (Γ : context) (t : term) (Ht : welltyped Σ Γ t) : E.term by struct t := erase Γ t Ht with (is_erasable Σ HΣ Γ t Ht) := @@ -404,8 +409,7 @@ Section Erase. erase Γ (tCoFix mfix n) Ht _ := let mfix' := erase_mfix (erase) Γ mfix _ in E.tCoFix mfix' n; - erase Γ (tInt i) Ht _ := E.tInt i; - erase Γ (tFloat f) Ht _ := E.tFloat f + erase Γ (tPrim p) Ht _ := E.tPrim (erase_prim p) }. Proof. all:try clear b'; try clear f'; try clear brs'; try clear erase. diff --git a/pcuic/theories/PCUICAst.v b/pcuic/theories/PCUICAst.v index 21e587a85..789a49970 100644 --- a/pcuic/theories/PCUICAst.v +++ b/pcuic/theories/PCUICAst.v @@ -42,6 +42,8 @@ Inductive term := Derive NoConfusion for term. +Notation prim_val := (prim_val term). + Fixpoint mkApps t us := match us with | nil => t diff --git a/pcuic/theories/PCUICCanonicity.v b/pcuic/theories/PCUICCanonicity.v index df27bc024..ff9358915 100644 --- a/pcuic/theories/PCUICCanonicity.v +++ b/pcuic/theories/PCUICCanonicity.v @@ -1065,8 +1065,7 @@ Section WeakNormalization. - exfalso; eapply invert_ind_ind; eauto. - exfalso; eapply invert_fix_ind; eauto. - now rewrite head_mkApps /head /=. - - now eapply inversion_Int in typed. - - now eapply inversion_Float in typed. + - now eapply inversion_Prim in typed. Qed. Lemma wh_neutral_empty t ty : axiom_free Σ -> diff --git a/pcuic/theories/PCUICClosed.v b/pcuic/theories/PCUICClosed.v index 979270033..658b9ed1c 100644 --- a/pcuic/theories/PCUICClosed.v +++ b/pcuic/theories/PCUICClosed.v @@ -1212,8 +1212,7 @@ Lemma term_closedn_list_ind : (forall k (s : projection) (t : term), P k t -> P k (tProj s t)) -> (forall k (m : mfixpoint term) (n : nat), tFixProp (P k) (P (#|fix_context m| + k)) m -> P k (tFix m n)) -> (forall k (m : mfixpoint term) (n : nat), tFixProp (P k) (P (#|fix_context m| + k)) m -> P k (tCoFix m n)) -> - (forall k i, P k (tInt i)) -> - (forall k f, P k (tFloat f)) -> + (forall k p, P k (tPrim p)) -> forall k (t : term), closedn k t -> P k t. Proof. intros until t. revert k t. diff --git a/pcuic/theories/PCUICEquality.v b/pcuic/theories/PCUICEquality.v index 5d953c008..684d9b0da 100644 --- a/pcuic/theories/PCUICEquality.v +++ b/pcuic/theories/PCUICEquality.v @@ -203,8 +203,7 @@ Inductive eq_term_upto_univ_napp Σ (Re Rle : Universe.t -> Universe.t -> Prop) ) mfix mfix' -> eq_term_upto_univ_napp Σ Re Rle napp (tCoFix mfix idx) (tCoFix mfix' idx) -| eq_Int i : eq_term_upto_univ_napp Σ Re Rle napp (tInt i) (tInt i) -| eq_Float f : eq_term_upto_univ_napp Σ Re Rle napp (tFloat f) (tFloat f). +| eq_Prim i : eq_term_upto_univ_napp Σ Re Rle napp (tPrim i) (tPrim i). Notation eq_term_upto_univ Σ Re Rle := (eq_term_upto_univ_napp Σ Re Rle 0). @@ -893,8 +892,7 @@ Fixpoint eqb_term_upto_univ_napp Σ (equ lequ : Universe.t -> Universe.t -> bool eqb_annot x.(dname) y.(dname) ) mfix mfix' - | tInt i, tInt i' => eqb i i' - | tFloat f, tFloat f' => eqb f f' + | tPrim p, tPrim p' => eqb p p' | _, _ => false end. @@ -1037,7 +1035,6 @@ Proof. intro. rtoProp. split; tas. split;tas. split; eapply X0; tea. now apply eqb_annot_spec. - eqspec; [|discriminate]. constructor. - - eqspec; [|discriminate]. constructor. Qed. Lemma reflect_eq_term_upto_univ Σ equ lequ (Re Rle : Universe.t -> Universe.t -> Prop) napp : @@ -1231,7 +1228,6 @@ Proof. -- constructor. intro bot. apply f. inversion bot. subst. inversion X0. subst. apply X2. - cbn - [eqb]. eqspecs. do 2 constructor. - - cbn - [eqb]. eqspecs. do 2 constructor. Qed. Lemma compare_global_instance_refl : @@ -1301,7 +1297,6 @@ Proof. rewrite -> e1 by assumption. rewrite -> e2 by assumption. rewrite eqb_annot_refl; assumption. - apply eq_dec_to_bool_refl. - - apply eq_dec_to_bool_refl. Qed. (** ** Behavior on mkApps and it_mkLambda_or_LetIn ** *) diff --git a/pcuic/theories/PCUICInduction.v b/pcuic/theories/PCUICInduction.v index b9f097965..22194a6b9 100644 --- a/pcuic/theories/PCUICInduction.v +++ b/pcuic/theories/PCUICInduction.v @@ -12,6 +12,7 @@ Set Asymmetric Patterns. Allows to get the right induction principle on lists of terms appearing in the term syntax (in evar, applications, branches of cases and (co-)fixpoints. *) +Notation prim_ind P p := (P (tPrim p)). (** Custom induction principle on syntax, dealing with the various lists appearing in terms. *) @@ -35,7 +36,7 @@ Lemma term_forall_list_ind : (forall (s : projection) (t : term), P t -> P (tProj s t)) -> (forall (m : mfixpoint term) (n : nat), tFixProp P P m -> P (tFix m n)) -> (forall (m : mfixpoint term) (n : nat), tFixProp P P m -> P (tCoFix m n)) -> - (forall p, P (tPrim p)) -> + (forall p, prim_ind P p) -> forall t : term, P t. Proof. intros until t. revert t. @@ -232,12 +233,11 @@ Lemma term_forall_mkApps_ind : (forall (s : projection) (t : term), P t -> P (tProj s t)) -> (forall (m : mfixpoint term) (n : nat), tFixProp P P m -> P (tFix m n)) -> (forall (m : mfixpoint term) (n : nat), tFixProp P P m -> P (tCoFix m n)) -> - (forall i, P (tInt i)) -> - (forall f, P (tFloat f)) -> + (forall i, prim_ind P i) -> forall t : term, P t. Proof. intros until t. - rename X14 into Pint. rename X15 into Pfloat. + rename X14 into Pprim. assert (Acc (MR lt size) t) by eapply measure_wf, Wf_nat.lt_wf. induction H. rename X14 into auxt. clear H. rename x into t. move auxt at top. diff --git a/pcuic/theories/PCUICInversion.v b/pcuic/theories/PCUICInversion.v index 04565ada9..8044a4e00 100644 --- a/pcuic/theories/PCUICInversion.v +++ b/pcuic/theories/PCUICInversion.v @@ -239,17 +239,10 @@ Section Inversion. intros Γ mfix idx T h. invtac h. Qed. - (** At this stage we don't typecheck primitive types *) - Lemma inversion_Int : + (** At this stage we don't typecheck primitive values *) + Lemma inversion_Prim : forall {Γ i T}, - Σ ;;; Γ |- tInt i : T -> False. - Proof. - intros Γ i T h. now depind h. - Qed. - - Lemma inversion_Float : - forall {Γ f T}, - Σ ;;; Γ |- tFloat f : T -> False. + Σ ;;; Γ |- tPrim i : T -> False. Proof. intros Γ i T h. now depind h. Qed. diff --git a/pcuic/theories/PCUICLiftSubst.v b/pcuic/theories/PCUICLiftSubst.v index 3ad96ba01..bae8a0770 100644 --- a/pcuic/theories/PCUICLiftSubst.v +++ b/pcuic/theories/PCUICLiftSubst.v @@ -1793,6 +1793,7 @@ Hint Rewrite @subst_inst : sigma. Hint Rewrite shiftk_shift_l shiftk_shift : sigma. (* Hint Rewrite Upn_eq : sigma. *) +(** Can't move to PCUICInduction because of fix_context definition *) Lemma term_forall_ctx_list_ind : forall P : context -> term -> Type, (forall Γ (n : nat), P Γ (tRel n)) -> @@ -1813,8 +1814,7 @@ Lemma term_forall_ctx_list_ind : (forall Γ (s : projection) (t : term), P Γ t -> P Γ (tProj s t)) -> (forall Γ (m : mfixpoint term) (n : nat), tFixProp (P Γ) (P (Γ ,,, fix_context m)) m -> P Γ (tFix m n)) -> (forall Γ (m : mfixpoint term) (n : nat), tFixProp (P Γ) (P (Γ ,,, fix_context m)) m -> P Γ (tCoFix m n)) -> - (forall Γ i, P Γ (tInt i)) -> - (forall Γ f, P Γ (tFloat f)) -> + (forall Γ p, P Γ (tPrim p)) -> forall Γ (t : term), P Γ t. Proof. intros. revert Γ t0. @@ -1843,6 +1843,7 @@ Proof. split. apply auxt. apply auxt. apply auxm. Defined. + Fixpoint subst_app (t : term) (us : list term) : term := match t, us with | tLambda _ A t, u :: us => subst_app (t {0 := u}) us diff --git a/pcuic/theories/PCUICNameless.v b/pcuic/theories/PCUICNameless.v index e4df6614c..2a0d407dc 100644 --- a/pcuic/theories/PCUICNameless.v +++ b/pcuic/theories/PCUICNameless.v @@ -47,7 +47,7 @@ Fixpoint nameless (t : term) : bool := | tCoFix mfix idx => forallb (fun d => banon d.(dname)) mfix && forallb (test_def nameless nameless) mfix - | tInt _ | tFloat _ => true + | tPrim _ => true end. Definition anonymize (b : binder_annot name) : binder_annot name := @@ -77,8 +77,7 @@ Fixpoint nl (t : term) : term := | tProj p c => tProj p (nl c) | tFix mfix idx => tFix (map (map_def_anon nl nl) mfix) idx | tCoFix mfix idx => tCoFix (map (map_def_anon nl nl) mfix) idx - | tInt n => tInt n - | tFloat f => tFloat f + | tPrim p => tPrim p end. Definition map_decl_anon f (d : context_decl) := {| diff --git a/pcuic/theories/PCUICNormal.v b/pcuic/theories/PCUICNormal.v index bec0519be..679a65f37 100644 --- a/pcuic/theories/PCUICNormal.v +++ b/pcuic/theories/PCUICNormal.v @@ -52,8 +52,7 @@ Section Normal. end -> whnf Γ (mkApps (tFix mfix idx) v) | whnf_cofixapp mfix idx v : whnf Γ (mkApps (tCoFix mfix idx) v) - | whnf_int i : whnf Γ (tInt i) - | whnf_float f : whnf Γ (tFloat f) + | whnf_prim p : whnf Γ (tPrim p) with whne (Γ : context) : term -> Type := | whne_rel i : @@ -253,8 +252,6 @@ Proof. apply mkApps_eq_inj in eq as (<-&<-); auto. - destruct l using MCList.rev_ind; [|now rewrite <- mkApps_nested in eq]. cbn in *; subst; auto. - - destruct l using MCList.rev_ind; [|now rewrite <- mkApps_nested in eq]. - cbn in *; subst; auto. Qed. Lemma whnf_fixapp' {flags} Σ Γ mfix idx narg body v : @@ -391,11 +388,6 @@ Proof with eauto using sq with pcuic. eapply whne_mkApps_inv in w as []... -- depelim w. help. -- destruct s0 as [? [? [? [? [? [? ?]]]]]]. congruence. - * destruct v as [ | ? v]... - right. intros [w]. depelim w. depelim w. all:help. clear IHt. - eapply whne_mkApps_inv in w as []... - -- depelim w. help. - -- destruct s0 as [? [? [? [? [? [? ?]]]]]]. congruence. + right. intros [w]. eapply n. constructor. now eapply whnf_mkApps_inv. - destruct (IHt Γ) as [_ []]. + left. destruct s as [w]. constructor. now eapply whne_mkApps. @@ -937,7 +929,6 @@ Proof. now inv e. - eapply red1_mkApps_tCoFix_inv in r as [[(?&->&?)|(?&->&?)]|(?&->&?)]; eauto. - depelim r. solve_discr. - - depelim r; solve_discr. Qed. Lemma whnf_pres Σ Γ t t' : @@ -1002,8 +993,7 @@ Inductive whnf_red Σ Γ : term -> term -> Type := red Σ (Γ,,, fix_context mfix) (dbody d) (dbody d')) mfix mfix' -> whnf_red Σ Γ (tCoFix mfix idx) (tCoFix mfix' idx) -| whnf_red_tInt i : whnf_red Σ Γ (tInt i) (tInt i) -| whnf_red_tFloat f : whnf_red Σ Γ (tFloat f) (tFloat f). +| whnf_red_tPrim i : whnf_red Σ Γ (tPrim i) (tPrim i). Derive Signature for whnf_red. @@ -1290,7 +1280,6 @@ Proof. intros ? ? (?&[= -> -> ->]). auto. - depelim r; solve_discr. - - depelim r; solve_discr. Qed. Lemma whnf_red_inv Σ Γ t t' : @@ -1381,7 +1370,6 @@ Proof. depelim e. apply whnf_cofixapp. - depelim eq; auto. - - depelim eq; auto. Qed. Lemma whnf_eq_term {cf:checker_flags} f Σ φ Γ t t' : diff --git a/pcuic/theories/PCUICParallelReduction.v b/pcuic/theories/PCUICParallelReduction.v index 518578733..db1043884 100644 --- a/pcuic/theories/PCUICParallelReduction.v +++ b/pcuic/theories/PCUICParallelReduction.v @@ -96,8 +96,7 @@ Lemma term_forall_ctx_list_ind : (forall Γ (m : mfixpoint term) (n : nat), All_local_env (on_local_decl (fun Γ' t => P (Γ ,,, Γ') t)) (fix_context m) -> tFixProp (P Γ) (P (Γ ,,, fix_context m)) m -> P Γ (tCoFix m n)) -> - (forall Γ i, P Γ (tInt i)) -> - (forall Γ f, P Γ (tFloat f)) -> + (forall Γ p, P Γ (tPrim p)) -> forall Γ (t : term), P Γ t. Proof. intros. @@ -389,8 +388,7 @@ Section ParallelReduction. | tSort _ | tInd _ _ | tConstruct _ _ _ - | tInt _ - | tFloat _ => true + | tPrim _ => true | _ => false end. diff --git a/pcuic/theories/PCUICParallelReductionConfluence.v b/pcuic/theories/PCUICParallelReductionConfluence.v index 2f34692da..f12427caa 100644 --- a/pcuic/theories/PCUICParallelReductionConfluence.v +++ b/pcuic/theories/PCUICParallelReductionConfluence.v @@ -244,8 +244,7 @@ Lemma term_ind_size_app : tFixProp P P m -> P (tFix m n)) -> (forall (m : mfixpoint term) (n : nat), tFixProp (P) P m -> P (tCoFix m n)) -> - (forall i, P (tInt i)) -> - (forall f, P (tFloat f)) -> + (forall p, P (tPrim p)) -> forall (t : term), P t. Proof. intros. @@ -338,32 +337,13 @@ Ltac finish_discr := | [ H : pred_atom (mkApps _ _) |- _ ] => apply pred_atom_mkApps in H; intuition subst end. -Definition application_atom t := - match t with - | tVar _ - | tSort _ - | tInd _ _ - | tConstruct _ _ _ - | tLambda _ _ _ => true - | _ => false - end. - -Lemma application_atom_mkApps {t l} : application_atom (mkApps t l) -> application_atom t /\ l = []. -Proof. - induction l in t |- *; simpl; auto. - intros. destruct (IHl _ H). discriminate. -Qed. - Ltac solve_discr ::= (try (progress (prepare_discr; finish_discr; cbn [mkApps] in * ))); (try (match goal with - | [ H : is_true (application_atom _) |- _ ] => discriminate | [ H : is_true (atom _) |- _ ] => discriminate | [ H : is_true (atom (mkApps _ _)) |- _ ] => destruct (atom_mkApps H); subst; try discriminate | [ H : is_true (pred_atom _) |- _ ] => discriminate | [ H : is_true (pred_atom (mkApps _ _)) |- _ ] => destruct (pred_atom_mkApps H); subst; try discriminate - | [ H : is_true (application_atom (mkApps _ _)) |- _ ] => - destruct (application_atom_mkApps H); subst; try discriminate end)). Lemma is_constructor_app_ge n l l' : is_constructor n l -> is_constructor n (l ++ l'). @@ -1522,7 +1502,7 @@ Section Rho. rename r (rho Γ t) = rho Δ (rename r t). Proof. revert t Γ Δ r. - refine (term_ind_size_app _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _); + refine (term_ind_size_app _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _); intros; try subst Γ; try rename Γ0 into Γ(* ; rename_all_hyps *). all:auto 2. diff --git a/pcuic/theories/PCUICPretty.v b/pcuic/theories/PCUICPretty.v index df6dc897f..408b3f8ab 100644 --- a/pcuic/theories/PCUICPretty.v +++ b/pcuic/theories/PCUICPretty.v @@ -190,10 +190,7 @@ Section print_term. | tCoFix l n => parens top ("let cofix " ^ print_defs print_term Γ l ^ nl ^ " in " ^ List.nth_default (string_of_nat n) (map (string_of_aname ∘ dname) l) n) - | tInt i => - parens top (string_of_uint63_model i) - | tFloat f => - parens top (string_of_float64_model f) + | tPrim i => parens top (string_of_prim (print_term Γ true false) i) end. End print_term. diff --git a/pcuic/theories/PCUICPrimitive.v b/pcuic/theories/PCUICPrimitive.v index 9edd16344..92d60ada7 100644 --- a/pcuic/theories/PCUICPrimitive.v +++ b/pcuic/theories/PCUICPrimitive.v @@ -1,13 +1,13 @@ (* Distributed under the terms of the MIT license. *) -From MetaCoq.Template Require Export utils Universes BasicAst Reflect +From MetaCoq.Template Require Import utils Universes BasicAst Reflect Environment EnvironmentTyping. From Equations Require Import Equations. From Coq Require Import ssreflect. Variant prim_tag := | primInt - | primFloat - | primArray. + | primFloat. + (* | primArray. *) Derive NoConfusion EqDec for prim_tag. (** We don't enforce the type of the array here*) @@ -26,15 +26,15 @@ Inductive prim_model (term : Type) : prim_tag -> Type := (* | primArrayModel (a : array_model term) : prim_model term primArray. *) Arguments primIntModel {term}. Arguments primFloatModel {term}. -Arguments primArrayModel {term}. +(* Arguments primArrayModel {term}. *) Derive Signature NoConfusion for prim_model. -Definition prim_model_of term (p : prim_tag) : Type := +Definition prim_model_of (term : Type) (p : prim_tag) : Type := match p with | primInt => uint63_model | primFloat => float64_model - | primArray => array_model term + (* | primArray => array_model term *) end. Definition prim_val term := ∑ t : prim_tag, prim_model term t. @@ -45,7 +45,7 @@ Definition prim_model_val {term} (p : prim_val term) : prim_model_of term (prim_ match prim_val_model p in prim_model _ t return prim_model_of term t with | primIntModel i => i | primFloatModel f => f - | primArrayModel a => a + (* | primArrayModel a => a *) end. Lemma exist_irrel_eq {A} (P : A -> bool) (x y : sig P) : proj1_sig x = proj1_sig y -> x = y. @@ -84,12 +84,14 @@ Qed. (** Propositional UIP is needed below *) Set Equations With UIP. -Instance prim_model_eqdec {term} (e : EqDec term) : forall p : prim_tag, EqDec (prim_model term p). +Instance prim_model_eqdec {term} (*e : EqDec term*) : forall p : prim_tag, EqDec (prim_model term p). Proof. eqdec_proof. Qed. -Instance prim_tag_model_eqdec {term} (e : EqDec term) : EqDec (prim_val term). +Instance prim_tag_model_eqdec term : EqDec (prim_val term). Proof. eqdec_proof. Defined. +Instance prim_val_reflect_eq term : ReflectEq (prim_val term) := EqDec_ReflectEq _. + (** Printing *) Definition string_of_float64_model (f : float64_model) := @@ -99,5 +101,5 @@ Definition string_of_prim {term} (soft : term -> string) (p : prim_val term) : s match p.π2 return string with | primIntModel f => "(int: " ^ string_of_Z (proj1_sig f) ^ ")" | primFloatModel f => "(float: " ^ string_of_float64_model f ^ ")" - | primArrayModel a => "(array:" ^ ")" + (* | primArrayModel a => "(array:" ^ ")" *) end. diff --git a/pcuic/theories/PCUICPrincipality.v b/pcuic/theories/PCUICPrincipality.v index 08bd0e832..76fc8fe02 100644 --- a/pcuic/theories/PCUICPrincipality.v +++ b/pcuic/theories/PCUICPrincipality.v @@ -343,8 +343,7 @@ Section Principality. rewrite nthe' in nthe; noconf nthe. repeat split; eauto. eapply type_CoFix; eauto. - - now apply inversion_Int in hA. - - now apply inversion_Float in hA. + - now apply inversion_Prim in hA. Qed. (** A weaker version that is often convenient to use. *) diff --git a/pcuic/theories/PCUICReflect.v b/pcuic/theories/PCUICReflect.v index b92ea01e5..b430b53f7 100644 --- a/pcuic/theories/PCUICReflect.v +++ b/pcuic/theories/PCUICReflect.v @@ -34,8 +34,7 @@ Local Ltac term_dec_tac term_dec := | i : string, i' : kername |- _ => fcase (string_dec i i') | n : name, n' : name |- _ => fcase (eq_dec n n') | n : aname, n' : aname |- _ => fcase (eq_dec n n') - | i : uint63_model, j : uint63_model |- _ => fcase (eq_dec i j) - | i : float64_model, j : float64_model |- _ => fcase (eq_dec i j) + | i : prim_val, j : prim_val |- _ => fcase (eq_dec i j) | i : inductive, i' : inductive |- _ => fcase (eq_dec i i') | x : inductive * nat, y : inductive * nat |- _ => fcase (eq_dec x y) diff --git a/pcuic/theories/PCUICToTemplate.v b/pcuic/theories/PCUICToTemplate.v index fefc5a675..add6facdd 100644 --- a/pcuic/theories/PCUICToTemplate.v +++ b/pcuic/theories/PCUICToTemplate.v @@ -11,11 +11,10 @@ Definition uint63_from_model (i : uint63_model) : Int63.int := Definition float64_from_model (f : float64_model) : PrimFloat.float := FloatOps.SF2Prim (proj1_sig f). -Definition trans_prim {term} (t : prim_val term) : Ast.term := +Definition trans_prim (t : prim_val) : Ast.term := match t.π2 with | primIntModel i => Ast.tInt (uint63_from_model i) | primFloatModel f => Ast.tFloat (float64_from_model f) - | primArrayModel a => Ast.tRel 0 (* todo *) end. Fixpoint trans (t : PCUICAst.term) : Ast.term := diff --git a/pcuic/theories/PCUICToTemplateCorrectness.v b/pcuic/theories/PCUICToTemplateCorrectness.v index fb83909cf..bf798add1 100644 --- a/pcuic/theories/PCUICToTemplateCorrectness.v +++ b/pcuic/theories/PCUICToTemplateCorrectness.v @@ -59,6 +59,7 @@ Proof. - f_equal; auto. red in X. solve_list. - f_equal; auto; red in X; solve_list. - f_equal; auto; red in X; solve_list. + - destruct p as [? []]; eauto. Qed. Definition on_fst {A B C} (f:A->C) (p:A×B) := (f p.1, p.2). @@ -296,6 +297,7 @@ Proof. cbn in *. now rewrite e, e0. + apply IHX. + - destruct p as [? []]; eauto. Qed. @@ -355,6 +357,7 @@ Proof. destruct p. now rewrite e, e0. + apply IHX. + - destruct p as [? []]; eauto. Qed. Lemma trans_cst_type decl: @@ -475,10 +478,12 @@ Proof. 2: destruct (trans ty1);cbn;trivial. cbn. rewrite IHparams. cbn. now rewrite trans_subst. + destruct prim as [? []]; eauto. + destruct ty;cbn;trivial. 2: destruct (trans ty1);cbn;trivial. cbn. destruct pars;trivial. cbn. now rewrite IHparams. + destruct prim as [? []]; eauto. Qed. @@ -538,6 +543,7 @@ Proof. - rewrite <- IHx3. reflexivity. - destruct (trans x1);cbn;trivial. + - destruct prim as [? []]; eauto. Qed. Lemma trans_mkProd_or_LetIn a t: diff --git a/pcuic/theories/PCUICUnivSubst.v b/pcuic/theories/PCUICUnivSubst.v index 2e79b4583..857c69f5e 100644 --- a/pcuic/theories/PCUICUnivSubst.v +++ b/pcuic/theories/PCUICUnivSubst.v @@ -32,7 +32,7 @@ Instance subst_instance_constr : UnivSubst term := | tCoFix mfix idx => let mfix' := List.map (map_def (subst_instance_constr u) (subst_instance_constr u)) mfix in tCoFix mfix' idx - | tInt _ | tFloat _ => c + | tPrim _ => c end. Instance subst_instance_decl : UnivSubst context_decl diff --git a/safechecker/_PluginProject.in b/safechecker/_PluginProject.in index d4ffe1b33..870755842 100644 --- a/safechecker/_PluginProject.in +++ b/safechecker/_PluginProject.in @@ -27,6 +27,8 @@ src/typing0.ml # From PCUIC +src/pCUICPrimitive.mli +src/pCUICPrimitive.ml src/pCUICAst.ml src/pCUICAst.mli src/pCUICAstUtils.ml diff --git a/safechecker/src/metacoq_safechecker_plugin.mlpack b/safechecker/src/metacoq_safechecker_plugin.mlpack index 9233d9ebc..0868323b5 100644 --- a/safechecker/src/metacoq_safechecker_plugin.mlpack +++ b/safechecker/src/metacoq_safechecker_plugin.mlpack @@ -14,6 +14,7 @@ Classes0 Logic1 Relation Relation_Properties +PCUICPrimitive PCUICAst PCUICAstUtils PCUICInduction diff --git a/safechecker/theories/Extraction.v b/safechecker/theories/Extraction.v index a5e51d625..60e85911a 100644 --- a/safechecker/theories/Extraction.v +++ b/safechecker/theories/Extraction.v @@ -31,6 +31,7 @@ Extract Constant Equations.Init.pr1 => "fst". Extract Constant Equations.Init.pr2 => "snd". Extraction Inline Equations.Init.pr1 Equations.Init.pr2. Extraction Inline Equations.Prop.Logic.transport Equations.Prop.Logic.transport_r MCEquality.transport. +Extraction Inline Equations.Prop.Logic.True_rect_dep Equations.Prop.Logic.False_rect_dep. Extract Constant PCUICTyping.guard_checking => "{ fix_guard = (fun _ _ _ -> true); cofix_guard = (fun _ _ _ -> true) }". diff --git a/safechecker/theories/PCUICSafeConversion.v b/safechecker/theories/PCUICSafeConversion.v index 8992b5272..f19d4c291 100644 --- a/safechecker/theories/PCUICSafeConversion.v +++ b/safechecker/theories/PCUICSafeConversion.v @@ -4058,31 +4058,14 @@ Section Conversion. Qed. (* TODO move to PCUICNormal *) - Lemma whnf_mkApps_tInt_inv : - forall (f : RedFlags.t) (Σ : global_env) (Γ : context) i (args : list term), - whnf f Σ Γ (mkApps (tInt i) args) -> args = []. + Lemma whnf_mkApps_tPrim_inv : + forall (f : RedFlags.t) (Σ : global_env) (Γ : context) p (args : list term), + whnf f Σ Γ (mkApps (tPrim p) args) -> args = []. Proof. intros * wh. inversion wh; solve_discr. clear -X. - remember (mkApps (tInt i) args) eqn:teq. - exfalso. - revert teq. - induction X in args |- *; intros; solve_discr. - destruct args as [|? ? _] using MCList.rev_ind; [easy|]. - rewrite <- mkApps_nested in teq. - cbn in teq. noconf teq. - eauto. - Qed. - - Lemma whnf_mkApps_tFloat_inv : - forall (rf : RedFlags.t) (Σ : global_env) (Γ : context) f (args : list term), - whnf rf Σ Γ (mkApps (tFloat f) args) -> args = []. - Proof. - intros * wh. - inversion wh; solve_discr. - clear -X. - remember (mkApps (tFloat f) args) eqn:teq. + remember (mkApps (tPrim p) args) eqn:teq. exfalso. revert teq. induction X in args |- *; intros; solve_discr. @@ -4150,10 +4133,7 @@ Section Conversion. - constructor; eexists _, (decompose_stack π).1. split; [constructor; eauto with pcuic|]. eauto with pcuic. - - apply whnf_mkApps_tInt_inv in wh as ->. - constructor; eexists _, []. - eauto using whnf_red with pcuic. - - apply whnf_mkApps_tFloat_inv in wh as ->. + - apply whnf_mkApps_tPrim_inv in wh as ->. constructor; eexists _, []. eauto using whnf_red with pcuic. - constructor; eexists _, (decompose_stack π).1. @@ -4540,7 +4520,6 @@ Section Conversion. apply inversion_Sort in h1 as (_&h1&_); auto. eapply conv_pb_relb_complete in H0; eauto. - now rewrite eq_dec_to_bool_refl in noteq. - - now rewrite eq_dec_to_bool_refl in noteq. Qed. Equations _isconv (s : state) (Γ : context) diff --git a/safechecker/theories/PCUICSafeReduce.v b/safechecker/theories/PCUICSafeReduce.v index f4c14f156..5f72d038f 100644 --- a/safechecker/theories/PCUICSafeReduce.v +++ b/safechecker/theories/PCUICSafeReduce.v @@ -1256,8 +1256,7 @@ Section Reduce. unfold is_true in typ. unfold PCUICAst.fst_ctx in *. congruence. - - now eapply inversion_Int in typ. - - now eapply inversion_Float in typ. + - now eapply inversion_Prim in typ. Qed. Definition isCoFix_app t := @@ -1289,8 +1288,7 @@ Section Reduce. - exfalso; eapply invert_fix_ind; eauto. - unfold isCoFix_app in cof. now rewrite decompose_app_mkApps in cof. - - now eapply inversion_Int in typ. - - now eapply inversion_Float in typ. + - now eapply inversion_Prim in typ. Qed. Lemma whnf_fix_arg_whne mfix idx body Γ t before args aftr ty : @@ -1441,9 +1439,7 @@ Section Reduce. eapply PCUICConversion.cumul_Sort_Prod_inv; eauto. + exfalso. eapply welltyped_context in h as [s Hs]; tas. - now eapply inversion_Int in Hs. - + exfalso; eapply welltyped_context in h as [s Hs]; tas. - now eapply inversion_Float in Hs. + now eapply inversion_Prim in Hs. - unfold zipp. case_eq (decompose_stack π0). intros l ρ e. constructor. constructor. eapply whne_mkApps. eapply whne_rel_nozeta. assumption. diff --git a/safechecker/theories/PCUICSafeRetyping.v b/safechecker/theories/PCUICSafeRetyping.v index 02b003fdc..318aef85b 100644 --- a/safechecker/theories/PCUICSafeRetyping.v +++ b/safechecker/theories/PCUICSafeRetyping.v @@ -263,8 +263,7 @@ Section TypeOf. { | ret (Some f) => ret f.(dtype); | ret None => ! }; - infer Γ (tInt i) wt := ! ; - infer Γ (tFloat f) wt := ! + infer Γ (tPrim p) wt := ! }. Proof. all:try clear infer. @@ -659,8 +658,7 @@ Section TypeOf. - now eapply inversion_CoFix in HT as [decl [fg [hnth [htys [hbods [wf cum]]]]]]; auto. - - now eapply inversion_Int in HT. - - now eapply inversion_Float in HT. + - now eapply inversion_Prim in HT. Defined. Definition type_of Γ t wt : term := (infer Γ t wt). diff --git a/safechecker/theories/PCUICTypeChecker.v b/safechecker/theories/PCUICTypeChecker.v index 344470aac..a79de73d6 100644 --- a/safechecker/theories/PCUICTypeChecker.v +++ b/safechecker/theories/PCUICTypeChecker.v @@ -456,7 +456,7 @@ Section Typecheck. ret (dtype decl; _) end - | tInt _ | tFloat _ => raise (Msg "Primitive types are not supported") + | tPrim _ => raise (Msg "Primitive types are not supported") end. (* tRel *) From aa097dd96ae9eebd722167d7abf6ab7fd3adbda3 Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Thu, 10 Dec 2020 03:40:20 +0100 Subject: [PATCH 45/70] Another weak type variable problem --- safechecker/theories/Extraction.v | 3 +++ 1 file changed, 3 insertions(+) diff --git a/safechecker/theories/Extraction.v b/safechecker/theories/Extraction.v index 60e85911a..7e3820ecf 100644 --- a/safechecker/theories/Extraction.v +++ b/safechecker/theories/Extraction.v @@ -33,6 +33,9 @@ Extraction Inline Equations.Init.pr1 Equations.Init.pr2. Extraction Inline Equations.Prop.Logic.transport Equations.Prop.Logic.transport_r MCEquality.transport. Extraction Inline Equations.Prop.Logic.True_rect_dep Equations.Prop.Logic.False_rect_dep. +(** This Inline is because of a problem of weak type variables (partial application?) *) +Extraction Inline PCUICPrimitive.prim_val_reflect_eq. + Extract Constant PCUICTyping.guard_checking => "{ fix_guard = (fun _ _ _ -> true); cofix_guard = (fun _ _ _ -> true) }". Cd "src". From 40aea2fef5d68c6a33e7ed078d04eb27f454673d Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Wed, 9 Dec 2020 01:13:30 +0100 Subject: [PATCH 46/70] Update Template-Coq's typing derivations to match PCUIC more closely --- TODO.md | 9 + checker/theories/Checker.v | 2 +- checker/theories/Closed.v | 32 +-- checker/theories/Generation.v | 2 +- checker/theories/Substitution.v | 250 ++++++++++++++++---- checker/theories/Weakening.v | 161 ++++++++----- checker/theories/WeakeningEnv.v | 44 +++- pcuic/theories/PCUICAlpha.v | 5 +- pcuic/theories/PCUICAstUtils.v | 10 - pcuic/theories/PCUICClosed.v | 2 +- pcuic/theories/PCUICGeneration.v | 4 +- pcuic/theories/PCUICInductives.v | 8 +- pcuic/theories/PCUICSigmaCalculus.v | 19 +- pcuic/theories/PCUICSubstitution.v | 2 +- pcuic/theories/PCUICTyping.v | 13 +- pcuic/theories/PCUICUnivSubstitution.v | 3 +- pcuic/theories/PCUICValidity.v | 12 +- pcuic/theories/PCUICWeakening.v | 11 - pcuic/theories/PCUICWfUniverses.v | 2 +- pcuic/theories/TemplateToPCUICCorrectness.v | 101 +++++--- template-coq/theories/LiftSubst.v | 21 ++ template-coq/theories/Typing.v | 200 +++++++++------- template-coq/theories/TypingWf.v | 64 +---- template-coq/theories/utils/MCList.v | 19 ++ template-coq/theories/utils/MCPrelude.v | 1 + 25 files changed, 645 insertions(+), 352 deletions(-) diff --git a/TODO.md b/TODO.md index 9ccba9f5c..8596882d8 100644 --- a/TODO.md +++ b/TODO.md @@ -33,6 +33,12 @@ - Finish the PCUICSigmaCalculus proofs. +# Medium Projects + +- Change Template-PCUIC translations to translate casts to applications of + identity functions (vm_cast, default_cast etc) to make the back and forth + the identity and derive weakening/substitution/etc.. from the PCUIC theorems. + Is that really better than identity functions? # Big projects - Refine the longest-simple-path algorithm on universes with the @@ -48,6 +54,9 @@ be definable. Probably not very useful though because if the elimination is restricted then it means some Type is in the constructor and won't be projectable. +- Verify the substitution calculus of P.M Pédrot using skewed lists at + https://github.com/coq/coq/pull/13537 and try to use it to implement efficient explicit + substitutions. ## Website diff --git a/checker/theories/Checker.v b/checker/theories/Checker.v index a1acfb784..139a18def 100644 --- a/checker/theories/Checker.v +++ b/checker/theories/Checker.v @@ -957,7 +957,7 @@ Section InferOk. specialize (IH' _ _ Heqt0). intros. eapply type_Conv. apply IH'. - right. apply infer_type_correct in H; eauto. + apply infer_type_correct in H; eauto. destruct a0. eapply cumul_convert_leq; eassumption. Qed. diff --git a/checker/theories/Closed.v b/checker/theories/Closed.v index 98ec0fba9..21b9f0c65 100644 --- a/checker/theories/Closed.v +++ b/checker/theories/Closed.v @@ -8,7 +8,6 @@ From Equations Require Import Equations. (** * Lemmas about the [closedn] predicate *) - Definition closed_decl n d := option_default (closedn n) d.(decl_body) true && closedn n d.(decl_type). @@ -526,7 +525,7 @@ Proof. apply closedn_mkApps; auto. rewrite forallb_app. simpl. rewrite H1. rewrite forallb_skipn; auto. - now apply closedn_mkApps_inv in H7. + now apply closedn_mkApps_inv in H8. - intuition auto. apply closedn_subst0. @@ -542,36 +541,25 @@ Proof. unfold test_def. simpl. rtoProp. split. rewrite -> app_context_length in *. rewrite -> Nat.add_comm in *. - eapply closedn_lift_inv in H2; eauto. lia. + eapply closedn_lift_inv in H3; eauto. lia. subst types. - now rewrite app_context_length fix_context_length in H1. + now rewrite app_context_length fix_context_length in H2. eapply nth_error_all in H0; eauto. simpl in H0. intuition. rtoProp. - subst types. rewrite app_context_length in H1. - rewrite Nat.add_comm in H1. - now eapply closedn_lift_inv in H1. + subst types. rewrite app_context_length in H2. + rewrite Nat.add_comm in H2. + now eapply closedn_lift_inv in H2. - split. solve_all. destruct x; simpl in *. unfold test_def. simpl. rtoProp. split. rewrite -> app_context_length in *. rewrite -> Nat.add_comm in *. - eapply closedn_lift_inv in H1; eauto. lia. + eapply closedn_lift_inv in H2; eauto. lia. subst types. - now rewrite -> app_context_length, fix_context_length in H0. + now rewrite -> app_context_length, fix_context_length in H1. eapply (nth_error_all) in H; eauto. simpl in *. intuition. rtoProp. - subst types. rewrite app_context_length in H0. - rewrite Nat.add_comm in H0. - now eapply closedn_lift_inv in H0. - - - destruct X2; intuition eauto. - + destruct i as [[u [ctx [Heq Hi]]] Hwfi]. simpl in Hwfi. - generalize (destArity_spec [] B). rewrite Heq. - simpl; intros ->. - apply closedn_All_local_closed in Hwfi. - rewrite closedn_ctx_app in Hwfi. - move/andb_and: Hwfi => [] clΓ clctx. - apply closedn_it_mkProd_or_LetIn => //. - + destruct s. rewrite andb_true_r in p. intuition auto. + subst types. rewrite app_context_length Nat.add_comm in H1. + now eapply closedn_lift_inv in H1. Qed. Lemma declared_decl_closed `{checker_flags} {Σ : global_env} {cst decl} : diff --git a/checker/theories/Generation.v b/checker/theories/Generation.v index db01d128f..c1ae9ffd1 100644 --- a/checker/theories/Generation.v +++ b/checker/theories/Generation.v @@ -15,7 +15,7 @@ Proof. intros Hty. dependent induction Hty. - exists t_ty, t'. intuition. - - destruct IHHty as [T' [U' [H' H'']]]. + - destruct IHHty1 as [T' [U' [H' H'']]]. exists T', U'. split; auto. eapply cumul_trans; eauto. Qed. diff --git a/checker/theories/Substitution.v b/checker/theories/Substitution.v index 7b6ae4a7b..7807ad583 100644 --- a/checker/theories/Substitution.v +++ b/checker/theories/Substitution.v @@ -1117,6 +1117,187 @@ Qed. Hint Unfold subst1 : subst. Hint Rewrite subst_mkApps distr_subst: subst. +Lemma subst_decompose_prod_assum_rec ctx t s k : + let (ctx', t') := decompose_prod_assum ctx t in + ∑ ctx'' t'', + (decompose_prod_assum [] (subst s (#|ctx'| + k) t') = (ctx'', t'')) * + (decompose_prod_assum (subst_context s k ctx) (subst s (length ctx + k) t) = + (subst_context s k ctx' ,,, ctx'', t'')). +Proof. + induction t in ctx, k |- *; simpl; try solve [ eexists _, _; firstorder eauto ]. + - elim: leb_spec_Set => comp. + + destruct (nth_error s (n - (#|ctx| + k))) eqn:Heq. + * destruct decompose_prod_assum eqn:Heq'. + eexists _, _; intuition eauto. + now rewrite decompose_prod_assum_ctx Heq'. + * eexists _,_; firstorder eauto. + + eexists _,_; firstorder eauto. + - destruct decompose_prod_assum eqn:Heq. + rewrite decompose_prod_assum_ctx in Heq. + destruct (decompose_prod_assum [] t1) eqn:Heq'. + noconf Heq. + specialize (IHt1 ctx k). + rewrite decompose_prod_assum_ctx in IHt1. + rewrite Heq' in IHt1. + destruct IHt1 as [ctx'' [t'' [eqt eqt1]]]. + exists ctx'', t''. rewrite -eqt. + split. + * unfold snoc; simpl. rewrite !app_context_length. + simpl. lia_f_equal. + * rewrite decompose_prod_assum_ctx in eqt1. + rewrite decompose_prod_assum_ctx. + destruct (decompose_prod_assum [] (subst s _ t1)) eqn:Heq''. + rewrite subst_context_app in eqt1. + rewrite !subst_context_app. + injection eqt1. intros <-. + intros eqctx. f_equal. + unfold app_context in eqctx. + rewrite app_assoc in eqctx. + apply app_inv_tail in eqctx. + subst c. rewrite app_context_assoc. + unfold snoc. simpl. lia_f_equal. + - destruct decompose_prod_assum eqn:Heq. + rewrite decompose_prod_assum_ctx in Heq. + destruct (decompose_prod_assum [] t2) eqn:Heq'. + noconf Heq. + specialize (IHt2 ctx (S k)). + rewrite decompose_prod_assum_ctx in IHt2. + rewrite Heq' in IHt2. + destruct IHt2 as [ctx'' [t'' [eqt eqt2]]]. + exists ctx'', t''. rewrite -eqt. + split. + * unfold snoc; simpl. rewrite !app_context_length. + simpl. lia_f_equal. + * rewrite decompose_prod_assum_ctx in eqt2. + rewrite decompose_prod_assum_ctx. + rewrite Nat.add_succ_r in eqt2. + destruct (decompose_prod_assum [] (subst s _ t2)) eqn:Heq''. + rewrite subst_context_app in eqt2. + rewrite !subst_context_app subst_context_snoc. + injection eqt2. intros <-. + intros eqctx. f_equal. + unfold app_context in eqctx. + rewrite app_assoc in eqctx. + apply app_inv_tail in eqctx. + subst c. rewrite app_context_assoc. + unfold snoc. simpl. lia_f_equal. + + - destruct decompose_prod_assum eqn:Heq. + rewrite decompose_prod_assum_ctx in Heq. + destruct (decompose_prod_assum [] t3) eqn:Heq'. + noconf Heq. + specialize (IHt3 ctx (S k)). + rewrite decompose_prod_assum_ctx in IHt3. + rewrite Heq' in IHt3. + destruct IHt3 as [ctx'' [t'' [eqt eqt3]]]. + exists ctx'', t''. rewrite -eqt. + split. + * unfold snoc; simpl. rewrite !app_context_length. + simpl. lia_f_equal. + * rewrite decompose_prod_assum_ctx in eqt3. + rewrite decompose_prod_assum_ctx. + rewrite Nat.add_succ_r in eqt3. + destruct (decompose_prod_assum [] (subst s _ t3)) eqn:Heq''. + rewrite subst_context_app in eqt3. + rewrite !subst_context_app subst_context_snoc. + injection eqt3. intros <-. + intros eqctx. f_equal. + unfold app_context in eqctx. + rewrite app_assoc in eqctx. + apply app_inv_tail in eqctx. + subst c. rewrite app_context_assoc. + unfold snoc. simpl. lia_f_equal. + + - todo "applications". +Qed. + +Lemma map_option_out_impl {A B} (l : list A) (f g : A -> option B) x : + (forall x y, f x = Some y -> g x = Some y) -> + map_option_out (map f l) = Some x -> + map_option_out (map g l) = Some x. +Proof. + intros Hfg. + induction l in x |- *; simpl; auto. + destruct (f a) eqn:fa. + - rewrite (Hfg _ _ fa). + move: IHl; destruct map_option_out. + * move=> H'. specialize (H' _ eq_refl). + rewrite H'. congruence. + * discriminate. + - discriminate. +Qed. +Lemma smash_context_app Δ Γ Γ' : + smash_context Δ (Γ ++ Γ') = smash_context (smash_context Δ Γ) Γ'. +Proof. + revert Δ; induction Γ as [|[na [b|] ty]]; intros Δ; simpl; auto. +Qed. + +Lemma substitution_check_one_fix s k mfix inds : + map_option_out (map check_one_fix mfix) = Some inds -> + map_option_out (map (fun x : def term => + check_one_fix (map_def (subst s k) (subst s (#|mfix| + k)) x)) mfix) = Some inds. +Proof. + apply map_option_out_impl. + move=> [na ty def rarg] /=. + rewrite decompose_prod_assum_ctx. + destruct (decompose_prod_assum _ ty) eqn:decomp. + rewrite decompose_prod_assum_ctx in decomp. + destruct (decompose_prod_assum [] ty) eqn:decty. + noconf decomp. rewrite !app_context_nil_l. + pose proof (subst_decompose_prod_assum_rec [] ty s k). + rewrite decty in X. + destruct X as [ctx'' [t'' [dect decty']]]. + rewrite -> subst_context_nil in decty'. simpl in decty'. + rewrite decty'. intros ind. + rewrite smash_context_app. +Admitted. + (* rewrite (smash_context_acc _ (smash_context _ _)). + rewrite List.rev_app_distr. + destruct (nth_error_spec (List.rev (smash_context [] c0)) rarg) => /= //; + autorewrite with len in l; simpl in *. + rewrite nth_error_app_lt; autorewrite with len; simpl; try lia. + rewrite (smash_context_subst []) /=. + rewrite nth_error_rev_inv; autorewrite with len; simpl; try lia. + rewrite nth_error_subst_context /=. + autorewrite with len. + rewrite nth_error_rev_inv in e; autorewrite with len; auto. + autorewrite with len in e. simpl in e. rewrite e. + simpl. + destruct (decompose_app (decl_type x)) eqn:Happ. + destruct t0; try discriminate. simpl in *. + erewrite decompose_app_subst; eauto. simpl. auto. +Qed. *) + +Lemma decompose_prod_assum_mkApps ctx ind u args : + decompose_prod_assum ctx (mkApps (tInd ind u) args) = (ctx, mkApps (tInd ind u) args). +Proof. + apply (decompose_prod_assum_it_mkProd ctx []). + now rewrite is_ind_app_head_mkApps. +Qed. + + +Lemma substitution_check_one_cofix s k mfix inds : + map_option_out (map check_one_cofix mfix) = Some inds -> + map_option_out (map (fun x : def term => + check_one_cofix (map_def (subst s k) (subst s (#|mfix| + k)) x)) mfix) = Some inds. +Proof. + apply map_option_out_impl. move=> [na ty def rarg] /= ind. + destruct (decompose_prod_assum [] ty) eqn:decty. + destruct (decompose_app t) eqn:eqapp. + destruct t0; try discriminate. simpl. + pose proof (subst_decompose_prod_assum_rec [] ty s k). + rewrite decty in X. + destruct X as [ctx'' [t'' [dect decty']]]. + rewrite decty'. +Admitted. + (* apply decompose_app_mkApps in eqapp. => //. + subst t. + rewrite subst_mkApps /= in dect. + rewrite decompose_prod_assum_mkApps in dect. noconf dect. + rewrite decompose_app_mkApps //. +Qed. *) + + Lemma subs_nth_error `{checker_flags} Σ Γ s Δ decl n t : subs Σ Γ s Δ -> nth_error Δ n = Some decl -> @@ -1795,8 +1976,8 @@ Proof. -- simpl. destruct (on_declared_inductive wfΣ isdecl) as [oind obod]. pose obod.(onConstructors) as onc. - eapply (subst_build_branches_type s #|Δ|) in H3; eauto. - subst params. rewrite firstn_map. exact H3. + eapply (subst_build_branches_type s #|Δ|) in H4; eauto. + subst params. rewrite firstn_map. exact H4. 4: now rewrite closedn_subst_instance_context. all: eauto with wf. admit. admit. @@ -1840,6 +2021,12 @@ Proof. rewrite subst_context_length fix_context_length. rewrite commut_lift_subst_rec; try lia. now rewrite (Nat.add_comm #|Δ|). now rewrite isLambda_subst. + * move: H2. + rewrite /wf_fixpoint. + pose proof (substitution_check_one_fix s #|Δ| mfix). + destruct map_option_out eqn:Heq => //. + specialize (H2 _ eq_refl). + rewrite map_map_compose. now rewrite H2. - rewrite -> (map_dtype _ (subst s (#|mfix| + #|Δ|))). eapply type_CoFix; auto. @@ -1858,54 +2045,17 @@ Proof. rewrite app_context_length fix_context_length in IH. rewrite subst_context_length fix_context_length. rewrite commut_lift_subst_rec; try lia. now rewrite (Nat.add_comm #|Δ|). - - - assert(wfB : Ast.wf B). - { destruct X2 as [Bs|[u Hu]]. - destruct Bs as [[ctx [u [Hd IH]]]]. simpl in *. - generalize (destArity_spec [] B); rewrite Hd. - move => /= ->. clear -wfΣ IH. - eapply (it_mkProd_or_LetIn_wf (Γ ,,, Γ' ,,, Δ)). - rewrite -it_mkProd_or_LetIn_app. - eapply (wf_it_mkProd_or_LetIn _ _ IH); auto. - induction IH; constructor; auto. - destruct t0. split; try constructor. - eapply typing_wf in t0. intuition. auto. - eapply typing_wf in t1. intuition. auto. - eapply typing_wf in t1. intuition. auto. constructor. - destruct Hu. apply typing_wf in t0; intuition auto. } - econstructor; eauto. - destruct X2 as [Bs|[u Hu]]. - + left. destruct Bs as [[ctx [u [Hd IH]]]]. simpl in *. - exists (subst_context s #|Δ| ctx), u. - pose proof (subst_destArity [] B s #|Δ|). rewrite Hd in H0. - rewrite {}H0; auto. - split; auto. - apply All_local_env_app; intuition auto. - clear -sub a. - induction ctx; try constructor; depelim a. - -- rewrite subst_context_snoc. - unfold snoc. - econstructor; auto. - eapply IHctx. eapply a. - simpl. destruct tu as [u tu]. exists u. - specialize (t0 _ _ (Δ ,,, ctx) _ sub). forward t0. - now rewrite app_context_assoc. simpl in t0. - now rewrite subst_context_app Nat.add_0_r app_context_assoc app_length in t0. - -- rewrite subst_context_snoc. - constructor; auto. - ++ eapply IHctx. eapply a. - ++ simpl. - specialize (t1 _ _ (Δ ,,, ctx) _ sub). - forward t1. 1: now rewrite app_context_assoc. - simpl in t1. - now rewrite subst_context_app Nat.add_0_r app_context_assoc app_length in t1. - ++ simpl. - specialize (t0 _ _ (Δ ,,, ctx) _ sub). forward t0. - 1: now rewrite app_context_assoc. simpl in t0. - now rewrite subst_context_app Nat.add_0_r app_context_assoc app_length in t0. - + right; exists u; intuition eauto. - + eapply substitution_cumul; eauto. - now eapply typing_wf in X0. + * move: H1. + rewrite /wf_cofixpoint. + pose proof (substitution_check_one_cofix s #|Δ| mfix). + destruct map_option_out eqn:Heq => //. + specialize (H1 _ eq_refl). + rewrite map_map_compose. now rewrite H1. + + - econstructor; eauto. + eapply substitution_cumul; eauto. + now eapply typing_wf in X0. + now eapply typing_wf in X2. Admitted. Lemma substitution0 `{checker_flags} Σ Γ n u U (t : term) T : diff --git a/checker/theories/Weakening.v b/checker/theories/Weakening.v index fa2447cfa..fdea27fd0 100644 --- a/checker/theories/Weakening.v +++ b/checker/theories/Weakening.v @@ -61,13 +61,6 @@ Proof. Qed. Hint Rewrite lift_context_snoc : lift. -Lemma lift_context_alt n k Γ : - lift_context n k Γ = - mapi (fun k' d => lift_decl n (Nat.pred #|Γ| - k' + k) d) Γ. -Proof. - unfold lift_context. apply fold_context_alt. -Qed. - Lemma lift_context_app n k Γ Δ : lift_context n k (Γ ,,, Δ) = lift_context n k Γ ,,, lift_context n (#|Γ| + k) Δ. Proof. @@ -522,15 +515,28 @@ Proof. Qed. Hint Rewrite lift_instantiate_params : lift. -(* bug eauto with let .. in hypothesis failing *) +Lemma decompose_prod_assum_ctx ctx t : decompose_prod_assum ctx t = + let (ctx', t') := decompose_prod_assum [] t in + (ctx ,,, ctx', t'). +Proof. + induction t in ctx |- *; simpl; auto. + - simpl. rewrite IHt2. + rewrite (IHt2 ([] ,, vass _ _)). + destruct (decompose_prod_assum [] t2). simpl. + unfold snoc. now rewrite app_context_assoc. + - simpl. rewrite IHt3. + rewrite (IHt3 ([] ,, vdef _ _ _)). + destruct (decompose_prod_assum [] t3). simpl. + unfold snoc. now rewrite app_context_assoc. +Qed. + Lemma lift_decompose_prod_assum_rec ctx t n k : - let (ctx', t') := decompose_prod_assum ctx t in - (lift_context n k ctx', lift n (length ctx' + k) t') = + (let (ctx', t') := decompose_prod_assum ctx t in + (lift_context n k ctx', lift n (length ctx' + k) t')) = decompose_prod_assum (lift_context n k ctx) (lift n (length ctx + k) t). Proof. induction t in n, k, ctx |- *; simpl; try rewrite -> Nat.sub_diag, Nat.add_0_r; try (eauto; congruence). - - eapply IHt1. - specialize (IHt2 (ctx ,, vass na t1) n k). destruct decompose_prod_assum. rewrite IHt2. simpl. rewrite lift_context_snoc. reflexivity. @@ -540,8 +546,8 @@ Proof. Qed. Lemma lift_decompose_prod_assum t n k : - let (ctx', t') := decompose_prod_assum [] t in - (lift_context n k ctx', lift n (length ctx' + k) t') = + (let (ctx', t') := decompose_prod_assum [] t in + (lift_context n k ctx', lift n (length ctx' + k) t')) = decompose_prod_assum [] (lift n k t). Proof. apply lift_decompose_prod_assum_rec. Qed. @@ -899,6 +905,83 @@ Proof. simpl. rewrite Nat.add_0_r. apply t0; auto. Qed. +Lemma destInd_lift n k t : destInd (lift n k t) = destInd t. +Proof. + destruct t; simpl; try congruence. +Qed. + +Lemma smash_context_lift Δ k n Γ : + smash_context (lift_context n (k + #|Γ|) Δ) (lift_context n k Γ) = + lift_context n k (smash_context Δ Γ). +Proof. + revert Δ. induction Γ as [|[na [b|] ty]]; intros Δ; simpl; auto. + - now rewrite Nat.add_0_r. + - rewrite -IHΓ. + rewrite lift_context_snoc /=. f_equal. + rewrite !subst_context_alt !lift_context_alt !mapi_compose. + apply mapi_ext=> n' x. + destruct x as [na' [b'|] ty']; simpl. + * rewrite !mapi_length /lift_decl /subst_decl /= /map_decl /=; f_equal. + + f_equal. rewrite Nat.add_0_r distr_lift_subst_rec /=. + lia_f_equal. + + rewrite Nat.add_0_r distr_lift_subst_rec; simpl. lia_f_equal. + * rewrite !mapi_length /lift_decl /subst_decl /= /map_decl /=; f_equal. + rewrite Nat.add_0_r distr_lift_subst_rec /=. + repeat (lia || f_equal). + - rewrite -IHΓ. + rewrite lift_context_snoc /= // /lift_decl /subst_decl /map_decl /=. + f_equal. + rewrite lift_context_app. simpl. + rewrite /app_context; lia_f_equal. + rewrite /lift_context // /fold_context /= /map_decl /=. + now lia_f_equal. +Qed. + +Lemma weakening_check_one_fix (Γ' Γ'' : context) mfix : + map + (fun x : def term => + check_one_fix (map_def (lift #|Γ''| #|Γ'|) (lift #|Γ''| (#|mfix| + #|Γ'|)) x)) mfix = + map check_one_fix mfix. +Proof. + apply map_ext. move=> [na ty def rarg] /=. + rewrite decompose_prod_assum_ctx. + destruct (decompose_prod_assum _ ty) eqn:decomp. + rewrite decompose_prod_assum_ctx in decomp. + rewrite -lift_decompose_prod_assum. + destruct (decompose_prod_assum [] ty) eqn:decty. + noconf decomp. rewrite !app_context_nil_l (smash_context_lift []). + destruct (nth_error_spec (List.rev (smash_context [] c0)) rarg). + rewrite -> List.rev_length, ?smash_context_length in *; simpl in *. + - rewrite nth_error_rev_inv; rewrite !List.rev_length mapi_length List.rev_length smash_context_length; simpl; auto. + rewrite nth_error_lift_context_eq. + simpl. + rewrite nth_error_rev_inv ?List.rev_length smash_context_length in e; auto. + simpl in e. rewrite e. simpl. + destruct (decompose_app (decl_type x)) eqn:Happ. + erewrite decompose_app_lift; eauto. + rewrite destInd_lift. reflexivity. + - erewrite (proj2 (nth_error_None _ _)); auto. + rewrite List.rev_length lift_context_length. + now rewrite List.rev_length in l. +Qed. + +Lemma weakening_check_one_cofix (Γ' Γ'' : context) mfix : + map + (fun x : def term => + check_one_cofix (map_def (lift #|Γ''| #|Γ'|) (lift #|Γ''| (#|mfix| + #|Γ'|)) x)) mfix = + map check_one_cofix mfix. +Proof. + apply map_ext. move=> [na ty def rarg] /=. + rewrite decompose_prod_assum_ctx. + destruct (decompose_prod_assum _ ty) eqn:decomp. + rewrite decompose_prod_assum_ctx in decomp. + rewrite -lift_decompose_prod_assum. + destruct (decompose_prod_assum [] ty) eqn:decty. + noconf decomp. + destruct (decompose_app t) eqn:Happ. + erewrite decompose_app_lift; eauto. + rewrite destInd_lift. reflexivity. +Qed. Lemma weakening_typing `{cf : checker_flags} Σ Γ Γ' Γ'' (t : term) : wf Σ.1 -> @@ -990,7 +1073,7 @@ Proof. rewrite -> closedn_subst_instance_context. eapply closed_wf_local in Hmdecl; eauto. } simpl. econstructor. - 7:{ cbn. rewrite -> firstn_map. + 8:{ cbn. rewrite -> firstn_map. erewrite lift_build_branches_type; tea. rewrite map_option_out_map_option_map. subst params. erewrite heq_map_option_out. reflexivity. } @@ -1039,6 +1122,9 @@ Proof. rewrite lift_context_length fix_context_length. rewrite permute_lift; try lia. now rewrite (Nat.add_comm #|Γ'|). now rewrite isLambda_lift. + * red; rewrite <-H1. unfold wf_fixpoint. + rewrite map_map_compose. + now rewrite weakening_check_one_fix. - rewrite -> (map_dtype _ (lift #|Γ''| (#|mfix| + #|Γ'|))). eapply type_CoFix; auto. @@ -1057,51 +1143,12 @@ Proof. rewrite app_context_length fix_context_length in IH. rewrite lift_context_length fix_context_length. rewrite permute_lift; try lia. now rewrite (Nat.add_comm #|Γ'|). + * red; rewrite <- H0. unfold wf_cofixpoint. + rewrite map_map_compose. + now rewrite weakening_check_one_cofix. - econstructor; eauto. - destruct IHB. - + left. destruct i as [[ctx [u [Hd IH]]]]. simpl in *. - exists (lift_context #|Γ''| #|Γ'| ctx), u. - rewrite (lift_destArity [] B #|Γ''| #|Γ'|) ?Hd. - { generalize (destArity_spec [] B); rewrite Hd. - move => /= ->. clear -wfΣ IH. - eapply (it_mkProd_or_LetIn_wf (Γ ,,, Γ')). - rewrite -it_mkProd_or_LetIn_app. - eapply (wf_it_mkProd_or_LetIn _ _ IH); auto. - induction IH; constructor; auto. - destruct t0. split; try constructor. - eapply typing_wf in t0. intuition. auto. - eapply typing_wf in t1. intuition. auto. - eapply typing_wf in t1. intuition. auto. constructor. } - split; auto. - apply All_local_env_app; intuition auto. - clear -wf a. - induction ctx; try constructor; depelim a. - -- rewrite lift_context_snoc. - constructor; auto. - eapply IHctx. eapply a. - simpl. destruct tu as [u tu]. exists u. - specialize (t0 Γ (Γ' ,,, ctx) Γ''). forward t0. auto. - rewrite app_context_assoc in t0. - specialize (t0 eq_refl). simpl in t0. - rewrite app_context_length lift_context_app app_context_assoc Nat.add_0_r in t0. apply t0. - -- rewrite lift_context_snoc. - constructor; auto. - ++ eapply IHctx. eapply a. - ++ simpl. - specialize (t1 Γ (Γ' ,,, ctx) Γ''). forward t1 by auto. - rewrite app_context_assoc in t1. - specialize (t1 eq_refl). simpl in t1. - rewrite app_context_length lift_context_app app_context_assoc Nat.add_0_r in t1. - eexists. apply t1. - ++ simpl. - specialize (t0 Γ (Γ' ,,, ctx) Γ'' wf). - rewrite app_context_assoc in t0. - specialize (t0 eq_refl). simpl in t0. - rewrite app_context_length lift_context_app app_context_assoc Nat.add_0_r in t0. - apply t0. - + right. destruct s as [u Hu]; exists u. intuition; now eapply weakening_cumul. - + now eapply weakening_cumul. + now eapply weakening_cumul. Qed. Lemma weakening `{cf : checker_flags} Σ Γ Γ' (t : term) T : diff --git a/checker/theories/WeakeningEnv.v b/checker/theories/WeakeningEnv.v index 2b212f77c..b198cfaac 100644 --- a/checker/theories/WeakeningEnv.v +++ b/checker/theories/WeakeningEnv.v @@ -331,6 +331,37 @@ Proof. Qed. Hint Resolve weakening_env_consistent_instance : extends. +Lemma extends_check_recursivity_kind {cf:checker_flags} Σ ind k Σ' : extends Σ Σ' -> wf Σ' -> + check_recursivity_kind Σ ind k -> check_recursivity_kind Σ' ind k. +Proof. + intros ext wfΣ'. + rewrite /check_recursivity_kind. + destruct lookup_env eqn:Heq => //. + eapply extends_lookup in Heq; eauto. + now rewrite Heq. +Qed. + +Lemma extends_wf_fixpoint {cf:checker_flags} Σ mfix Σ' : extends Σ Σ' -> wf Σ' -> + wf_fixpoint Σ mfix -> wf_fixpoint Σ' mfix. +Proof. + intros ext wfΣ'. + unfold wf_fixpoint. + destruct map_option_out as [[|ind inds]|]; auto. + move/andb_and => [->] /=. + now apply extends_check_recursivity_kind. +Qed. + +Lemma extends_wf_cofixpoint {cf:checker_flags} Σ mfix Σ' : extends Σ Σ' -> wf Σ' -> + wf_cofixpoint Σ mfix -> wf_cofixpoint Σ' mfix. +Proof. + intros ext wfΣ'. + unfold wf_cofixpoint. + destruct map_option_out as [[|ind inds]|]; auto. + move/andb_and => [->] /=. + now apply extends_check_recursivity_kind. +Qed. + +Hint Resolve extends_wf_fixpoint extends_wf_cofixpoint : extends. Lemma global_levels_Set Σ : LevelSet.In Level.lSet (global_levels Σ). @@ -408,9 +439,7 @@ Proof. rename_all_hyps; try solve [econstructor; eauto 2 with extends]. - econstructor; eauto 2 with extends. - intuition auto. - destruct H1 as [l' [inl' eq]]. right; right. - exists l'. split; eauto 2 with extends. + intuition auto. eapply extends_wf_universe; eauto. - econstructor; eauto 2 with extends. destruct Σ as [Σ φ]. clear typet heq_isApp forall_Σ' hneq_l. @@ -422,16 +451,13 @@ Proof. eapply (All_impl X0); intuition eauto. destruct X2 as [s Hs]; exists s; intuition eauto. eapply All_impl; eauto; simpl; intuition eauto with extends. + - econstructor; eauto with extends. auto. eapply (All_impl X0); intuition eauto. destruct X2 as [s Hs]; exists s; intuition eauto. eapply All_impl; eauto; simpl; intuition eauto with extends. - - econstructor. eauto. - destruct X2 as [isB|[u [Hu Ps]]]. - + left; auto. destruct isB. destruct x as [ctx [u [Heq Hu]]]. - exists ctx, u. split; eauto with extends. - + right. exists u. eapply Ps; auto. - + destruct Σ as [Σ φ]. eapply weakening_env_cumul in cumulA; eauto. + - econstructor; eauto with extends. + destruct Σ as [Σ φ]. eapply weakening_env_cumul in cumulA; eauto. Qed. Definition weaken_env_prop `{checker_flags} diff --git a/pcuic/theories/PCUICAlpha.v b/pcuic/theories/PCUICAlpha.v index d21c1e243..d2ead3eb2 100644 --- a/pcuic/theories/PCUICAlpha.v +++ b/pcuic/theories/PCUICAlpha.v @@ -348,13 +348,14 @@ Section Alpha. constructor. assumption. all: try (eapply upto_names_impl_eq_term ; assumption). all: eapply eq_term_refl. - - intros t na A B u ih ht iht hu ihu v e; invs e. + - intros t na A B s u ih hty ihty ht iht hu ihu v e; invs e. eapply type_Cumul'. - + econstructor. + + econstructor; cycle 1. * eapply iht. eapply eq_term_upto_univ_empty_impl in X; eauto. all:typeclasses eauto. * eapply ihu. assumption. + * eapply hty. + eapply validity_term ; eauto. econstructor ; eauto. + constructor. diff --git a/pcuic/theories/PCUICAstUtils.v b/pcuic/theories/PCUICAstUtils.v index 4d2889a20..4c4754bad 100644 --- a/pcuic/theories/PCUICAstUtils.v +++ b/pcuic/theories/PCUICAstUtils.v @@ -301,16 +301,6 @@ Qed. Hint Rewrite context_assumptions_map context_assumptions_mapi : len. -Lemma mapi_rec_compose {A B C} (g : nat -> B -> C) (f : nat -> A -> B) k l : - mapi_rec g (mapi_rec f l k) k = mapi_rec (fun k x => g k (f k x)) l k. -Proof. - induction l in k |- *; simpl; auto. now rewrite IHl. -Qed. - -Lemma mapi_compose {A B C} (g : nat -> B -> C) (f : nat -> A -> B) l : - mapi g (mapi f l) = mapi (fun k x => g k (f k x)) l. -Proof. apply mapi_rec_compose. Qed. - Lemma compose_map_decl f g x : map_decl f (map_decl g x) = map_decl (f ∘ g) x. Proof. destruct x as [? [?|] ?]; reflexivity. diff --git a/pcuic/theories/PCUICClosed.v b/pcuic/theories/PCUICClosed.v index 658b9ed1c..f3101aacd 100644 --- a/pcuic/theories/PCUICClosed.v +++ b/pcuic/theories/PCUICClosed.v @@ -713,7 +713,7 @@ Proof. - intuition auto. generalize (closedn_subst [u] #|Γ| 0 B). rewrite Nat.add_0_r. - move=> Hs. apply: Hs => /=. rewrite H0 => //. + move=> Hs. apply: Hs => /=. rewrite H1 => //. rewrite Nat.add_1_r. auto. - rewrite closedn_subst_instance_constr. diff --git a/pcuic/theories/PCUICGeneration.v b/pcuic/theories/PCUICGeneration.v index ecd8976f6..40755651e 100644 --- a/pcuic/theories/PCUICGeneration.v +++ b/pcuic/theories/PCUICGeneration.v @@ -38,9 +38,9 @@ Section Generation. intros. specialize (IHHsp (tApp t0 hd)). apply IHHsp. - eapply type_App. + destruct i as [s Hs]. + eapply type_App; eauto. eapply type_Cumul; eauto. - eapply i.π2. eauto. Qed. Lemma type_it_mkLambda_or_LetIn : diff --git a/pcuic/theories/PCUICInductives.v b/pcuic/theories/PCUICInductives.v index c3c9983a8..8cdfe1dd0 100644 --- a/pcuic/theories/PCUICInductives.v +++ b/pcuic/theories/PCUICInductives.v @@ -1190,10 +1190,10 @@ Lemma invert_type_mkApps_ind {cf:checker_flags} Σ Γ ind u args T mdecl idecl : Proof. intros wfΣ decli. intros H; dependent induction H; solve_discr. - - destruct args using rev_case; solve_discr. noconf H1. - rewrite -PCUICAstUtils.mkApps_nested in H1. simpl in H1. - noconf H1. clear IHtyping2. - specialize (IHtyping1 _ _ _ _ _ _ _ wfΣ decli eq_refl) as [IH cu]; + - destruct args using rev_case; solve_discr. noconf H2. + rewrite -PCUICAstUtils.mkApps_nested in H2. simpl in H2. + noconf H2. clear IHtyping1 IHtyping3. + specialize (IHtyping2 _ _ _ _ _ _ _ wfΣ decli eq_refl) as [IH cu]; split; auto. destruct (on_declared_inductive wfΣ decli) as [onmind oib]. eapply typing_spine_app; eauto. diff --git a/pcuic/theories/PCUICSigmaCalculus.v b/pcuic/theories/PCUICSigmaCalculus.v index 352f95e68..e3f99837a 100644 --- a/pcuic/theories/PCUICSigmaCalculus.v +++ b/pcuic/theories/PCUICSigmaCalculus.v @@ -1071,6 +1071,15 @@ Proof. intros Σ Γ t A B h []. assumption. Qed. +Lemma meta_conv_term : + forall Σ Γ t t' A, + Σ ;;; Γ |- t : A -> + t = t' -> + Σ ;;; Γ |- t' : A. +Proof. + intros Σ Γ t A B h []. assumption. +Qed. + (* Could be more precise *) Lemma instantiate_params_subst_length : forall params pars s t s' t', @@ -1664,9 +1673,10 @@ Proof. * destruct hf. assumption. * simpl. eexists. eapply ihB. assumption. * simpl. eapply ihb. assumption. - - intros Σ wfΣ Γ wfΓ t na A B u X ht iht hu ihu Δ f hf. + - intros Σ wfΣ Γ wfΓ t na A B s u X hty ihty ht iht hu ihu Δ f hf. simpl. eapply meta_conv. - + econstructor. + + eapply type_App. + * simpl in ihty. eapply ihty; eassumption. * simpl in iht. eapply iht. assumption. * eapply ihu. assumption. + autorewrite with sigma. rewrite !subst1_inst. sigma. @@ -2232,9 +2242,12 @@ Proof. constructor; auto. ** exists s1. apply ihB; auto. ** apply ihb; auto. - - intros Σ wfΣ Γ wfΓ t na A B u X ht iht hu ihu Δ σ hΔ hσ. + - intros Σ wfΣ Γ wfΓ t na A B s u X hty ihty ht iht hu ihu Δ σ hΔ hσ. autorewrite with sigma. econstructor. + * specialize (ihty _ _ hΔ hσ). + simpl in ihty. eapply meta_conv_term; [eapply ihty|]. + now rewrite up_Up. * specialize (iht _ _ hΔ hσ). simpl in iht. eapply meta_conv; [eapply iht|]. now rewrite up_Up. diff --git a/pcuic/theories/PCUICSubstitution.v b/pcuic/theories/PCUICSubstitution.v index caeff121c..b8192fd6e 100644 --- a/pcuic/theories/PCUICSubstitution.v +++ b/pcuic/theories/PCUICSubstitution.v @@ -2567,7 +2567,7 @@ Proof. rewrite subst_context_snoc0 in X5. econstructor; eauto. - - specialize (X1 Γ Γ' Δ s sub eq_refl). + - specialize (X3 _ _ _ s0 sub eq_refl). eapply refine_type. 1: econstructor; eauto. unfold subst1. rewrite -> distr_subst. simpl. reflexivity. diff --git a/pcuic/theories/PCUICTyping.v b/pcuic/theories/PCUICTyping.v index 444c99784..d2bc5b7d0 100644 --- a/pcuic/theories/PCUICTyping.v +++ b/pcuic/theories/PCUICTyping.v @@ -356,7 +356,10 @@ Inductive typing `{checker_flags} (Σ : global_env_ext) (Γ : context) : term -> Σ ;;; Γ ,, vdef na b B |- t : A -> Σ ;;; Γ |- tLetIn na b B t : tLetIn na b B A -| type_App t na A B u : +| type_App t na A B s u : + (* Paranoid assumption, allows to show equivalence with template-coq, + but eventually unnecessary thanks to validity. *) + Σ ;;; Γ |- tProd na A B : tSort s -> Σ ;;; Γ |- t : tProd na A B -> Σ ;;; Γ |- u : A -> Σ ;;; Γ |- tApp t u : B{0 := u} @@ -698,6 +701,7 @@ Lemma typing_ind_env `{cf : checker_flags} : nth_error Γ n = Some decl -> PΓ Σ Γ wfΓ -> P Σ Γ (tRel n) (lift0 (S n) decl.(decl_type))) -> + (forall Σ (wfΣ : wf Σ.1) (Γ : context) (wfΓ : wf_local Σ Γ) (u : Universe.t), PΓ Σ Γ wfΓ -> wf_universe Σ u -> @@ -727,8 +731,9 @@ Lemma typing_ind_env `{cf : checker_flags} : Σ ;;; Γ,, vdef n b b_ty |- b' : b'_ty -> P Σ (Γ,, vdef n b b_ty) b' b'_ty -> P Σ Γ (tLetIn n b b_ty b') (tLetIn n b b_ty b'_ty)) -> - (forall Σ (wfΣ : wf Σ.1) (Γ : context) (wfΓ : wf_local Σ Γ) (t : term) na A B u, + (forall Σ (wfΣ : wf Σ.1) (Γ : context) (wfΓ : wf_local Σ Γ) (t : term) na A B u s, PΓ Σ Γ wfΓ -> + Σ ;;; Γ |- tProd na A B : tSort s -> P Σ Γ (tProd na A B) (tSort s) -> Σ ;;; Γ |- t : tProd na A B -> P Σ Γ t (tProd na A B) -> Σ ;;; Γ |- u : A -> P Σ Γ u A -> P Σ Γ (tApp t u) (B{0 := u})) -> @@ -988,6 +993,10 @@ Proof. -- match reverse goal with H : _ |- _ => eapply H + end; eauto; unshelve eapply X14; simpl; auto; try lia. + + -- match reverse goal with + H : _ |- _ => eapply H end; eauto. simpl in Hdecls. apply Hdecls; lia. diff --git a/pcuic/theories/PCUICUnivSubstitution.v b/pcuic/theories/PCUICUnivSubstitution.v index aed89cfc8..282cc39d8 100644 --- a/pcuic/theories/PCUICUnivSubstitution.v +++ b/pcuic/theories/PCUICUnivSubstitution.v @@ -1580,10 +1580,11 @@ Proof. + eapply X3; aa. - intros n b b_ty b' s1 b'_ty X X0 X1 X2 X3 X4 X5 u univs wfΣ' HSub H. econstructor; eauto. eapply X5; aa. - - intros t0 na A B u X X0 X1 X2 X3 u0 univs wfΣ' HSub H. + - intros t0 na A B s u X X0 X1 X2 X3 X4 X5 u0 univs wfΣ' HSub H. rewrite <- subst_subst_instance_constr. cbn. econstructor. + eapply X1; eauto. + eapply X3; eauto. + + eapply X5; eauto. - intros. rewrite subst_instance_constr_two. econstructor; [aa|aa|]. clear X X0; cbn in *. eapply consistent_ext_trans; eauto. diff --git a/pcuic/theories/PCUICValidity.v b/pcuic/theories/PCUICValidity.v index a68266978..dd01730c4 100644 --- a/pcuic/theories/PCUICValidity.v +++ b/pcuic/theories/PCUICValidity.v @@ -160,7 +160,7 @@ Section Validity. reflexivity. - (* Application *) - destruct X1 as [u' Hu']. exists u'. + destruct X3 as [u' Hu']. exists u'. move: (typing_wf_universe wf Hu') => wfu'. eapply (substitution0 _ _ na _ _ _ (tSort u')); eauto. apply inversion_Prod in Hu' as [na' [s1 [s2 Hs]]]; tas. intuition. @@ -314,3 +314,13 @@ Proof. clear -H'' HA''' wfΣ. depind H''. econstructor; eauto. eapply cumul_trans; eauto. Qed. + +(** "Economical" typing rule for applications, not requiring to check the product type *) +Lemma type_App' {cf:checker_flags} {Σ : global_env_ext} {wfΣ : wf Σ} {Γ t na A B u} : + Σ;;; Γ |- t : tProd na A B -> + Σ;;; Γ |- u : A -> Σ;;; Γ |- tApp t u : B {0 := u}. +Proof. + intros Ht Hu. + have [s Hs] := validity_term wfΣ Ht. + eapply type_App; eauto. +Qed. \ No newline at end of file diff --git a/pcuic/theories/PCUICWeakening.v b/pcuic/theories/PCUICWeakening.v index 253d04b27..533339ec6 100644 --- a/pcuic/theories/PCUICWeakening.v +++ b/pcuic/theories/PCUICWeakening.v @@ -118,8 +118,6 @@ Proof. * destruct H2. rewrite H2. simpl. now rewrite Nat.sub_0_r. Qed. -Ltac lia_f_equal := repeat (lia || f_equal). - Lemma smash_context_lift Δ k n Γ : smash_context (lift_context n (k + #|Γ|) Δ) (lift_context n k Γ) = lift_context n k (smash_context Δ Γ). @@ -887,15 +885,6 @@ Proof. destruct t; simpl; try congruence. Qed. -Lemma nth_error_rev_inv {A} (l : list A) i : - i < #|l| -> - nth_error (List.rev l) i = nth_error l (#|l| - S i). -Proof. - intros Hi. - rewrite nth_error_rev; autorewrite with len; auto. - now rewrite List.rev_involutive. -Qed. - Lemma weakening_check_one_fix (Γ' Γ'' : context) mfix : map (fun x : def term => diff --git a/pcuic/theories/PCUICWfUniverses.v b/pcuic/theories/PCUICWfUniverses.v index c0d345cf3..2bf2fb4cc 100644 --- a/pcuic/theories/PCUICWfUniverses.v +++ b/pcuic/theories/PCUICWfUniverses.v @@ -677,7 +677,7 @@ Section CheckerFlags. - simpl in *; to_wfu; eauto with pcuic. - rewrite wf_universes_subst. constructor. to_wfu; auto. constructor. - now move/andP: H3 => []. + now move/andP: H4 => []. - apply/andP; split. { apply/wf_universe_instanceP. diff --git a/pcuic/theories/TemplateToPCUICCorrectness.v b/pcuic/theories/TemplateToPCUICCorrectness.v index b2eff5476..1e643fe8b 100644 --- a/pcuic/theories/TemplateToPCUICCorrectness.v +++ b/pcuic/theories/TemplateToPCUICCorrectness.v @@ -3,7 +3,7 @@ From MetaCoq.Template Require Import config utils Ast TypingWf WfInv. Set Warnings "-notation-overridden". From MetaCoq.PCUIC Require Import PCUICAst PCUICAstUtils PCUICCumulativity PCUICLiftSubst PCUICEquality PCUICUnivSubst PCUICTyping TemplateToPCUIC - PCUICSubstitution PCUICGeneration. + PCUICWeakening PCUICSubstitution PCUICGeneration PCUICValidity. Set Warnings "+notation-overridden". From Equations.Prop Require Import DepElim. @@ -1042,18 +1042,21 @@ Lemma trans_wf_local {cf}: forall (Σ : Template.Ast.global_env_ext) (Γ : Tcontext) (wfΓ : TTy.wf_local Σ Γ), let P := (fun Σ0 (Γ0 : Tcontext) _ (t T : Tterm) _ => + wf (trans_global Σ0).1 -> trans_global Σ0;;; trans_local Γ0 |- trans t : trans T) in + wf (trans_global Σ).1 -> TTy.All_local_env_over TTy.typing P Σ Γ wfΓ -> wf_local (trans_global Σ) (trans_local Γ). Proof. intros. - induction X. + induction X0. - simpl. constructor. - simpl. econstructor. - + eapply IHX. - + simpl. destruct tu. exists x. eapply p. - - simpl. constructor; auto. red. destruct tu. exists x. auto. + + eapply IHX0. + + simpl. destruct tu. exists x. now eapply p. + - simpl. constructor; auto. red. destruct tu. exists x; auto. + simpl. eauto. Qed. Lemma trans_wf_local_env {cf} Σ Γ : @@ -1131,11 +1134,29 @@ Proof. eapply typing_wf; eauto. constructor. Qed. +Lemma trans_global_decl_universes d : + TTy.universes_decl_of_decl d = + universes_decl_of_decl (trans_global_decl d). +Proof. + destruct d; reflexivity. +Qed. + +Lemma trans_consistent_instance_ext {cf:checker_flags} Σ d u : + TTy.consistent_instance_ext Σ (TTy.universes_decl_of_decl d) u -> + consistent_instance_ext (trans_global Σ) (universes_decl_of_decl (trans_global_decl d)) u. +Proof. + unfold TTy.consistent_instance_ext, consistent_instance_ext. + rewrite global_ext_levels_trans global_ext_constraints_trans trans_global_decl_universes. + trivial. +Qed. + Theorem template_to_pcuic {cf} : TTy.env_prop (fun Σ Γ t T => + wf (trans_global Σ).1 -> typing (trans_global Σ) (trans_local Γ) (trans t) (trans T)). Proof. apply (TTy.typing_ind_env (fun Σ Γ t T => + wf (trans_global Σ).1 -> typing (trans_global Σ) (trans_local Γ) (trans t) (trans T) )%type). all: simpl. @@ -1156,48 +1177,68 @@ Proof. (* now rewrite global_ext_levels_trans. *) - (* Casts *) - eapply refine_type. eapply type_App with _ (trans t). - eapply type_Lambda; eauto. eapply type_Rel. econstructor; auto. - eapply typing_wf_local. eauto. eauto. simpl. exists s; auto. reflexivity. eauto. + eapply refine_type. eapply type_App with _ (trans t) _. + 2:{ eapply type_Lambda; eauto. eapply type_Rel. econstructor; auto. + eapply typing_wf_local. eauto. eauto. simpl. exists s; auto. reflexivity. } + eapply type_Prod. eauto. + instantiate (1 := s). simpl. + eapply (weakening _ _ [_] _ (tSort _)); eauto. + constructor; eauto. eapply typing_wf_local; eauto. red. + exists s; eauto. auto. simpl. unfold subst1. rewrite simpl_subst; auto. now rewrite lift0_p. - (* The interesting application case *) eapply type_mkApps; eauto. + specialize (X0 X2). eapply typing_wf in X; eauto. destruct X. - clear H1 X0 H H0. revert H2. - induction X1. econstructor; eauto. - (* Need updated typing_spine in template-coq *) admit. reflexivity. - simpl in p. - destruct (TypingWf.typing_wf _ wfΣ _ _ _ typrod) as [wfAB _]. - intros wfT. - econstructor; eauto. exists s; eauto. - change (tProd na (trans A) (trans B)) with (trans (T.tProd na A B)). - apply trans_cumul; auto with trans. - apply TypingWf.typing_wf_sigma; auto. - eapply Forall_impl. eapply TypingWf.typing_all_wf_decl; eauto. - intros. auto. - eapply typing_wf in ty; eauto. destruct ty as [wfhd _]. - rewrite trans_subst in IHX1; eauto with wf. - eapply IHX1. apply Template.LiftSubst.wf_subst; try constructor; auto. now inv wfAB. + eapply PCUICValidity.validity in X0. + clear H1 H H0. revert H2. + induction X1. + * econstructor; eauto. reflexivity. + * simpl in p. + destruct (TypingWf.typing_wf _ wfΣ _ _ _ typrod) as [wfAB _]. + intros wfT. + econstructor; eauto. + + exists s; eauto. eapply p; eauto. + + change (tProd na (trans A) (trans B)) with (trans (T.tProd na A B)). + apply trans_cumul; auto with trans. + apply TypingWf.typing_wf_sigma; auto. + eapply Forall_impl. eapply TypingWf.typing_all_wf_decl; eauto. + intros. auto. + + eapply typing_wf in ty; eauto. destruct ty as [wfhd _]. + rewrite trans_subst in IHX1; eauto with wf. + eapply IHX1; cycle 1. + apply Template.LiftSubst.wf_subst; try constructor; auto. now inv wfAB. + specialize (p X2). specialize (p0 X2). + eapply PCUICInversion.inversion_Prod in p as [s1 [s2 [HA [HB Hs]]]]. + eapply PCUICArities.isType_subst with [vass na (trans A)]; eauto. + constructor; eauto with pcuic. + constructor; eauto with pcuic. now rewrite subst_empty. + now exists s2. + apply X2. + * apply X2. - rewrite trans_subst_instance_constr. pose proof (forall_decls_declared_constant _ _ _ H). replace (trans (Template.Ast.cst_type decl)) with (cst_type (trans_constant_body decl)) by (destruct decl; reflexivity). - constructor; eauto with trans. admit. + constructor; eauto with trans. + now apply (trans_consistent_instance_ext _ (T.ConstantDecl decl)). - rewrite trans_subst_instance_constr. pose proof (forall_decls_declared_inductive _ _ _ _ isdecl). replace (trans (Template.Ast.ind_type idecl)) with (ind_type (trans_one_ind_body idecl)) by (destruct idecl; reflexivity). - eapply type_Ind; eauto. eauto with trans. admit. + eapply type_Ind; eauto. eauto with trans. + now apply (trans_consistent_instance_ext _ (T.InductiveDecl mdecl)). - pose proof (forall_decls_declared_constructor _ _ _ _ _ isdecl). unfold TTy.type_of_constructor in *. rewrite trans_subst. rewrite trans_subst_instance_constr. rewrite trans_inds. simpl. - eapply refine_type. econstructor; eauto with trans. admit. + eapply refine_type. econstructor; eauto with trans. + now apply (trans_consistent_instance_ext _ (T.InductiveDecl mdecl)). unfold type_of_constructor. simpl. f_equal. f_equal. destruct cdecl as [[id t] p]; simpl; auto. @@ -1208,9 +1249,9 @@ Proof. apply forall_decls_declared_inductive; eauto. destruct mdecl; auto. -- simpl. rewrite firstn_map. rewrite trans_build_case_predicate_type. erewrite H0. reflexivity. - -- eapply X2. + -- eapply X1. -- rewrite global_ext_constraints_trans; exact H1. - -- rewrite trans_mkApps in X4; auto with wf. + -- rewrite trans_mkApps in X2; auto with wf. -- admit. -- apply trans_build_branches_type in H2. rewrite firstn_map. exact H2. @@ -1245,8 +1286,8 @@ Proof. -- apply All_map. eapply All_impl; eauto. intuition eauto 3 with wf; cbn. rewrite H1. rewrite /trans_local map_length. - rewrite /trans_local map_app in X2. - rewrite <- trans_lift. apply X2. + rewrite /trans_local map_app in X3. + rewrite <- trans_lift. apply X3; auto. rdest. destruct (dbody x); simpl in *; congruence. -- admit. -- destruct decl; reflexivity. diff --git a/template-coq/theories/LiftSubst.v b/template-coq/theories/LiftSubst.v index 07025fb88..5571fc022 100644 --- a/template-coq/theories/LiftSubst.v +++ b/template-coq/theories/LiftSubst.v @@ -41,6 +41,13 @@ Definition lift_decl n k d := (map_decl (lift n k) d). Definition lift_context n k (Γ : context) : context := fold_context (fun k' => lift n (k' + k)) Γ. +Lemma lift_context_alt n k Γ : + lift_context n k Γ = + mapi (fun k' d => lift_decl n (Nat.pred #|Γ| - k' + k) d) Γ. +Proof. + unfold lift_context. apply fold_context_alt. +Qed. + (** Parallel substitution: it assumes that all terms in the substitution live in the same context *) @@ -83,6 +90,8 @@ Notation "M { j := N }" := (subst1 N j M) (at level 10, right associativity). Definition subst_context s k (Γ : context) : context := fold_context (fun k' => subst s (k' + k)) Γ. +Definition subst_decl s k (d : context_decl) := map_decl (subst s k) d. + Lemma subst_context_length s n Γ : #|subst_context s n Γ| = #|Γ|. Proof. induction Γ as [|[na [body|] ty] tl] in Γ |- *; cbn; eauto. @@ -92,6 +101,17 @@ Proof. lia. Qed. +Lemma subst_context_nil s n : subst_context s n [] = []. +Proof. reflexivity. Qed. + +Lemma subst_context_alt s k Γ : + subst_context s k Γ = + mapi (fun k' d => subst_decl s (Nat.pred #|Γ| - k' + k) d) Γ. +Proof. + unfold subst_context, fold_context. rewrite rev_mapi. rewrite List.rev_involutive. + apply mapi_ext. intros. f_equal. now rewrite List.rev_length. +Qed. + Definition subst_telescope s k (Γ : context) : context := mapi (fun k' decl => map_decl (subst s (k' + k)) decl) Γ. @@ -711,3 +731,4 @@ Lemma noccur_between_subst k n t : noccur_between k n t -> closedn (n + k) t -> closedn k t. Proof. Admitted. *) + diff --git a/template-coq/theories/Typing.v b/template-coq/theories/Typing.v index b123bbc4e..a273f4e03 100644 --- a/template-coq/theories/Typing.v +++ b/template-coq/theories/Typing.v @@ -1,7 +1,7 @@ (* Distributed under the terms of the MIT license. *) From Coq Require Import ssreflect Wellfounded Relation_Operators. From MetaCoq.Template Require Import config utils Ast AstUtils LiftSubst UnivSubst - EnvironmentTyping. + EnvironmentTyping Reflect. (** * Typing derivations @@ -627,20 +627,6 @@ Definition eq_context `{checker_flags} φ (Γ Δ : context) := Module TemplateEnvTyping := EnvTyping TemplateTerm TemplateEnvironment. Include TemplateEnvTyping. -Section WfArity. - Context (typing : forall (Σ : global_env_ext) (Γ : context), term -> term -> Type). - - Definition isWfArity Σ (Γ : context) T := - { ctx & { s & (destArity [] T = Some (ctx, s)) * All_local_env (lift_typing typing Σ) (Γ ,,, ctx) } }. - - Context (property : forall (Σ : global_env_ext) (Γ : context), - All_local_env (lift_typing typing Σ) Γ -> - forall (t T : term), typing Σ Γ t T -> Type). - - Definition isWfArity_prop Σ (Γ : context) T := - { wfa : isWfArity Σ Γ T & All_local_env_over typing property Σ _ (snd (projT2 (projT2 wfa))) }. -End WfArity. - (* AXIOM GUARD CONDITION *) Axiom fix_guard : mfixpoint term -> bool. @@ -765,27 +751,100 @@ Definition build_case_predicate_type ind mdecl idecl params u ps : option term : decl_type := mkApps (tInd ind u) (map (lift0 #|X.1|) params ++ to_extended_list X.1) |} in ret (it_mkProd_or_LetIn (X.1 ,, inddecl) (tSort ps)). -Definition wf_universe Σ s := +Definition destInd (t : term) := + match t with + | tInd ind u => Some (ind, u) + | _ => None + end. + +Definition isFinite (r : recursivity_kind) := + match r with + | Finite => true + | _ => false + end. + +Definition isCoFinite (r : recursivity_kind) := + match r with + | CoFinite => true + | _ => false + end. + +Definition check_recursivity_kind (Σ : global_env) ind r := + match lookup_env Σ ind with + | Some (InductiveDecl mib) => Reflect.eqb mib.(ind_finite) r + | _ => false + end. + +Definition check_one_fix d := + let '{| dname := na; + dtype := ty; + dbody := b; + rarg := arg |} := d in + let '(ctx, ty) := decompose_prod_assum [] ty in + match nth_error (List.rev (smash_context [] ctx)) arg with + | Some argd => + let (hd, args) := decompose_app argd.(decl_type) in + match destInd hd with + | Some (mkInd mind _, u) => Some mind + | None => None (* Not recursive on an inductive type *) + end + | None => None (* Recursive argument not found *) + end. + +Definition wf_fixpoint (Σ : global_env) mfix := + let checks := map check_one_fix mfix in + match map_option_out checks with + | Some (ind :: inds) => + (* Check that mutually recursive fixpoints are all on the same mututal + inductive block *) + forallb (Reflect.eqb ind) inds && + check_recursivity_kind Σ ind Finite + | _ => false + end. + +Definition check_one_cofix d := + let '{| dname := na; + dtype := ty; + dbody := b; + rarg := arg |} := d in + let '(ctx, ty) := decompose_prod_assum [] ty in + let (hd, args) := decompose_app ty in + match destInd hd with + | Some (mkInd ind _, u) => Some ind + | None => None (* Not recursive on an inductive type *) + end. + +Definition wf_cofixpoint (Σ : global_env) mfix := + let checks := map check_one_cofix mfix in + match map_option_out checks with + | Some (ind :: inds) => + (* Check that mutually recursive cofixpoints are all producing + coinductives in the same mututal coinductive block *) + forallb (Reflect.eqb ind) inds && + check_recursivity_kind Σ ind CoFinite + | _ => false + end. + +Definition wf_universe Σ s := match s with - | Universe.lProp + | Universe.lProp | Universe.lSProp => True - | Universe.lType u => + | Universe.lType u => forall l, UnivExprSet.In l u -> LevelSet.In (UnivExpr.get_level l) (global_ext_levels Σ) end. +Reserved Notation "'wf_local' Σ Γ " (at level 9, Σ, Γ at next level). Inductive typing `{checker_flags} (Σ : global_env_ext) (Γ : context) : term -> term -> Type := | type_Rel n decl : - All_local_env (lift_typing typing Σ) Γ -> + wf_local Σ Γ -> nth_error Γ n = Some decl -> Σ ;;; Γ |- tRel n : lift0 (S n) decl.(decl_type) -| type_Sort l : - All_local_env (lift_typing typing Σ) Γ -> - (l = inl PropLevel.lSProp \/ - l = inl PropLevel.lProp \/ - (exists l', LevelSet.In l' (global_ext_levels Σ) /\ l = inr l')) -> - Σ ;;; Γ |- tSort (Universe.of_levels l) : tSort (Universe.super (Universe.of_levels l)) +| type_Sort s : + wf_local Σ Γ -> + wf_universe Σ s -> + Σ ;;; Γ |- tSort s : tSort (Universe.super s) | type_Cast c k t s : Σ ;;; Γ |- t : tSort s -> @@ -815,19 +874,19 @@ Inductive typing `{checker_flags} (Σ : global_env_ext) (Γ : context) : term -> Σ ;;; Γ |- tApp t l : t' | type_Const cst u : - All_local_env (lift_typing typing Σ) Γ -> + wf_local Σ Γ -> forall decl (isdecl : declared_constant Σ.1 cst decl), consistent_instance_ext Σ decl.(cst_universes) u -> Σ ;;; Γ |- (tConst cst u) : subst_instance_constr u decl.(cst_type) | type_Ind ind u : - All_local_env (lift_typing typing Σ) Γ -> + wf_local Σ Γ -> forall mdecl idecl (isdecl : declared_inductive Σ.1 mdecl ind idecl), consistent_instance_ext Σ mdecl.(ind_universes) u -> Σ ;;; Γ |- (tInd ind u) : subst_instance_constr u idecl.(ind_type) | type_Construct ind i u : - All_local_env (lift_typing typing Σ) Γ -> + wf_local Σ Γ -> forall mdecl idecl cdecl (isdecl : declared_constructor Σ.1 mdecl idecl (ind, i) cdecl), consistent_instance_ext Σ mdecl.(ind_universes) u -> Σ ;;; Γ |- (tConstruct ind i u) : type_of_constructor mdecl cdecl (ind, i) u @@ -841,6 +900,7 @@ Inductive typing `{checker_flags} (Σ : global_env_ext) (Γ : context) : term -> forall ps pty, build_case_predicate_type ind mdecl idecl params u ps = Some pty -> Σ ;;; Γ |- p : pty -> is_allowed_elimination Σ ps idecl.(ind_kelim) -> + isCoFinite mdecl.(ind_finite) = false -> Σ ;;; Γ |- c : mkApps (tInd ind u) args -> forall btys, map_option_out (build_branches_type ind mdecl idecl params u p) = Some btys -> All2 (fun br bty => (br.1 = bty.1) * (Σ ;;; Γ |- br.2 : bty.2) * (Σ ;;; Γ |- bty.2 : tSort ps)) brs btys -> @@ -853,27 +913,30 @@ Inductive typing `{checker_flags} (Σ : global_env_ext) (Γ : context) : term -> Σ ;;; Γ |- tProj p c : subst0 (c :: List.rev args) (subst_instance_constr u pdecl.2) | type_Fix mfix n decl : - fix_guard mfix -> - nth_error mfix n = Some decl -> - All_local_env (lift_typing typing Σ) Γ -> - All (fun d => {s & Σ ;;; Γ |- d.(dtype) : tSort s}) mfix -> - All (fun d => (Σ ;;; Γ ,,, fix_context mfix |- d.(dbody) : lift0 #|fix_context mfix| d.(dtype)) - * (isLambda d.(dbody) = true)%type) mfix -> - Σ ;;; Γ |- tFix mfix n : decl.(dtype) + fix_guard mfix -> + nth_error mfix n = Some decl -> + wf_local Σ Γ -> + All (fun d => {s & Σ ;;; Γ |- d.(dtype) : tSort s}) mfix -> + All (fun d => (Σ ;;; Γ ,,, fix_context mfix |- d.(dbody) : lift0 #|fix_context mfix| d.(dtype)) + * (isLambda d.(dbody) = true)%type) mfix -> + wf_fixpoint Σ mfix -> + Σ ;;; Γ |- tFix mfix n : decl.(dtype) | type_CoFix mfix n decl : nth_error mfix n = Some decl -> - All_local_env (lift_typing typing Σ) Γ -> + wf_local Σ Γ -> All (fun d => {s & Σ ;;; Γ |- d.(dtype) : tSort s}) mfix -> All (fun d => Σ ;;; Γ ,,, fix_context mfix |- d.(dbody) : lift0 #|fix_context mfix| d.(dtype)) mfix -> + wf_cofixpoint Σ mfix -> Σ ;;; Γ |- tCoFix mfix n : decl.(dtype) -| type_Conv t A B : +| type_Conv t A B s : Σ ;;; Γ |- t : A -> - (isWfArity typing Σ Γ B + {s & Σ ;;; Γ |- B : tSort s})%type -> + Σ ;;; Γ |- B : tSort s -> Σ ;;; Γ |- A <= B -> Σ ;;; Γ |- t : B where " Σ ;;; Γ |- t : T " := (typing Σ Γ t T) : type_scope + and "'wf_local' Σ Γ " := (All_local_env (lift_typing typing Σ) Γ) : type_scope (* Typing of "spines", currently just the arguments of applications *) @@ -886,8 +949,6 @@ with typing_spine `{checker_flags} (Σ : global_env_ext) (Γ : context) : term - typing_spine Σ Γ (subst10 hd B) tl B' -> typing_spine Σ Γ T (cons hd tl) B'. -Notation wf_local Σ Γ := (All_local_env (lift_typing typing Σ) Γ). - (** ** Typechecking of global environments *) Definition has_nparams npars ty := @@ -974,16 +1035,11 @@ Proof. (all2_size _ (fun x y p => Nat.max (typing_size Σ Γ (snd x) (snd y) (snd (fst p))) (typing_size _ _ _ _ (snd p))) a)))). - exact (S (Nat.max (Nat.max (wf_local_size _ typing_size _ a) (all_size _ (fun x p => typing_size Σ _ _ _ p.π2) a0)) (all_size _ (fun x p => typing_size Σ _ _ _ (fst p)) a1))). - exact (S (Nat.max (Nat.max (wf_local_size _ typing_size _ a) (all_size _ (fun x p => typing_size Σ _ _ _ p.π2) a0)) (all_size _ (fun x p => typing_size Σ _ _ _ p) a1))). - - destruct s. - + red in i. - exact (S (Nat.max (wf_local_size _ typing_size _ (snd (projT2 (projT2 i)))) d)). - + destruct s as [u Hu]. apply typing_size in Hu. - exact (S (Nat.max d Hu)). Defined. Lemma typing_size_pos `{checker_flags} {Σ Γ t T} (d : Σ ;;; Γ |- t : T) : typing_size d > 0. Proof. - induction d; simpl; try lia. destruct s as [s | [u Hu]]; try lia. + induction d; simpl; try lia. Qed. Fixpoint globenv_size (Σ : global_env) : size := @@ -1014,7 +1070,7 @@ Proof. intros. now apply X. Qed. Lemma type_Prop `{checker_flags} Σ : Σ ;;; [] |- tSort Universe.lProp : tSort Universe.type1. change ( Σ ;;; [] |- tSort (Universe.of_levels (inl PropLevel.lProp)) : tSort Universe.type1); - constructor;auto. constructor. + constructor;auto. constructor. constructor. Defined. Lemma env_prop_sigma `{checker_flags} P : env_prop P -> @@ -1047,7 +1103,6 @@ Proof. change (fun (x : global_env_ext) (x0 : context) (x1 x2 : term) (x3 : x;;; x0 |- x1 : x2) => typing_size x3) with (@typing_size H); try lia. - destruct indnparrel as ((ind' & npar') & ?); cbn in *; subst ind npar. lia. - - destruct s as [s | [u Hu]]; try lia. Qed. Lemma wf_local_inv `{checker_flags} {Σ Γ'} (w : wf_local Σ Γ') : @@ -1106,7 +1161,6 @@ Inductive Forall_typing_spine `{checker_flags} Σ Γ (P : term -> term -> Type) Forall_typing_spine Σ Γ P T (hd :: tl) B' (type_spine_cons Σ Γ hd tl na A B s T B' typrod cumul ty tls). - Lemma typing_ind_env `{cf : checker_flags} : forall (P : global_env_ext -> context -> term -> term -> Type) (Pdecl := fun Σ Γ wfΓ t T tyT => P Σ Γ t T), @@ -1114,14 +1168,10 @@ Lemma typing_ind_env `{cf : checker_flags} : nth_error Γ n = Some decl -> All_local_env_over typing Pdecl Σ Γ wfΓ -> P Σ Γ (tRel n) (lift0 (S n) decl.(decl_type))) -> - (forall Σ (wfΣ : wf Σ.1) (Γ : context) (wfΓ : wf_local Σ Γ) - (l : PropLevel.t + Level.t), - All_local_env_over typing Pdecl Σ Γ wfΓ -> - (l = inl PropLevel.lSProp \/ - l = inl PropLevel.lProp \/ - (exists l', LevelSet.In l' (global_ext_levels Σ) /\ l = inr l')) -> - - P Σ Γ (tSort (Universe.of_levels l)) (tSort (Universe.super (Universe.of_levels l)))) -> + (forall Σ (wfΣ : wf Σ.1) (Γ : context) (wfΓ : wf_local Σ Γ) (u : Universe.t), + All_local_env_over typing Pdecl Σ Γ wfΓ -> + wf_universe Σ u -> + P Σ Γ (tSort u) (tSort (Universe.super u))) -> (forall Σ (wfΣ : wf Σ.1) (Γ : context) (wfΓ : wf_local Σ Γ) (c : term) (k : cast_kind) (t : term) (s : Universe.t), @@ -1192,6 +1242,7 @@ Lemma typing_ind_env `{cf : checker_flags} : is_allowed_elimination (global_ext_constraints Σ) ps idecl.(ind_kelim) -> Σ ;;; Γ |- c : mkApps (tInd ind u) args -> P Σ Γ c (mkApps (tInd ind u) args) -> + isCoFinite mdecl.(ind_finite) = false -> forall btys, map_option_out (build_branches_type ind mdecl idecl params u p) = Some btys -> All2 (fun br bty => (br.1 = bty.1) * (Σ ;;; Γ |- br.2 : bty.2) * P Σ Γ br.2 bty.2 * @@ -1216,6 +1267,7 @@ Lemma typing_ind_env `{cf : checker_flags} : All (fun d => (Σ ;;; Γ ,,, types |- d.(dbody) : lift0 #|types| d.(dtype))%type * (isLambda d.(dbody) = true)%type * P Σ (Γ ,,, types) d.(dbody) (lift0 #|types| d.(dtype)))%type mfix -> + wf_fixpoint Σ.1 mfix -> P Σ Γ (tFix mfix n) decl.(dtype)) -> (forall Σ (wfΣ : wf Σ.1) (Γ : context) (wfΓ : wf_local Σ Γ) (mfix : list (def term)) (n : nat) decl, @@ -1225,13 +1277,15 @@ Lemma typing_ind_env `{cf : checker_flags} : All (fun d => {s & (Σ ;;; Γ |- d.(dtype) : tSort s)%type * P Σ Γ d.(dtype) (tSort s)})%type mfix -> All (fun d => (Σ ;;; Γ ,,, types |- d.(dbody) : lift0 #|types| d.(dtype))%type * P Σ (Γ ,,, types) d.(dbody) (lift0 #|types| d.(dtype)))%type mfix -> + wf_cofixpoint Σ.1 mfix -> P Σ Γ (tCoFix mfix n) decl.(dtype)) -> - (forall Σ (wfΣ : wf Σ.1) (Γ : context) (wfΓ : wf_local Σ Γ) (t A B : term), + (forall Σ (wfΣ : wf Σ.1) (Γ : context) (wfΓ : wf_local Σ Γ) (t A B : term) s, All_local_env_over typing Pdecl Σ Γ wfΓ -> Σ ;;; Γ |- t : A -> P Σ Γ t A -> - (isWfArity_prop typing Pdecl Σ Γ B + {s & (Σ ;;; Γ |- B : tSort s) * P Σ Γ B (tSort s)})%type -> + Σ ;;; Γ |- B : tSort s -> + P Σ Γ B (tSort s) -> Σ ;;; Γ |- A <= B -> P Σ Γ t B) -> @@ -1478,7 +1532,7 @@ Proof. Forall_decls_typing P Σ.1 * P Σ Γ0 t T). {intros. eapply (X14 _ X _ _ Hty); eauto. lia. } clear X14 X13. - clear e decl i a0. + clear e decl i a0 i0. remember (fix_context mfix) as mfixcontext. clear Heqmfixcontext. induction a1; econstructor; eauto. @@ -1516,7 +1570,7 @@ Proof. Forall_decls_typing P Σ.1 * P Σ Γ0 t T). {intros. eapply (X14 _ X _ _ Hty); eauto. lia. } clear X14 X13. - clear e decl a0. + clear e decl a0 i. remember (fix_context mfix) as mfixcontext. clear Heqmfixcontext. induction a1; econstructor; eauto. @@ -1524,28 +1578,8 @@ Proof. eapply (X _ (typing_wf_local p) _ _ p). simpl. lia. ++ eapply IHa1. intros. eapply (X _ X0 _ _ Hty). simpl; lia. - - -- eapply X12; eauto. - ++ eapply (X14 _ wfΓ _ _ H); simpl. destruct s as [s | [u Hu]]; lia. - ++ simpl in X14, X13. - destruct s as [s | [u Hu]]. - ** left. - red. exists s. red in s. revert X14. - generalize (snd (projT2 (projT2 s))). - induction a; simpl in *; intros X14 *; constructor. - --- apply IHa. intros. eapply (X14 _ wfΓ0 _ _ Hty). lia. - --- red. eapply (X14 _ a _ _ (projT2 t1)). clear. - destruct t1. simpl. lia. - --- apply IHa. intros. eapply (X14 _ wfΓ0 _ _ Hty). lia. - --- red. destruct t1. unshelve eapply X14. all: eauto. - simpl. lia. - --- red. destruct t1. unshelve eapply X14. all: eauto. - simpl. lia. - ** right. - exists u. intuition eauto. unshelve eapply X14. all: eauto. lia. Qed. - (** * Lemmas about All_local_env *) Lemma nth_error_All_local_env {P Γ n} (isdecl : n < #|Γ|) : @@ -1626,7 +1660,7 @@ Qed. Definition property `{checker_flags} := forall (Σ : global_env_ext) (Γ : context), - All_local_env (lift_typing typing Σ) Γ -> forall t T : term, typing Σ Γ t T -> Type. + wf_local Σ Γ -> forall t T : term, typing Σ Γ t T -> Type. Definition lookup_wf_local {Γ P} (wfΓ : All_local_env P Γ) (n : nat) (isdecl : n < #|Γ|) : All_local_env P (skipn (S n) Γ). @@ -1666,7 +1700,7 @@ Definition on_wf_local_decl `{checker_flags} {Σ Γ} end H. -Lemma nth_error_All_local_env_over `{checker_flags} {P Σ Γ n decl} (eq : nth_error Γ n = Some decl) {wfΓ : All_local_env (lift_typing typing Σ) Γ} : +Lemma nth_error_All_local_env_over `{checker_flags} {P Σ Γ n decl} (eq : nth_error Γ n = Some decl) {wfΓ : wf_local Σ Γ} : All_local_env_over typing P Σ Γ wfΓ -> let Γ' := skipn (S n) Γ in let p := lookup_wf_local_decl wfΓ n eq in diff --git a/template-coq/theories/TypingWf.v b/template-coq/theories/TypingWf.v index 298e683d1..ee69a6d85 100644 --- a/template-coq/theories/TypingWf.v +++ b/template-coq/theories/TypingWf.v @@ -1,6 +1,7 @@ (* Distributed under the terms of the MIT license. *) From MetaCoq.Template Require Import config utils Ast AstUtils Induction LiftSubst UnivSubst Typing. +From Equations Require Import Equations. Require Import ssreflect. (** * Well-formedness of terms and types in typing derivations @@ -523,7 +524,7 @@ Proof. apply wf_subst; auto with wf. apply wf_subst_instance_constr. eapply declared_constructor_wf; eauto. - split. wf. constructor; eauto. solve_all. - apply wf_mkApps. wf. solve_all. apply wf_mkApps_inv in H7. solve_all. + apply wf_mkApps. wf. solve_all. apply wf_mkApps_inv in H8. solve_all. apply All_app_inv; solve_all. now apply All_skipn. - split. wf. apply wf_subst. solve_all. constructor. wf. apply wf_mkApps_inv in H2. apply All_rev. solve_all. @@ -544,15 +545,6 @@ Proof. solve_all. destruct a. intuition. + eapply All_nth_error in X0; eauto. destruct X0 as [s ?]; intuition. - - - split. apply H. destruct X1 as [X1|[s X1]]; [|apply X1]. - destruct X1 as [[Γ' [s [X1 X1']]] XX]; cbn in *. - assert (HB : B = it_mkProd_or_LetIn Γ' (tSort s)). { - clear -X1. pose proof (destArity_spec [] B) as HH. - rewrite X1 in HH. assumption. } - rewrite HB. clear -XX. - eapply wf_it_mkProd_or_LetIn in XX. rewrite it_mkProd_or_LetIn_app in XX. - apply it_mkProd_or_LetIn_wf in XX. exact XX. constructor. Qed. Lemma typing_all_wf_decl {cf:checker_flags} Σ (wfΣ : wf Σ.1) Γ (wfΓ : wf_local Σ Γ) : @@ -568,49 +560,6 @@ Proof. Qed. Hint Resolve typing_all_wf_decl : wf. -(* TODO MOVE? *) -Definition sort_irrelevant - (P : global_env_ext -> context -> term -> option term -> Type) := - forall Σ Γ b s s', P Σ Γ (tSort s) b -> P Σ Γ (tSort s') b. - - -(* TODO MOVE? *) -Lemma on_global_env_mix `{checker_flags} {Σ P Q} : - sort_irrelevant Q -> - on_global_env P Σ -> - on_global_env Q Σ -> - on_global_env (fun Σ Γ t T => (P Σ Γ t T * Q Σ Γ t T)%type) Σ. -Proof. - intros iQ hP hQ. - induction hP in Q, iQ, hQ |- *. - 1: constructor. - invs hQ. constructor. - - eapply IHhP. all: eauto. - - assumption. - - assumption. - (* - destruct d. all: simpl in *. - + destruct c as [ty [bo|] un]. all: simpl in *. - all: unfold on_constant_decl in *. - all: simpl in *. - * intuition eauto. - * unfold on_type in *. intuition eauto. - + destruct o0 as [oi op onpars ong]. - destruct o2 as [oi' op' onpars' ong']. - constructor. all: auto. - * clear - oi oi'. revert oi oi'. - generalize (TemplateEnvironment.ind_bodies m). - intros l h1 h2. - induction h1 in h2 |- *. 1: constructor. - dependent destruction h2. - constructor. 2: auto. - destruct p, o. econstructor. - -- eassumption. - -- unfold on_type in *. intuition eauto. - -- admit. - -- *) - - todo "simplify onConstructors"%string. -Qed. - Lemma on_global_env_impl `{checker_flags} Σ P Q : (forall Σ Γ t T, on_global_env P Σ.1 -> P Σ Γ t T -> Q Σ Γ t T) -> on_global_env P Σ -> on_global_env Q Σ. @@ -662,13 +611,8 @@ Proof. intros. pose proof (env_prop_sigma _ typing_wf_gen _ wfΣ). red in X. unfold lift_typing in X. do 2 red in wfΣ. - unshelve eapply (on_global_env_mix _ wfΣ) in X. - red. intros. destruct b; intuition auto with wf. - destruct X0 as [u Hu]. exists u. intuition auto with wf. - clear wfΣ. - eapply on_global_env_impl; eauto; simpl; intros. clear X. - destruct X1 as [Hty Ht]. - destruct T. apply Ht. destruct Ht; wf. + eapply on_global_env_impl; eauto; simpl; intros. + destruct T. red. apply X1. red. destruct X1 as [x [a wfs]]. split; auto. Qed. Lemma typing_wf {cf:checker_flags} Σ (wfΣ : wf Σ.1) Γ t T : diff --git a/template-coq/theories/utils/MCList.v b/template-coq/theories/utils/MCList.v index e3c3b6f24..79094596f 100644 --- a/template-coq/theories/utils/MCList.v +++ b/template-coq/theories/utils/MCList.v @@ -236,6 +236,16 @@ Proof. destruct l; simpl in *; congruence. Qed. +Lemma mapi_rec_compose {A B C} (g : nat -> B -> C) (f : nat -> A -> B) k l : + mapi_rec g (mapi_rec f l k) k = mapi_rec (fun k x => g k (f k x)) l k. +Proof. + induction l in k |- *; simpl; auto. now rewrite IHl. +Qed. + +Lemma mapi_compose {A B C} (g : nat -> B -> C) (f : nat -> A -> B) l : + mapi g (mapi f l) = mapi (fun k x => g k (f k x)) l. +Proof. apply mapi_rec_compose. Qed. + Lemma map_ext {A B : Type} (f g : A -> B) (l : list A) : (forall x, f x = g x) -> map f l = map g l. @@ -770,6 +780,15 @@ Proof. reflexivity. Qed. +Lemma nth_error_rev_inv {A} (l : list A) i : + i < #|l| -> + nth_error (List.rev l) i = nth_error l (#|l| - S i). +Proof. + intros Hi. + rewrite nth_error_rev ?List.rev_length; auto. + now rewrite List.rev_involutive. +Qed. + Lemma nth_error_snoc {A} (l : list A) (a : A) (l' : list A) i : i = #|l| -> nth_error (l ++ a :: l') i = Some a. diff --git a/template-coq/theories/utils/MCPrelude.v b/template-coq/theories/utils/MCPrelude.v index 81f3ffe07..5b8768dea 100644 --- a/template-coq/theories/utils/MCPrelude.v +++ b/template-coq/theories/utils/MCPrelude.v @@ -33,6 +33,7 @@ Notation "x .π2" := (@projT2 _ _ x) (at level 3, format "x '.π2'"). Create HintDb terms. Ltac arith_congr := repeat (try lia; progress f_equal). +Ltac lia_f_equal := repeat (lia || f_equal). Ltac easy0 := let rec use_hyp H := From cb5aaebb8e049fe8f0d5ba84d95c2b7b3da4d25e Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Wed, 9 Dec 2020 02:31:13 +0100 Subject: [PATCH 47/70] Template -> PCUIC -> Template proofs --- erasure/theories/ESubstitution.v | 4 +- erasure/theories/Erasure.v | 4 +- erasure/theories/ErasureCorrectness.v | 11 +- pcuic/theories/PCUICCanonicity.v | 2 +- pcuic/theories/PCUICClosed.v | 76 +++++++++++ pcuic/theories/PCUICCumulProp.v | 10 +- pcuic/theories/PCUICLiftSubst.v | 2 +- pcuic/theories/PCUICPrincipality.v | 21 +-- pcuic/theories/PCUICSR.v | 5 +- pcuic/theories/PCUICSigmaCalculus.v | 16 +-- pcuic/theories/PCUICToTemplateCorrectness.v | 81 +++++------ pcuic/theories/TemplateToPCUICCorrectness.v | 141 +++++++++----------- safechecker/theories/PCUICSafeRetyping.v | 2 +- safechecker/theories/PCUICTypeChecker.v | 2 +- template-coq/theories/LiftSubst.v | 2 +- template-coq/theories/Typing.v | 5 +- 16 files changed, 225 insertions(+), 159 deletions(-) diff --git a/erasure/theories/ESubstitution.v b/erasure/theories/ESubstitution.v index 941f35bee..bd2880ce2 100644 --- a/erasure/theories/ESubstitution.v +++ b/erasure/theories/ESubstitution.v @@ -399,10 +399,10 @@ Proof. eapply substitution; eauto. + econstructor. eapply is_type_subst; eauto. - - inv H1. + - inv H2. + cbn. econstructor. - eapply H; eauto. eapply H0; eauto. + eapply H1; eauto. + econstructor. eapply is_type_subst; eauto. - inv H1. diff --git a/erasure/theories/Erasure.v b/erasure/theories/Erasure.v index e062b81d5..b3a5baf10 100644 --- a/erasure/theories/Erasure.v +++ b/erasure/theories/Erasure.v @@ -25,7 +25,7 @@ Program Definition erase_template_program (p : Ast.program) Next Obligation. sq. - apply (template_to_pcuic_env (Ast.empty_ext p.1) wfΣ). + apply (template_to_pcuic_env_ext (Ast.empty_ext p.1) wfΣ). Qed. Next Obligation. @@ -36,7 +36,7 @@ Next Obligation. apply Ht. Defined. Next Obligation. - sq. apply (template_to_pcuic_env (Ast.empty_ext p.1) wfΣ). + sq. apply (template_to_pcuic_env_ext (Ast.empty_ext p.1) wfΣ). Defined. Local Open Scope string_scope. diff --git a/erasure/theories/ErasureCorrectness.v b/erasure/theories/ErasureCorrectness.v index d5f531381..6f9bb01b7 100644 --- a/erasure/theories/ErasureCorrectness.v +++ b/erasure/theories/ErasureCorrectness.v @@ -1097,7 +1097,7 @@ Proof. destruct H2. eapply (Is_type_app _ _ _ (x5 ++ [av])) in X as []; eauto; first last. - rewrite mkApps_nested app_assoc mkApps_snoc. - eapply type_App; eauto. + eapply PCUICValidity.type_App'; eauto. eapply subject_reduction; eauto. eapply wcbeval_red; eauto. - eapply erases_box. @@ -1149,7 +1149,8 @@ Proof. subst. unfold is_constructor. rewrite nth_error_snoc. lia. assert(Σ ;;; [] |- mkApps (tFix mfix idx) (argsv ++ [av]) : PCUICLiftSubst.subst [av] 0 x1). - { rewrite -mkApps_nested. eapply type_App; eauto. eapply subject_reduction_eval;eauto. } + { rewrite -mkApps_nested. eapply PCUICValidity.type_App'; eauto. + eapply subject_reduction_eval; eauto. } epose proof (fix_app_is_constructor Σ (args:=argsv ++ [av]) axfree X). rewrite /unfold_fix e0 in X0. specialize (X0 eq_refl). simpl in X0. @@ -1223,7 +1224,7 @@ Proof. eauto. -- eauto. -- rewrite mkApps_snoc. - eapply type_App; eauto. + eapply PCUICValidity.type_App'; eauto. eapply subject_reduction; eauto. eapply wcbeval_red; eauto. @@ -1264,7 +1265,7 @@ Proof. -- eauto. -- eauto. -- cbn. - eapply type_App; eauto. + eapply PCUICValidity.type_App'; eauto. * depelim H1. -- exists (E.tApp (E.mkApps (E.tFix mfix' idx) x7) x5). split; [eauto using erases_tApp, erases_mkApps|]. @@ -1289,7 +1290,7 @@ Proof. ++ eauto. ++ eauto. ++ rewrite mkApps_snoc. - eapply type_App; eauto. + eapply PCUICValidity.type_App'; eauto. - destruct ip. assert (Hty' := Hty). diff --git a/pcuic/theories/PCUICCanonicity.v b/pcuic/theories/PCUICCanonicity.v index ff9358915..abc7b956d 100644 --- a/pcuic/theories/PCUICCanonicity.v +++ b/pcuic/theories/PCUICCanonicity.v @@ -1219,7 +1219,7 @@ Section WeakNormalization. rewrite closedn_mkApps in Ht2. now move/andP: Ht2 => [clf _]. eapply red_fix; eauto. assert (Σ ;;; [] |- mkApps (tFix mfix idx) (argsv ++ [av]) : B {0 := av}). - { rewrite -mkApps_nested /=. eapply type_App; eauto. } + { rewrite -mkApps_nested /=. eapply type_App'; eauto. } epose proof (fix_app_is_constructor axfree X0 e); eauto. rewrite /is_constructor. destruct nth_error eqn:hnth => //. diff --git a/pcuic/theories/PCUICClosed.v b/pcuic/theories/PCUICClosed.v index f3101aacd..35a50d762 100644 --- a/pcuic/theories/PCUICClosed.v +++ b/pcuic/theories/PCUICClosed.v @@ -1262,3 +1262,79 @@ Proof. simpl in clt. move/andP: clt. intuition auto. move/andP: clt => [cd cmfix]. apply auxm; auto. Defined. + +Lemma term_noccur_between_list_ind : + forall (P : nat -> nat -> term -> Type), + (forall k n (i : nat), i < k \/ k + n <= i -> P k n (tRel i)) -> + (forall k n (i : ident), P k n (tVar i)) -> + (forall k n (id : nat) (l : list term), All (P k n) l -> P k n (tEvar id l)) -> + (forall k n s, P k n (tSort s)) -> + (forall k n (na : aname) (t : term), P k n t -> forall t0 : term, P (S k) n t0 -> P k n (tProd na t t0)) -> + (forall k n (na : aname) (t : term), P k n t -> forall t0 : term, P (S k) n t0 -> P k n (tLambda na t t0)) -> + (forall k n (na : aname) (t : term), + P k n t -> forall t0 : term, P k n t0 -> forall t1 : term, P (S k) n t1 -> P k n (tLetIn na t t0 t1)) -> + (forall k n (t u : term), P k n t -> P k n u -> P k n (tApp t u)) -> + (forall k n s (u : list Level.t), P k n (tConst s u)) -> + (forall k n (i : inductive) (u : list Level.t), P k n (tInd i u)) -> + (forall k n (i : inductive) (c : nat) (u : list Level.t), P k n (tConstruct i c u)) -> + (forall k n (p : inductive * nat) (t : term), + P k n t -> forall t0 : term, P k n t0 -> forall l : list (nat * term), + tCaseBrsProp (P k n) l -> P k n (tCase p t t0 l)) -> + (forall k n (s : projection) (t : term), P k n t -> P k n (tProj s t)) -> + (forall k n (m : mfixpoint term) (i : nat), tFixProp (P k n) (P (#|fix_context m| + k) n) m -> P k n (tFix m i)) -> + (forall k n (m : mfixpoint term) (i : nat), tFixProp (P k n) (P (#|fix_context m| + k) n) m -> P k n (tCoFix m i)) -> + (forall k n p, P k n (tPrim p)) -> + forall k n (t : term), noccur_between k n t -> P k n t. +Proof. + intros until t. revert k n t. + fix auxt 3. + move auxt at top. + intros k n t. + destruct t; intros clt; match goal with + H : _ |- _ => apply H + end; auto; simpl in clt; + try move/andP: clt => [cl1 cl2]; + try move/andP: cl1 => [cl1 cl1']; + try solve[apply auxt; auto]; + simpl in *. + + - move/orP: clt => [cl|cl]. + now apply Nat.ltb_lt in cl; eauto. + now apply Nat.leb_le in cl; eauto. + + - revert l clt. + fix auxl' 1. + destruct l; constructor; [|apply auxl']. + apply auxt. simpl in clt. now move/andP: clt => [clt cll]. + now move/andP: clt => [clt cll]. + + - red. + revert brs cl2. + fix auxl' 1. + destruct brs; constructor; [|apply auxl']. + simpl in cl2. move/andP: cl2 => [clt cll]. + apply auxt, clt. move/andP: cl2 => [clt cll]. + apply cll. + + - red. + rewrite fix_context_length. + revert clt. + generalize (#|mfix|). + revert mfix. + fix auxm 1. + destruct mfix; intros; constructor. + simpl in clt. move/andP: clt => [clt cll]. + simpl in clt. move/andP: clt. intuition auto. + move/andP: clt => [cd cmfix]. apply auxm; auto. + + - red. + rewrite fix_context_length. + revert clt. + generalize (#|mfix|). + revert mfix. + fix auxm 1. + destruct mfix; intros; constructor. + simpl in clt. move/andP: clt => [clt cll]. + simpl in clt. move/andP: clt. intuition auto. + move/andP: clt => [cd cmfix]. apply auxm; auto. +Defined. diff --git a/pcuic/theories/PCUICCumulProp.v b/pcuic/theories/PCUICCumulProp.v index 174ba913c..5de299dce 100644 --- a/pcuic/theories/PCUICCumulProp.v +++ b/pcuic/theories/PCUICCumulProp.v @@ -904,14 +904,14 @@ Proof. 14:{ specialize (X1 _ _ H X5 _ X6). now eapply cumul_prop_cum_l. } - 6:{ eapply inversion_App in X4 as (na' & A' & B' & hf & ha & cum); auto. - specialize (X1 _ _ H hf _ X5_1). - specialize (X3 _ _ H ha _ (eq_term_upto_univ_napp_leq X5_2)). + 6:{ eapply inversion_App in X6 as (na' & A' & B' & hf & ha & cum); auto. + specialize (X3 _ _ H hf _ X7_1). + specialize (X5 _ _ H ha _ (eq_term_upto_univ_napp_leq X7_2)). eapply cumul_cumul_prop in cum; auto. transitivity (B' {0 := u0}) => //. - eapply cumul_prop_prod_inv in X1 => //. + eapply cumul_prop_prod_inv in X3 => //. transitivity (B' {0 := u}). - now eapply substitution1_untyped_cumul_prop in X1. + now eapply substitution1_untyped_cumul_prop in X3. constructor. eapply eq_term_eq_term_prop_impl => //. eapply PCUICEquality.eq_term_upto_univ_substs. diff --git a/pcuic/theories/PCUICLiftSubst.v b/pcuic/theories/PCUICLiftSubst.v index bae8a0770..cdf0c1567 100644 --- a/pcuic/theories/PCUICLiftSubst.v +++ b/pcuic/theories/PCUICLiftSubst.v @@ -189,7 +189,7 @@ Notation closed t := (closedn 0 t). Fixpoint noccur_between k n (t : term) : bool := match t with - | tRel i => Nat.leb k i && Nat.ltb i (k + n) + | tRel i => Nat.ltb i k || Nat.leb (k + n) i | tEvar ev args => List.forallb (noccur_between k n) args | tLambda _ T M | tProd _ T M => noccur_between k n T && noccur_between (S k) n M | tApp u v => noccur_between k n u && noccur_between k n v diff --git a/pcuic/theories/PCUICPrincipality.v b/pcuic/theories/PCUICPrincipality.v index 76fc8fe02..90b81cdb5 100644 --- a/pcuic/theories/PCUICPrincipality.v +++ b/pcuic/theories/PCUICPrincipality.v @@ -178,7 +178,8 @@ Section Principality. eapply cumul_conv_ctx; eauto. constructor. apply conv_ctx_refl. constructor. assumption. eapply conv_trans; eauto. now apply conv_sym. - econstructor. eapply type_reduction; eauto. + eapply type_App'. + eapply type_reduction; eauto. eapply type_Cumul'; eauto. 2:transitivity dom; auto; now apply conv_cumul. eapply type_reduction in t0. 2:eapply redA. @@ -522,22 +523,22 @@ Proof. econstructor; eauto. eapply cum_LetIn; pcuic. - - eapply inversion_App in X4 as (na' & A' & B' & hf & ha & cum); auto. + - eapply inversion_App in X6 as (na' & A' & B' & hf & ha & cum); auto. unfold leq_term in X1. - eapply eq_term_upto_univ_empty_impl in X5_1. - specialize (X1 onu _ _ hf X5_1). all:try typeclasses eauto. - specialize (X3 onu _ _ ha (eq_term_empty_leq_term X5_2)). - eapply leq_term_empty_leq_term in X5_1. - eapply eq_term_empty_eq_term in X5_2. + eapply eq_term_upto_univ_empty_impl in X7_1. + specialize (X3 onu _ _ hf X7_1). all:try typeclasses eauto. + specialize (X5 onu _ _ ha (eq_term_empty_leq_term X7_2)). + eapply leq_term_empty_leq_term in X7_1. + eapply eq_term_empty_eq_term in X7_2. eapply type_Cumul'. - econstructor; [eapply X1|eapply X3]. + eapply type_App'; [eapply X3|eapply X5]. eapply PCUICValidity.validity; pcuic. eapply type_App; eauto. eapply conv_cumul. eapply (subst_conv Γ [vass na A] [vass na A] []); pcuic. repeat constructor. now rewrite subst_empty. repeat constructor. now rewrite subst_empty. - eapply PCUICValidity.validity in X0; auto. - apply PCUICArities.isType_tProd in X0 as [tyA]; auto. + eapply PCUICValidity.validity in X2; auto. + apply PCUICArities.isType_tProd in X2 as [tyA]; auto. constructor; auto. - eapply inversion_Const in X1 as [decl' [wf [declc [cu cum]]]]; auto. diff --git a/pcuic/theories/PCUICSR.v b/pcuic/theories/PCUICSR.v index b9d288b5f..c65ea3e01 100644 --- a/pcuic/theories/PCUICSR.v +++ b/pcuic/theories/PCUICSR.v @@ -273,10 +273,9 @@ Proof. specialize (validity _ wf _ _ _ appty) as [_ vT']. eapply type_tFix_inv in appty as [T [arg [fn' [[[Hnth wffix] Hty]]]]]; auto. rewrite e in Hnth. noconf Hnth. - eapply type_App. + eapply type_App; eauto. eapply type_mkApps. eapply type_Cumul'; eauto. eapply spty. - eauto. - + - (* Congruence *) eapply type_Cumul'; [eapply type_App| |]; eauto with wf. eapply validity. eauto. eauto. diff --git a/pcuic/theories/PCUICSigmaCalculus.v b/pcuic/theories/PCUICSigmaCalculus.v index e3f99837a..849927a2f 100644 --- a/pcuic/theories/PCUICSigmaCalculus.v +++ b/pcuic/theories/PCUICSigmaCalculus.v @@ -5,7 +5,7 @@ From MetaCoq.PCUIC Require Import PCUICAst PCUICAstUtils PCUICInduction PCUICLiftSubst PCUICUnivSubst PCUICTyping PCUICClosed PCUICEquality. -Require Import ssreflect. +Require Import ssreflect ssrbool. From Equations Require Import Equations. Require Import Equations.Prop.DepElim. Set Equations With UIP. @@ -749,15 +749,15 @@ Proof. Qed. Lemma rename_shiftn : - forall f t, - rename (shiftn 1 f) (lift0 1 t) = lift0 1 (rename f t). + forall f k t, + rename (shiftn k f) (lift0 k t) = lift0 k (rename f t). Proof. - intros f t. + intros f k t. autorewrite with sigma. eapply inst_ext. intro i. unfold ren, lift_renaming, shiftn, subst_compose. simpl. - replace (i - 0) with i by lia. - reflexivity. + destruct (Nat.ltb_spec (k + i) k); try lia. + unfold shiftk. lia_f_equal. Qed. Lemma urenaming_vass : @@ -1801,7 +1801,7 @@ Proof. + eapply ihB. assumption. + eapply cumul_rename. all: try eassumption. apply hf. -Abort. +Admitted. Lemma typing_rename : forall Σ Γ Δ f t A, @@ -1810,7 +1810,7 @@ Lemma typing_rename : Σ ;;; Γ |- t : A -> Σ ;;; Δ |- rename f t : rename f A. Proof. -Abort. +Admitted. (* intros Σ Γ Δ f t A hΣ hf h. revert Σ hΣ Γ t A h Δ f hf. apply typing_rename_prop. diff --git a/pcuic/theories/PCUICToTemplateCorrectness.v b/pcuic/theories/PCUICToTemplateCorrectness.v index bf798add1..27a7c53c2 100644 --- a/pcuic/theories/PCUICToTemplateCorrectness.v +++ b/pcuic/theories/PCUICToTemplateCorrectness.v @@ -629,6 +629,8 @@ Proof. - apply IHmfix. Qed. +Definition TTwf_local Σ Γ := TT.All_local_env (TT.lift_typing TT.typing Σ) Γ. + Lemma trans_wf_local': forall (Σ : PCUICAst.global_env_ext) Γ (wfΓ : wf_local Σ Γ), let P := @@ -636,7 +638,7 @@ Lemma trans_wf_local': TT.typing (trans_global Σ0) (trans_local Γ0) (trans t) (trans T)) in PT.All_local_env_over PT.typing P Σ Γ wfΓ -> - TT.wf_local (trans_global Σ) (trans_local Γ). + TTwf_local (trans_global Σ) (trans_local Γ). Proof. intros. induction X. @@ -653,7 +655,7 @@ Lemma trans_wf_local_env Σ Γ : (fun (Σ : PCUICAst.global_env_ext) Γ b ty => PT.typing Σ Γ b ty × TT.typing (trans_global Σ) (trans_local Γ) (trans b) (trans ty)) Σ) Γ -> - TT.wf_local (trans_global Σ) (trans_local Γ). + TTwf_local (trans_global Σ) (trans_local Γ). Proof. intros. induction X. @@ -666,18 +668,18 @@ Proof. Qed. Lemma trans_branches Σ Γ brs btys ps: -All2 - (fun br bty : nat × PCUICAst.term => - (((br.1 = bty.1 × PT.typing Σ Γ br.2 bty.2) - × TT.typing (trans_global Σ) (trans_local Γ) (trans br.2) (trans bty.2)) - × PT.typing Σ Γ bty.2 (PCUICAst.tSort ps)) - × TT.typing (trans_global Σ) (trans_local Γ) (trans bty.2) - (trans (PCUICAst.tSort ps))) brs btys -> -All2 - (fun br bty : nat × term => - (br.1 = bty.1 × TT.typing (trans_global Σ) (trans_local Γ) br.2 bty.2) - × TT.typing (trans_global Σ) (trans_local Γ) bty.2 (tSort ps)) - (map (on_snd trans) brs) (map (fun '(x, y) => (x, trans y)) btys). + All2 + (fun br bty : nat × PCUICAst.term => + (((br.1 = bty.1 × PT.typing Σ Γ br.2 bty.2) + × TT.typing (trans_global Σ) (trans_local Γ) (trans br.2) (trans bty.2)) + × PT.typing Σ Γ bty.2 (PCUICAst.tSort ps)) + × TT.typing (trans_global Σ) (trans_local Γ) (trans bty.2) + (trans (PCUICAst.tSort ps))) brs btys -> + All2 + (fun br bty : nat × term => + (br.1 = bty.1 × TT.typing (trans_global Σ) (trans_local Γ) br.2 bty.2) + × TT.typing (trans_global Σ) (trans_local Γ) bty.2 (tSort ps)) + (map (on_snd trans) brs) (map (fun '(x, y) => (x, trans y)) btys). Proof. induction 1;cbn. - constructor. @@ -689,23 +691,21 @@ Proof. + apply IHX. Qed. - - Lemma trans_mfix_All Σ Γ mfix: -PT.All_local_env - (PT.lift_typing - (fun (Σ : PCUICEnvironment.global_env_ext) - (Γ : PCUICEnvironment.context) (b ty : PCUICAst.term) => - PT.typing Σ Γ b ty - × TT.typing (trans_global Σ) (trans_local Γ) (trans b) (trans ty)) Σ) - (PCUICAst.app_context Γ (PCUICLiftSubst.fix_context mfix)) -> -TT.wf_local (trans_global Σ) - (trans_local Γ ,,, TT.fix_context (map (map_def trans trans) mfix)). + PT.All_local_env + (PT.lift_typing + (fun (Σ : PCUICEnvironment.global_env_ext) + (Γ : PCUICEnvironment.context) (b ty : PCUICAst.term) => + PT.typing Σ Γ b ty + × TT.typing (trans_global Σ) (trans_local Γ) (trans b) (trans ty)) Σ) + (PCUICAst.app_context Γ (PCUICLiftSubst.fix_context mfix)) -> + TTwf_local (trans_global Σ) + (trans_local Γ ,,, TT.fix_context (map (map_def trans trans) mfix)). Proof. intros. rewrite <- trans_fix_context. match goal with - |- TT.wf_local _ ?A => + |- TTwf_local _ ?A => replace A with (trans_local (PCUICAst.app_context Γ (PCUICLiftSubst.fix_context mfix))) end. 2: { @@ -798,7 +798,7 @@ Proof. intros Hty. dependent induction Hty. - exists t_ty, t'. intuition. - - edestruct IHHty as [T' [U' [H' H'']]]. + - edestruct IHHty1 as [T' [U' [H' H'']]]. exists T', U'. split; auto. eapply TT.cumul_trans; eauto. Qed. @@ -859,9 +859,10 @@ Proof. Qed. - - - +Axiom fix_guard_trans : + forall Σ Γ mfix, + PT.fix_guard Σ Γ mfix -> + TT.fix_guard (map (map_def trans trans) mfix). Theorem template_to_pcuic (Σ : P.global_env_ext) Γ t T : PT.wf Σ -> @@ -887,9 +888,9 @@ in All (for wf_local assumptions) rewrite trans_decl_type. eapply TT.type_Rel; eauto. + now apply map_nth_error. - - admit. (* TODO adapt Template Coq to new sort typing rule *) - (* eapply TT.type_Sort; eauto. - now apply trans_in_level_set. *) + - econstructor; eauto. + destruct u; auto. simpl in H |- *. + intros l inl. now rewrite <-trans_global_ext_levels. - eapply TT.type_Prod;assumption. - eapply TT.type_Lambda;eassumption. - eapply TT.type_LetIn;eassumption. @@ -944,9 +945,8 @@ in All (for wf_local assumptions) + eassumption. + rewrite <- trans_global_ext_constraints. eassumption. - + rewrite trans_mkApps in X4. - cbn in X4. - apply X4. + + auto. + + now rewrite trans_mkApps in X4. + admit. (* map_option_out build branche type *) (* this should be similar to trans_build_case_predicate_type *) + admit. (* now apply trans_branches.*) @@ -965,7 +965,7 @@ in All (for wf_local assumptions) reflexivity. - rewrite trans_dtype. simpl. eapply TT.type_Fix; auto. - + admit. (* fix guard *) + + now rewrite fix_guard_trans. + erewrite map_nth_error. 2: apply H0. destruct decl. @@ -977,7 +977,8 @@ in All (for wf_local assumptions) + fold trans. subst types. eapply trans_mfix_All2;eassumption. - - rewrite trans_dtype. + + admit. + - rewrite trans_dtype. simpl. eapply TT.type_CoFix; auto. + erewrite map_nth_error. 2: eassumption. @@ -990,8 +991,8 @@ in All (for wf_local assumptions) + fold trans;subst types. (* like trans_mfix_All2 without isLambda *) admit. + + admit. - eapply TT.type_Conv. + eassumption. - + admit. (* trans isWfArity *) - + admit. (* trans_cumul *) + + admit. (* eapply trans_cumul. *) Admitted. diff --git a/pcuic/theories/TemplateToPCUICCorrectness.v b/pcuic/theories/TemplateToPCUICCorrectness.v index 1e643fe8b..5c2b3a4b6 100644 --- a/pcuic/theories/TemplateToPCUICCorrectness.v +++ b/pcuic/theories/TemplateToPCUICCorrectness.v @@ -1038,8 +1038,10 @@ Definition Tlift_typing (P : Template.Ast.global_env_ext -> Tcontext -> Tterm -> | None => { s : Universe.t & P Σ Γ t (T.tSort s) } end. +Definition TTy_wf_local {cf : checker_flags} Σ Γ := TTy.All_local_env (TTy.lift_typing TTy.typing Σ) Γ. + Lemma trans_wf_local {cf}: - forall (Σ : Template.Ast.global_env_ext) (Γ : Tcontext) (wfΓ : TTy.wf_local Σ Γ), + forall (Σ : Template.Ast.global_env_ext) (Γ : Tcontext) (wfΓ : TTy_wf_local Σ Γ), let P := (fun Σ0 (Γ0 : Tcontext) _ (t T : Tterm) _ => wf (trans_global Σ0).1 -> @@ -1118,22 +1120,11 @@ Axiom fix_guard_trans : TTy.fix_guard mfix -> fix_guard Σ Γ (map (map_def trans trans) mfix). -Lemma isWFArity_wf {cf} (Σ : Ast.global_env_ext) Γ T : Typing.wf Σ -> TTy.isWfArity TTy.typing Σ Γ T -> T.wf T. -Proof. - intros wfΣ []. - destruct s as [s [eq wf]]. - generalize (destArity_spec [] T). rewrite eq. - simpl. move => ->. - apply (it_mkProd_or_LetIn_wf Γ). - rewrite -TEnv.it_mkProd_or_LetIn_app. - eapply wf_it_mkProd_or_LetIn. instantiate (1:=wf). - induction wf; constructor; auto. - destruct t0. eapply typing_wf; eauto. - eapply typing_wf; eauto. simpl. - destruct t0. - eapply typing_wf; eauto. constructor. -Qed. - +Axiom cofix_guard_trans : + forall Σ Γ mfix, + TTy.cofix_guard mfix -> + cofix_guard Σ Γ (map (map_def trans trans) mfix). + Lemma trans_global_decl_universes d : TTy.universes_decl_of_decl d = universes_decl_of_decl (trans_global_decl d). @@ -1173,8 +1164,9 @@ Proof. - (* Sorts *) constructor; eauto. eapply trans_wf_local; eauto. - admit. (* todo *) - (* now rewrite global_ext_levels_trans. *) + destruct u; simpl in *; eauto. + intros. + now rewrite global_ext_levels_trans. - (* Casts *) eapply refine_type. eapply type_App with _ (trans t) _. @@ -1252,9 +1244,9 @@ Proof. -- eapply X1. -- rewrite global_ext_constraints_trans; exact H1. -- rewrite trans_mkApps in X2; auto with wf. - -- admit. - -- apply trans_build_branches_type in H2. - rewrite firstn_map. exact H2. + -- apply H2. + -- apply trans_build_branches_type in H3. + rewrite firstn_map. exact H3. -- eapply All2_map. solve_all. - destruct pdecl as [arity ty]; simpl in *. @@ -1285,11 +1277,11 @@ Proof. now exists s. -- apply All_map. eapply All_impl; eauto. intuition eauto 3 with wf; cbn. - rewrite H1. rewrite /trans_local map_length. + rewrite H2. rewrite /trans_local map_length. rewrite /trans_local map_app in X3. rewrite <- trans_lift. apply X3; auto. rdest. destruct (dbody x); simpl in *; congruence. - -- admit. + -- todo "wffix". -- destruct decl; reflexivity. - eapply refine_type. @@ -1300,52 +1292,27 @@ Proof. f_equal. apply mapi_ext => i x. simpl. rewrite trans_lift. reflexivity. } econstructor; eauto. - -- admit. + -- eapply cofix_guard_trans. -- now rewrite nth_error_map H. -- eapply trans_wf_local; eauto. -- eapply All_map, (All_impl X0). intros x [s [Hs Hts]]. now exists s. -- apply All_map. eapply All_impl; eauto. intuition eauto 3 with wf. - rewrite H0. rewrite /trans_local map_length. - unfold Template.Ast.app_context in X2. - rewrite /trans_local map_app in X2. - cbn. rewrite <- trans_lift. apply X2. - -- admit. + rewrite H1. rewrite /trans_local map_length. + unfold Template.Ast.app_context in X3. + rewrite /trans_local map_app in X3. + cbn. rewrite <- trans_lift. now apply X3. + -- todo "wfcofix". -- destruct decl; reflexivity. - assert (T.wf B). - { destruct X2. destruct i as [wfa allwfa]. - now apply (isWFArity_wf _ _ _ wfΣ wfa). - destruct s as [s [H ?]]. - eapply typing_wf in H; intuition eauto. } - destruct X2. red in i. - destruct i as [wfa allwfa]. - destruct wfa as [ctx [s ?]]. - * admit. - (* exists (trans_local ctx), s. destruct p. - generalize (trans_destArity [] B); rewrite e. - intros. split; auto. - eapply trans_wf_local in allwfa. simpl in allwfa. - rewrite /trans_local in allwfa. - now rewrite map_app in allwfa. - right. *) - * destruct s as [s [? ?]]; eauto. - eapply type_Cumul; eauto. - eapply trans_cumul; eauto with trans. - eapply typing_wf_sigma; auto. - clear X. apply typing_all_wf_decl in wfΓ; auto. - eapply typing_wf in X0; eauto. destruct X0. auto. -Admitted. - -Theorem template_to_pcuic_typing {cf} Σ Γ t T : - TTy.wf Σ.1 -> - TTy.typing Σ Γ t T -> - typing (trans_global Σ) (trans_local Γ) (trans t) (trans T). -Proof. - intros wf ty. - apply (TTy.env_prop_typing _ template_to_pcuic _ wf); auto. - now eapply TTy.typing_wf_local. + { now apply typing_wf in X2. } + eapply type_Cumul; eauto. + eapply trans_cumul; eauto with trans. + eapply typing_wf_sigma; auto. + clear X. apply typing_all_wf_decl in wfΓ; auto. + eapply typing_wf in X0; eauto. destruct X0. auto. Qed. Lemma Alli_map {A B} (P : nat -> B -> Type) n (f : A -> B) l : @@ -1395,7 +1362,9 @@ Proof. Qed. Lemma trans_on_global_env `{checker_flags} Σ P Q : - (forall Σ Γ t T, TTy.on_global_env P Σ.1 -> P Σ Γ t T -> Q (trans_global Σ) (trans_local Γ) (trans t) (option_map trans T)) -> + (forall Σ Γ t T, TTy.on_global_env P Σ.1 -> P Σ Γ t T -> + on_global_env Q (trans_global_decls Σ.1) -> + Q (trans_global Σ) (trans_local Γ) (trans t) (option_map trans T)) -> TTy.on_global_env P Σ -> on_global_env Q (trans_global_decls Σ). Proof. intros X X0. @@ -1452,7 +1421,7 @@ Proof. red. move: (X (Σ, Ast.ind_universes m) (Ast.arities_context (Ast.ind_bodies m)) t None). now rewrite trans_arities_context. - + clear -X0 X on_cargs. revert on_cargs. simpl. + + clear -X0 IHX0 X on_cargs. revert on_cargs. simpl. generalize (TTy.cshape_args cs), (TTy.cshape_sorts cs). have foo := (X (Σ, udecl) _ _ _ X0). rewrite -trans_arities_context. @@ -1467,7 +1436,7 @@ Proof. now apply (foo ty None). now apply (foo b (Some ty)). now apply (foo ty (Some (Ast.tSort _))). - + clear -X0 X on_cindices. + + clear -X0 IHX0 X on_cindices. revert on_cindices. rewrite trans_lift_context /trans_local -map_rev. simpl. rewrite {2}/trans_local map_length. @@ -1482,7 +1451,7 @@ Proof. now apply (foo i (Some t)). now rewrite (trans_subst_telescope [i] 0) in IHon_cindices. now rewrite (trans_subst_telescope [b] 0) in IHon_cindices. - + clear -on_ctype_positive. + + clear -IHX0 on_ctype_positive. unfold TTy.cdecl_type in *. unfold cdecl_type. simpl in *. change [] with (map trans_decl []). revert on_ctype_positive. generalize (@nil Ast.context_decl). induction 1; simpl. @@ -1511,24 +1480,40 @@ Proof. -- admit. Admitted. -Lemma template_to_pcuic_env {cf} Σ : Template.Typing.wf_ext Σ -> wf_ext (trans_global Σ). +Lemma template_to_pcuic_env {cf} Σ : Template.Typing.wf Σ -> wf (trans_global_decls Σ). Proof. - intros [H Hu]. - split; auto. + intros Hu. eapply trans_on_global_env; eauto. simpl; intros. epose proof (TTy.env_prop_typing _ template_to_pcuic _ X Γ). - forward X1. + forward X2. red in X0. destruct T. now eapply TTy.typing_wf_local. destruct X0 as [s Hs]. eapply TTy.typing_wf_local; eauto. destruct T; simpl in *. - - eapply X1; eauto. + - eapply X2; eauto. - destruct X0 as [s Hs]. exists s. - eapply (X1 _ (Ast.tSort s)); eauto. - - destruct Hu as [? [? [? ?]]]. - split; rewrite global_levels_trans //. - repeat split => //. - red in H3 |- *. - rewrite -global_ext_constraints_trans in H3. - apply H3. -Qed. \ No newline at end of file + eapply (X2 _ (Ast.tSort s)); eauto. +Qed. + +Lemma template_to_pcuic_env_ext {cf} Σ : Template.Typing.wf_ext Σ -> wf_ext (trans_global Σ). +Proof. + intros [u Hu]. + split. now apply template_to_pcuic_env. + destruct Hu as [? [? [? ?]]]. + split; rewrite global_levels_trans //. + repeat split => //. + red in H2 |- *. + rewrite -global_ext_constraints_trans in H2. + apply H2. +Qed. + +Theorem template_to_pcuic_typing {cf} Σ Γ t T : + TTy.wf Σ.1 -> + TTy.typing Σ Γ t T -> + typing (trans_global Σ) (trans_local Γ) (trans t) (trans T). +Proof. + intros wf ty. + apply (TTy.env_prop_typing _ template_to_pcuic _ wf); auto. + now eapply TTy.typing_wf_local. + now apply template_to_pcuic_env. +Qed. diff --git a/safechecker/theories/PCUICSafeRetyping.v b/safechecker/theories/PCUICSafeRetyping.v index 318aef85b..800dbc0e4 100644 --- a/safechecker/theories/PCUICSafeRetyping.v +++ b/safechecker/theories/PCUICSafeRetyping.v @@ -344,7 +344,7 @@ Section TypeOf. sq. split. * simpl. eapply type_reduction in Htty; eauto. - eapply type_App; eauto. + eapply type_App'; eauto. specialize (pbty _ t0). assert (Σ ;;; Γ |- tProd na' A' B' <= tProd x x0 x1). eapply cumul_red_l_inv; eauto. diff --git a/safechecker/theories/PCUICTypeChecker.v b/safechecker/theories/PCUICTypeChecker.v index a79de73d6..3a8a94876 100644 --- a/safechecker/theories/PCUICTypeChecker.v +++ b/safechecker/theories/PCUICTypeChecker.v @@ -508,7 +508,7 @@ Section Typecheck. eexists. eassumption. Defined. Next Obligation. - cbn in *; sq; econstructor. + cbn in *; sq; eapply type_App'. 2: eassumption. eapply type_reduction; eassumption. Defined. diff --git a/template-coq/theories/LiftSubst.v b/template-coq/theories/LiftSubst.v index 5571fc022..d689cd832 100644 --- a/template-coq/theories/LiftSubst.v +++ b/template-coq/theories/LiftSubst.v @@ -140,7 +140,7 @@ Notation closed t := (closedn 0 t). Fixpoint noccur_between k n (t : term) : bool := match t with - | tRel i => Nat.leb k i && Nat.ltb i (k + n) + | tRel i => Nat.ltb i k && Nat.leb (k + n) i | tEvar ev args => List.forallb (noccur_between k n) args | tLambda _ T M | tProd _ T M => noccur_between k n T && noccur_between (S k) n M | tApp u v => noccur_between k n u && List.forallb (noccur_between k n) v diff --git a/template-coq/theories/Typing.v b/template-coq/theories/Typing.v index a273f4e03..48ed81d95 100644 --- a/template-coq/theories/Typing.v +++ b/template-coq/theories/Typing.v @@ -629,6 +629,7 @@ Include TemplateEnvTyping. (* AXIOM GUARD CONDITION *) Axiom fix_guard : mfixpoint term -> bool. +Axiom cofix_guard : mfixpoint term -> bool. Axiom fix_guard_red1 : forall Σ Γ mfix mfix' idx, @@ -923,6 +924,7 @@ Inductive typing `{checker_flags} (Σ : global_env_ext) (Γ : context) : term -> Σ ;;; Γ |- tFix mfix n : decl.(dtype) | type_CoFix mfix n decl : + cofix_guard mfix -> nth_error mfix n = Some decl -> wf_local Σ Γ -> All (fun d => {s & Σ ;;; Γ |- d.(dtype) : tSort s}) mfix -> @@ -1272,6 +1274,7 @@ Lemma typing_ind_env `{cf : checker_flags} : (forall Σ (wfΣ : wf Σ.1) (Γ : context) (wfΓ : wf_local Σ Γ) (mfix : list (def term)) (n : nat) decl, let types := fix_context mfix in + cofix_guard mfix -> nth_error mfix n = Some decl -> All_local_env_over typing Pdecl Σ Γ wfΓ -> All (fun d => {s & (Σ ;;; Γ |- d.(dtype) : tSort s)%type * P Σ Γ d.(dtype) (tSort s)})%type mfix -> @@ -1570,7 +1573,7 @@ Proof. Forall_decls_typing P Σ.1 * P Σ Γ0 t T). {intros. eapply (X14 _ X _ _ Hty); eauto. lia. } clear X14 X13. - clear e decl a0 i. + clear e decl a0 i i0. remember (fix_context mfix) as mfixcontext. clear Heqmfixcontext. induction a1; econstructor; eauto. From 326ed83844fa1b3f60415e7f5f47cde8daa5b7d7 Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Wed, 9 Dec 2020 21:37:03 +0100 Subject: [PATCH 48/70] Before removing isLambda --- checker/theories/Closed.v | 10 +- checker/theories/Weakening.v | 3 +- checker/theories/WeakeningEnv.v | 5 +- pcuic/theories/PCUICToTemplateCorrectness.v | 476 ++++++++++++++++---- template-coq/theories/Typing.v | 106 +++-- 5 files changed, 461 insertions(+), 139 deletions(-) diff --git a/checker/theories/Closed.v b/checker/theories/Closed.v index 21b9f0c65..9f0a98142 100644 --- a/checker/theories/Closed.v +++ b/checker/theories/Closed.v @@ -553,13 +553,13 @@ Proof. unfold test_def. simpl. rtoProp. split. rewrite -> app_context_length in *. rewrite -> Nat.add_comm in *. - eapply closedn_lift_inv in H2; eauto. lia. + eapply closedn_lift_inv in H3; eauto. lia. subst types. - now rewrite -> app_context_length, fix_context_length in H1. - eapply (nth_error_all) in H; eauto. simpl in *. + now rewrite -> app_context_length, fix_context_length in H2. + eapply (nth_error_all) in H0; eauto. simpl in *. intuition. rtoProp. - subst types. rewrite app_context_length Nat.add_comm in H1. - now eapply closedn_lift_inv in H1. + subst types. rewrite app_context_length Nat.add_comm in H2. + now eapply closedn_lift_inv in H2. Qed. Lemma declared_decl_closed `{checker_flags} {Σ : global_env} {cst decl} : diff --git a/checker/theories/Weakening.v b/checker/theories/Weakening.v index fdea27fd0..bb40ea917 100644 --- a/checker/theories/Weakening.v +++ b/checker/theories/Weakening.v @@ -1128,6 +1128,7 @@ Proof. - rewrite -> (map_dtype _ (lift #|Γ''| (#|mfix| + #|Γ'|))). eapply type_CoFix; auto. + * eapply cofix_guard_lift; eauto. * rewrite -> nth_error_map, heq_nth_error. reflexivity. * eapply All_map. eapply (All_impl X0); simpl. @@ -1143,7 +1144,7 @@ Proof. rewrite app_context_length fix_context_length in IH. rewrite lift_context_length fix_context_length. rewrite permute_lift; try lia. now rewrite (Nat.add_comm #|Γ'|). - * red; rewrite <- H0. unfold wf_cofixpoint. + * red; rewrite <- H1. unfold wf_cofixpoint. rewrite map_map_compose. now rewrite weakening_check_one_cofix. diff --git a/checker/theories/WeakeningEnv.v b/checker/theories/WeakeningEnv.v index b198cfaac..f6bdd3d9e 100644 --- a/checker/theories/WeakeningEnv.v +++ b/checker/theories/WeakeningEnv.v @@ -5,11 +5,8 @@ Require Import ssreflect. (** * Weakening lemmas w.r.t. the global environment *) - Generalizable Variables Σ Γ t T. -Definition extends (Σ Σ' : global_env) := { Σ'' & Σ' = Σ'' ++ Σ }. - Lemma weakening_env_global_ext_levels Σ Σ' φ (H : extends Σ Σ') l : LevelSet.In l (global_ext_levels (Σ, φ)) -> LevelSet.In l (global_ext_levels (Σ', φ)). @@ -448,11 +445,13 @@ Proof. - econstructor; eauto 2 with extends. close_Forall. intros; intuition eauto with extends. - econstructor; eauto with extends. + eapply fix_guard_extends; eauto. eapply (All_impl X0); intuition eauto. destruct X2 as [s Hs]; exists s; intuition eauto. eapply All_impl; eauto; simpl; intuition eauto with extends. - econstructor; eauto with extends. auto. + eapply cofix_guard_extends; eauto. eapply (All_impl X0); intuition eauto. destruct X2 as [s Hs]; exists s; intuition eauto. eapply All_impl; eauto; simpl; intuition eauto with extends. diff --git a/pcuic/theories/PCUICToTemplateCorrectness.v b/pcuic/theories/PCUICToTemplateCorrectness.v index 27a7c53c2..631934c99 100644 --- a/pcuic/theories/PCUICToTemplateCorrectness.v +++ b/pcuic/theories/PCUICToTemplateCorrectness.v @@ -1,13 +1,15 @@ (* Distributed under the terms of the MIT license. *) From MetaCoq.PCUIC Require Import PCUICAst PCUICAstUtils PCUICInduction - PCUICLiftSubst PCUICEquality PCUICUnivSubst PCUICTyping PCUICGeneration. + PCUICLiftSubst PCUICEquality PCUICReduction PCUICUnivSubst PCUICTyping PCUICGeneration. Set Warnings "-notation-overridden". From MetaCoq.Template Require Import config utils Ast TypingWf WfInv UnivSubst LiftSubst. + Set Warnings "+notation_overridden". Require Import PCUICToTemplate. +From Coq Require Import ssreflect. (* from Checker Generation to avoid dependencies *) @@ -17,19 +19,20 @@ Derive NoConfusion for term. From Equations Require Import Equations. Require Import Equations.Prop.DepElim. -Module P := PCUICAst. -Module PT := PCUICTyping. +(** Source = PCUIC, Target = Coq *) +Module S := PCUICAst. +Module ST := PCUICTyping. Module T := Template.Ast. Module TT := Template.Typing. Local Existing Instance default_checker_flags. -Module PL := PCUICLiftSubst. +Module SL := PCUICLiftSubst. Module TL := Template.LiftSubst. Ltac solve_list := - rewrite !map_map_compose, ?compose_on_snd, ?compose_map_def; + rewrite !map_map_compose ?compose_on_snd ?compose_map_def; try rewrite !map_length; try solve_all; try typeclasses eauto with core. @@ -46,12 +49,12 @@ Proof. reflexivity. Qed. -Lemma trans_lift (t:P.term) n k: - trans(PL.lift n k t) = TL.lift n k (trans t). +Lemma trans_lift (t : S.term) n k: + trans (SL.lift n k t) = TL.lift n k (trans t). Proof. revert k. induction t using PCUICInduction.term_forall_list_ind; simpl; intros; try congruence. - f_equal. rewrite !map_map_compose. solve_all. - - rewrite IHt1, IHt2. + - rewrite IHt1 IHt2. rewrite mkAppMkApps. rewrite <- mapOne. rewrite <- TL.lift_mkApps. @@ -75,22 +78,22 @@ Proof. Defined. Lemma trans_global_ext_levels Σ: -PT.global_ext_levels Σ = TT.global_ext_levels (trans_global Σ). +ST.global_ext_levels Σ = TT.global_ext_levels (trans_global Σ). Proof. - unfold TT.global_ext_levels, PT.global_ext_levels. + unfold TT.global_ext_levels, ST.global_ext_levels. destruct Σ. cbn [trans_global fst snd]. f_equal. induction g. - reflexivity. - - unfold PT.global_levels in IHg. + - unfold ST.global_levels in IHg. cbn. rewrite IHg. f_equal. destruct a. cbn. unfold TT.monomorphic_levels_decl, TT.monomorphic_udecl_decl, TT.on_udecl_decl. - unfold PT.monomorphic_levels_decl, PT.monomorphic_udecl_decl, PT.on_udecl_decl. + unfold ST.monomorphic_levels_decl, ST.monomorphic_udecl_decl, ST.on_udecl_decl. destruct g0. + cbn. destruct c. @@ -101,15 +104,15 @@ Proof. Qed. Lemma trans_global_ext_constraints Σ : - PT.global_ext_constraints Σ = TT.global_ext_constraints (trans_global Σ). + ST.global_ext_constraints Σ = TT.global_ext_constraints (trans_global Σ). Proof. destruct Σ. - unfold PT.global_ext_constraints, trans_global. + unfold ST.global_ext_constraints, trans_global. cbn [fst snd]. Admitted. Lemma trans_mem_level_set l Σ: -LevelSet.mem l (PT.global_ext_levels Σ) -> +LevelSet.mem l (ST.global_ext_levels Σ) -> LevelSet.mem l (TT.global_ext_levels (trans_global Σ)). Proof. intros. @@ -118,7 +121,7 @@ Proof. Qed. Lemma trans_in_level_set l Σ: -LevelSet.In l (PT.global_ext_levels Σ) -> +LevelSet.In l (ST.global_ext_levels Σ) -> LevelSet.In l (TT.global_ext_levels (trans_global Σ)). Proof. intros. @@ -128,8 +131,8 @@ Qed. Lemma trans_lookup Σ cst decl: -P.lookup_env Σ.1 cst = Some decl -> -Ast.lookup_env (trans_global Σ).1 cst = +S.lookup_env Σ.1 cst = Some decl -> +Ast .lookup_env (trans_global Σ).1 cst = Some (trans_global_decl decl). Proof. intros H. @@ -147,18 +150,18 @@ Proof. Qed. Lemma trans_declared_constant Σ cst decl: -PT.declared_constant Σ.1 cst decl -> +ST.declared_constant Σ.1 cst decl -> TT.declared_constant (trans_global Σ).1 cst (trans_constant_body decl). Proof. intros H. unfold TT.declared_constant. - unfold PT.declared_constant in H. + unfold ST.declared_constant in H. apply trans_lookup in H as ->. reflexivity. Qed. Lemma trans_constraintSet_in x Σ: -ConstraintSet.In x (PT.global_ext_constraints Σ) -> +ConstraintSet.In x (ST.global_ext_constraints Σ) -> ConstraintSet.In x (TT.global_ext_constraints (trans_global Σ)). Proof. rewrite trans_global_ext_constraints. @@ -166,12 +169,12 @@ Proof. Qed. Lemma trans_consistent_instance_ext Σ decl u: -PT.consistent_instance_ext Σ decl u -> +ST.consistent_instance_ext Σ decl u -> TT.consistent_instance_ext (trans_global Σ) decl u. Proof. intros H. - unfold consistent_instance_ext, PT.consistent_instance_ext in *. - unfold consistent_instance, PT.consistent_instance in *. + unfold consistent_instance_ext, ST.consistent_instance_ext in *. + unfold consistent_instance, ST.consistent_instance in *. destruct decl;trivial. destruct H as (?&?&?). repeat split;trivial. @@ -193,12 +196,12 @@ Proof. Qed. Lemma trans_declared_inductive Σ mdecl ind idecl: -PT.declared_inductive Σ.1 mdecl ind idecl -> +ST.declared_inductive Σ.1 mdecl ind idecl -> TT.declared_inductive (trans_global Σ).1 (trans_minductive_body mdecl) ind (trans_one_ind_body idecl). Proof. intros []. split. - - unfold TT.declared_minductive, PT.declared_minductive in *. + - unfold TT.declared_minductive, ST.declared_minductive in *. apply trans_lookup in H as ->. reflexivity. - now apply map_nth_error. @@ -240,7 +243,7 @@ Qed. Lemma trans_subst xs k t: - trans (PL.subst xs k t) = + trans (SL.subst xs k t) = TL.subst (map trans xs) k (trans t). Proof. induction t in k |- * using PCUICInduction.term_forall_list_ind. @@ -256,7 +259,7 @@ Proof. apply All_map_eq. eapply All_forall in X. apply X. - - rewrite IHt1, IHt2. + - rewrite IHt1 IHt2. destruct (trans t1);cbn;trivial. rewrite AstUtils.mkApp_mkApps. do 2 f_equal. @@ -283,7 +286,7 @@ Proof. destruct x. unfold map_def. cbn in *. - now rewrite e, e0. + now rewrite e e0. + apply IHX. - f_equal. rewrite map_length. @@ -295,17 +298,17 @@ Proof. destruct x. unfold map_def. cbn in *. - now rewrite e, e0. + now rewrite e e0. + apply IHX. - destruct p as [? []]; eauto. Qed. Lemma trans_subst10 u B: -trans (PL.subst1 u 0 B)= +trans (SL.subst1 u 0 B)= TL.subst10 (trans u) (trans B). Proof. - unfold PL.subst1. + unfold SL.subst1. rewrite trans_subst. reflexivity. Qed. @@ -319,7 +322,7 @@ Proof. f_equal. apply All_map_eq. apply X. - - rewrite IHt1, IHt2. + - rewrite IHt1 IHt2. do 2 rewrite mkAppMkApps. rewrite subst_instance_constr_mkApps. cbn. @@ -346,7 +349,7 @@ Proof. + destruct x;cbn in *. unfold map_def;cbn. destruct p. - now rewrite e, e0. + now rewrite e e0. + apply IHX. - f_equal. unfold tFixProp in X. @@ -355,7 +358,7 @@ Proof. + destruct x;cbn in *. unfold map_def;cbn. destruct p. - now rewrite e, e0. + now rewrite e e0. + apply IHX. - destruct p as [? []]; eauto. Qed. @@ -375,19 +378,19 @@ Proof. Qed. Lemma trans_type_of_constructor mdecl cdecl ind i u: -trans (PT.type_of_constructor mdecl cdecl (ind, i) u) = +trans (ST.type_of_constructor mdecl cdecl (ind, i) u) = TT.type_of_constructor (trans_minductive_body mdecl) (trans_ctor cdecl) (ind,i) u. Proof. - unfold PT.type_of_constructor. + unfold ST.type_of_constructor. rewrite trans_subst. unfold TT.type_of_constructor. f_equal. - cbn [fst]. - rewrite PT.inds_spec. + rewrite ST.inds_spec. rewrite TT.inds_spec. rewrite map_rev. rewrite map_mapi. @@ -423,7 +426,7 @@ Proof. Qed. Lemma trans_declared_projection Σ mdecl idecl p pdecl : -PT.declared_projection Σ.1 mdecl idecl p pdecl -> +ST.declared_projection Σ.1 mdecl idecl p pdecl -> TT.declared_projection (trans_global Σ).1 (trans_minductive_body mdecl) (trans_one_ind_body idecl) p (on_snd trans pdecl). Proof. intros (?&?&?). @@ -455,11 +458,11 @@ Qed. Lemma trans_instantiate_params params pars ty: option_map trans - (PT.instantiate_params + (ST.instantiate_params params pars ty) = TT.instantiate_params (trans_local params) (map trans pars) (trans ty). Proof. - rewrite TT.instantiate_params_, PT.instantiate_params_. + rewrite TT.instantiate_params_ ST.instantiate_params_. rewrite option_map_two. match goal with |- option_map _ (_ _ _ ?A _) = option_map _ (_ _ _ ?B _) => change B with (map trans A) @@ -488,7 +491,7 @@ Qed. Lemma trans_instantiate_params' u mdecl idecl args npar x: -PT.instantiate_params +ST.instantiate_params (PCUICUnivSubst.subst_instance_context u (PCUICAst.ind_params mdecl)) (firstn npar args) (PCUICUnivSubst.subst_instance_constr u (PCUICAst.ind_type idecl)) = @@ -564,8 +567,250 @@ Proof. Qed. +Lemma trans_nth n l x : trans (nth n l x) = nth n (List.map trans l) (trans x). +Proof. + induction l in n |- *; destruct n; trivial. + simpl in *. congruence. +Qed. + +Lemma trans_iota_red pars c args brs : + trans (iota_red pars c args brs) = + TT.iota_red pars c (List.map trans args) (List.map (on_snd trans) brs). +Proof. + unfold iota_red, TT.iota_red. + rewrite trans_mkApps. + f_equal. induction brs in c |- *; simpl; destruct c; trivial. + now rewrite map_skipn. +Qed. + +Lemma trans_isLambda t : + T.isLambda (trans t) = S.isLambda t. +Proof. + destruct t; cbnr. + generalize (trans t1) (trans t2); clear. + induction t; intros; cbnr. + destruct prim as [? []]; cbnr. +Qed. + +Lemma trans_unfold_fix mfix idx narg fn : + List.Forall (fun def : def S.term => S.isLambda (dbody def) = true) mfix -> + unfold_fix mfix idx = Some (narg, fn) -> + TT.unfold_fix (map (map_def trans trans) mfix) idx = Some (narg, trans fn). +Proof. + unfold TT.unfold_fix, unfold_fix. intros wffix. + rewrite nth_error_map. destruct (nth_error mfix idx) eqn:Hdef => //. + cbn. + intros [= <- <-]. simpl. + eapply nth_error_forall in wffix; eauto. simpl in wffix. + rewrite trans_isLambda wffix. + repeat f_equal. + rewrite trans_subst. + f_equal. clear Hdef. simpl. + unfold fix_subst, TT.fix_subst. rewrite map_length. + generalize mfix at 1 3. + induction mfix; trivial. + simpl; intros mfix'. f_equal. + eapply IHmfix. +Qed. + +Lemma trans_unfold_cofix mfix idx narg fn : + unfold_cofix mfix idx = Some (narg, fn) -> + TT.unfold_cofix (map (map_def trans trans) mfix) idx = Some (narg, trans fn). +Proof. + unfold TT.unfold_cofix, unfold_cofix. + rewrite nth_error_map. destruct (nth_error mfix idx) eqn:Hdef => //. + intros [= <- <-]. simpl. repeat f_equal. + rewrite trans_subst. + f_equal. clear Hdef. + unfold cofix_subst, TT.cofix_subst. rewrite map_length. + generalize mfix at 1 3. + induction mfix; trivial. + simpl; intros mfix'. f_equal. + eapply IHmfix. +Qed. + +Definition isApp t := match t with tApp _ _ => true | _ => false end. + +Lemma trans_is_constructor: + forall (args : list S.term) (narg : nat), + is_constructor narg args = true -> TT.is_constructor narg (map trans args) = true. +Proof. + intros args narg. + unfold TT.is_constructor, is_constructor. + rewrite nth_error_map //. destruct nth_error => //. simpl. intros. + unfold AstUtils.isConstruct_app, isConstruct_app, decompose_app in *. + destruct (decompose_app_rec t []) eqn:da. simpl in H. + destruct t0 => //. + apply decompose_app_rec_inv in da. simpl in da. subst t. + rewrite trans_mkApps /=. + rewrite decompose_app_mkApps //. +Qed. + +Lemma refine_red1_r Σ Γ t u u' : u = u' -> TT.red1 Σ Γ t u -> TT.red1 Σ Γ t u'. +Proof. + intros ->. trivial. +Qed. + +Lemma refine_red1_Γ Σ Γ Γ' t u : Γ = Γ' -> TT.red1 Σ Γ t u -> TT.red1 Σ Γ' t u. +Proof. + intros ->. trivial. +Qed. +Ltac wf_inv H := try apply wf_inv in H; simpl in H; rdest. + +Lemma trans_red1 Σ Γ T U : + red1 Σ Γ T U -> + TT.red1 (map (on_snd trans_global_decl) Σ) (trans_local Γ) (trans T) (trans U). +Proof. + induction 1 using red1_ind_all; simpl in *; + try solve [econstructor; eauto]. + + - simpl. + rewrite trans_subst; auto. constructor. + + - rewrite trans_subst; eauto. repeat constructor. + - rewrite trans_lift; eauto. repeat constructor. + rewrite nth_error_map. + destruct nth_error eqn:Heq => //. simpl in H. noconf H. + simpl. destruct c; noconf H => //. + + - rewrite trans_mkApps; eauto with wf; simpl. + erewrite trans_iota_red; eauto. repeat constructor. + + - simpl. rewrite !trans_mkApps /=. + unfold is_constructor in H0. + destruct nth_error eqn:hnth. + pose proof (nth_error_Some_length hnth). + destruct args. simpl. elimtype False; depelim H1. + cbn -[mkApps]. + eapply refine_red1_r; cycle 1. + eapply TT.red_fix. + apply trans_unfold_fix; eauto. admit. + eapply (trans_is_constructor (t0 :: args)). + now rewrite /is_constructor hnth. + + + - apply wf_mkApps_napp in H1; auto. + intuition. + pose proof (unfold_cofix_wf _ _ _ _ H H3). wf_inv H3. + rewrite !trans_mkApps; eauto with wf. + apply trans_unfold_cofix in H; eauto with wf. + eapply red_cofix_case; eauto. + + - eapply wf_mkApps_napp in Hwf; auto. + intuition. pose proof (unfold_cofix_wf _ _ _ _ H H0). wf_inv H0. + rewrite !trans_mkApps; intuition eauto with wf. + eapply red_cofix_proj; eauto. + apply trans_unfold_cofix; eauto with wf. + + - rewrite trans_subst_instance_constr. econstructor. + apply (forall_decls_declared_constant _ c decl H). + destruct decl. now simpl in *; subst cst_body. + + - rewrite trans_mkApps; eauto with wf. + simpl. constructor. now rewrite nth_error_map H. + + - constructor. apply IHX. constructor; hnf; simpl; auto. hnf. auto. + + - constructor. apply IHX. constructor; hnf; simpl; auto. auto. + + - constructor. solve_all. + apply OnOne2_map. apply (OnOne2_All_mix_left H1) in X. clear H1. + solve_all. red. simpl in *. + intuition eauto. + apply b2. all: solve_all. + + - rewrite !trans_mkApps; auto with wf. eapply wf_red1 in X; auto. + apply red1_mkApps_l. auto. + + - apply Forall_All in H2. clear H H0 H1. revert M1. induction X. + simpl. intuition. inv H2. specialize (X H). + apply red1_mkApps_l. apply app_red_r. auto. + inv H2. specialize (IHX X0). + simpl. intros. + eapply (IHX (T.tApp M1 [hd])). + + - constructor. apply IHX. constructor; hnf; simpl; auto. auto. + - constructor. induction X; simpl; repeat constructor. apply p; auto. now inv Hwf. + apply IHX. now inv Hwf. + + - constructor. constructor. eapply IHX; auto. + - eapply refine_red1_r; [|constructor]. unfold subst1. simpl. now rewrite lift0_p. + + - constructor. apply OnOne2_map. repeat toAll. + apply (OnOne2_All_mix_left Hwf) in X. clear Hwf. + solve_all. + red. rewrite <- !map_dtype. rewrite <- !map_dbody. + inversion b0. clear b0. + intuition eauto. + + eapply b. all: solve_all. + + unfold map_def. simpl. + f_equal. 2: auto. + f_equal. assumption. + + - apply fix_red_body. apply OnOne2_map. repeat toAll. + apply (OnOne2_All_mix_left Hwf) in X. + solve_all. + red. rewrite <- !map_dtype. rewrite <- !map_dbody. intuition eauto. + + unfold Template.Ast.app_context, trans_local in b. + simpl in a. rewrite -> map_app in b. + unfold app_context. unfold TTy.fix_context in b. + rewrite map_rev map_mapi in b. simpl in b. + unfold fix_context. rewrite mapi_map. simpl. + forward b. + { clear b. solve_all. eapply All_app_inv; auto. + apply All_rev. apply All_mapi. + clear -Hwf; generalize 0 at 2; induction mfix0; constructor; hnf; simpl; auto. + intuition auto. depelim a. simpl. depelim Hwf. simpl in *. intuition auto. + now eapply LiftSubst.wf_lift. + depelim a. simpl. depelim Hwf. simpl in *. intuition auto. + } + forward b by auto. + eapply (refine_red1_Γ); [|apply b]. + f_equal. f_equal. apply mapi_ext; intros [] []. + rewrite lift0_p. simpl. rewrite LiftSubst.lift0_p. reflexivity. + rewrite trans_lift. simpl. reflexivity. + + simpl. inversion b0. reflexivity. + + - constructor. apply OnOne2_map. repeat toAll. + apply (OnOne2_All_mix_left Hwf) in X. clear Hwf. + solve_all. + red. rewrite <- !map_dtype. rewrite <- !map_dbody. + inversion b0. clear b0. + intuition eauto. + + eapply b. all: solve_all. + + unfold map_def. simpl. + f_equal. 2: auto. + f_equal. assumption. + + - apply cofix_red_body. apply OnOne2_map. repeat toAll. + apply (OnOne2_All_mix_left Hwf) in X. + solve_all. + red. rewrite <- !map_dtype. rewrite <- !map_dbody. intuition eauto. + + unfold Template.Ast.app_context, trans_local in b. + simpl in a. rewrite -> map_app in b. + unfold app_context. unfold TTy.fix_context in b. + rewrite map_rev map_mapi in b. simpl in b. + unfold fix_context. rewrite mapi_map. simpl. + forward b. + { clear b. solve_all. eapply All_app_inv; auto. + apply All_rev. apply All_mapi. + clear -Hwf; generalize 0 at 2; induction mfix0; constructor; hnf; simpl; auto. + intuition auto. depelim a. simpl. depelim Hwf. simpl in *. intuition auto. + now eapply LiftSubst.wf_lift. + depelim a. simpl. depelim Hwf. simpl in *. intuition auto. + } + forward b by auto. + eapply (refine_red1_Γ); [|apply b]. + f_equal. f_equal. apply mapi_ext; intros [] []. + rewrite lift0_p. simpl. rewrite LiftSubst.lift0_p. reflexivity. + rewrite trans_lift. simpl. reflexivity. + + simpl. inversion b0. reflexivity. +Qed. + + + Lemma trans_build_case_predicate_type ind mdecl idecl npar args u ps pty: -PT.build_case_predicate_type ind mdecl idecl (firstn npar args) u ps = Some pty -> +ST.build_case_predicate_type ind mdecl idecl (firstn npar args) u ps = Some pty -> TT.build_case_predicate_type ind (trans_minductive_body mdecl) (trans_one_ind_body idecl) (firstn npar (map trans args)) u ps = Some (trans pty). @@ -616,7 +861,7 @@ Proof. 2: { destruct d. cbn. rewrite lift0_p. - rewrite PL.lift0_p. + rewrite SL.lift0_p. unfold vass. reflexivity. } @@ -637,7 +882,7 @@ Lemma trans_wf_local': (fun Σ0 Γ0 _ (t T : PCUICAst.term) _ => TT.typing (trans_global Σ0) (trans_local Γ0) (trans t) (trans T)) in - PT.All_local_env_over PT.typing P Σ Γ wfΓ -> + ST.All_local_env_over ST.typing P Σ Γ wfΓ -> TTwf_local (trans_global Σ) (trans_local Γ). Proof. intros. @@ -650,10 +895,10 @@ Proof. Qed. Lemma trans_wf_local_env Σ Γ : - PT.All_local_env - (PT.lift_typing + ST.All_local_env + (ST.lift_typing (fun (Σ : PCUICAst.global_env_ext) Γ b ty => - PT.typing Σ Γ b ty × TT.typing (trans_global Σ) (trans_local Γ) (trans b) (trans ty)) Σ) + ST.typing Σ Γ b ty × TT.typing (trans_global Σ) (trans_local Γ) (trans b) (trans ty)) Σ) Γ -> TTwf_local (trans_global Σ) (trans_local Γ). Proof. @@ -670,9 +915,9 @@ Qed. Lemma trans_branches Σ Γ brs btys ps: All2 (fun br bty : nat × PCUICAst.term => - (((br.1 = bty.1 × PT.typing Σ Γ br.2 bty.2) + (((br.1 = bty.1 × ST.typing Σ Γ br.2 bty.2) × TT.typing (trans_global Σ) (trans_local Γ) (trans br.2) (trans bty.2)) - × PT.typing Σ Γ bty.2 (PCUICAst.tSort ps)) + × ST.typing Σ Γ bty.2 (PCUICAst.tSort ps)) × TT.typing (trans_global Σ) (trans_local Γ) (trans bty.2) (trans (PCUICAst.tSort ps))) brs btys -> All2 @@ -692,11 +937,11 @@ Proof. Qed. Lemma trans_mfix_All Σ Γ mfix: - PT.All_local_env - (PT.lift_typing + ST.All_local_env + (ST.lift_typing (fun (Σ : PCUICEnvironment.global_env_ext) (Γ : PCUICEnvironment.context) (b ty : PCUICAst.term) => - PT.typing Σ Γ b ty + ST.typing Σ Γ b ty × TT.typing (trans_global Σ) (trans_local Γ) (trans b) (trans ty)) Σ) (PCUICAst.app_context Γ (PCUICLiftSubst.fix_context mfix)) -> TTwf_local (trans_global Σ) @@ -724,28 +969,28 @@ Proof. Qed. Lemma trans_mfix_All2 Σ Γ mfix xfix: -All - (fun d : def PCUICAst.term => - (PT.typing Σ (PCUICAst.app_context Γ (PCUICLiftSubst.fix_context xfix)) - (dbody d) - (PCUICLiftSubst.lift0 #|PCUICLiftSubst.fix_context xfix| (dtype d)) - × PCUICAst.isLambda (dbody d) = true) - × TT.typing (trans_global Σ) - (trans_local (PCUICAst.app_context Γ (PCUICLiftSubst.fix_context xfix))) - (trans (dbody d)) - (trans - (PCUICLiftSubst.lift0 #|PCUICLiftSubst.fix_context xfix| - (dtype d)))) mfix -> -All - (fun d : def term => - TT.typing (trans_global Σ) - (trans_local Γ ,,, TT.fix_context (map (map_def trans trans) xfix)) - (dbody d) (TL.lift0 #|TT.fix_context (map (map_def trans trans) xfix)| (dtype d)) - × isLambda (dbody d) = true) (map (map_def trans trans) mfix). + All + (fun d : def PCUICAst.term => + (ST.typing Σ (PCUICAst.app_context Γ (PCUICLiftSubst.fix_context xfix)) + (dbody d) + (PCUICLiftSubst.lift0 #|PCUICLiftSubst.fix_context xfix| (dtype d)) + × PCUICAst.isLambda (dbody d) = true) + × TT.typing (trans_global Σ) + (trans_local (PCUICAst.app_context Γ (PCUICLiftSubst.fix_context xfix))) + (trans (dbody d)) + (trans + (PCUICLiftSubst.lift0 #|PCUICLiftSubst.fix_context xfix| + (dtype d)))) mfix -> + All + (fun d : def term => + TT.typing (trans_global Σ) + (trans_local Γ ,,, TT.fix_context (map (map_def trans trans) xfix)) + (dbody d) (TL.lift0 #|TT.fix_context (map (map_def trans trans) xfix)| (dtype d)) + × isLambda (dbody d) = true) (map (map_def trans trans) mfix). Proof. induction 1. - constructor. - - constructor. + - simpl; constructor. + destruct p as [[]]. unfold app_context, PCUICAst.app_context in *. split. @@ -754,22 +999,59 @@ Proof. rewrite trans_dbody, trans_lift, trans_dtype in t0. replace(#|PCUICLiftSubst.fix_context xfix|) with (#|TT.fix_context (map(map_def trans trans) xfix)|) in t0. - 2: admit. -Admitted. + 2:now rewrite TT.fix_context_length, map_length, fix_context_length. + now destruct x. + * destruct x; simpl in *; auto. + now destruct dbody. + + auto. +Qed. +Lemma trans_mfix_All2' Σ Γ mfix xfix: + All + (fun d : def PCUICAst.term => + (ST.typing Σ (PCUICAst.app_context Γ (PCUICLiftSubst.fix_context xfix)) + (dbody d) + (PCUICLiftSubst.lift0 #|PCUICLiftSubst.fix_context xfix| (dtype d))) + × TT.typing (trans_global Σ) + (trans_local (PCUICAst.app_context Γ (PCUICLiftSubst.fix_context xfix))) + (trans (dbody d)) + (trans + (PCUICLiftSubst.lift0 #|PCUICLiftSubst.fix_context xfix| + (dtype d)))) mfix -> + All + (fun d : def term => + TT.typing (trans_global Σ) + (trans_local Γ ,,, TT.fix_context (map (map_def trans trans) xfix)) + (dbody d) (TL.lift0 #|TT.fix_context (map (map_def trans trans) xfix)| (dtype d))) + (map (map_def trans trans) mfix). +Proof. + induction 1. + - constructor. + - simpl; constructor. + + destruct p as []. + unfold app_context, PCUICAst.app_context in *. + unfold trans_local in t0. + rewrite map_app, trans_fix_context in t0. + rewrite trans_dbody, trans_lift, trans_dtype in t0. + replace(#|PCUICLiftSubst.fix_context xfix|) with + (#|TT.fix_context (map(map_def trans trans) xfix)|) in t0. + 2:now rewrite TT.fix_context_length, map_length, fix_context_length. + now destruct x. + + auto. +Qed. Lemma All_over_All Σ Γ wfΓ : -PT.All_local_env_over PT.typing - (fun (Σ : PCUICAst.global_env_ext) (Γ : PCUICAst.context) - (_ : wf_local Σ Γ) (t T : PCUICAst.term) - (_ : PT.typing Σ Γ t T) => - TT.typing (trans_global Σ) (trans_local Γ) (trans t) (trans T)) Σ Γ wfΓ -> -PT.All_local_env - (PT.lift_typing - (fun (Σ0 : PCUICAst.global_env_ext) (Γ0 : PCUICEnvironment.context) - (b ty : PCUICAst.term) => - PT.typing Σ0 Γ0 b ty - × TT.typing (trans_global Σ0) (trans_local Γ0) (trans b) (trans ty)) Σ) Γ. + ST.All_local_env_over ST.typing + (fun (Σ : PCUICAst.global_env_ext) (Γ : PCUICAst.context) + (_ : wf_local Σ Γ) (t T : PCUICAst.term) + (_ : ST.typing Σ Γ t T) => + TT.typing (trans_global Σ) (trans_local Γ) (trans t) (trans T)) Σ Γ wfΓ -> + ST.All_local_env + (ST.lift_typing + (fun (Σ0 : PCUICAst.global_env_ext) (Γ0 : PCUICEnvironment.context) + (b ty : PCUICAst.term) => + ST.typing Σ0 Γ0 b ty + × TT.typing (trans_global Σ0) (trans_local Γ0) (trans b) (trans ty)) Σ) Γ. Proof. intros H. induction H;cbn. @@ -789,6 +1071,9 @@ Proof. Qed. + + + Lemma invert_type_App `{checker_flags} Σ Γ f u T : TT.typing Σ Γ (tApp f u) T -> { T' : term & { U' & ((TT.typing Σ Γ f T') * TT.typing_spine Σ Γ T' u U' * @@ -858,21 +1143,25 @@ Proof. - intro; apply leq_universe_refl. Qed. - Axiom fix_guard_trans : forall Σ Γ mfix, - PT.fix_guard Σ Γ mfix -> - TT.fix_guard (map (map_def trans trans) mfix). + ST.fix_guard Σ Γ mfix -> + TT.fix_guard (trans_global Σ) (trans_local Γ) (map (map_def trans trans) mfix). -Theorem template_to_pcuic (Σ : P.global_env_ext) Γ t T : - PT.wf Σ -> - PT.typing Σ Γ t T -> +Axiom cofix_guard_trans : + forall Σ Γ mfix, + ST.cofix_guard Σ Γ mfix -> + TT.cofix_guard (trans_global Σ) (trans_local Γ) (map (map_def trans trans) mfix). + +Theorem template_to_pcuic (Σ : S.global_env_ext) Γ t T : + ST .wf Σ -> + ST.typing Σ Γ t T -> TT.typing (trans_global Σ) (trans_local Γ) (trans t) (trans T). Proof. intros X X0. revert Σ X Γ t T X0. - apply (PT.typing_ind_env (fun Σ Γ t T => + apply (ST.typing_ind_env (fun Σ Γ t T => TT.typing (trans_global Σ) (trans_local Γ) (trans t) (trans T) )%type (fun Σ Γ wfΓ => @@ -980,6 +1269,7 @@ in All (for wf_local assumptions) + admit. - rewrite trans_dtype. simpl. eapply TT.type_CoFix; auto. + + now eapply cofix_guard_trans. + erewrite map_nth_error. 2: eassumption. destruct decl. @@ -990,7 +1280,7 @@ in All (for wf_local assumptions) intros x [s ?]; exists s; intuition auto. + fold trans;subst types. (* like trans_mfix_All2 without isLambda *) - admit. + now apply trans_mfix_All2'. + admit. - eapply TT.type_Conv. + eassumption. diff --git a/template-coq/theories/Typing.v b/template-coq/theories/Typing.v index 48ed81d95..8f629717a 100644 --- a/template-coq/theories/Typing.v +++ b/template-coq/theories/Typing.v @@ -167,7 +167,7 @@ Inductive red1 (Σ : global_env) (Γ : context) : term -> term -> Type := | red_fix mfix idx args narg fn : unfold_fix mfix idx = Some (narg, fn) -> is_constructor narg args = true -> - red1 Σ Γ (tApp (tFix mfix idx) args) (tApp fn args) + red1 Σ Γ (tApp (tFix mfix idx) args) (mkApps fn args) (** CoFix-case unfolding *) | red_cofix_case ip p mfix idx args narg fn brs : @@ -263,7 +263,7 @@ Lemma red1_ind_all : (forall (Γ : context) (mfix : mfixpoint term) (idx : nat) (args : list term) (narg : nat) (fn : term), unfold_fix mfix idx = Some (narg, fn) -> - is_constructor narg args = true -> P Γ (tApp (tFix mfix idx) args) (tApp fn args)) -> + is_constructor narg args = true -> P Γ (tApp (tFix mfix idx) args) (mkApps fn args)) -> (forall (Γ : context) (ip : inductive * nat * relevance) (p : term) (mfix : mfixpoint term) (idx : nat) (args : list term) (narg : nat) (fn : term) (brs : list (nat * term)), unfold_cofix mfix idx = Some (narg, fn) -> @@ -627,40 +627,73 @@ Definition eq_context `{checker_flags} φ (Γ Δ : context) := Module TemplateEnvTyping := EnvTyping TemplateTerm TemplateEnvironment. Include TemplateEnvTyping. -(* AXIOM GUARD CONDITION *) -Axiom fix_guard : mfixpoint term -> bool. -Axiom cofix_guard : mfixpoint term -> bool. - -Axiom fix_guard_red1 : - forall Σ Γ mfix mfix' idx, - fix_guard mfix -> - red1 Σ Γ (tFix mfix idx) (tFix mfix' idx) -> - fix_guard mfix'. - -Axiom fix_guard_lift : - forall mfix n k, +Definition extends (Σ Σ' : global_env) := { Σ'' & Σ' = Σ'' ++ Σ }. + +Class GuardChecker := +{ (* Structural recursion check *) + fix_guard : global_env_ext -> context -> mfixpoint term -> bool ; + (* Guarded by destructors check *) + cofix_guard : global_env_ext -> context -> mfixpoint term -> bool ; + + fix_guard_red1 Σ Γ mfix mfix' idx : + fix_guard Σ Γ mfix -> + red1 Σ Γ (tFix mfix idx) (tFix mfix' idx) -> + fix_guard Σ Γ mfix' ; + + fix_guard_lift Σ Γ Γ' Γ'' mfix : + let k' := (#|mfix| + #|Γ'|)%nat in + let mfix' := map (map_def (lift #|Γ''| #|Γ'|) (lift #|Γ''| k')) mfix in + fix_guard Σ (Γ ,,, Γ') mfix -> + fix_guard Σ (Γ ,,, Γ'' ,,, lift_context #|Γ''| 0 Γ') mfix' ; + + fix_guard_subst Σ Γ Γ' Δ mfix s k : let k' := (#|mfix| + k)%nat in - let mfix' := map (map_def (lift n k) (lift n k')) mfix in - fix_guard mfix -> - fix_guard mfix'. - -Axiom fix_guard_subst : - forall mfix s k, + let mfix' := map (map_def (subst s k) (subst s k')) mfix in + fix_guard Σ (Γ ,,, Γ' ,,, Δ) mfix -> + fix_guard Σ (Γ ,,, subst_context s 0 Δ) mfix' ; + + fix_guard_subst_instance {cf:checker_flags} Σ Γ mfix u univs : + consistent_instance_ext (Σ.1, univs) Σ.2 u -> + fix_guard Σ Γ mfix -> + fix_guard (Σ.1, univs) (subst_instance_context u Γ) (map (map_def (subst_instance_constr u) (subst_instance_constr u)) + mfix) ; + + fix_guard_extends Σ Γ mfix (Σ' : global_env_ext) : + fix_guard Σ Γ mfix -> + extends Σ.1 Σ' -> + fix_guard Σ' Γ mfix ; + + cofix_guard_red1 Σ Γ mfix mfix' idx : + cofix_guard Σ Γ mfix -> + red1 Σ Γ (tCoFix mfix idx) (tCoFix mfix' idx) -> + cofix_guard Σ Γ mfix' ; + + cofix_guard_lift Σ Γ Γ' Γ'' mfix : + let k' := (#|mfix| + #|Γ'|)%nat in + let mfix' := map (map_def (lift #|Γ''| #|Γ'|) (lift #|Γ''| k')) mfix in + cofix_guard Σ (Γ ,,, Γ') mfix -> + cofix_guard Σ (Γ ,,, Γ'' ,,, lift_context #|Γ''| 0 Γ') mfix' ; + + cofix_guard_subst Σ Γ Γ' Δ mfix s k : let k' := (#|mfix| + k)%nat in let mfix' := map (map_def (subst s k) (subst s k')) mfix in - fix_guard mfix -> - fix_guard mfix'. - -(* AXIOM INDUCTIVE GUARD CONDITION *) -Axiom ind_guard : mutual_inductive_body -> bool. - -Extract Constant fix_guard => "fun m -> assert false". -Extract Constant fix_guard_red1 => "fun s g m m' i -> assert false". -Extract Constant fix_guard_lift => "fun m n k -> assert false". -Extract Constant fix_guard_subst => "fun m s k -> assert false". - -Extract Constant ind_guard => "fun m -> assert false". + cofix_guard Σ (Γ ,,, Γ' ,,, Δ) mfix -> + cofix_guard Σ (Γ ,,, subst_context s 0 Δ) mfix' ; + + cofix_guard_subst_instance {cf:checker_flags} Σ Γ mfix u univs : + consistent_instance_ext (Σ.1, univs) Σ.2 u -> + cofix_guard Σ Γ mfix -> + cofix_guard (Σ.1, univs) (subst_instance_context u Γ) (map (map_def (subst_instance_constr u) (subst_instance_constr u)) + mfix) ; + + cofix_guard_extends Σ Γ mfix (Σ' : global_env_ext) : + cofix_guard Σ Γ mfix -> + extends Σ.1 Σ' -> + cofix_guard Σ' Γ mfix }. +(* AXIOM GUARD CONDITION *) +Axiom guard_checking : GuardChecker. +Existing Instance guard_checking. (** Compute the type of a case from the predicate [p], actual parameters [pars] and an inductive declaration. *) @@ -914,7 +947,7 @@ Inductive typing `{checker_flags} (Σ : global_env_ext) (Γ : context) : term -> Σ ;;; Γ |- tProj p c : subst0 (c :: List.rev args) (subst_instance_constr u pdecl.2) | type_Fix mfix n decl : - fix_guard mfix -> + fix_guard Σ Γ mfix -> nth_error mfix n = Some decl -> wf_local Σ Γ -> All (fun d => {s & Σ ;;; Γ |- d.(dtype) : tSort s}) mfix -> @@ -924,7 +957,7 @@ Inductive typing `{checker_flags} (Σ : global_env_ext) (Γ : context) : term -> Σ ;;; Γ |- tFix mfix n : decl.(dtype) | type_CoFix mfix n decl : - cofix_guard mfix -> + cofix_guard Σ Γ mfix -> nth_error mfix n = Some decl -> wf_local Σ Γ -> All (fun d => {s & Σ ;;; Γ |- d.(dtype) : tSort s}) mfix -> @@ -963,7 +996,6 @@ Definition unlift_opt_pred (P : global_env_ext -> context -> option term -> term Module TemplateTyping <: Typing TemplateTerm TemplateEnvironment TemplateEnvTyping. - Definition ind_guard := ind_guard. Definition typing := @typing. Definition wf_universe := @wf_universe. Definition conv := @conv. @@ -1262,7 +1294,7 @@ Lemma typing_ind_env `{cf : checker_flags} : (forall Σ (wfΣ : wf Σ.1) (Γ : context) (wfΓ : wf_local Σ Γ) (mfix : list (def term)) (n : nat) decl, let types := fix_context mfix in - fix_guard mfix -> + fix_guard Σ Γ mfix -> nth_error mfix n = Some decl -> All_local_env_over typing Pdecl Σ Γ wfΓ -> All (fun d => {s & (Σ ;;; Γ |- d.(dtype) : tSort s)%type * P Σ Γ d.(dtype) (tSort s)})%type mfix -> @@ -1274,7 +1306,7 @@ Lemma typing_ind_env `{cf : checker_flags} : (forall Σ (wfΣ : wf Σ.1) (Γ : context) (wfΓ : wf_local Σ Γ) (mfix : list (def term)) (n : nat) decl, let types := fix_context mfix in - cofix_guard mfix -> + cofix_guard Σ Γ mfix -> nth_error mfix n = Some decl -> All_local_env_over typing Pdecl Σ Γ wfΓ -> All (fun d => {s & (Σ ;;; Γ |- d.(dtype) : tSort s)%type * P Σ Γ d.(dtype) (tSort s)})%type mfix -> From 14b1cb3a42c670dabb7d18300817aab6c3a54e9c Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Wed, 9 Dec 2020 21:48:15 +0100 Subject: [PATCH 49/70] Remove isLambda condition on fixpoint bodies --- template-coq/theories/Ast.v | 2 +- template-coq/theories/Induction.v | 3 +-- template-coq/theories/LiftSubst.v | 2 +- template-coq/theories/Typing.v | 20 ++++++-------------- template-coq/theories/TypingWf.v | 18 +++++------------- template-coq/theories/WfInv.v | 2 +- 6 files changed, 15 insertions(+), 32 deletions(-) diff --git a/template-coq/theories/Ast.v b/template-coq/theories/Ast.v index a7d03bd8a..8efdd5707 100644 --- a/template-coq/theories/Ast.v +++ b/template-coq/theories/Ast.v @@ -124,7 +124,7 @@ Inductive wf : term -> Prop := | wf_tConstruct i k u : wf (tConstruct i k u) | wf_tCase ci p c brs : wf p -> wf c -> Forall (wf ∘ snd) brs -> wf (tCase ci p c brs) | wf_tProj p t : wf t -> wf (tProj p t) -| wf_tFix mfix k : Forall (fun def => wf def.(dtype) /\ wf def.(dbody) /\ isLambda def.(dbody) = true) mfix -> +| wf_tFix mfix k : Forall (fun def => wf def.(dtype) /\ wf def.(dbody)) mfix -> wf (tFix mfix k) | wf_tCoFix mfix k : Forall (fun def => wf def.(dtype) /\ wf def.(dbody)) mfix -> wf (tCoFix mfix k) | wf_tInt i : wf (tInt i) diff --git a/template-coq/theories/Induction.v b/template-coq/theories/Induction.v index 6d8f12934..7182c9f1e 100644 --- a/template-coq/theories/Induction.v +++ b/template-coq/theories/Induction.v @@ -87,7 +87,7 @@ Lemma term_wf_forall_list_ind : P t -> forall t0 : term, P t0 -> forall l : list (nat * term), tCaseBrsProp P l -> P (tCase p t t0 l)) -> (forall (s : projection) (t : term), P t -> P (tProj s t)) -> - (forall (m : mfixpoint term) (n : nat), tFixProp P P m -> Forall (fun def => isLambda (dbody def) = true) m -> P (tFix m n)) -> + (forall (m : mfixpoint term) (n : nat), tFixProp P P m -> P (tFix m n)) -> (forall (m : mfixpoint term) (n : nat), tFixProp P P m -> P (tCoFix m n)) -> (forall i, P (tInt i)) -> (forall f, P (tFloat f)) -> @@ -123,7 +123,6 @@ Proof. induction X; constructor. + split; inv H18; intuition. + apply IHX. now inv H18. - + eapply Forall_impl; tea. clear; intros; cbn in *; intuition. - inv H16; auto. apply H15. red. red in X. diff --git a/template-coq/theories/LiftSubst.v b/template-coq/theories/LiftSubst.v index d689cd832..dfb5cbb78 100644 --- a/template-coq/theories/LiftSubst.v +++ b/template-coq/theories/LiftSubst.v @@ -634,7 +634,7 @@ Proof. - apply wf_mkApps; auto. apply Forall_map. eapply Forall_impl; eauto. - apply Forall_map. apply All_Forall. eapply All_impl; tea. intros [] XX; cbn in *; apply XX. - - solve_all. induction dbody; try discriminate. reflexivity. + - solve_all. - apply Forall_map. eapply All_Forall, All_impl; eauto. intros [] XX; cbn in *; split; apply XX. Qed. diff --git a/template-coq/theories/Typing.v b/template-coq/theories/Typing.v index 8f629717a..0f2fb1483 100644 --- a/template-coq/theories/Typing.v +++ b/template-coq/theories/Typing.v @@ -80,13 +80,7 @@ Definition fix_subst (l : mfixpoint term) := Definition unfold_fix (mfix : mfixpoint term) (idx : nat) := match List.nth_error mfix idx with - | Some d => - if isLambda d.(dbody) then - Some (d.(rarg), subst0 (fix_subst mfix) d.(dbody)) - else None (* We don't unfold ill-formed fixpoints, which would - render confluence unprovable, creating an infinite - number of critical pairs between unfoldings of fixpoints. - e.g. [fix f := f] is not allowed. *) + | Some d => Some (d.(rarg), subst0 (fix_subst mfix) d.(dbody)) | None => None end. @@ -951,8 +945,7 @@ Inductive typing `{checker_flags} (Σ : global_env_ext) (Γ : context) : term -> nth_error mfix n = Some decl -> wf_local Σ Γ -> All (fun d => {s & Σ ;;; Γ |- d.(dtype) : tSort s}) mfix -> - All (fun d => (Σ ;;; Γ ,,, fix_context mfix |- d.(dbody) : lift0 #|fix_context mfix| d.(dtype)) - * (isLambda d.(dbody) = true)%type) mfix -> + All (fun d => (Σ ;;; Γ ,,, fix_context mfix |- d.(dbody) : lift0 #|fix_context mfix| d.(dtype))) mfix -> wf_fixpoint Σ mfix -> Σ ;;; Γ |- tFix mfix n : decl.(dtype) @@ -1067,7 +1060,7 @@ Proof. - exact (S (S (wf_local_size _ typing_size _ a))). - exact (S (Nat.max d1 (Nat.max d2 (all2_size _ (fun x y p => Nat.max (typing_size Σ Γ (snd x) (snd y) (snd (fst p))) (typing_size _ _ _ _ (snd p))) a)))). - - exact (S (Nat.max (Nat.max (wf_local_size _ typing_size _ a) (all_size _ (fun x p => typing_size Σ _ _ _ p.π2) a0)) (all_size _ (fun x p => typing_size Σ _ _ _ (fst p)) a1))). + - exact (S (Nat.max (Nat.max (wf_local_size _ typing_size _ a) (all_size _ (fun x p => typing_size Σ _ _ _ p.π2) a0)) (all_size _ (fun x p => typing_size Σ _ _ _ p) a1))). - exact (S (Nat.max (Nat.max (wf_local_size _ typing_size _ a) (all_size _ (fun x p => typing_size Σ _ _ _ p.π2) a0)) (all_size _ (fun x p => typing_size Σ _ _ _ p) a1))). Defined. @@ -1299,7 +1292,6 @@ Lemma typing_ind_env `{cf : checker_flags} : All_local_env_over typing Pdecl Σ Γ wfΓ -> All (fun d => {s & (Σ ;;; Γ |- d.(dtype) : tSort s)%type * P Σ Γ d.(dtype) (tSort s)})%type mfix -> All (fun d => (Σ ;;; Γ ,,, types |- d.(dbody) : lift0 #|types| d.(dtype))%type * - (isLambda d.(dbody) = true)%type * P Σ (Γ ,,, types) d.(dbody) (lift0 #|types| d.(dtype)))%type mfix -> wf_fixpoint Σ.1 mfix -> P Σ Γ (tFix mfix n) decl.(dtype)) -> @@ -1562,8 +1554,8 @@ Proof. typing_size Hty < S (all_size (fun x : def term => (Σ;;; Γ ,,, fix_context mfix |- dbody x : lift0 #|fix_context mfix| (dtype x))%type - * (isLambda (dbody x) = true)%type)%type - (fun (x : def term) p => typing_size (fst p)) a1) -> + )%type + (fun (x : def term) p => typing_size p) a1) -> Forall_decls_typing P Σ.1 * P Σ Γ0 t T). {intros. eapply (X14 _ X _ _ Hty); eauto. lia. } clear X14 X13. @@ -1572,7 +1564,7 @@ Proof. induction a1; econstructor; eauto. ++ split; auto. - eapply (X _ (typing_wf_local (fst p)) _ _ (fst p)). simpl. lia. + eapply (X _ (typing_wf_local p) _ _ p). simpl. lia. ++ eapply IHa1. intros. eapply (X _ X0 _ _ Hty). simpl; lia. diff --git a/template-coq/theories/TypingWf.v b/template-coq/theories/TypingWf.v index ee69a6d85..29dcecfbd 100644 --- a/template-coq/theories/TypingWf.v +++ b/template-coq/theories/TypingWf.v @@ -93,18 +93,15 @@ Lemma unfold_fix_wf: forall (mfix : mfixpoint term) (idx : nat) (narg : nat) (fn : term), unfold_fix mfix idx = Some (narg, fn) -> Ast.wf (tFix mfix idx) -> - Ast.wf fn /\ isApp fn = false. + Ast.wf fn. Proof. intros mfix idx narg fn Hf Hwf. unfold unfold_fix in Hf. inv Hwf. destruct nth_error eqn:eqnth; try congruence. pose proof (nth_error_forall eqnth H). simpl in H0. - destruct H0 as [ _ [ wfd islamd ] ]. - rewrite islamd in Hf. + destruct H0 as [ _ wfd]. injection Hf. intros <- <-. - apply (isLambda_subst (fix_subst mfix) 0) in islamd. - apply isLambda_isApp in islamd. split; try congruence. - apply wf_subst; auto. clear wfd islamd Hf eqnth. + apply wf_subst; auto. clear wfd Hf eqnth. assert(forall n, Ast.wf (tFix mfix n)). constructor; auto. unfold fix_subst. generalize #|mfix|; intros. induction n; auto. Qed. @@ -134,8 +131,6 @@ Proof. now apply Forall_map. - constructor; auto. solve_all. - constructor. solve_all. - destruct x; simpl in *. repeat split; tas. - destruct dbody; simpl in *; congruence. - constructor. solve_all. Qed. @@ -204,7 +199,7 @@ Proof. induction brs in c, H1 |- *; destruct c; simpl in *. constructor. constructor. inv H1; auto. inv H1; auto. induction H0 in pars |- *; destruct pars; try constructor; auto. simpl. auto. - - apply unfold_fix_wf in H; auto. constructor; intuition auto. + - apply unfold_fix_wf in H; auto. eapply wf_mkApps; auto. - constructor; auto. apply wf_mkApps_napp in H1 as [Hcof Hargs]; auto. apply unfold_cofix_wf in H; auto. apply wf_mkApps; intuition auto. @@ -235,7 +230,7 @@ Proof. - constructor; auto. solve_all. pose proof H as H'. revert H. apply (OnOne2_All_All X). clear X. - intros [na bo ty ra] [nb bb tb rb] [[r ih] e] [? [? ?]]. + intros [na bo ty ra] [nb bb tb rb] [[r ih] e] [? ?]. simpl in *. inversion e. subst. clear e. intuition eauto. @@ -246,7 +241,6 @@ Proof. cbn. unfold wf_decl. simpl. intros ? [? ? ? ?] ?. simpl in *. intuition eauto with wf. - + eapply red1_isLambda. all: eassumption. - constructor; auto. induction X; inv H; constructor; intuition auto; congruence. - constructor; auto. solve_all. @@ -299,8 +293,6 @@ Proof. - destruct t; try reflexivity. discriminate. - destruct l; simpl in *; congruence. - - destruct x; simpl in *; intuition eauto. - destruct dbody; simpl in *; try discriminate. destruct Nat.leb; auto. Qed. Lemma declared_inductive_wf {cf:checker_flags} : diff --git a/template-coq/theories/WfInv.v b/template-coq/theories/WfInv.v index 8e982e7aa..9fff63947 100644 --- a/template-coq/theories/WfInv.v +++ b/template-coq/theories/WfInv.v @@ -17,7 +17,7 @@ Fixpoint wf_Inv (t : term) := | tConst _ _ | tInd _ _ | tConstruct _ _ _ => True | tCase ci p c brs => wf p /\ wf c /\ Forall (wf ∘ snd) brs | tProj p t => wf t - | tFix mfix k => Forall (fun def => wf def.(dtype) /\ wf def.(dbody) /\ isLambda def.(dbody) = true) mfix + | tFix mfix k => Forall (fun def => wf def.(dtype) /\ wf def.(dbody)) mfix | tCoFix mfix k => Forall (fun def => wf def.(dtype) /\ wf def.(dbody)) mfix end. From 319a3601dfc3c108c74a5ce55fd0615889285d8d Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Thu, 10 Dec 2020 02:09:20 +0100 Subject: [PATCH 50/70] Finished PCUIC -> Template proofs --- checker/theories/Substitution.v | 164 ++--- checker/theories/Weakening.v | 64 +- checker/theories/WeakeningEnv.v | 138 ++-- pcuic/theories/PCUICContextConversion.v | 2 +- pcuic/theories/PCUICEquality.v | 1 - pcuic/theories/PCUICNameless.v | 1 - pcuic/theories/PCUICSigmaCalculus.v | 18 +- pcuic/theories/PCUICSubstitution.v | 12 +- pcuic/theories/PCUICToTemplateCorrectness.v | 660 ++++++++++++-------- pcuic/theories/PCUICTyping.v | 14 +- pcuic/theories/PCUICUnivSubstitution.v | 19 +- pcuic/theories/PCUICWeakening.v | 12 +- pcuic/theories/PCUICWeakeningEnv.v | 2 +- pcuic/theories/TemplateToPCUICCorrectness.v | 2 +- template-coq/_CoqProject | 1 + template-coq/theories/TermEquality.v | 443 +++++++++++++ template-coq/theories/Typing.v | 137 +--- 17 files changed, 1080 insertions(+), 610 deletions(-) create mode 100644 template-coq/theories/TermEquality.v diff --git a/checker/theories/Substitution.v b/checker/theories/Substitution.v index 7807ad583..41be803e5 100644 --- a/checker/theories/Substitution.v +++ b/checker/theories/Substitution.v @@ -1,6 +1,6 @@ (* Distributed under the terms of the MIT license. *) From MetaCoq.Template Require Import config utils Ast AstUtils Induction LiftSubst - UnivSubst Typing TypingWf. + UnivSubst TermEquality Typing TypingWf. From MetaCoq.Checker Require Import Generation Closed WeakeningEnv Weakening. From Equations Require Import Equations. @@ -221,10 +221,8 @@ Lemma subst_unfold_fix n k mfix idx narg fn : Proof. unfold unfold_fix. intros wfn. rewrite nth_error_map. destruct (nth_error mfix idx) eqn:Hdef; try congruence. - case_eq (isLambda (dbody d)); [|discriminate]. - move=> Hlam [= <- <-] /=. rewrite isLambda_subst; tas. + move=> [= <- <-] /=. f_equal. f_equal. - solve_all. erewrite (distr_subst_rec _ _ _ wfn k 0). rewrite fix_subst_length. simpl. f_equal. unfold fix_subst. rewrite !map_length. @@ -1338,6 +1336,7 @@ Proof. rewrite mkApp_mkApps. constructor. intros. + rewrite mkApp_mkApps. econstructor; eauto. inv wfM1. simpl. clear -H1. @@ -1388,7 +1387,7 @@ Qed. Lemma wf_fix : forall (mfix : list (def term)) (k : nat), Ast.wf (tFix mfix k) -> Forall - (fun def : def term => Ast.wf (dtype def) /\ Ast.wf (dbody def) /\ isLambda (dbody def) = true) + (fun def : def term => Ast.wf (dtype def) /\ Ast.wf (dbody def)) mfix. Proof. intros. inv H. auto. @@ -1468,20 +1467,9 @@ Proof. constructor. - rewrite mkApps_tApp; simpl; auto with wf. - inv wfM. auto with wf. rewrite -> mkApps_tApp; simpl. + inv wfM. auto with wf. + eapply red_fix. erewrite subst_unfold_fix; eauto. now apply subst_is_constructor. - + inv wfM. inv H3. - unfold unfold_fix in H. - destruct nth_error eqn:Heq. - destruct (isLambda (dbody d)); [|discriminate]. - injection H. intros <- <-. - eapply nth_error_forall in H5; eauto. - destruct d as [na b ty]; simpl in *. - destruct H5 as [_ [_ Hty]]. - destruct ty; try discriminate. reflexivity. - discriminate. - + apply not_empty_map. now inv wfM. - pose proof (subst_declared_constant _ _ _ s #|Γ''| u wfΣ H). apply (f_equal cst_body) in H1. @@ -1592,113 +1580,79 @@ Proof. + inversion b0. auto. Qed. -Lemma eq_term_upto_univ_refl Re Rle : - RelationClasses.Reflexive Re -> - RelationClasses.Reflexive Rle -> - forall t, eq_term_upto_univ Re Rle t t. -Proof. - intros hRe hRle. - induction t in Rle, hRle |- * using term_forall_list_rect; simpl; - try constructor; try apply Forall_Forall2; try apply All_All2 ; try easy; - try now (try apply Forall_All ; apply Forall_True). - - eapply All_All2. 1: eassumption. - intros. easy. - - eapply All_All2. 1: eassumption. - intros. easy. - - destruct p. constructor; try easy. - eapply All_All2. 1: eassumption. - intros. split ; auto. - - eapply All_All2. 1: eassumption. - intros x [? ?]. repeat split ; auto. - - eapply All_All2. 1: eassumption. - intros x [? ?]. repeat split ; auto. -Qed. - -Lemma eq_term_refl `{checker_flags} φ t : eq_term φ t t. +Lemma eq_term_leq_term `{checker_flags} Σ φ t u : + eq_term Σ φ t u -> leq_term Σ φ t u. Proof. - apply eq_term_upto_univ_refl. - - intro; apply eq_universe_refl. - - intro; apply eq_universe_refl. -Qed. - - -Lemma leq_term_refl `{checker_flags} φ t : leq_term φ t t. -Proof. - apply eq_term_upto_univ_refl. - - intro; apply eq_universe_refl. - - intro; apply leq_universe_refl. -Qed. - - -Lemma eq_term_leq_term `{checker_flags} φ t u : eq_term φ t u -> leq_term φ t u. -Proof. - induction t in u |- * using term_forall_list_rect; simpl; inversion 1; - subst; constructor; try (now unfold eq_term, leq_term in * ); - try eapply Forall2_impl' ; try eapply All2_impl' ; try easy. + eapply eq_term_upto_univ_morphism. auto. + intros. now apply eq_universe_leq_universe. - all: try (apply Forall_True, eq_universe_leq_universe). Qed. -Lemma eq_term_upto_univ_App `{checker_flags} Re Rle f f' : - eq_term_upto_univ Re Rle f f' -> +Lemma eq_term_upto_univ_App `{checker_flags} Σ Re Rle napp f f' : + eq_term_upto_univ_napp Σ Re Rle napp f f' -> isApp f = isApp f'. Proof. inversion 1; reflexivity. Qed. -Lemma eq_term_App `{checker_flags} φ f f' : - eq_term φ f f' -> +Lemma eq_term_App `{checker_flags} Σ φ f f' : + eq_term Σ φ f f' -> isApp f = isApp f'. Proof. inversion 1; reflexivity. Qed. -Lemma eq_term_upto_univ_mkApps `{checker_flags} Re Rle f l f' l' : - eq_term_upto_univ Re Rle f f' -> - All2 (eq_term_upto_univ Re Re) l l' -> - eq_term_upto_univ Re Rle (mkApps f l) (mkApps f' l'). +Lemma eq_term_upto_univ_mkApps `{checker_flags} Σ Re Rle napp f l f' l' : + eq_term_upto_univ_napp Σ Re Rle (#|l| + napp) f f' -> + All2 (eq_term_upto_univ Σ Re Re) l l' -> + eq_term_upto_univ_napp Σ Re Rle napp (mkApps f l) (mkApps f' l'). Proof. induction l in f, f' |- *; intro e; inversion_clear 1. - assumption. - - pose proof (eq_term_upto_univ_App _ _ _ _ e). + - pose proof (eq_term_upto_univ_App _ _ _ _ _ _ e). case_eq (isApp f). + intro X; rewrite X in H0. destruct f; try discriminate. destruct f'; try discriminate. - cbn. inversion_clear e. constructor. assumption. + cbn. inversion_clear e. constructor. + rewrite app_length /= -Nat.add_assoc //. apply All2_app. assumption. now constructor. + intro X; rewrite X in H0. rewrite !mkApps_tApp; eauto. intro; discriminate. intro; discriminate. - constructor. assumption. + constructor. simpl. now simpl in e. now constructor. Qed. -Lemma leq_term_mkApps `{checker_flags} φ f l f' l' : - leq_term φ f f' -> - All2 (eq_term φ) l l' -> - leq_term φ (mkApps f l) (mkApps f' l'). +Lemma leq_term_mkApps `{checker_flags} Σ φ f l f' l' : + leq_term Σ φ f f' -> + All2 (eq_term Σ φ) l l' -> + leq_term Σ φ (mkApps f l) (mkApps f' l'). Proof. + intros. eapply eq_term_upto_univ_mkApps. + eapply eq_term_upto_univ_impl. 5:eauto. 4:auto with arith. + 1-3:typeclasses eauto. + apply X0. Qed. -Lemma leq_term_App `{checker_flags} φ f f' : - leq_term φ f f' -> +Lemma leq_term_App `{checker_flags} Σ φ f f' : + leq_term Σ φ f f' -> isApp f = isApp f'. Proof. inversion 1; reflexivity. Qed. -Lemma subst_eq_term_upto_univ `{checker_flags} Re Rle n k T U : +Lemma subst_eq_term_upto_univ `{checker_flags} Σ Re Rle napp n k T U : RelationClasses.Reflexive Re -> RelationClasses.Reflexive Rle -> - eq_term_upto_univ Re Rle T U -> - eq_term_upto_univ Re Rle (subst n k T) (subst n k U). + eq_term_upto_univ_napp Σ Re Rle napp T U -> + eq_term_upto_univ_napp Σ Re Rle napp (subst n k T) (subst n k U). Proof. intros hRe hRle h. - induction T in n, k, U, h, Rle, hRle |- * using term_forall_list_rect. + induction T in napp, n, k, U, h, Rle, hRle |- * using term_forall_list_rect. all: simpl ; inversion h ; simpl. all: try (eapply eq_term_upto_univ_refl ; easy). all: try (constructor ; easy). @@ -1706,7 +1660,8 @@ Proof. eapply All2_map. eapply All2_impl' ; try eassumption. eapply All_impl ; try eassumption. cbn. intros x HH y HH'. now eapply HH. - - subst. eapply eq_term_upto_univ_mkApps. all: try easy. + - subst. eapply eq_term_upto_univ_mkApps. + rewrite map_length. eauto. eapply All2_map. eapply All2_impl' ; try eassumption. eapply All_impl ; try eassumption. cbn. intros x HH y HH'. now eapply HH. @@ -1729,9 +1684,9 @@ Proof. intros x [] y []; now split. Qed. -Lemma subst_eq_term `{checker_flags} ϕ n k T U : - eq_term ϕ T U -> - eq_term ϕ (subst n k T) (subst n k U). +Lemma subst_eq_term `{checker_flags} Σ ϕ n k T U : + eq_term Σ ϕ T U -> + eq_term Σ ϕ (subst n k T) (subst n k U). Proof. intros Hleq. eapply subst_eq_term_upto_univ. @@ -1740,9 +1695,9 @@ Proof. - assumption. Qed. -Lemma subst_leq_term `{checker_flags} ϕ n k T U : - leq_term ϕ T U -> - leq_term ϕ (subst n k T) (subst n k U). +Lemma subst_leq_term `{checker_flags} Σ ϕ n k T U : + leq_term Σ ϕ T U -> + leq_term Σ ϕ (subst n k T) (subst n k U). Proof. intros Hleq. eapply subst_eq_term_upto_univ. @@ -1752,16 +1707,16 @@ Proof. Qed. -Lemma subst_eq_decl `{checker_flags} ϕ l k d d' : - eq_decl ϕ d d' -> eq_decl ϕ (subst_decl l k d) (subst_decl l k d'). +Lemma subst_eq_decl `{checker_flags} Σ ϕ l k d d' : + eq_decl Σ ϕ d d' -> eq_decl Σ ϕ (subst_decl l k d) (subst_decl l k d'). Proof. destruct d, d', decl_body, decl_body0; unfold eq_decl, map_decl; cbn; intuition auto using subst_eq_term. Qed. -Lemma subst_eq_context `{checker_flags} φ l l' n k : - eq_context φ l l' -> - eq_context φ (subst_context n k l) (subst_context n k l'). +Lemma subst_eq_context `{checker_flags} Σ φ l l' n k : + eq_context Σ φ l l' -> + eq_context Σ φ (subst_context n k l) (subst_context n k l'). Proof. induction l in l', n, k |- *; inversion 1. constructor. rewrite !subst_context_snoc. constructor. @@ -1980,8 +1935,14 @@ Proof. subst params. rewrite firstn_map. exact H4. 4: now rewrite closedn_subst_instance_context. all: eauto with wf. - admit. admit. + subst params. eapply All_firstn. + eapply typing_wf in X3; auto. + destruct X3 as [wfc wfargs]. + eapply Forall_All. + now eapply wf_mkApps_inv in wfargs. + now eapply subs_wf in sub. -- solve_all. + destruct b0 as [s' [Hs IHs]]; eauto. - specialize (X2 Γ Γ' Δ s sub eq_refl). eapply refine_type. econstructor. @@ -2011,16 +1972,14 @@ Proof. now specialize (Hs' _ _ _ _ sub eq_refl). * eapply All_map. eapply (All_impl X1); simpl. - intros x [[Hb Hlam] IH]. + intros x [Hb IH]. rewrite subst_fix_context. specialize (IH Γ Γ' (Δ ,,, (fix_context mfix)) _ sub). rewrite app_context_assoc in IH. specialize (IH eq_refl). - split; auto. rewrite subst_context_app Nat.add_0_r app_context_assoc in IH. rewrite app_context_length fix_context_length in IH. rewrite subst_context_length fix_context_length. rewrite commut_lift_subst_rec; try lia. now rewrite (Nat.add_comm #|Δ|). - now rewrite isLambda_subst. * move: H2. rewrite /wf_fixpoint. pose proof (substitution_check_one_fix s #|Δ| mfix). @@ -2030,7 +1989,8 @@ Proof. - rewrite -> (map_dtype _ (subst s (#|mfix| + #|Δ|))). eapply type_CoFix; auto. - * now rewrite -> nth_error_map, H0. + * eapply cofix_guard_subst; eauto. + * now rewrite -> nth_error_map, H1. * eapply All_map. eapply (All_impl X0); simpl. intros x [u [Hs Hs']]; exists u. @@ -2045,18 +2005,18 @@ Proof. rewrite app_context_length fix_context_length in IH. rewrite subst_context_length fix_context_length. rewrite commut_lift_subst_rec; try lia. now rewrite (Nat.add_comm #|Δ|). - * move: H1. + * move: H2. rewrite /wf_cofixpoint. pose proof (substitution_check_one_cofix s #|Δ| mfix). destruct map_option_out eqn:Heq => //. - specialize (H1 _ eq_refl). - rewrite map_map_compose. now rewrite H1. + specialize (H2 _ eq_refl). + rewrite map_map_compose. now rewrite H2. - econstructor; eauto. eapply substitution_cumul; eauto. now eapply typing_wf in X0. now eapply typing_wf in X2. -Admitted. +Qed. Lemma substitution0 `{checker_flags} Σ Γ n u U (t : term) T : wf Σ.1 -> diff --git a/checker/theories/Weakening.v b/checker/theories/Weakening.v index bb40ea917..ddd4d2bc3 100644 --- a/checker/theories/Weakening.v +++ b/checker/theories/Weakening.v @@ -1,6 +1,6 @@ (* Distributed under the terms of the MIT license. *) From MetaCoq.Template Require Import config utils Ast AstUtils Reflect Induction - LiftSubst UnivSubst Typing TypingWf LibHypsNaming. + LiftSubst UnivSubst TermEquality Typing TypingWf LibHypsNaming. From MetaCoq.Checker Require Import WeakeningEnv Closed. Require Import ssreflect. @@ -176,9 +176,7 @@ Lemma lift_unfold_fix n k mfix idx narg fn : Proof. unfold unfold_fix. rewrite nth_error_map. destruct (nth_error mfix idx) eqn:Hdef; try congruence. - case_eq (isLambda (dbody d)); [|discriminate]. - intros Hlam [= <- <-]. simpl. - rewrite isLambda_lift; tas. + intros [= <- <-]. simpl. repeat f_equal. rewrite (distr_lift_subst_rec _ _ n 0 k). rewrite fix_subst_length. f_equal. @@ -686,19 +684,19 @@ Proof. + inversion b. eauto. Qed. -Lemma lift_eq_term_upto_univ Re Rl n k T U : - eq_term_upto_univ Re Rl T U -> - eq_term_upto_univ Re Rl (lift n k T) (lift n k U). +Lemma lift_eq_term_upto_univ Σ Re Rl n k T U napp : + eq_term_upto_univ_napp Σ Re Rl napp T U -> + eq_term_upto_univ_napp Σ Re Rl napp (lift n k T) (lift n k U). Proof. - induction T in n, k, U, Rl |- * using term_forall_list_rect; + induction T in napp, n, k, U, Rl |- * using term_forall_list_rect; inversion 1; simpl; try (now constructor). - constructor. subst. clear - X X1. induction l in X, args', X1 |- *. + inversion X1; constructor. + inversion X1. inversion X. subst. simpl. constructor. all: easy. - - constructor. easy. clear - X X2. - induction l in X, args', X2 |- *. + - constructor. rewrite map_length; easy. clear - X X2. + induction l in X, u', X2 |- *. + inversion X2; constructor. + inversion X2; inversion X; subst. now constructor. @@ -708,49 +706,48 @@ Proof. + inversion X3; inversion X; subst. constructor. cbn; easy. easy. - - constructor; try easy. clear - X X1. + - constructor; try easy. clear -napp X X1. assert (XX:forall k k', All2 - (fun x y => eq_term_upto_univ Re Re (dtype x) (dtype y) × - eq_term_upto_univ Re Re (dbody x) (dbody y) × - rarg x = rarg y) + (fun x y => ((eq_term_upto_univ Σ Re Re (dtype x) (dtype y) × + eq_term_upto_univ Σ Re Re (dbody x) (dbody y)) × + rarg x = rarg y) * eq_binder_annot (dname x) (dname y)) (map (map_def (lift n k) (lift n (#|m| + k'))) m) (map (map_def (lift n k) (lift n (#|mfix'| + k'))) mfix')); [|now apply XX]. clear k. induction m in X, mfix', X1 |- *. + inversion X1; constructor. + inversion X1; inversion X; subst. - simpl. constructor. split. cbn; easy. + simpl. constructor. split. split. split. cbn; easy. cbn; erewrite All2_length by eassumption. - easy. + easy. easy. easy. unfold tFixProp in IHm. cbn. rewrite !plus_n_Sm. now apply IHm. - constructor; try easy. clear - X X1. assert (XX:forall k k', All2 - (fun x y => eq_term_upto_univ Re Re (dtype x) (dtype y) × - eq_term_upto_univ Re Re (dbody x) (dbody y) × - rarg x = rarg y) + (fun x y => ((eq_term_upto_univ Σ Re Re (dtype x) (dtype y) × + eq_term_upto_univ Σ Re Re (dbody x) (dbody y)) × + rarg x = rarg y) * eq_binder_annot (dname x) (dname y)) (map (map_def (lift n k) (lift n (#|m| + k'))) m) (map (map_def (lift n k) (lift n (#|mfix'| + k'))) mfix')); [|now apply XX]. clear k. induction m in X, mfix', X1 |- *. + inversion X1; constructor. + inversion X1; inversion X; subst. - simpl. constructor. split. cbn; easy. + simpl. constructor. split. split. split. cbn; easy. cbn; erewrite All2_length by eassumption. - easy. + easy. easy. easy. unfold tFixProp in IHm. cbn. rewrite !plus_n_Sm. now apply IHm. Qed. - -Lemma lift_eq_term `{checker_flags} ϕ n k T U : - eq_term ϕ T U -> eq_term ϕ (lift n k T) (lift n k U). +Lemma lift_eq_term `{checker_flags} Σ ϕ n k T U : + eq_term Σ ϕ T U -> eq_term Σ ϕ (lift n k T) (lift n k U). Proof. apply lift_eq_term_upto_univ. Qed. -Lemma lift_leq_term `{checker_flags} ϕ n k T U : - leq_term ϕ T U -> leq_term ϕ (lift n k T) (lift n k U). +Lemma lift_leq_term `{checker_flags} Σ ϕ n k T U : + leq_term Σ ϕ T U -> leq_term Σ ϕ (lift n k T) (lift n k U). Proof. apply lift_eq_term_upto_univ. Qed. @@ -769,16 +766,16 @@ Proof. econstructor 3; eauto. Qed. -Lemma lift_eq_decl `{checker_flags} ϕ n k d d' : - eq_decl ϕ d d' -> eq_decl ϕ (lift_decl n k d) (lift_decl n k d'). +Lemma lift_eq_decl `{checker_flags} Σ ϕ n k d d' : + eq_decl Σ ϕ d d' -> eq_decl Σ ϕ (lift_decl n k d) (lift_decl n k d'). Proof. destruct d, d', decl_body, decl_body0; unfold eq_decl, map_decl; cbn; intuition auto using lift_eq_term. Qed. -Lemma lift_eq_context `{checker_flags} φ l l' n k : - eq_context φ l l' -> - eq_context φ (lift_context n k l) (lift_context n k l'). +Lemma lift_eq_context `{checker_flags} Σ φ l l' n k : + eq_context Σ φ l l' -> + eq_context Σ φ (lift_context n k l) (lift_context n k l'). Proof. induction l in l', n, k |- *; intros; destruct l'; rewrite -> ?lift_context_snoc0. - constructor. @@ -1084,6 +1081,7 @@ Proof. -- destruct idecl; simpl in *; auto. -- now rewrite -> !lift_mkApps in IHc. -- solve_all. + destruct b0 as [s [Hs IHs]]. exists s; eauto. - simpl. erewrite (distr_lift_subst_rec _ _ _ 0 #|Γ'|). @@ -1112,16 +1110,14 @@ Proof. now specialize (Hs' _ _ _ wf eq_refl). * eapply All_map. eapply (All_impl X1); simpl. - intros x [[Hb Hlam] IH]. + intros x [Hb IH]. rewrite lift_fix_context. specialize (IH Γ (Γ' ,,, (fix_context mfix)) Γ'' wf). rewrite app_context_assoc in IH. specialize (IH eq_refl). - split; auto. rewrite lift_context_app Nat.add_0_r app_context_assoc in IH. rewrite app_context_length fix_context_length in IH. rewrite lift_context_length fix_context_length. rewrite permute_lift; try lia. now rewrite (Nat.add_comm #|Γ'|). - now rewrite isLambda_lift. * red; rewrite <-H1. unfold wf_fixpoint. rewrite map_map_compose. now rewrite weakening_check_one_fix. diff --git a/checker/theories/WeakeningEnv.v b/checker/theories/WeakeningEnv.v index f6bdd3d9e..9e703f407 100644 --- a/checker/theories/WeakeningEnv.v +++ b/checker/theories/WeakeningEnv.v @@ -1,6 +1,7 @@ (* Distributed under the terms of the MIT license. *) +From Coq Require Import RelationClasses. From MetaCoq.Template Require Import config utils Ast AstUtils - LibHypsNaming Typing. + LibHypsNaming TermEquality Typing. Require Import ssreflect. (** * Weakening lemmas w.r.t. the global environment *) @@ -128,58 +129,95 @@ Proof. eapply satisfies_subset; eauto. Qed. - -Lemma eq_term_upto_univ_morphism0 (Re Re' : _ -> _ -> Prop) - (Hre : forall t u, Re t u -> Re' t u) - : forall t u, eq_term_upto_univ Re Re t u -> eq_term_upto_univ Re' Re' t u. -Proof. - fix aux 3. - destruct 1; constructor; eauto. - all: unfold R_universe_instance in *. - all: match goal with - | H : All2 _ _ _ |- _ => induction H; constructor; eauto - | H : Forall2 _ _ _ |- _ => induction H; constructor; eauto - end. - all: intuition eauto. -Qed. - -Lemma eq_term_upto_univ_morphism (Re Re' Rle Rle' : _ -> _ -> Prop) - (Hre : forall t u, Re t u -> Re' t u) - (Hrle : forall t u, Rle t u -> Rle' t u) - : forall t u, eq_term_upto_univ Re Rle t u -> eq_term_upto_univ Re' Rle' t u. -Proof. - fix aux 3. - destruct 1; constructor; eauto using eq_term_upto_univ_morphism0. - all: unfold R_universe_instance in *. - all: match goal with - | H : Forall2 _ _ _ |- _ => induction H; constructor; - eauto using eq_term_upto_univ_morphism0 - | H : All2 _ _ _ |- _ => induction H; constructor; - eauto using eq_term_upto_univ_morphism0 - end. - - destruct r. split; eauto using eq_term_upto_univ_morphism0. - - destruct r as [? [? ?]]. - repeat split; eauto using eq_term_upto_univ_morphism0. - - destruct r as [? [? ?]]. - repeat split; eauto using eq_term_upto_univ_morphism0. -Qed. - -Lemma eq_term_subset {cf:checker_flags} φ φ' t t' +Lemma eq_term_subset {cf:checker_flags} Σ φ φ' t t' : ConstraintSet.Subset φ φ' - -> eq_term φ t t' -> eq_term φ' t t'. + -> eq_term Σ φ t t' -> eq_term Σ φ' t t'. Proof. intro H. apply eq_term_upto_univ_morphism. all: intros u u'; eapply eq_universe_subset; assumption. Qed. -Lemma leq_term_subset {cf:checker_flags} ctrs ctrs' t u - : ConstraintSet.Subset ctrs ctrs' -> leq_term ctrs t u -> leq_term ctrs' t u. +Lemma leq_term_subset {cf:checker_flags} Σ ctrs ctrs' t u + : ConstraintSet.Subset ctrs ctrs' -> leq_term Σ ctrs t u -> leq_term Σ ctrs' t u. Proof. intro H. apply eq_term_upto_univ_morphism. intros t' u'; eapply eq_universe_subset; assumption. intros t' u'; eapply leq_universe_subset; assumption. Qed. +Lemma global_variance_sigma_mon {cf:checker_flags} {Σ Σ' gr napp v} : + wf Σ' -> extends Σ Σ' -> + global_variance Σ gr napp = Some v -> + global_variance Σ' gr napp = Some v. +Proof. + intros wf ext. + rewrite /global_variance /lookup_constructor /lookup_inductive /lookup_minductive. + destruct gr as [|ind|[ind i]|] => /= //. + - destruct (lookup_env Σ ind) eqn:look => //. + eapply extends_lookup in look; eauto. rewrite look //. + - destruct (lookup_env Σ (inductive_mind i)) eqn:look => //. + eapply extends_lookup in look; eauto. rewrite look //. +Qed. + + +(** The definition of [R_global_instance] is defined so that it is weakenable. *) +Lemma R_global_instance_weaken_env {cf:checker_flags} Σ Σ' Re Re' Rle Rle' gr napp : + wf Σ' -> extends Σ Σ' -> + RelationClasses.subrelation Re Re' -> + RelationClasses.subrelation Rle Rle' -> + RelationClasses.subrelation Re Rle' -> + subrelation (R_global_instance Σ Re Rle gr napp) (R_global_instance Σ' Re' Rle' gr napp). +Proof. + intros wfΣ ext he hle hele t t'. + rewrite /R_global_instance /R_opt_variance. + destruct global_variance as [v|] eqn:look. + - rewrite (global_variance_sigma_mon wfΣ ext look). + induction t in v, t' |- *; destruct v, t'; simpl; auto. + intros []; split; auto. + destruct t0; simpl; auto. + - destruct (global_variance Σ' gr napp) => //. + * induction t in l, t' |- *; destruct l, t'; simpl; intros H; inv H; auto. + split; auto. destruct t0; simpl; auto. + * eauto using R_universe_instance_impl'. +Qed. + +Instance eq_term_upto_univ_weaken_env {cf:checker_flags} Σ Σ' Re Re' Rle Rle' napp : + wf Σ' -> extends Σ Σ' -> + RelationClasses.subrelation Re Re' -> + RelationClasses.subrelation Rle Rle' -> + RelationClasses.subrelation Re Rle' -> + CRelationClasses.subrelation (eq_term_upto_univ_napp Σ Re Rle napp) + (eq_term_upto_univ_napp Σ' Re' Rle' napp). +Proof. + intros wfΣ ext he hele hle t t'. + induction t in napp, t', Rle, Rle', hle, hele |- * using Induction.term_forall_list_rect; + try (inversion 1; subst; constructor; + eauto using R_universe_instance_impl'; fail). + - inversion 1; subst; constructor. + eapply All2_impl'; tea. + eapply All_impl; eauto. + - inversion 1; subst; constructor. + eapply IHt. 3:eauto. all:auto. + eapply All2_impl'; tea. + eapply All_impl; eauto. + - inversion 1; subst; constructor. + eapply R_global_instance_weaken_env. 6:eauto. all:eauto. + - inversion 1; subst; constructor. + eapply R_global_instance_weaken_env. 6:eauto. all:eauto. + - inversion 1; subst; constructor; eauto. + eapply All2_impl'; tea. + eapply All_impl; eauto. + cbn. intros x ? y [? ?]. split; eauto. + - inversion 1; subst; constructor. + eapply All2_impl'; tea. + eapply All_impl; eauto. + cbn. intros x [? ?] y [[[? ?] ?] ?]. repeat split; eauto. + - inversion 1; subst; constructor. + eapply All2_impl'; tea. + eapply All_impl; eauto. + cbn. intros x [? ?] y [[[? ?] ?] ?]. repeat split; eauto. +Qed. + Lemma weakening_env_conv `{CF:checker_flags} Σ Σ' φ Γ M N : wf Σ' -> @@ -191,7 +229,8 @@ Proof. induction 1; simpl. - econstructor. eapply eq_term_subset. + eapply global_ext_constraints_app. - + assumption. + + eapply eq_term_upto_univ_weaken_env; eauto. exists Σ''; eauto. + all:typeclasses eauto. - econstructor 2; eauto. eapply weakening_env_red1; eauto. exists Σ''; eauto. - econstructor 3; eauto. eapply weakening_env_red1; eauto. exists Σ''; eauto. Qed. @@ -202,8 +241,10 @@ Lemma weakening_env_cumul `{CF:checker_flags} Σ Σ' φ Γ M N : Proof. intros wfΣ [Σ'' ->]. induction 1; simpl. - - econstructor. eapply leq_term_subset. eapply global_ext_constraints_app. - assumption. + - econstructor. eapply leq_term_subset. + + eapply global_ext_constraints_app. + + eapply eq_term_upto_univ_weaken_env; eauto. exists Σ''; eauto. + all:typeclasses eauto. - econstructor 2; eauto. eapply weakening_env_red1; eauto. exists Σ''; eauto. - econstructor 3; eauto. eapply weakening_env_red1; eauto. exists Σ''; eauto. Qed. @@ -292,18 +333,18 @@ Proof. apply global_ext_constraints_app. Qed. -Lemma eq_decl_subset {cf:checker_flags} φ φ' d d' +Lemma eq_decl_subset {cf:checker_flags} Σ φ φ' d d' : ConstraintSet.Subset φ φ' - -> eq_decl φ d d' -> eq_decl φ' d d'. + -> eq_decl Σ φ d d' -> eq_decl Σ φ' d d'. Proof. intros Hφ [H1 H2]. split; [|eapply eq_term_subset; eauto]. destruct d as [na [bd|] ty], d' as [na' [bd'|] ty']; cbn in *; trivial. eapply eq_term_subset; eauto. Qed. -Lemma eq_context_subset {cf:checker_flags} φ φ' Γ Γ' +Lemma eq_context_subset {cf:checker_flags} Σ φ φ' Γ Γ' : ConstraintSet.Subset φ φ' - -> eq_context φ Γ Γ' -> eq_context φ' Γ Γ'. + -> eq_context Σ φ Γ Γ' -> eq_context Σ φ' Γ Γ'. Proof. intros Hφ. induction 1; constructor. eapply eq_decl_subset; eassumption. assumption. @@ -444,6 +485,7 @@ Proof. eapply weakening_env_cumul in cumul; eauto. - econstructor; eauto 2 with extends. close_Forall. intros; intuition eauto with extends. + destruct b as [s [Hs IHs]]. exists s. eauto. - econstructor; eauto with extends. eapply fix_guard_extends; eauto. eapply (All_impl X0); intuition eauto. diff --git a/pcuic/theories/PCUICContextConversion.v b/pcuic/theories/PCUICContextConversion.v index 230dd9dd3..c226a00bd 100644 --- a/pcuic/theories/PCUICContextConversion.v +++ b/pcuic/theories/PCUICContextConversion.v @@ -967,7 +967,7 @@ Proof. intros x [s [Hs IH]]. exists s; eauto. eapply (All_impl X1). - intros x [[Hs Hl] IH]. split; auto. + intros x [Hs IH]. eapply IH. now apply cumul_context_app_same. eapply (All_mfix_wf); auto. diff --git a/pcuic/theories/PCUICEquality.v b/pcuic/theories/PCUICEquality.v index 684d9b0da..9f6ce36e5 100644 --- a/pcuic/theories/PCUICEquality.v +++ b/pcuic/theories/PCUICEquality.v @@ -8,7 +8,6 @@ Require Import ssreflect. From Equations.Prop Require Import DepElim. Set Equations With UIP. - Definition R_universe_instance R := fun u u' => Forall2 R (List.map Universe.make u) (List.map Universe.make u'). diff --git a/pcuic/theories/PCUICNameless.v b/pcuic/theories/PCUICNameless.v index 2a0d407dc..198c9d82d 100644 --- a/pcuic/theories/PCUICNameless.v +++ b/pcuic/theories/PCUICNameless.v @@ -1356,7 +1356,6 @@ Proof. * rewrite fix_context_length map_length. rewrite fix_context_length in Hs. now rewrite -> XX, <- nl_lift. - * destruct dbody; simpl in *; congruence. + now rewrite <-nl_wf_fixpoint. - replace (nl (dtype decl)) with (dtype (map_def_anon nl nl decl)); [|destruct decl; reflexivity]. diff --git a/pcuic/theories/PCUICSigmaCalculus.v b/pcuic/theories/PCUICSigmaCalculus.v index 849927a2f..e3b3cbc59 100644 --- a/pcuic/theories/PCUICSigmaCalculus.v +++ b/pcuic/theories/PCUICSigmaCalculus.v @@ -1753,17 +1753,15 @@ Proof. intros x [s [Hs IHs]]. exists s. now apply IHs. * apply All_map, (All_impl ihmfixb). - intros x [[Hb Hlam] IHb]. + intros x [Hb IHb]. destruct x as [na ty bo rarg]. simpl in *. - split. - -- rewrite rename_fix_context. - eapply meta_conv. - ++ apply (IHb (Δ ,,, rename_context f types) (shiftn #|mfix| f)). - split; auto. subst types. rewrite -(fix_context_length mfix). - apply urenaming_context; auto. apply hf. - ++ autorewrite with sigma. subst types. rewrite fix_context_length. - now rewrite -ren_shiftn up_Upn shiftn_consn_idsn. - -- eapply isLambda_rename. assumption. + rewrite rename_fix_context. + eapply meta_conv. + ++ apply (IHb (Δ ,,, rename_context f types) (shiftn #|mfix| f)). + split; auto. subst types. rewrite -(fix_context_length mfix). + apply urenaming_context; auto. apply hf. + ++ autorewrite with sigma. subst types. rewrite fix_context_length. + now rewrite -ren_shiftn up_Upn shiftn_consn_idsn. * admit (* wf_fixpoint renaming *). + reflexivity. diff --git a/pcuic/theories/PCUICSubstitution.v b/pcuic/theories/PCUICSubstitution.v index b8192fd6e..46164e095 100644 --- a/pcuic/theories/PCUICSubstitution.v +++ b/pcuic/theories/PCUICSubstitution.v @@ -2644,16 +2644,14 @@ Proof. now specialize (Hs' _ _ _ _ sub eq_refl). * eapply All_map. eapply (All_impl X1); simpl. - intros x [[Hb Hlam] IH]. + intros x [Hb IH]. rewrite subst_fix_context. specialize (IH Γ Γ' (Δ ,,, (fix_context mfix)) _ sub). rewrite app_context_assoc in IH. specialize (IH eq_refl). - split; auto. - + rewrite subst_context_app Nat.add_0_r app_context_assoc in IH. - rewrite app_context_length fix_context_length in IH. - rewrite subst_context_length fix_context_length. - rewrite commut_lift_subst_rec; try lia. now rewrite (Nat.add_comm #|Δ|). - + now rewrite isLambda_subst. + rewrite subst_context_app Nat.add_0_r app_context_assoc in IH. + rewrite app_context_length fix_context_length in IH. + rewrite subst_context_length fix_context_length. + rewrite commut_lift_subst_rec; try lia. now rewrite (Nat.add_comm #|Δ|). * move: H1. rewrite /wf_fixpoint. pose proof (substitution_check_one_fix s #|Δ| mfix). diff --git a/pcuic/theories/PCUICToTemplateCorrectness.v b/pcuic/theories/PCUICToTemplateCorrectness.v index 631934c99..09dbf85fa 100644 --- a/pcuic/theories/PCUICToTemplateCorrectness.v +++ b/pcuic/theories/PCUICToTemplateCorrectness.v @@ -4,7 +4,8 @@ From MetaCoq.PCUIC Require Import PCUICAst PCUICAstUtils PCUICInduction Set Warnings "-notation-overridden". From MetaCoq.Template Require Import config utils Ast TypingWf WfInv UnivSubst - LiftSubst. + TermEquality LiftSubst. +From MetaCoq.Checker Require Import Substitution. Set Warnings "+notation_overridden". @@ -107,9 +108,13 @@ Lemma trans_global_ext_constraints Σ : ST.global_ext_constraints Σ = TT.global_ext_constraints (trans_global Σ). Proof. destruct Σ. - unfold ST.global_ext_constraints, trans_global. - cbn [fst snd]. -Admitted. + unfold ST.global_ext_constraints, TT.global_ext_constraints. simpl. + f_equal. clear u. + induction g. + - reflexivity. + - simpl. rewrite IHg. f_equal. clear. + destruct a as [? []]; reflexivity. +Qed. Lemma trans_mem_level_set l Σ: LevelSet.mem l (ST.global_ext_levels Σ) -> @@ -129,34 +134,26 @@ Proof. apply H. Qed. - -Lemma trans_lookup Σ cst decl: -S.lookup_env Σ.1 cst = Some decl -> -Ast .lookup_env (trans_global Σ).1 cst = -Some (trans_global_decl decl). +Lemma trans_lookup Σ cst : + Ast.lookup_env (trans_global_decls Σ) cst = option_map trans_global_decl (S.lookup_env Σ cst). Proof. - intros H. - destruct Σ. cbn in *. - induction g;cbn in H. - - discriminate H. + induction Σ. + - reflexivity. - cbn. unfold eq_kername in *; destruct kername_eq_dec; subst. - + destruct a. - cbn in *. - injection H as ->. - reflexivity. - + apply IHg, H. + + destruct a; auto. + + now rewrite IHΣ. Qed. Lemma trans_declared_constant Σ cst decl: -ST.declared_constant Σ.1 cst decl -> -TT.declared_constant (trans_global Σ).1 cst (trans_constant_body decl). + ST.declared_constant Σ cst decl -> + TT.declared_constant (trans_global_decls Σ) cst (trans_constant_body decl). Proof. - intros H. unfold TT.declared_constant. - unfold ST.declared_constant in H. - apply trans_lookup in H as ->. + rewrite trans_lookup. + unfold ST.declared_constant. + intros ->. reflexivity. Qed. @@ -196,20 +193,19 @@ Proof. Qed. Lemma trans_declared_inductive Σ mdecl ind idecl: -ST.declared_inductive Σ.1 mdecl ind idecl -> -TT.declared_inductive (trans_global Σ).1 (trans_minductive_body mdecl) ind (trans_one_ind_body idecl). + ST.declared_inductive Σ mdecl ind idecl -> + TT.declared_inductive (trans_global_decls Σ) (trans_minductive_body mdecl) ind (trans_one_ind_body idecl). Proof. intros []. split. - unfold TT.declared_minductive, ST.declared_minductive in *. - apply trans_lookup in H as ->. - reflexivity. + now rewrite trans_lookup H. - now apply map_nth_error. Qed. Lemma trans_mkApps t args: -trans (PCUICAst.mkApps t args) = -mkApps (trans t) (map trans args). + trans (PCUICAst.mkApps t args) = + mkApps (trans t) (map trans args). Proof. induction args in t |- *. - reflexivity. @@ -489,22 +485,20 @@ Proof. destruct prim as [? []]; eauto. Qed. - -Lemma trans_instantiate_params' u mdecl idecl args npar x: +Lemma trans_instantiate_params' u mdecl args npar x ty : ST.instantiate_params (PCUICUnivSubst.subst_instance_context u (PCUICAst.ind_params mdecl)) (firstn npar args) - (PCUICUnivSubst.subst_instance_constr u (PCUICAst.ind_type idecl)) = + ty = Some x -> TT.instantiate_params (subst_instance_context u (trans_local (PCUICAst.ind_params mdecl))) (firstn npar (map trans args)) - (subst_instance_constr u (trans (PCUICAst.ind_type idecl))) = + (trans ty) = Some (trans x). Proof. intros H. - rewrite <- trans_subst_instance_constr. rewrite firstn_map. match goal with |- TT.instantiate_params ?A _ _ = _ => @@ -593,16 +587,13 @@ Proof. Qed. Lemma trans_unfold_fix mfix idx narg fn : - List.Forall (fun def : def S.term => S.isLambda (dbody def) = true) mfix -> unfold_fix mfix idx = Some (narg, fn) -> TT.unfold_fix (map (map_def trans trans) mfix) idx = Some (narg, trans fn). Proof. - unfold TT.unfold_fix, unfold_fix. intros wffix. + unfold TT.unfold_fix, unfold_fix. rewrite nth_error_map. destruct (nth_error mfix idx) eqn:Hdef => //. cbn. intros [= <- <-]. simpl. - eapply nth_error_forall in wffix; eauto. simpl in wffix. - rewrite trans_isLambda wffix. repeat f_equal. rewrite trans_subst. f_equal. clear Hdef. simpl. @@ -657,9 +648,43 @@ Proof. Qed. Ltac wf_inv H := try apply wf_inv in H; simpl in H; rdest. +Lemma trans_wf t : wf (trans t). +Proof. + induction t using term_forall_list_ind; simpl; try constructor; auto; + solve_all. + now eapply wf_mkApp. + destruct p as [? []]; constructor. +Qed. +Hint Resolve trans_wf : wf. + +Lemma trans_fix_context mfix: + map trans_decl (PCUICLiftSubst.fix_context mfix) = + TT.fix_context (map (map_def trans trans) mfix). +Proof. + unfold trans_local. + destruct mfix;trivial. + unfold TT.fix_context, PCUICLiftSubst.fix_context. + rewrite map_rev map_mapi. + cbn. f_equal. + 2: { + destruct d. cbn. + rewrite lift0_p. + rewrite SL.lift0_p. + unfold vass. + reflexivity. + } + f_equal. + unfold vass. + remember 1 as k. + induction mfix in k |- *;trivial. + cbn;f_equal. + - now rewrite trans_lift. + - apply IHmfix. +Qed. + Lemma trans_red1 Σ Γ T U : red1 Σ Γ T U -> - TT.red1 (map (on_snd trans_global_decl) Σ) (trans_local Γ) (trans T) (trans U). + TT.red1 (trans_global_decls Σ) (trans_local Γ) (trans T) (trans U). Proof. induction 1 using red1_ind_all; simpl in *; try solve [econstructor; eauto]. @@ -682,132 +707,131 @@ Proof. pose proof (nth_error_Some_length hnth). destruct args. simpl. elimtype False; depelim H1. cbn -[mkApps]. - eapply refine_red1_r; cycle 1. eapply TT.red_fix. - apply trans_unfold_fix; eauto. admit. + apply trans_unfold_fix; eauto. eapply (trans_is_constructor (t0 :: args)). now rewrite /is_constructor hnth. + discriminate. - - - apply wf_mkApps_napp in H1; auto. - intuition. - pose proof (unfold_cofix_wf _ _ _ _ H H3). wf_inv H3. + - rewrite trans_mkApps. rewrite !trans_mkApps; eauto with wf. apply trans_unfold_cofix in H; eauto with wf. - eapply red_cofix_case; eauto. - - - eapply wf_mkApps_napp in Hwf; auto. - intuition. pose proof (unfold_cofix_wf _ _ _ _ H H0). wf_inv H0. - rewrite !trans_mkApps; intuition eauto with wf. - eapply red_cofix_proj; eauto. - apply trans_unfold_cofix; eauto with wf. + eapply TT.red_cofix_case; eauto. + - rewrite !trans_mkApps. + apply trans_unfold_cofix in H; eauto with wf. + eapply TT.red_cofix_proj; eauto. + - rewrite trans_subst_instance_constr. econstructor. - apply (forall_decls_declared_constant _ c decl H). + apply (trans_declared_constant _ c decl H). destruct decl. now simpl in *; subst cst_body. - rewrite trans_mkApps; eauto with wf. simpl. constructor. now rewrite nth_error_map H. - - constructor. apply IHX. constructor; hnf; simpl; auto. hnf. auto. - - - constructor. apply IHX. constructor; hnf; simpl; auto. auto. - - constructor. solve_all. - apply OnOne2_map. apply (OnOne2_All_mix_left H1) in X. clear H1. + apply OnOne2_map. solve_all. red. simpl in *. intuition eauto. - apply b2. all: solve_all. - - - rewrite !trans_mkApps; auto with wf. eapply wf_red1 in X; auto. - apply red1_mkApps_l. auto. - - - apply Forall_All in H2. clear H H0 H1. revert M1. induction X. - simpl. intuition. inv H2. specialize (X H). - apply red1_mkApps_l. apply app_red_r. auto. - inv H2. specialize (IHX X0). - simpl. intros. - eapply (IHX (T.tApp M1 [hd])). - - - constructor. apply IHX. constructor; hnf; simpl; auto. auto. - - constructor. induction X; simpl; repeat constructor. apply p; auto. now inv Hwf. - apply IHX. now inv Hwf. - - - constructor. constructor. eapply IHX; auto. - - eapply refine_red1_r; [|constructor]. unfold subst1. simpl. now rewrite lift0_p. - - - constructor. apply OnOne2_map. repeat toAll. - apply (OnOne2_All_mix_left Hwf) in X. clear Hwf. - solve_all. - red. rewrite <- !map_dtype. rewrite <- !map_dbody. - inversion b0. clear b0. - intuition eauto. - + eapply b. all: solve_all. - + unfold map_def. simpl. - f_equal. 2: auto. - f_equal. assumption. - - - apply fix_red_body. apply OnOne2_map. repeat toAll. - apply (OnOne2_All_mix_left Hwf) in X. - solve_all. - red. rewrite <- !map_dtype. rewrite <- !map_dbody. intuition eauto. - + unfold Template.Ast.app_context, trans_local in b. - simpl in a. rewrite -> map_app in b. - unfold app_context. unfold TTy.fix_context in b. - rewrite map_rev map_mapi in b. simpl in b. - unfold fix_context. rewrite mapi_map. simpl. - forward b. - { clear b. solve_all. eapply All_app_inv; auto. - apply All_rev. apply All_mapi. - clear -Hwf; generalize 0 at 2; induction mfix0; constructor; hnf; simpl; auto. - intuition auto. depelim a. simpl. depelim Hwf. simpl in *. intuition auto. - now eapply LiftSubst.wf_lift. - depelim a. simpl. depelim Hwf. simpl in *. intuition auto. - } - forward b by auto. - eapply (refine_red1_Γ); [|apply b]. - f_equal. f_equal. apply mapi_ext; intros [] []. - rewrite lift0_p. simpl. rewrite LiftSubst.lift0_p. reflexivity. - rewrite trans_lift. simpl. reflexivity. - + simpl. inversion b0. reflexivity. - - - constructor. apply OnOne2_map. repeat toAll. - apply (OnOne2_All_mix_left Hwf) in X. clear Hwf. - solve_all. - red. rewrite <- !map_dtype. rewrite <- !map_dbody. - inversion b0. clear b0. - intuition eauto. - + eapply b. all: solve_all. - + unfold map_def. simpl. - f_equal. 2: auto. - f_equal. assumption. - - - apply cofix_red_body. apply OnOne2_map. repeat toAll. - apply (OnOne2_All_mix_left Hwf) in X. - solve_all. - red. rewrite <- !map_dtype. rewrite <- !map_dbody. intuition eauto. - + unfold Template.Ast.app_context, trans_local in b. - simpl in a. rewrite -> map_app in b. - unfold app_context. unfold TTy.fix_context in b. - rewrite map_rev map_mapi in b. simpl in b. - unfold fix_context. rewrite mapi_map. simpl. - forward b. - { clear b. solve_all. eapply All_app_inv; auto. - apply All_rev. apply All_mapi. - clear -Hwf; generalize 0 at 2; induction mfix0; constructor; hnf; simpl; auto. - intuition auto. depelim a. simpl. depelim Hwf. simpl in *. intuition auto. - now eapply LiftSubst.wf_lift. - depelim a. simpl. depelim Hwf. simpl in *. intuition auto. - } - forward b by auto. - eapply (refine_red1_Γ); [|apply b]. - f_equal. f_equal. apply mapi_ext; intros [] []. - rewrite lift0_p. simpl. rewrite LiftSubst.lift0_p. reflexivity. - rewrite trans_lift. simpl. reflexivity. - + simpl. inversion b0. reflexivity. + + - eapply (red1_mkApps_l _ _ _ _ [_]); auto with wf. + - eapply (red1_mkApps_r _ _ _ [_] [_]); auto with wf. + + - constructor. eapply OnOne2_map. solve_all. + + - constructor. eapply OnOne2_map. solve_all. + red. intuition auto. destruct x, y; simpl in *. noconf b. + reflexivity. + + - apply TT.fix_red_body. eapply OnOne2_map; solve_all. + red. destruct x, y; simpl in *. noconf b. + intuition auto. + rewrite /trans_local map_app in b0. + now rewrite -trans_fix_context. + + - constructor. eapply OnOne2_map. solve_all. + red. intuition auto. destruct x, y; simpl in *. noconf b. + reflexivity. + + - apply TT.cofix_red_body. eapply OnOne2_map; solve_all. + red. destruct x, y; simpl in *. noconf b. + intuition auto. + rewrite /trans_local map_app in b0. + now rewrite -trans_fix_context. Qed. +Lemma context_assumptions_map ctx : Ast.context_assumptions (map trans_decl ctx) = PCUICAst.context_assumptions ctx. +Proof. + induction ctx as [|[na [b|] ty] ctx]; simpl; auto. +Qed. +Lemma trans_R_global_instance Σ Re Rle gref napp u u' : + PCUICEquality.R_global_instance Σ Re Rle gref napp u u' -> + R_global_instance (trans_global_decls Σ) Re Rle gref napp u u'. +Proof. + unfold PCUICEquality.R_global_instance, PCUICEquality.global_variance. + unfold R_global_instance, global_variance. + destruct gref; simpl; auto. + - unfold PCUICEquality.lookup_inductive, PCUICEquality.lookup_minductive. + unfold lookup_inductive, lookup_minductive. + rewrite trans_lookup. destruct PCUICAst.lookup_env => //; simpl. + destruct g => /= //. rewrite nth_error_map. + destruct nth_error => /= //. + rewrite [destArity _ _]trans_destr_arity. + destruct PCUICAstUtils.destArity as [[ctx ps]|] => /= //. + now rewrite context_assumptions_map. + - unfold PCUICEquality.lookup_constructor, PCUICEquality.lookup_inductive, PCUICEquality.lookup_minductive. + unfold lookup_constructor, lookup_inductive, lookup_minductive. + rewrite trans_lookup. destruct PCUICAst.lookup_env => //; simpl. + destruct g => /= //. rewrite nth_error_map. + destruct nth_error => /= //. + rewrite nth_error_map. + destruct nth_error => /= //. + destruct p as [[id t] nargs]; simpl. + destruct Nat.leb => //. +Qed. + +Lemma trans_eq_term_upto_univ : + forall Σ Re Rle t u napp, + PCUICEquality.eq_term_upto_univ_napp Σ Re Rle napp t u -> + eq_term_upto_univ_napp (trans_global_decls Σ) Re Rle napp (trans t) (trans u). +Proof. + intros Σ Re Rle t u napp e. + induction t using term_forall_list_ind in Rle, napp, u, e |- *. + all: invs e; cbn. + all: try solve [ constructor ; auto ]. + all: try solve [ + repeat constructor ; + match goal with + | ih : forall Rle u (napp : nat), _ |- _ => + eapply ih ; auto + end + ]. + all: try solve [ constructor; solve_all ]. + all: try solve [ constructor; now eapply trans_R_global_instance ]. + - eapply (eq_term_upto_univ_mkApps _ _ _ _ _ [_] _ [_]); simpl; eauto. + - destruct p as [? []]; constructor. +Qed. + +Lemma trans_leq_term Σ ϕ T U : + PCUICEquality.leq_term Σ ϕ T U -> + leq_term (trans_global_decls Σ) ϕ (trans T) (trans U). +Proof. + eapply trans_eq_term_upto_univ ; eauto. +Qed. + +Lemma trans_cumul Σ Γ T U : + cumul Σ Γ T U -> + TT.cumul (trans_global Σ) (trans_local Γ) (trans T) (trans U). +Proof. + induction 1. constructor; auto. + eapply trans_leq_term in l. + now rewrite -trans_global_ext_constraints. + apply trans_red1 in r; auto. econstructor 2; eauto. + econstructor 3. + apply IHX; auto. + apply trans_red1 in r; auto. +Qed. Lemma trans_build_case_predicate_type ind mdecl idecl npar args u ps pty: ST.build_case_predicate_type ind mdecl idecl (firstn npar args) u ps = Some pty -> @@ -819,13 +843,13 @@ Proof. apply inv_opt_monad in H as (?&?&?&?&[=]). unfold TT.build_case_predicate_type. simpl in *. - apply trans_instantiate_params' in H as ->. + apply trans_instantiate_params' in H. + rewrite trans_subst_instance_constr in H. rewrite H. simpl. - rewrite trans_destr_arity, H0. + rewrite trans_destr_arity H0. simpl. f_equal. rewrite <- H2. - rewrite trans_it_mkProd_or_LetIn, - trans_mkProd_or_LetIn. + rewrite trans_it_mkProd_or_LetIn trans_mkProd_or_LetIn. f_equal. - now destruct x0. - f_equal. cbn. @@ -839,7 +863,7 @@ Proof. f_equal. + rewrite firstn_map. induction (firstn npar args);cbn;trivial. - now rewrite IHl0, map_length, trans_lift. + now rewrite IHl0 map_length trans_lift. + remember 0 as n;clear Heqn. remember (@nil PCUICAst.term) as xs. replace (@nil term) with (map trans xs) by (now subst). @@ -849,30 +873,6 @@ Proof. Qed. -Lemma trans_fix_context mfix: -map trans_decl (PCUICLiftSubst.fix_context mfix) = -TT.fix_context (map (map_def trans trans) mfix). -Proof. - unfold trans_local. - destruct mfix;trivial. - unfold TT.fix_context, PCUICLiftSubst.fix_context. - rewrite map_rev, map_mapi. - cbn. f_equal. - 2: { - destruct d. cbn. - rewrite lift0_p. - rewrite SL.lift0_p. - unfold vass. - reflexivity. - } - f_equal. - unfold vass. - remember 1 as k. - induction mfix in k |- *;trivial. - cbn;f_equal. - - now rewrite trans_lift. - - apply IHmfix. -Qed. Definition TTwf_local Σ Γ := TT.All_local_env (TT.lift_typing TT.typing Σ) Γ. @@ -969,44 +969,6 @@ Proof. Qed. Lemma trans_mfix_All2 Σ Γ mfix xfix: - All - (fun d : def PCUICAst.term => - (ST.typing Σ (PCUICAst.app_context Γ (PCUICLiftSubst.fix_context xfix)) - (dbody d) - (PCUICLiftSubst.lift0 #|PCUICLiftSubst.fix_context xfix| (dtype d)) - × PCUICAst.isLambda (dbody d) = true) - × TT.typing (trans_global Σ) - (trans_local (PCUICAst.app_context Γ (PCUICLiftSubst.fix_context xfix))) - (trans (dbody d)) - (trans - (PCUICLiftSubst.lift0 #|PCUICLiftSubst.fix_context xfix| - (dtype d)))) mfix -> - All - (fun d : def term => - TT.typing (trans_global Σ) - (trans_local Γ ,,, TT.fix_context (map (map_def trans trans) xfix)) - (dbody d) (TL.lift0 #|TT.fix_context (map (map_def trans trans) xfix)| (dtype d)) - × isLambda (dbody d) = true) (map (map_def trans trans) mfix). -Proof. - induction 1. - - constructor. - - simpl; constructor. - + destruct p as [[]]. - unfold app_context, PCUICAst.app_context in *. - split. - * unfold trans_local in t0. - rewrite map_app, trans_fix_context in t0. - rewrite trans_dbody, trans_lift, trans_dtype in t0. - replace(#|PCUICLiftSubst.fix_context xfix|) with - (#|TT.fix_context (map(map_def trans trans) xfix)|) in t0. - 2:now rewrite TT.fix_context_length, map_length, fix_context_length. - now destruct x. - * destruct x; simpl in *; auto. - now destruct dbody. - + auto. -Qed. - -Lemma trans_mfix_All2' Σ Γ mfix xfix: All (fun d : def PCUICAst.term => (ST.typing Σ (PCUICAst.app_context Γ (PCUICLiftSubst.fix_context xfix)) @@ -1031,11 +993,11 @@ Proof. + destruct p as []. unfold app_context, PCUICAst.app_context in *. unfold trans_local in t0. - rewrite map_app, trans_fix_context in t0. - rewrite trans_dbody, trans_lift, trans_dtype in t0. + rewrite map_app trans_fix_context in t0. + rewrite trans_dbody trans_lift trans_dtype in t0. replace(#|PCUICLiftSubst.fix_context xfix|) with (#|TT.fix_context (map(map_def trans trans) xfix)|) in t0. - 2:now rewrite TT.fix_context_length, map_length, fix_context_length. + 2:now rewrite TT.fix_context_length map_length fix_context_length. now destruct x. + auto. Qed. @@ -1109,38 +1071,220 @@ Proof. econstructor; eauto. Qed. +Lemma mkApp_ex t u : ∑ f args, mkApp t u = tApp f args. +Proof. + induction t; simpl; eexists _, _; reflexivity. +Qed. + +Lemma trans_decompose_prod_assum : + forall Γ t, + let '(Δ, c) := decompose_prod_assum Γ t in + AstUtils.decompose_prod_assum (trans_local Γ) (trans t) = (trans_local Δ, trans c). +Proof. + intros Γ t. + destruct decompose_prod_assum as [Δ c] eqn:e. + induction t in Γ, Δ, c, e |- *. + all: simpl in *. + all: try solve [ inversion e ; subst ; reflexivity ]. + - eapply IHt2 in e as e'. apply e'. + - eapply IHt3 in e as e'. assumption. + - noconf e. simpl. + now destruct (mkApp_ex (trans t1) (trans t2)) as [f [args ->]]. + - noconf e. now destruct prim as [? []] => /=. +Qed. -(* from Checker Substitution *) +Lemma trans_subst_context s k Γ : + trans_local (SL.subst_context s k Γ) = TL.subst_context (map trans s) k (trans_local Γ). +Proof. + induction Γ as [|[na [b|] ty] Γ]; simpl; auto. + - rewrite SL.subst_context_snoc /=. rewrite [TL.subst_context _ _ _ ]subst_context_snoc. + f_equal; auto. rewrite IHΓ /snoc /subst_decl /map_decl /=; f_equal. + now rewrite !trans_subst map_length. + - rewrite SL.subst_context_snoc /=. rewrite [TL.subst_context _ _ _ ]subst_context_snoc. + f_equal; auto. rewrite IHΓ /snoc /subst_decl /map_decl /=; f_equal. + now rewrite !trans_subst map_length. +Qed. +Lemma trans_smash_context Γ Δ : trans_local (smash_context Γ Δ) = TT.smash_context (trans_local Γ) (trans_local Δ). +Proof. + induction Δ in Γ |- *; simpl; auto. + destruct a as [na [b|] ty] => /=. + rewrite IHΔ. f_equal. + now rewrite (trans_subst_context [_]). + rewrite IHΔ. f_equal. rewrite /trans_local map_app //. +Qed. +Lemma trans_isApp t : PCUICAst.isApp t = false -> Ast.isApp (trans t) = false. +Proof. + destruct t => //. + now destruct prim as [? []]. +Qed. -Lemma eq_term_upto_univ_refl Re Rle : - RelationClasses.Reflexive Re -> - RelationClasses.Reflexive Rle -> - forall t, TT.eq_term_upto_univ Re Rle t t. +Lemma trans_destInd t : ST.destInd t = TT.destInd (trans t). Proof. - intros hRe hRle. - induction t in Rle, hRle |- * using Induction.term_forall_list_rect; simpl; - try constructor; try apply Forall_Forall2; try apply All_All2 ; try easy; - try now (try apply Forall_All ; apply Forall_True). - - eapply All_All2. 1: eassumption. - intros. easy. - - eapply All_All2. 1: eassumption. - intros. easy. - - destruct p. constructor; try easy. - eapply All_All2. 1: eassumption. - intros. split ; auto. - - eapply All_All2. 1: eassumption. - intros x [? ?]. repeat split ; auto. - - eapply All_All2. 1: eassumption. - intros x [? ?]. repeat split ; auto. + destruct t => //. simpl. + now destruct (mkApp_ex (trans t1) (trans t2)) as [f [u ->]]. + now destruct prim as [? []]. Qed. -Lemma leq_term_refl `{checker_flags} φ t : TT.leq_term φ t t. +Lemma trans_decompose_app t : + let '(hd, args) := decompose_app t in + AstUtils.decompose_app (trans t) = (trans hd, map trans args). Proof. - apply eq_term_upto_univ_refl. - - intro; apply eq_universe_refl. - - intro; apply leq_universe_refl. + destruct (decompose_app t) eqn:da. + pose proof (decompose_app_notApp _ _ _ da). + eapply decompose_app_rec_inv in da. simpl in da. subst t. + rewrite trans_mkApps. + apply AstUtils.decompose_app_mkApps. + now rewrite trans_isApp. +Qed. + + +Lemma All2_map_option_out_mapi_Some_spec : + forall {A B B'} (f : nat -> A -> option B) (g' : B -> B') + (g : nat -> A -> option B') l t, + (forall i x t, f i x = Some t -> g i x = Some (g' t)) -> + map_option_out (mapi f l) = Some t -> + map_option_out (mapi g l) = Some (map g' t). +Proof. + intros A B B' f g' g l t. + unfold mapi. generalize 0. + intros n h e. + induction l in n, e, t |- *. + - simpl in *. apply some_inj in e. subst. reflexivity. + - simpl in *. + destruct (f n a) eqn:e'. 2: discriminate. + eapply h in e' as h'. + rewrite h'. + match type of e with + | context [ map_option_out ?t ] => + destruct (map_option_out t) eqn:e'' + end. 2: discriminate. + eapply IHl in e''. rewrite e''. now noconf e. +Qed. + +Lemma trans_inds ind u mdecl : + map trans (ST.inds (inductive_mind ind) u (PCUICAst.ind_bodies mdecl)) = + TT.inds (inductive_mind ind) u (ind_bodies (trans_minductive_body mdecl)). +Proof. + rewrite ST.inds_spec TT.inds_spec. + rewrite map_rev map_mapi. simpl. + f_equal. rewrite mapi_map. apply mapi_ext => n //. +Qed. + +Lemma trans_reln l p Γ : map trans (PCUICAst.reln l p Γ) = + reln (map trans l) p (trans_local Γ). +Proof. + induction Γ as [|[na [b|] ty] Γ] in l, p |- *; simpl; auto. + now rewrite IHΓ. +Qed. + +Lemma trans_to_extended_list Γ n : map trans (PCUICAst.to_extended_list_k Γ n) = to_extended_list_k (trans_local Γ) n. +Proof. + now rewrite /to_extended_list_k trans_reln. +Qed. + +Lemma trans_build_branches_type ind mdecl idecl npar args u p brtys : + map_option_out (ST.build_branches_type ind mdecl idecl (firstn npar args) u p) + = Some brtys -> + map_option_out + (TT.build_branches_type ind (trans_minductive_body mdecl) + (trans_one_ind_body idecl) (firstn npar (map trans args)) u (trans p)) + = Some (map (on_snd trans) brtys). +Proof. + unfold ST.build_branches_type. + unfold TT.build_branches_type. + rewrite mapi_map. + apply All2_map_option_out_mapi_Some_spec. + intros i [[id ty] argn] [nargs br]. + simpl. + destruct ST.instantiate_params eqn:ipars => //. + apply trans_instantiate_params' in ipars. + rewrite trans_subst in ipars. + rewrite -trans_inds. + rewrite -trans_subst_instance_constr ipars. + move: (trans_decompose_prod_assum [] t). + destruct decompose_prod_assum => -> /=. + move: (trans_decompose_app t0). + destruct decompose_app => /= // ->. + simpl. destruct chop as [params argsl] eqn:ceq. + rewrite (chop_map _ _ _ _ _ ceq). + intros [= ->]. f_equal. unfold on_snd. simpl. f_equal. subst br. + rewrite trans_it_mkProd_or_LetIn trans_mkApps map_app /= trans_mkApps /= map_app. + now rewrite trans_to_extended_list trans_lift map_length. +Qed. + +Lemma trans_check_one_fix mfix : + TT.check_one_fix (map_def trans trans mfix) = ST.check_one_fix mfix. +Proof. + unfold ST.check_one_fix, TT.check_one_fix. + destruct mfix as [na ty arg rarg] => /=. + move: (trans_decompose_prod_assum [] ty). + destruct decompose_prod_assum as [ctx p] => -> /=. + rewrite -(trans_smash_context []) /trans_local. + rewrite -List.map_rev nth_error_map. + destruct nth_error => /= //. + move: (trans_decompose_app (PCUICAst.decl_type c)). + destruct decompose_app => /=. + simpl. destruct c. simpl. intros ->. + now rewrite -trans_destInd. +Qed. + +Lemma map_option_out_check_one_fix mfix : + map (fun x => TT.check_one_fix (map_def trans trans x)) mfix = + map ST.check_one_fix mfix. +Proof. + eapply map_ext => x. apply trans_check_one_fix. +Qed. + + +Lemma trans_check_one_cofix mfix : + TT.check_one_cofix (map_def trans trans mfix) = ST.check_one_cofix mfix. +Proof. + unfold ST.check_one_cofix, TT.check_one_cofix. + destruct mfix as [na ty arg rarg] => /=. + move: (trans_decompose_prod_assum [] ty). + destruct decompose_prod_assum as [ctx p] => -> /=. + move: (trans_decompose_app p). + destruct decompose_app => /= ->. + now rewrite -trans_destInd. +Qed. + +Lemma map_option_out_check_one_cofix mfix : + map (fun x => TT.check_one_cofix (map_def trans trans x)) mfix = + map ST.check_one_cofix mfix. +Proof. + eapply map_ext => x. apply trans_check_one_cofix. +Qed. + +Lemma trans_check_rec_kind Σ k f : + ST.check_recursivity_kind Σ k f = TT.check_recursivity_kind (trans_global_decls Σ) k f. +Proof. + unfold ST.check_recursivity_kind, TT.check_recursivity_kind. + rewrite trans_lookup. + destruct S.lookup_env as [[]|] => //. +Qed. + +Lemma trans_wf_fixpoint Σ mfix : + TT.wf_fixpoint (trans_global_decls Σ) (map (map_def trans trans) mfix) = + ST.wf_fixpoint Σ mfix. +Proof. + unfold ST.wf_fixpoint, TT.wf_fixpoint. + rewrite map_map_compose. + rewrite map_option_out_check_one_fix. + destruct map_option_out as [[]|] => //. + now rewrite trans_check_rec_kind. +Qed. + +Lemma trans_wf_cofixpoint Σ mfix : + TT.wf_cofixpoint (trans_global_decls Σ) (map (map_def trans trans) mfix) = + ST.wf_cofixpoint Σ mfix. +Proof. + unfold ST.wf_cofixpoint, TT.wf_cofixpoint. + rewrite map_map_compose. + rewrite map_option_out_check_one_cofix. + destruct map_option_out as [[]|] => //. + now rewrite trans_check_rec_kind. Qed. Axiom fix_guard_trans : @@ -1153,8 +1297,8 @@ Axiom cofix_guard_trans : ST.cofix_guard Σ Γ mfix -> TT.cofix_guard (trans_global Σ) (trans_local Γ) (map (map_def trans trans) mfix). -Theorem template_to_pcuic (Σ : S.global_env_ext) Γ t T : - ST .wf Σ -> +Theorem pcuic_to_template (Σ : S.global_env_ext) Γ t T : + ST.wf Σ -> ST.typing Σ Γ t T -> TT.typing (trans_global Σ) (trans_local Γ) (trans t) (trans T). Proof. @@ -1168,11 +1312,6 @@ Proof. TT.All_local_env (TT.lift_typing TT.typing (trans_global Σ)) (trans_local Γ)) );intros. - now eapply trans_wf_local_env, All_over_All. -(* -typing_ind_env is like induction but with -additional assumptions for the nested typing -in All (for wf_local assumptions) -*) - rewrite trans_lift. rewrite trans_decl_type. eapply TT.type_Rel; eauto. @@ -1195,11 +1334,7 @@ in All (for wf_local assumptions) cbn. constructor. apply leq_term_refl. } - admit. - (* - tProd na (trans A) (trans B) has a type - obtain with inversion from IHX0_1 - *) + eapply X1. - rewrite trans_subst_instance_constr. rewrite trans_cst_type. eapply TT.type_Const; eauto. @@ -1226,6 +1361,7 @@ in All (for wf_local assumptions) repeat f_equal. now rewrite map_skipn. } + simpl. eapply TT.type_Case. + now apply trans_declared_inductive. + cbn. assumption. @@ -1236,9 +1372,9 @@ in All (for wf_local assumptions) eassumption. + auto. + now rewrite trans_mkApps in X4. - + admit. (* map_option_out build branche type *) - (* this should be similar to trans_build_case_predicate_type *) - + admit. (* now apply trans_branches.*) + + now apply trans_build_branches_type in H3. + + eapply All2_map. solve_all. + destruct b0 as [s [Hs Hy]]. exists s; eauto. - rewrite trans_subst. rewrite trans_subst_instance_constr. cbn. @@ -1265,8 +1401,8 @@ in All (for wf_local assumptions) exists s; intuition auto. + fold trans. subst types. - eapply trans_mfix_All2;eassumption. - + admit. + eapply trans_mfix_All2; eassumption. + + now rewrite trans_wf_fixpoint. - rewrite trans_dtype. simpl. eapply TT.type_CoFix; auto. + now eapply cofix_guard_trans. @@ -1279,10 +1415,10 @@ in All (for wf_local assumptions) eapply All_map, (All_impl X0). intros x [s ?]; exists s; intuition auto. + fold trans;subst types. - (* like trans_mfix_All2 without isLambda *) - now apply trans_mfix_All2'. - + admit. + now apply trans_mfix_All2. + + now rewrite trans_wf_cofixpoint. - eapply TT.type_Conv. + eassumption. - + admit. (* eapply trans_cumul. *) -Admitted. + + eassumption. + + now eapply trans_cumul. +Qed. diff --git a/pcuic/theories/PCUICTyping.v b/pcuic/theories/PCUICTyping.v index d2bc5b7d0..4ee74367d 100644 --- a/pcuic/theories/PCUICTyping.v +++ b/pcuic/theories/PCUICTyping.v @@ -398,7 +398,9 @@ Inductive typing `{checker_flags} (Σ : global_env_ext) (Γ : context) : term -> Σ ;;; Γ |- c : mkApps (tInd ind u) args -> isCoFinite mdecl.(ind_finite) = false -> forall btys, map_option_out (build_branches_type ind mdecl idecl params u p) = Some btys -> - All2 (fun br bty => (br.1 = bty.1) * (Σ ;;; Γ |- br.2 : bty.2) * (∑ s, Σ ;;; Γ |- bty.2 : tSort s)) brs btys -> + All2 (fun br bty => (br.1 = bty.1) * (Σ ;;; Γ |- br.2 : bty.2) * + (* This is a paranoid assumption *) + (∑ s, Σ ;;; Γ |- bty.2 : tSort s)) brs btys -> Σ ;;; Γ |- tCase indnpar p c brs : mkApps p (skipn npar args ++ [c]) | type_Proj p c u : @@ -415,8 +417,7 @@ Inductive typing `{checker_flags} (Σ : global_env_ext) (Γ : context) : term -> nth_error mfix n = Some decl -> wf_local Σ Γ -> All (fun d => {s & Σ ;;; Γ |- d.(dtype) : tSort s}) mfix -> - All (fun d => (Σ ;;; Γ ,,, fix_context mfix |- d.(dbody) : lift0 #|fix_context mfix| d.(dtype)) - * (isLambda d.(dbody) = true)%type) mfix -> + All (fun d => (Σ ;;; Γ ,,, fix_context mfix |- d.(dbody) : lift0 #|fix_context mfix| d.(dtype))) mfix -> wf_fixpoint Σ.1 mfix -> Σ ;;; Γ |- tFix mfix n : decl.(dtype) @@ -515,7 +516,7 @@ Proof. - exact (S (S (wf_local_size _ typing_size _ a))). - exact (S (Nat.max d2 (Nat.max d3 (all2_size _ (fun x y p => Nat.max (typing_size Σ Γ (snd x) (snd y) (snd (fst p))) (typing_size _ _ _ _ (snd p).π2)) a)))). - - exact (S (Nat.max (Nat.max (wf_local_size _ typing_size _ a) (all_size _ (fun x p => typing_size Σ _ _ _ p.π2) a0)) (all_size _ (fun x p => typing_size Σ _ _ _ (fst p)) a1))). + - exact (S (Nat.max (Nat.max (wf_local_size _ typing_size _ a) (all_size _ (fun x p => typing_size Σ _ _ _ p.π2) a0)) (all_size _ (fun x p => typing_size Σ _ _ _ p) a1))). - exact (S (Nat.max (Nat.max (wf_local_size _ typing_size _ a) (all_size _ (fun x p => typing_size Σ _ _ _ p.π2) a0)) (all_size _ (fun x p => typing_size Σ _ _ _ p) a1))). Defined. @@ -795,7 +796,6 @@ Lemma typing_ind_env `{cf : checker_flags} : PΓ Σ Γ wfΓ -> All (fun d => {s & (Σ ;;; Γ |- d.(dtype) : tSort s)%type * P Σ Γ d.(dtype) (tSort s)})%type mfix -> All (fun d => (Σ ;;; Γ ,,, types |- d.(dbody) : lift0 #|types| d.(dtype))%type * - (isLambda d.(dbody) = true)%type * P Σ (Γ ,,, types) d.(dbody) (lift0 #|types| d.(dtype)))%type mfix -> wf_fixpoint Σ.1 mfix -> P Σ Γ (tFix mfix n) decl.(dtype)) -> @@ -1053,7 +1053,7 @@ Proof. forall (t T : term) (Hty : Σ;;; Γ0 |- t : T), typing_size Hty < S - (all_size _ (fun (x : def term) p => typing_size (fst p)) a1) -> + (all_size _ (fun (x : def term) p => typing_size p) a1) -> Forall_decls_typing P Σ.1 * P Σ Γ0 t T). {intros. eapply (X14 _ _ _ Hty); eauto. lia. } clear X14 X13. @@ -1062,7 +1062,7 @@ Proof. induction a1; econstructor; eauto. ++ split; auto. - eapply (X _ (typing_wf_local (fst p)) _ _ (fst p)). simpl. lia. + eapply (X _ (typing_wf_local p) _ _ p). simpl. lia. ++ eapply IHa1. intros. eapply (X _ X0 _ _ Hty). simpl; lia. diff --git a/pcuic/theories/PCUICUnivSubstitution.v b/pcuic/theories/PCUICUnivSubstitution.v index 282cc39d8..a3e6e7679 100644 --- a/pcuic/theories/PCUICUnivSubstitution.v +++ b/pcuic/theories/PCUICUnivSubstitution.v @@ -1656,16 +1656,15 @@ Proof. destruct X1 as [s Hs]. exists (subst_instance_univ u s). now apply Hs. + eapply All_map, All_impl; tea. - intros x [[X1 X2] X3]. split. - * specialize (X3 u univs wfΣ' HSub H2). erewrite map_dbody in X3. - rewrite <- lift_subst_instance_constr in X3. - rewrite fix_context_length, map_length in *. - erewrite map_dtype with (d := x) in X3. - unfold subst_instance_context, map_context in *. - rewrite map_app in *. - rewrite <- (fix_context_subst_instance u mfix). - eapply X3. - * destruct x as [? ? []]; cbn in *; tea. + intros x [X1 X3]. + specialize (X3 u univs wfΣ' HSub H2). erewrite map_dbody in X3. + rewrite <- lift_subst_instance_constr in X3. + rewrite fix_context_length, map_length in *. + erewrite map_dtype with (d := x) in X3. + unfold subst_instance_context, map_context in *. + rewrite map_app in *. + rewrite <- (fix_context_subst_instance u mfix). + eapply X3. + red; rewrite <- wffix. unfold wf_fixpoint. rewrite map_map_compose. diff --git a/pcuic/theories/PCUICWeakening.v b/pcuic/theories/PCUICWeakening.v index 533339ec6..e9f27ea0d 100644 --- a/pcuic/theories/PCUICWeakening.v +++ b/pcuic/theories/PCUICWeakening.v @@ -1055,16 +1055,14 @@ Proof. now specialize (Hs' _ _ _ wf eq_refl). * eapply All_map. eapply (All_impl X1); simpl. - intros x [[Hb Hlam] IH]. + intros x [Hb IH]. rewrite lift_fix_context. specialize (IH Γ (Γ' ,,, (fix_context mfix)) Γ'' wf). rewrite app_context_assoc in IH. specialize (IH eq_refl). - split; auto. - + rewrite lift_context_app Nat.add_0_r app_context_assoc in IH. - rewrite app_context_length fix_context_length in IH. - rewrite lift_context_length fix_context_length. - rewrite permute_lift; try lia. now rewrite (Nat.add_comm #|Γ'|). - + now rewrite isLambda_lift. + rewrite lift_context_app Nat.add_0_r app_context_assoc in IH. + rewrite app_context_length fix_context_length in IH. + rewrite lift_context_length fix_context_length. + rewrite permute_lift; try lia. now rewrite (Nat.add_comm #|Γ'|). * red; rewrite <-H1. unfold wf_fixpoint. rewrite map_map_compose. now rewrite weakening_check_one_fix. diff --git a/pcuic/theories/PCUICWeakeningEnv.v b/pcuic/theories/PCUICWeakeningEnv.v index c574debd3..f10496b07 100644 --- a/pcuic/theories/PCUICWeakeningEnv.v +++ b/pcuic/theories/PCUICWeakeningEnv.v @@ -213,7 +213,7 @@ Proof. eapply extends_lookup in look; eauto. rewrite look //. - destruct (lookup_env Σ (inductive_mind i)) eqn:look => //. eapply extends_lookup in look; eauto. rewrite look //. -Qed. +Qed. (** The definition of [R_global_instance] is defined so that it is weakenable. *) Lemma R_global_instance_weaken_env {cf:checker_flags} Σ Σ' Re Re' Rle Rle' gr napp : diff --git a/pcuic/theories/TemplateToPCUICCorrectness.v b/pcuic/theories/TemplateToPCUICCorrectness.v index 5c2b3a4b6..310bbcd6d 100644 --- a/pcuic/theories/TemplateToPCUICCorrectness.v +++ b/pcuic/theories/TemplateToPCUICCorrectness.v @@ -701,7 +701,7 @@ Admitted. Qed. *) Lemma trans_leq_term {cf} Σ ϕ T U : - T.wf T -> T.wf U -> TTy.leq_term ϕ T U -> + T.wf T -> T.wf U -> TTy.leq_term Σ ϕ T U -> leq_term Σ ϕ (trans T) (trans U). Proof. intros HT HU H. diff --git a/template-coq/_CoqProject b/template-coq/_CoqProject index 7e0f6be60..567a73559 100644 --- a/template-coq/_CoqProject +++ b/template-coq/_CoqProject @@ -37,6 +37,7 @@ theories/UnivSubst.v theories/Pretty.v theories/EnvironmentTyping.v theories/WfInv.v +theories/TermEquality.v theories/Typing.v theories/TypingWf.v diff --git a/template-coq/theories/TermEquality.v b/template-coq/theories/TermEquality.v new file mode 100644 index 000000000..23cbcd7e9 --- /dev/null +++ b/template-coq/theories/TermEquality.v @@ -0,0 +1,443 @@ +(* Distributed under the terms of the MIT license. *) +From Coq Require Import CMorphisms. +From MetaCoq.Template Require Import config utils Reflect Ast AstUtils Induction LiftSubst Reflect. + +Require Import ssreflect. +From Equations.Prop Require Import DepElim. +Set Equations With UIP. + +Definition R_universe_instance R := + fun u u' => Forall2 R (List.map Universe.make u) (List.map Universe.make u'). + +(** Cumulative inductive types: + + To simplify the development, we allow the variance list to not exactly + match the instances, so as to keep syntactic equality an equivalence relation + even on ill-formed terms. It corresponds to the right notion on well-formed terms. +*) + +Definition R_universe_variance (Re Rle : Universe.t -> Universe.t -> Prop) v u u' := + match v with + | Variance.Irrelevant => True + | Variance.Covariant => Rle (Universe.make u) (Universe.make u') + | Variance.Invariant => Re (Universe.make u) (Universe.make u') + end. + +Fixpoint R_universe_instance_variance Re Rle v u u' := + match u, u' return Prop with + | u :: us, u' :: us' => + match v with + | [] => R_universe_instance_variance Re Rle v us us' + (* Missing variance stands for irrelevance, we still check that the instances have + the same length. *) + | v :: vs => R_universe_variance Re Rle v u u' /\ + R_universe_instance_variance Re Rle vs us us' + end + | [], [] => True + | _, _ => False + end. + +Definition lookup_minductive Σ mind := + match lookup_env Σ mind with + | Some (InductiveDecl decl) => Some decl + | _ => None + end. + +Definition lookup_inductive Σ ind := + match lookup_minductive Σ (inductive_mind ind) with + | Some mdecl => + match nth_error mdecl.(ind_bodies) (inductive_ind ind) with + | Some idecl => Some (mdecl, idecl) + | None => None + end + | None => None + end. + +Definition lookup_constructor Σ ind k := + match lookup_inductive Σ ind with + | Some (mdecl, idecl) => + match nth_error idecl.(ind_ctors) k with + | Some cdecl => Some (mdecl, idecl, cdecl) + | None => None + end + | _ => None + end. + +Fixpoint destArity Γ (t : term) := + match t with + | tProd na t b => destArity (Γ ,, vass na t) b + | tLetIn na b b_ty b' => destArity (Γ ,, vdef na b b_ty) b' + | tSort s => Some (Γ, s) + | _ => None + end. +Definition global_variance Σ gr napp := + match gr with + | IndRef ind => + match lookup_inductive Σ ind with + | Some (mdecl, idecl) => + match destArity [] idecl.(ind_type) with + | Some (ctx, _) => if (context_assumptions ctx) <=? napp then mdecl.(ind_variance) + else None + | None => None + end + | None => None + end + | ConstructRef ind k => + match lookup_constructor Σ ind k with + | Some (mdecl, idecl, cdecl) => + if (cdecl.2 + mdecl.(ind_npars))%nat <=? napp then + (** Fully applied constructors are always compared at the same supertype, + which implies that no universe equality needs to be checked here. *) + Some [] + else None + | _ => None + end + | _ => None + end. + +Definition R_opt_variance Re Rle v := + match v with + | Some v => R_universe_instance_variance Re Rle v + | None => R_universe_instance Re + end. + +Definition R_global_instance Σ Re Rle gr napp := + R_opt_variance Re Rle (global_variance Σ gr napp). + +Lemma R_universe_instance_impl R R' : + RelationClasses.subrelation R R' -> + RelationClasses.subrelation (R_universe_instance R) (R_universe_instance R'). +Proof. + intros H x y xy. eapply Forall2_impl ; tea. +Qed. + +Lemma R_universe_instance_impl' R R' : + RelationClasses.subrelation R R' -> + forall u u', R_universe_instance R u u' -> R_universe_instance R' u u'. +Proof. + intros H x y xy. eapply Forall2_impl ; tea. +Qed. + +(** ** Syntactic equality up-to universes + We don't look at printing annotations *) + +(** Equality is indexed by a natural number that counts the number of applications + that surround the current term, used to implement cumulativity of inductive types + correctly (only fully applied constructors and inductives benefit from it). *) + +Inductive eq_term_upto_univ_napp Σ (Re Rle : Universe.t -> Universe.t -> Prop) (napp : nat) : term -> term -> Type := +| eq_Rel n : + eq_term_upto_univ_napp Σ Re Rle napp (tRel n) (tRel n) + +| eq_Evar e args args' : + All2 (eq_term_upto_univ_napp Σ Re Re 0) args args' -> + eq_term_upto_univ_napp Σ Re Rle napp (tEvar e args) (tEvar e args') + +| eq_Var id : + eq_term_upto_univ_napp Σ Re Rle napp (tVar id) (tVar id) + +| eq_Sort s s' : + Rle s s' -> + eq_term_upto_univ_napp Σ Re Rle napp (tSort s) (tSort s') + +| eq_App t t' u u' : + eq_term_upto_univ_napp Σ Re Rle (#|u| + napp) t t' -> + All2 (eq_term_upto_univ_napp Σ Re Re 0) u u' -> + eq_term_upto_univ_napp Σ Re Rle napp (tApp t u) (tApp t' u') + +| eq_Const c u u' : + R_universe_instance Re u u' -> + eq_term_upto_univ_napp Σ Re Rle napp (tConst c u) (tConst c u') + +| eq_Ind i u u' : + R_global_instance Σ Re Rle (IndRef i) napp u u' -> + eq_term_upto_univ_napp Σ Re Rle napp (tInd i u) (tInd i u') + +| eq_Construct i k u u' : + R_global_instance Σ Re Rle (ConstructRef i k) napp u u' -> + eq_term_upto_univ_napp Σ Re Rle napp (tConstruct i k u) (tConstruct i k u') + +| eq_Lambda na na' ty ty' t t' : + eq_binder_annot na na' -> + eq_term_upto_univ_napp Σ Re Re 0 ty ty' -> + eq_term_upto_univ_napp Σ Re Rle 0 t t' -> + eq_term_upto_univ_napp Σ Re Rle napp (tLambda na ty t) (tLambda na' ty' t') + +| eq_Prod na na' a a' b b' : + eq_binder_annot na na' -> + eq_term_upto_univ_napp Σ Re Re 0 a a' -> + eq_term_upto_univ_napp Σ Re Rle 0 b b' -> + eq_term_upto_univ_napp Σ Re Rle napp (tProd na a b) (tProd na' a' b') + +| eq_LetIn na na' t t' ty ty' u u' : + eq_binder_annot na na' -> + eq_term_upto_univ_napp Σ Re Re 0 t t' -> + eq_term_upto_univ_napp Σ Re Re 0 ty ty' -> + eq_term_upto_univ_napp Σ Re Rle 0 u u' -> + eq_term_upto_univ_napp Σ Re Rle napp (tLetIn na t ty u) (tLetIn na' t' ty' u') + +| eq_Case indn p p' c c' brs brs' : + eq_term_upto_univ_napp Σ Re Re 0 p p' -> + eq_term_upto_univ_napp Σ Re Re 0 c c' -> + All2 (fun x y => + (fst x = fst y) * + eq_term_upto_univ_napp Σ Re Re 0 (snd x) (snd y) + ) brs brs' -> + eq_term_upto_univ_napp Σ Re Rle napp (tCase indn p c brs) (tCase indn p' c' brs') + +| eq_Proj p c c' : + eq_term_upto_univ_napp Σ Re Re 0 c c' -> + eq_term_upto_univ_napp Σ Re Rle napp (tProj p c) (tProj p c') + +| eq_Fix mfix mfix' idx : + All2 (fun x y => + eq_term_upto_univ_napp Σ Re Re 0 x.(dtype) y.(dtype) * + eq_term_upto_univ_napp Σ Re Re 0 x.(dbody) y.(dbody) * + (x.(rarg) = y.(rarg)) * + eq_binder_annot x.(dname) y.(dname) + )%type mfix mfix' -> + eq_term_upto_univ_napp Σ Re Rle napp (tFix mfix idx) (tFix mfix' idx) + +| eq_CoFix mfix mfix' idx : + All2 (fun x y => + eq_term_upto_univ_napp Σ Re Re 0 x.(dtype) y.(dtype) * + eq_term_upto_univ_napp Σ Re Re 0 x.(dbody) y.(dbody) * + (x.(rarg) = y.(rarg)) * + eq_binder_annot x.(dname) y.(dname) + ) mfix mfix' -> + eq_term_upto_univ_napp Σ Re Rle napp (tCoFix mfix idx) (tCoFix mfix' idx) + +| eq_Cast t1 c t2 t1' c' t2' : + eq_term_upto_univ_napp Σ Re Rle napp t1 t1' -> + eq_cast_kind c c' -> + eq_term_upto_univ_napp Σ Re Re 0 t2 t2' -> + eq_term_upto_univ_napp Σ Re Rle napp (tCast t1 c t2) (tCast t1' c' t2') + +| eq_Int i : eq_term_upto_univ_napp Σ Re Rle napp (tInt i) (tInt i) +| eq_Float f : eq_term_upto_univ_napp Σ Re Rle napp (tFloat f) (tFloat f). + +Notation eq_term_upto_univ Σ Re Rle := (eq_term_upto_univ_napp Σ Re Rle 0). + +(* ** Syntactic conversion up-to universes *) + +Definition eq_term `{checker_flags} Σ φ := + eq_term_upto_univ Σ (eq_universe φ) (eq_universe φ). + +(* ** Syntactic cumulativity up-to universes *) + +Definition leq_term `{checker_flags} Σ φ := + eq_term_upto_univ Σ (eq_universe φ) (leq_universe φ). + + Lemma R_global_instance_refl Σ Re Rle gr napp u : + RelationClasses.Reflexive Re -> + RelationClasses.Reflexive Rle -> + R_global_instance Σ Re Rle gr napp u u. +Proof. + intros rRE rRle. + rewrite /R_global_instance. + destruct global_variance as [v|] eqn:lookup. + - induction u in v |- *; simpl; auto; + unfold R_opt_variance in IHu; destruct v; simpl; auto. + split; auto. + destruct t; simpl; auto. + - apply Forall2_same; eauto. +Qed. + +Instance eq_binder_annot_equiv {A} : RelationClasses.Equivalence (@eq_binder_annot A). +Proof. + split. + - red. reflexivity. + - red; now symmetry. + - intros x y z; unfold eq_binder_annot. + congruence. +Qed. + +Definition eq_binder_annot_refl {A} x : @eq_binder_annot A x x. +Proof. reflexivity. Qed. + +Hint Resolve @eq_binder_annot_refl : core. + +Lemma eq_term_upto_univ_refl Σ Re Rle : + RelationClasses.Reflexive Re -> + RelationClasses.Reflexive Rle -> + forall napp t, eq_term_upto_univ_napp Σ Re Rle napp t t. +Proof. + intros hRe hRle napp. + induction t in napp, Rle, hRle |- * using term_forall_list_rect; simpl; + try constructor; try apply Forall_Forall2; try apply All_All2 ; try easy; + try now (try apply Forall_All ; apply Forall_True). + - eapply All_All2. 1: eassumption. + intros. simpl in X0. easy. + - destruct c; constructor. + - eapply All_All2. 1: eassumption. + intros. easy. + - now apply R_global_instance_refl. + - now apply R_global_instance_refl. + - red in X. eapply All_All2. 1:eassumption. + intros; easy. + - eapply All_All2. 1: eassumption. + simpl. + intros x [? ?]. repeat split ; auto. + - eapply All_All2. 1: eassumption. + intros x [? ?]. repeat split ; auto. +Qed. + +Lemma eq_term_refl `{checker_flags} Σ φ t : eq_term Σ φ t t. +Proof. + apply eq_term_upto_univ_refl. + - intro; apply eq_universe_refl. + - intro; apply eq_universe_refl. +Qed. + + +Lemma leq_term_refl `{checker_flags} Σ φ t : leq_term Σ φ t t. +Proof. + apply eq_term_upto_univ_refl. + - intro; apply eq_universe_refl. + - intro; apply leq_universe_refl. +Qed. +(* +Lemma eq_term_leq_term `{checker_flags} Σ φ napp t u : + eq_term_upto_univ_napp Σ napp φ t u -> leq_term Σ φ t u. +Proof. + induction t in u |- * using term_forall_list_rect; simpl; inversion 1; + subst; constructor; try (now unfold eq_term, leq_term in * ); + try eapply Forall2_impl' ; try eapply All2_impl' ; try easy. + now apply eq_universe_leq_universe. + all: try (apply Forall_True, eq_universe_leq_universe). + apply IHt. +Qed. *) + + +Instance R_global_instance_impl_same_napp Σ Re Re' Rle Rle' gr napp : + RelationClasses.subrelation Re Re' -> + RelationClasses.subrelation Rle Rle' -> + subrelation (R_global_instance Σ Re Rle gr napp) (R_global_instance Σ Re' Rle' gr napp). +Proof. + intros he hle t t'. + rewrite /R_global_instance /R_opt_variance. + destruct global_variance as [v|] eqn:glob. + induction t in v, t' |- *; destruct v, t'; simpl; auto. + intros []; split; auto. + destruct t0; simpl; auto. + now eapply R_universe_instance_impl'. +Qed. + +Lemma eq_term_upto_univ_morphism0 Σ (Re Re' : _ -> _ -> Prop) + (Hre : forall t u, Re t u -> Re' t u) + : forall t u napp, eq_term_upto_univ_napp Σ Re Re napp t u -> eq_term_upto_univ_napp Σ Re' Re' napp t u. +Proof. + fix aux 4. + destruct 1; constructor; eauto. + all: unfold R_universe_instance in *. + all: try solve[ match goal with + | H : All2 _ _ _ |- _ => clear -H aux; induction H; constructor; eauto + | H : Forall2 _ _ _ |- _ => induction H; constructor; eauto + end]. + - eapply R_global_instance_impl_same_napp; eauto. + - eapply R_global_instance_impl_same_napp; eauto. + - induction a; constructor; auto. intuition auto. + - induction a; constructor; auto. intuition auto. + - induction a; constructor; auto. intuition auto. +Qed. + +Lemma eq_term_upto_univ_morphism Σ (Re Re' Rle Rle' : _ -> _ -> Prop) + (Hre : forall t u, Re t u -> Re' t u) + (Hrle : forall t u, Rle t u -> Rle' t u) + : forall t u napp, eq_term_upto_univ_napp Σ Re Rle napp t u -> eq_term_upto_univ_napp Σ Re' Rle' napp t u. +Proof. + fix aux 4. + destruct 1; constructor; eauto using eq_term_upto_univ_morphism0. + all: unfold R_universe_instance in *. + all: try solve [match goal with + | H : Forall2 _ _ _ |- _ => induction H; constructor; + eauto using eq_term_upto_univ_morphism0 + | H : All2 _ _ _ |- _ => induction H; constructor; + eauto using eq_term_upto_univ_morphism0 + end]. + - clear X. induction a; constructor; eauto using eq_term_upto_univ_morphism0. + - eapply R_global_instance_impl_same_napp; eauto. + - eapply R_global_instance_impl_same_napp; eauto. + - clear X1 X2. induction a; constructor; eauto using eq_term_upto_univ_morphism0. + destruct r. split; eauto using eq_term_upto_univ_morphism0. + - induction a; constructor; eauto using eq_term_upto_univ_morphism0. + destruct r as [[[? ?] ?] ?]. + repeat split; eauto using eq_term_upto_univ_morphism0. + - induction a; constructor; eauto using eq_term_upto_univ_morphism0. + destruct r as [[[? ?] ?] ?]. + repeat split; eauto using eq_term_upto_univ_morphism0. +Qed. + + +Lemma global_variance_napp_mon {Σ gr napp napp' v} : + napp <= napp' -> + global_variance Σ gr napp = Some v -> + global_variance Σ gr napp' = Some v. +Proof. + intros hnapp. + rewrite /global_variance. + destruct gr; try congruence. + - destruct lookup_inductive as [[mdecl idec]|] => //. + destruct destArity as [[ctx s]|] => //. + elim: Nat.leb_spec => // cass indv. + elim: Nat.leb_spec => //. lia. + - destruct lookup_constructor as [[[mdecl idecl] cdecl]|] => //. + elim: Nat.leb_spec => // cass indv. + elim: Nat.leb_spec => //. lia. +Qed. + +Instance R_global_instance_impl Σ Re Re' Rle Rle' gr napp napp' : + RelationClasses.subrelation Re Re' -> + RelationClasses.subrelation Re Rle' -> + RelationClasses.subrelation Rle Rle' -> + napp <= napp' -> + subrelation (R_global_instance Σ Re Rle gr napp) (R_global_instance Σ Re' Rle' gr napp'). +Proof. + intros he hle hele hnapp t t'. + rewrite /R_global_instance /R_opt_variance. + destruct global_variance as [v|] eqn:glob. + rewrite (global_variance_napp_mon hnapp glob). + induction t in v, t' |- *; destruct v, t'; simpl; auto. + intros []; split; auto. + destruct t0; simpl; auto. + destruct (global_variance _ _ napp') as [v|] eqn:glob'; eauto using R_universe_instance_impl'. + induction t in v, t' |- *; destruct v, t'; simpl; auto; intros H; inv H. + eauto. + split; auto. + destruct t0; simpl; auto. +Qed. + +Instance eq_term_upto_univ_impl Σ Re Re' Rle Rle' napp napp' : + RelationClasses.subrelation Re Re' -> + RelationClasses.subrelation Rle Rle' -> + RelationClasses.subrelation Re Rle' -> + napp <= napp' -> + subrelation (eq_term_upto_univ_napp Σ Re Rle napp) (eq_term_upto_univ_napp Σ Re' Rle' napp'). +Proof. + intros he hle hele hnapp t t'. + induction t in napp, napp', hnapp, t', Rle, Rle', hle, hele |- * using term_forall_list_rect; + try (inversion 1; subst; constructor; + eauto using R_universe_instance_impl'; fail). + - inversion 1; subst; constructor. + eapply All2_impl'; tea. + eapply All_impl; eauto. + - inversion 1; subst; constructor. + eapply IHt. 4:eauto. all:auto with arith. eauto. + solve_all. + - inversion 1; subst; constructor. + eapply R_global_instance_impl. 5:eauto. all:auto. + - inversion 1; subst; constructor. + eapply R_global_instance_impl. 5:eauto. all:eauto. + - inversion 1; subst; constructor; eauto. + eapply All2_impl'; tea. + eapply All_impl; eauto. + cbn. intros x ? y [? ?]. split; eauto. + - inversion 1; subst; constructor. + eapply All2_impl'; tea. + eapply All_impl; eauto. + cbn. intros x [? ?] y [[[? ?] ?] ?]. repeat split; eauto. + - inversion 1; subst; constructor. + eapply All2_impl'; tea. + eapply All_impl; eauto. + cbn. intros x [? ?] y [[[? ?] ?] ?]. repeat split; eauto. +Qed. diff --git a/template-coq/theories/Typing.v b/template-coq/theories/Typing.v index 0f2fb1483..34f240247 100644 --- a/template-coq/theories/Typing.v +++ b/template-coq/theories/Typing.v @@ -1,7 +1,7 @@ (* Distributed under the terms of the MIT license. *) From Coq Require Import ssreflect Wellfounded Relation_Operators. From MetaCoq.Template Require Import config utils Ast AstUtils LiftSubst UnivSubst - EnvironmentTyping Reflect. + EnvironmentTyping Reflect TermEquality. (** * Typing derivations @@ -417,107 +417,6 @@ Inductive red Σ Γ M : term -> Type := We hence implement first an equality which considers casts and do a stripping phase of casts before checking equality. *) -Definition R_universe_instance R := - fun u u' => Forall2 R (List.map Universe.make u) (List.map Universe.make u'). - -Inductive eq_term_upto_univ (Re Rle : Universe.t -> Universe.t -> Prop) : term -> term -> Type := -| eq_Rel n : - eq_term_upto_univ Re Rle (tRel n) (tRel n) - -| eq_Evar e args args' : - All2 (eq_term_upto_univ Re Re) args args' -> - eq_term_upto_univ Re Rle (tEvar e args) (tEvar e args') - -| eq_Var id : - eq_term_upto_univ Re Rle (tVar id) (tVar id) - -| eq_Sort s s' : - Rle s s' -> - eq_term_upto_univ Re Rle (tSort s) (tSort s') - -| eq_Cast f f' k T T' : - eq_term_upto_univ Re Re f f' -> - eq_term_upto_univ Re Re T T' -> - eq_term_upto_univ Re Rle (tCast f k T) (tCast f' k T') - -| eq_App t t' args args' : - eq_term_upto_univ Re Rle t t' -> - All2 (eq_term_upto_univ Re Re) args args' -> - eq_term_upto_univ Re Rle (tApp t args) (tApp t' args') - -| eq_Const c u u' : - R_universe_instance Re u u' -> - eq_term_upto_univ Re Rle (tConst c u) (tConst c u') - -| eq_Ind i u u' : - R_universe_instance Re u u' -> - eq_term_upto_univ Re Rle (tInd i u) (tInd i u') - -| eq_Construct i k u u' : - R_universe_instance Re u u' -> - eq_term_upto_univ Re Rle (tConstruct i k u) (tConstruct i k u') - -| eq_Lambda na na' ty ty' t t' : - eq_term_upto_univ Re Re ty ty' -> - eq_term_upto_univ Re Rle t t' -> - eq_term_upto_univ Re Rle (tLambda na ty t) (tLambda na' ty' t') - -| eq_Prod na na' a a' b b' : - eq_term_upto_univ Re Re a a' -> - eq_term_upto_univ Re Rle b b' -> - eq_term_upto_univ Re Rle (tProd na a b) (tProd na' a' b') - -| eq_LetIn na na' ty ty' t t' u u' : - eq_term_upto_univ Re Re ty ty' -> - eq_term_upto_univ Re Re t t' -> - eq_term_upto_univ Re Rle u u' -> - eq_term_upto_univ Re Rle (tLetIn na ty t u) (tLetIn na' ty' t' u') - -| eq_Case ind par p p' c c' brs brs' : - eq_term_upto_univ Re Re p p' -> - eq_term_upto_univ Re Re c c' -> - All2 (fun x y => - fst x = fst y × - eq_term_upto_univ Re Re (snd x) (snd y) - ) brs brs' -> - eq_term_upto_univ Re Rle (tCase (ind, par) p c brs) (tCase (ind, par) p' c' brs') - -| eq_Proj p c c' : - eq_term_upto_univ Re Re c c' -> - eq_term_upto_univ Re Rle (tProj p c) (tProj p c') - -| eq_Fix mfix mfix' idx : - All2 (fun x y => - eq_term_upto_univ Re Re x.(dtype) y.(dtype) × - eq_term_upto_univ Re Re x.(dbody) y.(dbody) × - x.(rarg) = y.(rarg) - ) mfix mfix' -> - eq_term_upto_univ Re Rle (tFix mfix idx) (tFix mfix' idx) - -| eq_CoFix mfix mfix' idx : - All2 (fun x y => - eq_term_upto_univ Re Re x.(dtype) y.(dtype) × - eq_term_upto_univ Re Re x.(dbody) y.(dbody) × - x.(rarg) = y.(rarg) - ) mfix mfix' -> - eq_term_upto_univ Re Rle (tCoFix mfix idx) (tCoFix mfix' idx) - -| eq_Int i : - eq_term_upto_univ Re Rle (tInt i) (tInt i) - - | eq_Float f : - eq_term_upto_univ Re Rle (tFloat f) (tFloat f). - -Definition eq_term `{checker_flags} φ := - eq_term_upto_univ (eq_universe φ) (eq_universe φ). - -(* ** Syntactic cumulativity up-to universes - - We shouldn't look at printing annotations *) - -Definition leq_term `{checker_flags} φ := - eq_term_upto_univ (eq_universe φ) (leq_universe φ). - Fixpoint strip_casts t := match t with | tEvar ev args => tEvar ev (List.map strip_casts args) @@ -540,11 +439,11 @@ Fixpoint strip_casts t := | tInt _ | tFloat _ => t end. -Definition eq_term_nocast `{checker_flags} (φ : ConstraintSet.t) (t u : term) := - eq_term φ (strip_casts t) (strip_casts u). +Definition eq_term_nocast `{checker_flags} (Σ : global_env) (φ : ConstraintSet.t) (t u : term) := + eq_term Σ φ (strip_casts t) (strip_casts u). -Definition leq_term_nocast `{checker_flags} (φ : ConstraintSet.t) (t u : term) := - leq_term φ (strip_casts t) (strip_casts u). +Definition leq_term_nocast `{checker_flags} (Σ : global_env) (φ : ConstraintSet.t) (t u : term) := + leq_term Σ φ (strip_casts t) (strip_casts u). (** ** Utilities for typing *) @@ -562,10 +461,11 @@ Fixpoint destArity Γ (t : term) := Reserved Notation " Σ ;;; Γ |- t : T " (at level 50, Γ, t, T at next level). Reserved Notation " Σ ;;; Γ |- t <= u " (at level 50, Γ, t, u at next level). Reserved Notation " Σ ;;; Γ |- t = u " (at level 50, Γ, t, u at next level). + (** ** Cumulativity *) Inductive cumul `{checker_flags} (Σ : global_env_ext) (Γ : context) : term -> term -> Type := -| cumul_refl t u : leq_term (global_ext_constraints Σ) t u -> Σ ;;; Γ |- t <= u +| cumul_refl t u : leq_term Σ (global_ext_constraints Σ) t u -> Σ ;;; Γ |- t <= u | cumul_red_l t u v : red1 Σ.1 Γ t v -> Σ ;;; Γ |- v <= u -> Σ ;;; Γ |- t <= u | cumul_red_r t u v : Σ ;;; Γ |- t <= v -> red1 Σ.1 Γ u v -> Σ ;;; Γ |- t <= u @@ -577,7 +477,7 @@ where " Σ ;;; Γ |- t <= u " := (cumul Σ Γ t u) : type_scope. *) Inductive conv `{checker_flags} (Σ : global_env_ext) (Γ : context) : term -> term -> Type := - | conv_refl t u : eq_term (global_ext_constraints Σ) t u -> Σ ;;; Γ |- t = u + | conv_refl t u : eq_term Σ (global_ext_constraints Σ) t u -> Σ ;;; Γ |- t = u | conv_red_l t u v : red1 Σ.1 Γ t v -> Σ ;;; Γ |- v = u -> Σ ;;; Γ |- t = u | conv_red_r t u v : Σ ;;; Γ |- t = v -> red1 Σ.1 Γ u v -> Σ ;;; Γ |- t = u @@ -603,18 +503,18 @@ Lemma congr_cumul_prod `{checker_flags} : forall Σ Γ na na' M1 M2 N1 N2, cumul Σ Γ (tProd na M1 M2) (tProd na' N1 N2). Proof. intros. todo "congr_cumul_prod". Defined. -Definition eq_opt_term `{checker_flags} φ (t u : option term) := +Definition eq_opt_term `{checker_flags} Σ φ (t u : option term) := match t, u with - | Some t, Some u => eq_term φ t u + | Some t, Some u => eq_term Σ φ t u | None, None => True | _, _ => False end. -Definition eq_decl `{checker_flags} φ (d d' : context_decl) := - eq_opt_term φ d.(decl_body) d'.(decl_body) * eq_term φ d.(decl_type) d'.(decl_type). +Definition eq_decl `{checker_flags} Σ φ (d d' : context_decl) := + eq_opt_term Σ φ d.(decl_body) d'.(decl_body) * eq_term Σ φ d.(decl_type) d'.(decl_type). -Definition eq_context `{checker_flags} φ (Γ Δ : context) := - All2 (eq_decl φ) Γ Δ. +Definition eq_context `{checker_flags} Σ φ (Γ Δ : context) := + All2 (eq_decl Σ φ) Γ Δ. (** ** Typing relation *) @@ -931,7 +831,7 @@ Inductive typing `{checker_flags} (Σ : global_env_ext) (Γ : context) : term -> isCoFinite mdecl.(ind_finite) = false -> Σ ;;; Γ |- c : mkApps (tInd ind u) args -> forall btys, map_option_out (build_branches_type ind mdecl idecl params u p) = Some btys -> - All2 (fun br bty => (br.1 = bty.1) * (Σ ;;; Γ |- br.2 : bty.2) * (Σ ;;; Γ |- bty.2 : tSort ps)) brs btys -> + All2 (fun br bty => (br.1 = bty.1) * (Σ ;;; Γ |- br.2 : bty.2) * (∑ s, Σ ;;; Γ |- bty.2 : tSort s)) brs btys -> Σ ;;; Γ |- tCase indnparrel p c brs : mkApps p (skipn npar args ++ [c]) | type_Proj p c u : @@ -1059,7 +959,7 @@ Proof. - exact (S (S (wf_local_size _ typing_size _ a))). - exact (S (S (wf_local_size _ typing_size _ a))). - exact (S (Nat.max d1 (Nat.max d2 - (all2_size _ (fun x y p => Nat.max (typing_size Σ Γ (snd x) (snd y) (snd (fst p))) (typing_size _ _ _ _ (snd p))) a)))). + (all2_size _ (fun x y p => Nat.max (typing_size Σ Γ (snd x) (snd y) (snd (fst p))) (typing_size _ _ _ _ (snd p).π2)) a)))). - exact (S (Nat.max (Nat.max (wf_local_size _ typing_size _ a) (all_size _ (fun x p => typing_size Σ _ _ _ p.π2) a0)) (all_size _ (fun x p => typing_size Σ _ _ _ p) a1))). - exact (S (Nat.max (Nat.max (wf_local_size _ typing_size _ a) (all_size _ (fun x p => typing_size Σ _ _ _ p.π2) a0)) (all_size _ (fun x p => typing_size Σ _ _ _ p) a1))). Defined. @@ -1273,7 +1173,7 @@ Lemma typing_ind_env `{cf : checker_flags} : forall btys, map_option_out (build_branches_type ind mdecl idecl params u p) = Some btys -> All2 (fun br bty => (br.1 = bty.1) * (Σ ;;; Γ |- br.2 : bty.2) * P Σ Γ br.2 bty.2 * - (Σ ;;; Γ |- bty.2 : tSort ps) * P Σ Γ bty.2 (tSort ps)) + ∑ s, (Σ ;;; Γ |- bty.2 : tSort s) * P Σ Γ bty.2 (tSort s)) brs btys -> P Σ Γ (tCase (ind, npar, r) p c brs) (mkApps p (skipn npar args ++ [c]))) -> @@ -1519,7 +1419,8 @@ Proof. --- intuition eauto. +++ eapply (X14 _ wfΓ _ _ t); eauto. simpl; auto with arith. lia. - +++ eapply (X14 _ wfΓ _ _ t0); eauto. simpl; auto with arith. + +++ destruct s as [s Hs]. exists s; split; [auto|]. + eapply (X14 _ wfΓ _ _ Hs); eauto. simpl; auto with arith. lia. --- apply IHa. auto. intros. eapply (X14 _ wfΓ0 _ _ Hty). lia. From 21e77a0ba45147d858a2655feeaa77db2def8179 Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Thu, 10 Dec 2020 03:09:04 +0100 Subject: [PATCH 51/70] Updating Template -> PCUIC --- erasure/theories/EDeps.v | 3 +- erasure/theories/ESubstitution.v | 6 +- erasure/theories/ErasureCorrectness.v | 6 +- erasure/theories/ErasureFunction.v | 4 +- pcuic/theories/PCUICAlpha.v | 33 ++-- pcuic/theories/PCUICInductiveInversion.v | 4 +- pcuic/theories/PCUICInversion.v | 4 +- pcuic/theories/PCUICSR.v | 15 +- pcuic/theories/TemplateToPCUICCorrectness.v | 180 ++++++++++++-------- safechecker/theories/PCUICTypeChecker.v | 11 +- template-coq/theories/TermEquality.v | 2 +- template-coq/theories/Typing.v | 9 - 12 files changed, 143 insertions(+), 134 deletions(-) diff --git a/erasure/theories/EDeps.v b/erasure/theories/EDeps.v index 5dda4f59d..982764c75 100644 --- a/erasure/theories/EDeps.v +++ b/erasure/theories/EDeps.v @@ -565,8 +565,7 @@ Proof. depelim typ. depelim er. depelim all_deps. - destruct p. - destruct p0 as (?&?&?). + destruct p as (?&?&?). now constructor; eauto. - constructor. apply inversion_CoFix in wt as (?&?&?&?&?&?&?); eauto. diff --git a/erasure/theories/ESubstitution.v b/erasure/theories/ESubstitution.v index bd2880ce2..87d7f5c81 100644 --- a/erasure/theories/ESubstitution.v +++ b/erasure/theories/ESubstitution.v @@ -108,7 +108,7 @@ Proof. - econstructor. eapply All2_All_mix_left in X1; eauto. eapply All2_impl. exact X1. - intros ? ? [[[]] [? []]]. + intros ? ? [[?] [? []]]. split; eauto. - econstructor. eapply All2_All_mix_left in X1; eauto. @@ -459,8 +459,8 @@ Proof. * cbn. now rewrite app_context_length, fix_context_length. * cbn. now erewrite app_context_length, fix_context_length, All2_length. * pose proof (substitution Σ Γ Γ' s (Δ ,,, PCUICLiftSubst.fix_context mfix)). - rewrite app_context_assoc in *. destruct Hs. - eapply X1 in t; eauto. + rewrite app_context_assoc in *. + eapply X1 in Hs; eauto. eapply typing_wf_local. eassumption. + econstructor. eapply is_type_subst; eauto. diff --git a/erasure/theories/ErasureCorrectness.v b/erasure/theories/ErasureCorrectness.v index 6f9bb01b7..ab746583e 100644 --- a/erasure/theories/ErasureCorrectness.v +++ b/erasure/theories/ErasureCorrectness.v @@ -141,11 +141,11 @@ Proof. eapply b0. subst types. eapply conv_context_app; auto. eapply typing_wf_local; eassumption. - eapply typing_wf_local in a1. subst types. + eapply typing_wf_local in a0. subst types. 2:eauto. eapply All_local_env_app. - eapply All_local_env_app_inv in a1. intuition auto. + eapply All_local_env_app_inv in a0. intuition auto. (* clear -wfΣ X2 a2 b4 X1. *) eapply All_local_env_impl; eauto. simpl; intros. @@ -283,7 +283,7 @@ Proof. eapply All2_impl. eapply All2_All_mix_left. eapply X1. exact X4. intros; cbn in *. destruct X5. destruct p0. destruct p0. - destruct p. destruct p. repeat split; eauto. + destruct p. repeat split; eauto. eapply e2 in e1. unfold PCUICUnivSubst.subst_instance_context in *. unfold map_context in *. rewrite ->map_app in *. subst types. 2:eauto. diff --git a/erasure/theories/ErasureFunction.v b/erasure/theories/ErasureFunction.v index 006ec8c63..31429f511 100644 --- a/erasure/theories/ErasureFunction.v +++ b/erasure/theories/ErasureFunction.v @@ -437,7 +437,7 @@ Section Erase. eexists; eauto. - eapply inversion_Fix in Ht as (? & ? & ? & ? & ? & ?); auto. eapply All_In in a0; eauto. - destruct a0 as [[a0 _]]. eexists; eauto. + destruct a0 as [a0]. eexists; eauto. - eapply inversion_CoFix in Ht as (? & ? & ? & ? & ? & ?); auto. eapply All_In in a0; eauto. destruct a0 as [a0]. eexists; eauto. @@ -800,7 +800,7 @@ Proof. eapply Forall2_All2 in H. eapply All2_All_mix_left in H; eauto. eapply All2_In_right in H; eauto. - destruct H as [[def [[Hty _] Hdef]]]. + destruct H as [[def [Hty Hdef]]]. eapply Hdef; eauto. - apply inversion_CoFix in wt as (?&?&?&?&?&?&?); eauto. diff --git a/pcuic/theories/PCUICAlpha.v b/pcuic/theories/PCUICAlpha.v index d2ead3eb2..d0161dca0 100644 --- a/pcuic/theories/PCUICAlpha.v +++ b/pcuic/theories/PCUICAlpha.v @@ -471,24 +471,21 @@ Section Alpha. destruct r as [[s [Hs IH]] [[[eqty eqann] eqbod] eqrarg]]. exists s; apply IH; eauto. * solve_all. - ** destruct a0 as [s [Hs IH]]. - specialize (IH _ a1). - specialize (b _ b3). - eapply context_conversion; eauto. - eapply (type_Cumul' (lift0 #|fix_context mfix| (dtype x))); auto. - exists s. rewrite <-H. - eapply (weakening _ _ _ _ (tSort _)); eauto. now eapply typing_wf_local in b. - apply cumul_refl. rewrite <- H. - eapply eq_term_upto_univ_lift. - eapply eq_term_upto_univ_empty_impl. - 4: intuition eauto. - all: intros ? ? []. - *** eapply eq_universe_refl. - *** eapply leq_universe_refl. - *** eapply leq_universe_refl. - ** eapply isLambda_eq_term_l. - --- eassumption. - --- intuition eauto. + destruct a0 as [s [Hs IH]]. + specialize (IH _ a). + specialize (b _ b2). + eapply context_conversion; eauto. + eapply (type_Cumul' (lift0 #|fix_context mfix| (dtype x))); auto. + exists s. rewrite <-H. + eapply (weakening _ _ _ _ (tSort _)); eauto. now eapply typing_wf_local in b. + apply cumul_refl. rewrite <- H. + eapply eq_term_upto_univ_lift. + eapply eq_term_upto_univ_empty_impl. + 4: intuition eauto. + all: intros ? ? []. + *** eapply eq_universe_refl. + *** eapply leq_universe_refl. + *** eapply leq_universe_refl. * revert wffix. unfold wf_fixpoint. enough (map check_one_fix mfix = map check_one_fix mfix') as ->; auto. diff --git a/pcuic/theories/PCUICInductiveInversion.v b/pcuic/theories/PCUICInductiveInversion.v index 34b790797..8a886151c 100644 --- a/pcuic/theories/PCUICInductiveInversion.v +++ b/pcuic/theories/PCUICInductiveInversion.v @@ -329,7 +329,7 @@ Proof. intros wfΣ H. depind H. - unfold unfold_fix. rewrite e. specialize (nth_error_all e a0) as [s Hs]. - specialize (nth_error_all e a1) as [Hty Hlam]. + specialize (nth_error_all e a1) as Hty. simpl. destruct decl as [name ty body rarg]; simpl in *. clear e. @@ -359,7 +359,7 @@ Proof. apply IHAll. --- intros. simpl in Hi. specialize (Hi (S i)). apply Hi. lia. --- lia. - ** clear IHAll. destruct p. + ** clear IHAll. simpl in Hlen. assert ((Nat.pred #|mfix| - (#|mfix| - S #|l|)) = #|l|) by lia. rewrite H0. rewrite simpl_subst_k. --- clear. induction l; simpl; auto with arith. diff --git a/pcuic/theories/PCUICInversion.v b/pcuic/theories/PCUICInversion.v index 8044a4e00..089f47d55 100644 --- a/pcuic/theories/PCUICInversion.v +++ b/pcuic/theories/PCUICInversion.v @@ -213,9 +213,7 @@ Section Inversion. nth_error mfix n = Some decl × All (fun d => isType Σ Γ (dtype d)) mfix × All (fun d => - Σ ;;; Γ ,,, types |- dbody d : (lift0 #|types|) (dtype d) × - isLambda (dbody d) = true - ) mfix × + Σ ;;; Γ ,,, types |- dbody d : (lift0 #|types|) (dtype d)) mfix × wf_fixpoint Σ mfix × Σ ;;; Γ |- dtype decl <= T. Proof. diff --git a/pcuic/theories/PCUICSR.v b/pcuic/theories/PCUICSR.v index c65ea3e01..b2e62e973 100644 --- a/pcuic/theories/PCUICSR.v +++ b/pcuic/theories/PCUICSR.v @@ -1157,12 +1157,11 @@ Proof. constructor; eauto. * eapply (OnOne2_All_mix_left X0) in o. apply (OnOne2_All_All o X1). - + intros x [[Hb Hlam] IH]. - split; auto. + + intros x [Hb IH]. eapply context_conversion; eauto. now rewrite -fixl. - + move=> [na ty b rarg] [na' ty' b' rarg'] /= [[red eq] [s [Hs IH]]] [[Hb Hlam] IH']. - noconf eq. split; auto. + + move=> [na ty b rarg] [na' ty' b' rarg'] /= [[red eq] [s [Hs IH]]] [Hb IH']. + noconf eq. eapply context_conversion; eauto. rewrite -fixl. eapply type_Cumul'. eapply Hb. @@ -1205,15 +1204,13 @@ Proof. apply fix_red_body; eauto. * eapply (OnOne2_All_mix_left X0) in o. apply (OnOne2_All_All o X1). - + intros x [[Hb Hlam] IH]. - split; auto. + + intros x [Hb IH]. eapply context_conversion; eauto. now rewrite -fixl. rewrite convctx. apply conv_ctx_refl. - + move=> [na ty b rarg] [na' ty' b' rarg'] /= [[red eq] [s [Hs IH]]] [[Hb Hlam] IH']. + + move=> [na ty b rarg] [na' ty' b' rarg'] /= [[red eq] [s [Hs IH]]] [Hb IH']. noconf eq. - rewrite -convctx. split; auto. - now eapply isLambda_red1. + now rewrite -convctx. * eapply wf_fixpoint_red1_body; eauto. * eapply All_nth_error in X2; eauto. * apply conv_cumul, conv_sym, red_conv. destruct disj as [<-|[_ eq]]. diff --git a/pcuic/theories/TemplateToPCUICCorrectness.v b/pcuic/theories/TemplateToPCUICCorrectness.v index 310bbcd6d..53e0a3536 100644 --- a/pcuic/theories/TemplateToPCUICCorrectness.v +++ b/pcuic/theories/TemplateToPCUICCorrectness.v @@ -1,5 +1,6 @@ (* Distributed under the terms of the MIT license. *) From MetaCoq.Template Require Import config utils Ast TypingWf WfInv. +From MetaCoq.Template Require TermEquality. Set Warnings "-notation-overridden". From MetaCoq.PCUIC Require Import PCUICAst PCUICAstUtils PCUICCumulativity PCUICLiftSubst PCUICEquality PCUICUnivSubst PCUICTyping TemplateToPCUIC @@ -7,10 +8,10 @@ From MetaCoq.PCUIC Require Import PCUICAst PCUICAstUtils PCUICCumulativity Set Warnings "+notation-overridden". From Equations.Prop Require Import DepElim. - Implicit Types cf : checker_flags. Module T := Template.Ast. +Module TEq := Template.TermEquality. Module TTy := Template.Typing. Module TEnv := Template.Ast.TemplateEnvironment. @@ -518,7 +519,7 @@ Proof. rewrite mkApps_app. simpl. reflexivity. Qed. -Derive Signature for TTy.eq_term_upto_univ. +Derive Signature for TEq.eq_term_upto_univ_napp. Lemma leq_term_mkApps {cf} Σ ϕ t u t' u' : eq_term Σ ϕ t t' -> All2 (eq_term Σ ϕ) u u' -> @@ -563,38 +564,78 @@ Proof. * assumption. Qed. +Lemma trans_lookup Σ cst : + lookup_env (trans_global_decls Σ) cst = option_map trans_global_decl (Ast.lookup_env Σ cst). +Proof. + cbn in *. + induction Σ. + - reflexivity. + - cbn. + unfold eq_kername in *; destruct kername_eq_dec; subst. + + destruct a; auto. + + now rewrite IHΣ. +Qed. + +Lemma trans_R_global_instance {cf} Σ Re Rle gref napp u u' : + TTy.on_global_env (fun Σ => wf_decl_pred) Σ -> + TEq.R_global_instance Σ Re Rle gref napp u u' -> + R_global_instance (trans_global_decls Σ) Re Rle gref napp u u'. +Proof. + intros wfe. + unfold PCUICEquality.R_global_instance, PCUICEquality.global_variance. + unfold TEq.R_global_instance, TEq.global_variance. + destruct gref; simpl; auto. + - unfold PCUICEquality.lookup_inductive, PCUICEquality.lookup_minductive. + unfold TEq.lookup_inductive, TEq.lookup_minductive. + rewrite trans_lookup. destruct Ast.lookup_env => //; simpl. + destruct g => /= //. rewrite nth_error_map. + destruct nth_error => /= //. + move: (trans_destArity [] (Ast.ind_type o)). + destruct TTy.destArity as [[ctx ps]|] => /= //. + admit. admit. + (* now rewrite context_assumptions_map. *) + - unfold PCUICEquality.lookup_constructor, PCUICEquality.lookup_inductive, PCUICEquality.lookup_minductive. + unfold TEq.lookup_constructor, TEq.lookup_inductive, TEq.lookup_minductive. + rewrite trans_lookup. destruct Ast.lookup_env => //; simpl. + destruct g => /= //. rewrite nth_error_map. + destruct nth_error => /= //. + rewrite nth_error_map. + destruct nth_error => /= //. + destruct p as [[id t] nargs]; simpl. + destruct Nat.leb => //. +Admitted. + + (* TODO update Template Coq's eq_term to reflect PCUIC's cumulativity *) Lemma trans_eq_term_upto_univ {cf} : forall Σ Re Rle t u napp, - T.wf t -> + TTy.on_global_env (fun Σ => wf_decl_pred) Σ -> + T.wf t -> T.wf u -> - TTy.eq_term_upto_univ Re Rle t u -> - eq_term_upto_univ_napp Σ Re Rle napp (trans t) (trans u). + TEq.eq_term_upto_univ_napp Σ Re Rle napp t u -> + eq_term_upto_univ_napp (trans_global_decls Σ) Re Rle napp (trans t) (trans u). Proof. -Admitted. -(* intros Σ Re Rle t u napp wt wu e. + intros Σ Re Rle t u napp wfΣ wt wu e. induction t using Induction.term_forall_list_rect in Rle, napp, wt, u, wu, e |- *. all: invs e; cbn. all: try solve [ constructor ; auto ]. + all: repeat (match goal with + | H : T.wf (_ _) |- _ => apply wf_inv in H; simpl in H + | H : _ /\ _ |- _ => destruct H + end). all: try solve [ - repeat constructor ; + repeat constructor ; auto ; match goal with | ih : forall Rle (u : Tterm) (napp : nat), _ |- _ => - eapply ih ; [ - inversion wt ; assumption - | inversion wu ; assumption - | assumption - ] + eapply ih ; eauto end ]. - constructor. - assert (w1 : All T.wf l). - { eapply Forall_All. inversion wt. assumption. } - assert (w2 : All T.wf args'). - { eapply Forall_All. inversion wu. assumption. } + apply Forall_All in wt. + apply Forall_All in wu. pose proof (All2_All_mix_left X X0) as h1. simpl in h1. - pose proof (All2_All_mix_left w1 h1) as h2. - pose proof (All2_All_mix_right w2 h2) as h3. + pose proof (All2_All_mix_left wt h1) as h2. + pose proof (All2_All_mix_right wu h2) as h3. simpl in h3. eapply All2_map. eapply All2_impl. 1: exact h3. @@ -602,43 +643,33 @@ Admitted. intros ? ? [[? [ih ?]] ?]. simpl in *. eapply ih. all: auto. - -s apply eq_term_eq_term_napp. - + eapply IHt. - * inversion wt. assumption. - * inversion wu. assumption. - * assumption. + - repeat constructor. + eapply eq_term_upto_univ_impl. 5:eauto. all:try typeclasses eauto. auto. + todo "update template". + - eapply eq_term_upto_univ_napp_mkApps. + + rewrite map_length. now eapply IHt. + pose proof (All2_All_mix_left X X1) as h. simpl in h. - assert (wl : Forall T.wf l). - { inversion wt. assumption. } - assert (wargs' : Forall T.wf args'). - { inversion wu. assumption. } - apply Forall_All in wl. - apply Forall_All in wargs'. - pose proof (All2_All_mix_left wl h) as h1. - pose proof (All2_All_mix_right wargs' h1) as h2. + apply Forall_All in H6. + apply Forall_All in H2. + pose proof (All2_All_mix_left H6 h) as h1. + pose proof (All2_All_mix_right H2 h1) as h2. simpl in h2. eapply All2_map. eapply All2_impl. 1: exact h2. simpl. intros u v [[? [ih ?]] ?]. eapply ih. all: auto. - - constructor. todounivs. - - constructor. todounivs. + - constructor. apply trans_R_global_instance; auto. + - constructor. apply trans_R_global_instance; auto. - constructor. all: try solve [ match goal with | ih : forall Rle u, _ |- _ => - eapply ih ; [ - inversion wt ; assumption - | inversion wu ; assumption - | assumption - ] + eapply ih ; auto end ]. - assert (wl : All (T.wf ∘ snd) l). - { eapply Forall_All. inversion wt. assumption. } - assert (wbrs' : All (T.wf ∘ snd) brs'). - { eapply Forall_All. inversion wu. assumption. } + assert (wl : All (T.wf ∘ snd) l) by solve_all. + assert (wbrs' : All (T.wf ∘ snd) brs') by solve_all. pose proof (All2_All_mix_left X X2) as h1. simpl in h1. pose proof (All2_All_mix_left wl h1) as h2. pose proof (All2_All_mix_right wbrs' h2) as h3. @@ -653,20 +684,17 @@ Admitted. w1 : All (fun def => T.wf (dtype def) /\ - T.wf (dbody def) /\ - T.isLambda (dbody def) = true + T.wf (dbody def) ) m ). - { eapply Forall_All. inversion wt. assumption. } + { solve_all. } assert ( w2 : All (fun def => T.wf (dtype def) /\ - T.wf (dbody def) /\ - T.isLambda (dbody def) = true - ) mfix' + T.wf (dbody def)) mfix' ). - { eapply Forall_All. inversion wu. assumption. } + { solve_all. } pose proof (All2_All_mix_left X X0) as h1. simpl in h1. pose proof (All2_All_mix_left w1 h1) as h2. pose proof (All2_All_mix_right w2 h2) as h3. @@ -674,7 +702,7 @@ Admitted. eapply All2_map. eapply All2_impl. 1: exact h3. simpl. - intros [? ? ? ?] [? ? ? ?] [[[? [? ?]] [[ih1 ih2] [? [? ?]]]] [? [? ?]]]. + intros [? ? ? ?] [? ? ? ?] [[[? ?] [[ih1 ih2] [? ?]]] [? ?]]. simpl in *. intuition eauto. - constructor. @@ -682,12 +710,12 @@ Admitted. w1 : All (fun def => T.wf (dtype def) /\ T.wf (dbody def)) m ). - { eapply Forall_All. inversion wt. assumption. } + { by eapply Forall_All. } assert ( w2 : All (fun def => T.wf (dtype def) /\ T.wf (dbody def)) mfix' ). - { eapply Forall_All. inversion wu. assumption. } + { by eapply Forall_All. } pose proof (All2_All_mix_left X X0) as h1. simpl in h1. pose proof (All2_All_mix_left w1 h1) as h2. pose proof (All2_All_mix_right w2 h2) as h3. @@ -695,22 +723,24 @@ Admitted. eapply All2_map. eapply All2_impl. 1: exact h3. simpl. - intros [? ? ? ?] [? ? ? ?] [[[? ?] [[ih1 ih2] [? [? ?]]]] [? ?]]. + intros [? ? ? ?] [? ? ? ?] [[[? ?] [[ih1 ih2] [? ?]]] [? ?]]. simpl in *. intuition eauto. -Qed. *) +Qed. Lemma trans_leq_term {cf} Σ ϕ T U : - T.wf T -> T.wf U -> TTy.leq_term Σ ϕ T U -> - leq_term Σ ϕ (trans T) (trans U). + TTy.on_global_env (fun Σ => wf_decl_pred) Σ -> + T.wf T -> T.wf U -> TEq.leq_term Σ ϕ T U -> + leq_term (trans_global_decls Σ) ϕ (trans T) (trans U). Proof. intros HT HU H. eapply trans_eq_term_upto_univ ; eauto. Qed. Lemma trans_eq_term {cf} Σ φ t u : - T.wf t -> T.wf u -> TTy.eq_term φ t u -> - eq_term Σ φ (trans t) (trans u). + TTy.on_global_env (fun Σ => wf_decl_pred) Σ -> + T.wf t -> T.wf u -> TEq.eq_term Σ φ t u -> + eq_term (trans_global_decls Σ) φ (trans t) (trans u). Proof. intros HT HU H. eapply trans_eq_term_upto_univ ; eauto. @@ -718,12 +748,13 @@ Qed. Lemma trans_eq_term_list {cf}: forall Σ φ l l', + TTy.on_global_env (fun Σ => wf_decl_pred) Σ -> List.Forall T.wf l -> List.Forall T.wf l' -> - All2 (TTy.eq_term φ) l l' -> - All2 (eq_term Σ φ) (List.map trans l) (List.map trans l'). + All2 (TEq.eq_term Σ φ) l l' -> + All2 (eq_term (trans_global_decls Σ) φ) (List.map trans l) (List.map trans l'). Proof. - intros Σ φ l l' w w' h. + intros Σ φ l l' wfΣ w w' h. eapply All2_map. apply Forall_All in w. apply Forall_All in w'. pose proof (All2_All_mix_left w h) as h1. @@ -773,15 +804,13 @@ Proof. Qed. Lemma trans_unfold_fix mfix idx narg fn : - List.Forall (fun def : def Tterm => T.wf (dtype def) /\ T.wf (dbody def) /\ - T.isLambda (dbody def) = true) mfix -> + List.Forall (fun def : def Tterm => T.wf (dtype def) /\ T.wf (dbody def)) mfix -> TTy.unfold_fix mfix idx = Some (narg, fn) -> unfold_fix (map (map_def trans trans) mfix) idx = Some (narg, trans fn). Proof. unfold TTy.unfold_fix, unfold_fix. intros wffix. rewrite nth_error_map. destruct (nth_error mfix idx) eqn:Hdef => //. cbn. - destruct (Ast.isLambda (dbody d)); [|discriminate]. intros [= <- <-]. simpl. repeat f_equal. rewrite trans_subst. @@ -863,8 +892,9 @@ Proof. - rewrite trans_mkApps; eauto with wf; simpl. erewrite trans_iota_red; eauto. repeat constructor. - - simpl. eapply red_fix. wf_inv H3. - now apply trans_unfold_fix; eauto. + - simpl. rewrite trans_mkApps. + eapply red_fix. wf_inv H3. + apply trans_unfold_fix; eauto. now apply trans_is_constructor. - apply wf_mkApps_napp in H1; auto. @@ -1117,13 +1147,13 @@ Qed. Axiom fix_guard_trans : forall Σ Γ mfix, - TTy.fix_guard mfix -> - fix_guard Σ Γ (map (map_def trans trans) mfix). + TTy.fix_guard Σ Γ mfix -> + fix_guard (trans_global Σ) (trans_local Γ) (map (map_def trans trans) mfix). Axiom cofix_guard_trans : forall Σ Γ mfix, - TTy.cofix_guard mfix -> - cofix_guard Σ Γ (map (map_def trans trans) mfix). + TTy.cofix_guard Σ Γ mfix -> + cofix_guard (trans_global Σ) (trans_local Γ) (map (map_def trans trans) mfix). Lemma trans_global_decl_universes d : TTy.universes_decl_of_decl d = @@ -1248,6 +1278,7 @@ Proof. -- apply trans_build_branches_type in H3. rewrite firstn_map. exact H3. -- eapply All2_map. solve_all. + destruct b0 as [s [Hs IHs]]; eauto. - destruct pdecl as [arity ty]; simpl in *. pose proof (TypingWf.declared_projection_wf _ _ _ _ _ isdecl). @@ -1280,7 +1311,6 @@ Proof. rewrite H2. rewrite /trans_local map_length. rewrite /trans_local map_app in X3. rewrite <- trans_lift. apply X3; auto. - rdest. destruct (dbody x); simpl in *; congruence. -- todo "wffix". -- destruct decl; reflexivity. @@ -1292,14 +1322,14 @@ Proof. f_equal. apply mapi_ext => i x. simpl. rewrite trans_lift. reflexivity. } econstructor; eauto. - -- eapply cofix_guard_trans. - -- now rewrite nth_error_map H. + -- now eapply cofix_guard_trans. + -- now rewrite nth_error_map H0. -- eapply trans_wf_local; eauto. -- eapply All_map, (All_impl X0). intros x [s [Hs Hts]]. now exists s. -- apply All_map. eapply All_impl; eauto. intuition eauto 3 with wf. - rewrite H1. rewrite /trans_local map_length. + rewrite H2. rewrite /trans_local map_length. unfold Template.Ast.app_context in X3. rewrite /trans_local map_app in X3. cbn. rewrite <- trans_lift. now apply X3. diff --git a/safechecker/theories/PCUICTypeChecker.v b/safechecker/theories/PCUICTypeChecker.v index 3a8a94876..2ce20f41c 100644 --- a/safechecker/theories/PCUICTypeChecker.v +++ b/safechecker/theories/PCUICTypeChecker.v @@ -406,17 +406,14 @@ Section Typecheck. (XX : ∥ All (fun x => isType Σ Γ (dtype x)) mfix' ∥) {struct mfix'} : typing_result (All (fun d => - ∥ Σ ;;; Γ ,,, fix_context mfix |- dbody d : (lift0 #|fix_context mfix|) (dtype d) ∥ - /\ isLambda (dbody d) = true) mfix') + ∥ Σ ;;; Γ ,,, fix_context mfix |- dbody d : (lift0 #|fix_context mfix|) (dtype d) ∥) mfix') := match mfix' with | [] => ret All_nil | def :: mfix' => W1 <- infer_cumul infer (Γ ,,, fix_context mfix) _ (dbody def) (lift0 #|fix_context mfix| (dtype def)) _ ;; - W2 <- check_eq_true (isLambda (dbody def)) - (Msg "not a lambda") ;; Z <- check_bodies mfix' _ ;; - ret (All_cons (conj W1 W2) Z) + ret (All_cons W1 Z) end) mfix _ ;; guarded <- check_eq_true (fix_guard Σ Γ mfix) (Msg "Unguarded fixpoint") ;; wffix <- check_eq_true (wf_fixpoint Σ.1 mfix) (Msg "Ill-formed fixpoint: not defined on a mutually inductive family") ;; @@ -680,9 +677,9 @@ Section Typecheck. now depelim XX. Qed. Next Obligation. - assert (∥ All (fun d => ((Σ;;; Γ ,,, fix_context mfix |- dbody d : (lift0 #|fix_context mfix|) (dtype d)) * (isLambda (dbody d) = true))%type) mfix ∥). { + assert (∥ All (fun d => ((Σ;;; Γ ,,, fix_context mfix |- dbody d : (lift0 #|fix_context mfix|) (dtype d)))%type) mfix ∥). { eapply All_sq, All_impl. exact YY. - cbn; intros ? []. sq; now constructor. } + cbn; intros ? ?. now sq. } sq; econstructor; try eassumption. symmetry; eassumption. Qed. diff --git a/template-coq/theories/TermEquality.v b/template-coq/theories/TermEquality.v index 23cbcd7e9..a734fb670 100644 --- a/template-coq/theories/TermEquality.v +++ b/template-coq/theories/TermEquality.v @@ -208,7 +208,7 @@ Inductive eq_term_upto_univ_napp Σ (Re Rle : Universe.t -> Universe.t -> Prop) eq_term_upto_univ_napp Σ Re Rle napp (tCoFix mfix idx) (tCoFix mfix' idx) | eq_Cast t1 c t2 t1' c' t2' : - eq_term_upto_univ_napp Σ Re Rle napp t1 t1' -> + eq_term_upto_univ_napp Σ Re Re napp t1 t1' -> eq_cast_kind c c' -> eq_term_upto_univ_napp Σ Re Re 0 t2 t2' -> eq_term_upto_univ_napp Σ Re Rle napp (tCast t1 c t2) (tCast t1' c' t2') diff --git a/template-coq/theories/Typing.v b/template-coq/theories/Typing.v index 34f240247..c1bfbe212 100644 --- a/template-coq/theories/Typing.v +++ b/template-coq/theories/Typing.v @@ -449,15 +449,6 @@ Definition leq_term_nocast `{checker_flags} (Σ : global_env) (φ : ConstraintSe (** Decompose an arity into a context and a sort *) -Fixpoint destArity Γ (t : term) := - match t with - | tProd na t b => destArity (Γ ,, vass na t) b - | tLetIn na b b_ty b' => destArity (Γ ,, vdef na b b_ty) b' - | tSort s => Some (Γ, s) - | _ => None - end. - - Reserved Notation " Σ ;;; Γ |- t : T " (at level 50, Γ, t, T at next level). Reserved Notation " Σ ;;; Γ |- t <= u " (at level 50, Γ, t, u at next level). Reserved Notation " Σ ;;; Γ |- t = u " (at level 50, Γ, t, u at next level). From bf81d71df6f61d57d6ec98196938fee823f8492b Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Thu, 10 Dec 2020 03:55:52 +0100 Subject: [PATCH 52/70] Move destArity to AstUtils --- pcuic/theories/PCUICToTemplateCorrectness.v | 6 +++--- pcuic/theories/TemplateToPCUICCorrectness.v | 4 ++-- template-coq/theories/AstUtils.v | 10 +++++++++- template-coq/theories/TermEquality.v | 7 ------- 4 files changed, 14 insertions(+), 13 deletions(-) diff --git a/pcuic/theories/PCUICToTemplateCorrectness.v b/pcuic/theories/PCUICToTemplateCorrectness.v index 09dbf85fa..3ec96d17f 100644 --- a/pcuic/theories/PCUICToTemplateCorrectness.v +++ b/pcuic/theories/PCUICToTemplateCorrectness.v @@ -528,8 +528,8 @@ Proof. Qed. Lemma trans_destr_arity x: -TT.destArity [] (trans x) -= option_map (fun '(xs,u) => (map trans_decl xs,u)) (PCUICAstUtils.destArity [] x). + AstUtils.destArity [] (trans x) + = option_map (fun '(xs,u) => (map trans_decl xs,u)) (PCUICAstUtils.destArity [] x). Proof. remember (@nil PCUICAst.context_decl) as xs. replace (@nil context_decl) with (map trans_decl xs) by (now subst). @@ -777,7 +777,7 @@ Proof. rewrite trans_lookup. destruct PCUICAst.lookup_env => //; simpl. destruct g => /= //. rewrite nth_error_map. destruct nth_error => /= //. - rewrite [destArity _ _]trans_destr_arity. + rewrite trans_destr_arity. destruct PCUICAstUtils.destArity as [[ctx ps]|] => /= //. now rewrite context_assumptions_map. - unfold PCUICEquality.lookup_constructor, PCUICEquality.lookup_inductive, PCUICEquality.lookup_minductive. diff --git a/pcuic/theories/TemplateToPCUICCorrectness.v b/pcuic/theories/TemplateToPCUICCorrectness.v index 53e0a3536..4661dc603 100644 --- a/pcuic/theories/TemplateToPCUICCorrectness.v +++ b/pcuic/theories/TemplateToPCUICCorrectness.v @@ -175,7 +175,7 @@ Qed. Lemma trans_destArity ctx t : T.wf t -> - match TTy.destArity ctx t with + match AstUtils.destArity ctx t with | Some (args, s) => destArity (trans_local ctx) (trans t) = Some (trans_local args, s) @@ -591,7 +591,7 @@ Proof. destruct g => /= //. rewrite nth_error_map. destruct nth_error => /= //. move: (trans_destArity [] (Ast.ind_type o)). - destruct TTy.destArity as [[ctx ps]|] => /= //. + destruct AstUtils.destArity as [[ctx ps]|] => /= //. admit. admit. (* now rewrite context_assumptions_map. *) - unfold PCUICEquality.lookup_constructor, PCUICEquality.lookup_inductive, PCUICEquality.lookup_minductive. diff --git a/template-coq/theories/AstUtils.v b/template-coq/theories/AstUtils.v index 5200f8ff7..317745221 100644 --- a/template-coq/theories/AstUtils.v +++ b/template-coq/theories/AstUtils.v @@ -55,7 +55,15 @@ Fixpoint string_of_term (t : term) := | tInt i => "Int(" ^ string_of_prim_int i ^ ")" | tFloat f => "Float(" ^ string_of_float f ^ ")" end. - + +Fixpoint destArity Γ (t : term) := + match t with + | tProd na t b => destArity (Γ ,, vass na t) b + | tLetIn na b b_ty b' => destArity (Γ ,, vdef na b b_ty) b' + | tSort s => Some (Γ, s) + | _ => None + end. + Definition decompose_app (t : term) := match t with | tApp f l => (f, l) diff --git a/template-coq/theories/TermEquality.v b/template-coq/theories/TermEquality.v index a734fb670..00b539216 100644 --- a/template-coq/theories/TermEquality.v +++ b/template-coq/theories/TermEquality.v @@ -63,13 +63,6 @@ Definition lookup_constructor Σ ind k := | _ => None end. -Fixpoint destArity Γ (t : term) := - match t with - | tProd na t b => destArity (Γ ,, vass na t) b - | tLetIn na b b_ty b' => destArity (Γ ,, vdef na b b_ty) b' - | tSort s => Some (Γ, s) - | _ => None - end. Definition global_variance Σ gr napp := match gr with | IndRef ind => From 80eb0fe8327ec6b44f81894447f2d3439aa16695 Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Thu, 10 Dec 2020 04:02:44 +0100 Subject: [PATCH 53/70] PCUIC -> Template relies on Substitution from the Checker --- Makefile | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Makefile b/Makefile index f69fca98e..d0caaa1e6 100644 --- a/Makefile +++ b/Makefile @@ -60,7 +60,7 @@ mrproper: template-coq: $(MAKE) -C template-coq -pcuic: template-coq +pcuic: template-coq checker $(MAKE) -C pcuic safechecker: template-coq pcuic From 054a3d72b0edf67d43d80d88751c51d40dd79106 Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Thu, 10 Dec 2020 10:54:14 +0100 Subject: [PATCH 54/70] Fix imports --- examples/metacoq_tour_prelude.v | 2 +- examples/typing_correctness.v | 3 +-- 2 files changed, 2 insertions(+), 3 deletions(-) diff --git a/examples/metacoq_tour_prelude.v b/examples/metacoq_tour_prelude.v index 14a04e9b2..a4083e74e 100644 --- a/examples/metacoq_tour_prelude.v +++ b/examples/metacoq_tour_prelude.v @@ -1,5 +1,5 @@ (* Distributed under the terms of the MIT license. *) -From MetaCoq.Template Require Import config Universes All. +From MetaCoq.Template Require Import config Universes Loader. From MetaCoq.PCUIC Require Import PCUICAst PCUICAstUtils PCUICTyping PCUICLiftSubst. From MetaCoq.SafeChecker Require Import PCUICErrors PCUICTypeChecker PCUICSafeChecker. From Equations Require Import Equations. diff --git a/examples/typing_correctness.v b/examples/typing_correctness.v index c14492b2b..e48d11e25 100644 --- a/examples/typing_correctness.v +++ b/examples/typing_correctness.v @@ -1,9 +1,8 @@ (* Distributed under the terms of the MIT license. *) -From MetaCoq.Template Require Import config Universes All. +From MetaCoq.Template Require Import config Universes Loader. From MetaCoq.PCUIC Require Import PCUICAst PCUICAstUtils PCUICTyping PCUICLiftSubst. From MetaCoq.SafeChecker Require Import PCUICErrors PCUICTypeChecker PCUICSafeChecker. From Equations Require Import Equations. - Existing Instance default_checker_flags. (* ********************************************************* *) From 0500201f7f3d8b1c08d849f9adabff91f14516c5 Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Thu, 10 Dec 2020 12:01:59 +0100 Subject: [PATCH 55/70] Cleanup dependencies, PCUIC -> Template does not need substitution --- Makefile | 2 +- checker/theories/Substitution.v | 158 +------------------- pcuic/theories/PCUICToTemplateCorrectness.v | 3 +- template-coq/_CoqProject | 1 + template-coq/theories/LiftSubst.v | 22 ++- template-coq/theories/Reduction.v | 77 ++++++++++ template-coq/theories/TermEquality.v | 66 ++++++++ template-coq/theories/TypingWf.v | 11 +- 8 files changed, 165 insertions(+), 175 deletions(-) create mode 100644 template-coq/theories/Reduction.v diff --git a/Makefile b/Makefile index d0caaa1e6..f69fca98e 100644 --- a/Makefile +++ b/Makefile @@ -60,7 +60,7 @@ mrproper: template-coq: $(MAKE) -C template-coq -pcuic: template-coq checker +pcuic: template-coq $(MAKE) -C pcuic safechecker: template-coq pcuic diff --git a/checker/theories/Substitution.v b/checker/theories/Substitution.v index 41be803e5..f2fd84fd8 100644 --- a/checker/theories/Substitution.v +++ b/checker/theories/Substitution.v @@ -1,6 +1,6 @@ (* Distributed under the terms of the MIT license. *) From MetaCoq.Template Require Import config utils Ast AstUtils Induction LiftSubst - UnivSubst TermEquality Typing TypingWf. + UnivSubst TermEquality Typing Reduction TypingWf. From MetaCoq.Checker Require Import Generation Closed WeakeningEnv Weakening. From Equations Require Import Equations. @@ -13,11 +13,6 @@ Generalizable Variables Σ Γ t T. Derive Signature for Ast.wf. -Definition subst_decl s k (d : context_decl) := map_decl (subst s k) d. - -Definition subst_context n k (Γ : context) : context := - fold_context (fun k' => subst n (k' + k)) Γ. - (** Well-typed substitution into a context with *no* let-ins *) Inductive subs `{cf : checker_flags} Σ (Γ : context) : list term -> context -> Type := @@ -82,20 +77,7 @@ Proof. unfold fold_context. now rewrite !List.rev_length mapi_length List.rev_length. Qed. -Lemma subst_context_length s k Γ : #|subst_context s k Γ| = #|Γ|. -Proof. - unfold subst_context. apply fold_context_length. -Qed. Hint Rewrite subst_context_length : subst. - -Lemma subst_context_snoc s k Γ d : subst_context s k (d :: Γ) = subst_context s k Γ ,, subst_decl s (#|Γ| + k) d. -Proof. - unfold subst_context, fold_context. - rewrite !rev_mapi !rev_involutive /mapi mapi_rec_eqn /snoc. - f_equal. now rewrite Nat.sub_0_r List.rev_length. - rewrite mapi_rec_Sk. simpl. apply mapi_rec_ext. intros. - rewrite app_length !List.rev_length. simpl. f_equal. f_equal. lia. -Qed. Hint Rewrite subst_context_snoc : subst. Lemma subst_context_snoc0 s Γ d : subst_context s 0 (Γ ,, d) = subst_context s 0 Γ ,, subst_decl s #|Γ| d. @@ -135,7 +117,7 @@ Proof. unfold closed_ctx, id. intros wfctx. inv wfctx. rewrite mapi_app forallb_app List.rev_length /= Nat.add_0_r. move/andb_and => /= [Hctx /andb_and [Ha _]]. - rewrite subst_context_snoc /snoc /= IHctx // subst_decl_closed //. + rewrite subst_context_snoc /snoc /= IHctx // /map_decl subst_decl_closed //. now apply: closed_decl_upwards. Qed. @@ -1313,77 +1295,6 @@ Proof. - apply IHX. Qed. -Lemma red1_tApp_mkApps_l Σ Γ M1 N1 M2 : - red1 Σ Γ M1 N1 -> red1 Σ Γ (tApp M1 M2) (mkApps N1 M2). -Proof. constructor. auto. Qed. - -Lemma red1_tApp_mkApp Σ Γ M1 N1 M2 : - red1 Σ Γ M1 N1 -> red1 Σ Γ (tApp M1 [M2]) (mkApp N1 M2). -Proof. - intros. - change (mkApp N1 M2) with (mkApps N1 [M2]). - apply app_red_l. auto. -Qed. - -Lemma red1_mkApp Σ Γ M1 N1 M2 : - Ast.wf M1 -> - red1 Σ Γ M1 N1 -> red1 Σ Γ (mkApp M1 M2) (mkApp N1 M2). -Proof. - intros wfM1 H. - destruct (isApp M1) eqn:Heq. - destruct M1; try discriminate. simpl. - revert wfM1. inv H. simpl. intros. - rewrite mkApp_mkApps. constructor. - - intros. - rewrite mkApp_mkApps. - econstructor; eauto. - inv wfM1. simpl. - clear -H1. - unfold is_constructor in *. - destruct (nth_error args narg) eqn:Heq. - eapply nth_error_app_left in Heq. now rewrite -> Heq. discriminate. - - intros. rewrite mkApp_mkApps. now constructor. - - intros. simpl. - constructor. clear -X. induction X; constructor; auto. - - rewrite mkApp_tApp; auto. - now apply red1_tApp_mkApp. -Qed. - -Lemma red1_mkApps_l Σ Γ M1 N1 M2 : - Ast.wf M1 -> All Ast.wf M2 -> - red1 Σ Γ M1 N1 -> red1 Σ Γ (mkApps M1 M2) (mkApps N1 M2). -Proof. - induction M2 in M1, N1 |- *. simpl; auto. - intros. specialize (IHM2 (mkApp M1 a) (mkApp N1 a)). - inv X. - forward IHM2. apply wf_mkApp; auto. - forward IHM2. auto. - rewrite <- !mkApps_mkApp; auto. - apply IHM2. - apply red1_mkApp; auto. -Qed. - -Lemma red1_mkApps_r Σ Γ M1 M2 N2 : - Ast.wf M1 -> All Ast.wf M2 -> - OnOne2 (red1 Σ Γ) M2 N2 -> red1 Σ Γ (mkApps M1 M2) (mkApps M1 N2). -Proof. - intros. induction X0 in M1, H, X |- *. - inv X. - destruct (isApp M1) eqn:Heq. destruct M1; try discriminate. - simpl. constructor. apply OnOne2_app. constructor. auto. - rewrite mkApps_tApp; try congruence. - rewrite mkApps_tApp; try congruence. - constructor. constructor. auto. - inv X. - specialize (IHX0 (mkApp M1 hd)). forward IHX0. - apply wf_mkApp; auto. forward IHX0; auto. - now rewrite !mkApps_mkApp in IHX0. -Qed. - Lemma wf_fix : forall (mfix : list (def term)) (k : nat), Ast.wf (tFix mfix k) -> Forall @@ -1580,71 +1491,6 @@ Proof. + inversion b0. auto. Qed. -Lemma eq_term_leq_term `{checker_flags} Σ φ t u : - eq_term Σ φ t u -> leq_term Σ φ t u. -Proof. - eapply eq_term_upto_univ_morphism. auto. - intros. - now apply eq_universe_leq_universe. -Qed. - -Lemma eq_term_upto_univ_App `{checker_flags} Σ Re Rle napp f f' : - eq_term_upto_univ_napp Σ Re Rle napp f f' -> - isApp f = isApp f'. -Proof. - inversion 1; reflexivity. -Qed. - -Lemma eq_term_App `{checker_flags} Σ φ f f' : - eq_term Σ φ f f' -> - isApp f = isApp f'. -Proof. - inversion 1; reflexivity. -Qed. - -Lemma eq_term_upto_univ_mkApps `{checker_flags} Σ Re Rle napp f l f' l' : - eq_term_upto_univ_napp Σ Re Rle (#|l| + napp) f f' -> - All2 (eq_term_upto_univ Σ Re Re) l l' -> - eq_term_upto_univ_napp Σ Re Rle napp (mkApps f l) (mkApps f' l'). -Proof. - induction l in f, f' |- *; intro e; inversion_clear 1. - - assumption. - - pose proof (eq_term_upto_univ_App _ _ _ _ _ _ e). - case_eq (isApp f). - + intro X; rewrite X in H0. - destruct f; try discriminate. - destruct f'; try discriminate. - cbn. inversion_clear e. constructor. - rewrite app_length /= -Nat.add_assoc //. - apply All2_app. assumption. - now constructor. - + intro X; rewrite X in H0. - rewrite !mkApps_tApp; eauto. - intro; discriminate. - intro; discriminate. - constructor. simpl. now simpl in e. - now constructor. -Qed. - -Lemma leq_term_mkApps `{checker_flags} Σ φ f l f' l' : - leq_term Σ φ f f' -> - All2 (eq_term Σ φ) l l' -> - leq_term Σ φ (mkApps f l) (mkApps f' l'). -Proof. - intros. - eapply eq_term_upto_univ_mkApps. - eapply eq_term_upto_univ_impl. 5:eauto. 4:auto with arith. - 1-3:typeclasses eauto. - apply X0. -Qed. - -Lemma leq_term_App `{checker_flags} Σ φ f f' : - leq_term Σ φ f f' -> - isApp f = isApp f'. -Proof. - inversion 1; reflexivity. -Qed. - Lemma subst_eq_term_upto_univ `{checker_flags} Σ Re Rle napp n k T U : RelationClasses.Reflexive Re -> RelationClasses.Reflexive Rle -> diff --git a/pcuic/theories/PCUICToTemplateCorrectness.v b/pcuic/theories/PCUICToTemplateCorrectness.v index 3ec96d17f..bb78f8f41 100644 --- a/pcuic/theories/PCUICToTemplateCorrectness.v +++ b/pcuic/theories/PCUICToTemplateCorrectness.v @@ -4,8 +4,7 @@ From MetaCoq.PCUIC Require Import PCUICAst PCUICAstUtils PCUICInduction Set Warnings "-notation-overridden". From MetaCoq.Template Require Import config utils Ast TypingWf WfInv UnivSubst - TermEquality LiftSubst. -From MetaCoq.Checker Require Import Substitution. + TermEquality LiftSubst Reduction. Set Warnings "+notation_overridden". diff --git a/template-coq/_CoqProject b/template-coq/_CoqProject index 567a73559..edc5cf783 100644 --- a/template-coq/_CoqProject +++ b/template-coq/_CoqProject @@ -39,6 +39,7 @@ theories/EnvironmentTyping.v theories/WfInv.v theories/TermEquality.v theories/Typing.v +theories/Reduction.v theories/TypingWf.v # The Template monad diff --git a/template-coq/theories/LiftSubst.v b/template-coq/theories/LiftSubst.v index dfb5cbb78..4c45c9c29 100644 --- a/template-coq/theories/LiftSubst.v +++ b/template-coq/theories/LiftSubst.v @@ -1,5 +1,6 @@ (* Distributed under the terms of the MIT license. *) From MetaCoq Require Import utils Ast AstUtils Induction. +From Coq Require Import ssreflect. (** * Lifting and substitution for the AST @@ -95,9 +96,9 @@ Definition subst_decl s k (d : context_decl) := map_decl (subst s k) d. Lemma subst_context_length s n Γ : #|subst_context s n Γ| = #|Γ|. Proof. induction Γ as [|[na [body|] ty] tl] in Γ |- *; cbn; eauto. - - rewrite !List.rev_length, !mapi_rec_length, !app_length, !List.rev_length. simpl. + - rewrite !List.rev_length !mapi_rec_length !app_length !List.rev_length. simpl. lia. - - rewrite !List.rev_length, !mapi_rec_length, !app_length, !List.rev_length. simpl. + - rewrite !List.rev_length !mapi_rec_length !app_length !List.rev_length. simpl. lia. Qed. @@ -112,6 +113,15 @@ Proof. apply mapi_ext. intros. f_equal. now rewrite List.rev_length. Qed. +Lemma subst_context_snoc s k Γ d : subst_context s k (d :: Γ) = subst_context s k Γ ,, subst_decl s (#|Γ| + k) d. +Proof. + unfold subst_context, fold_context. + rewrite !rev_mapi !rev_involutive /mapi mapi_rec_eqn /snoc. + f_equal. now rewrite Nat.sub_0_r List.rev_length. + rewrite mapi_rec_Sk. simpl. apply mapi_rec_ext. intros. + rewrite app_length !List.rev_length. simpl. f_equal. f_equal. lia. +Qed. + Definition subst_telescope s k (Γ : context) : context := mapi (fun k' decl => map_decl (subst s (k' + k)) decl) Γ. @@ -261,7 +271,7 @@ Lemma subst_rel_eq : subst u n (tRel p) = lift0 n t. Proof. intros; simpl in |- *. subst p. - elim (leb_spec n (n + i)). intros. assert (n + i - n = i) by lia. rewrite H1, H. + elim (leb_spec n (n + i)). intros. assert (n + i - n = i) by lia. rewrite H1 H. reflexivity. intros. lia. Qed. @@ -664,7 +674,7 @@ Lemma lift_to_extended_list_k Γ k : forall k', to_extended_list_k Γ (k' + k) = map (lift0 k') (to_extended_list_k Γ k). Proof. unfold to_extended_list_k. - intros k'. rewrite !reln_alt_eq, !app_nil_r. + intros k'. rewrite !reln_alt_eq !app_nil_r. induction Γ in k, k' |- *; simpl; auto. destruct a as [na [body|] ty]. now rewrite <- Nat.add_assoc, (IHΓ (k + 1) k'). @@ -722,9 +732,9 @@ Lemma map_vass_map_def g l n k : (map (map_def (lift n k) g) l)) = (mapi (fun i d => map_decl (lift n (i + k)) d) (mapi (fun i (d : def term) => vass (dname d) (lift0 i (dtype d))) l)). Proof. - rewrite mapi_mapi, mapi_map. apply mapi_ext. + rewrite mapi_mapi mapi_map. apply mapi_ext. intros. unfold map_decl, vass; simpl; f_equal. - rewrite permute_lift. f_equal; lia. lia. + rewrite permute_lift. lia. f_equal; lia. Qed. (* Lemma noccur_between_subst k n t : noccur_between k n t -> diff --git a/template-coq/theories/Reduction.v b/template-coq/theories/Reduction.v new file mode 100644 index 000000000..c138034ff --- /dev/null +++ b/template-coq/theories/Reduction.v @@ -0,0 +1,77 @@ +(* Distributed under the terms of the MIT license. *) +From MetaCoq.Template Require Import config utils Ast AstUtils Induction LiftSubst + UnivSubst TermEquality Typing. + +From Equations Require Import Equations. +Require Import ssreflect. + +Lemma red1_tApp_mkApps_l Σ Γ M1 N1 M2 : +red1 Σ Γ M1 N1 -> red1 Σ Γ (tApp M1 M2) (mkApps N1 M2). +Proof. constructor. auto. Qed. + +Lemma red1_tApp_mkApp Σ Γ M1 N1 M2 : + red1 Σ Γ M1 N1 -> red1 Σ Γ (tApp M1 [M2]) (mkApp N1 M2). +Proof. + intros. + change (mkApp N1 M2) with (mkApps N1 [M2]). + apply app_red_l. auto. +Qed. + +Lemma red1_mkApp Σ Γ M1 N1 M2 : + Ast.wf M1 -> + red1 Σ Γ M1 N1 -> red1 Σ Γ (mkApp M1 M2) (mkApp N1 M2). +Proof. + intros wfM1 H. + destruct (isApp M1) eqn:Heq. + destruct M1; try discriminate. simpl. + revert wfM1. inv H. simpl. intros. + rewrite mkApp_mkApps. constructor. + + intros. + rewrite mkApp_mkApps. + econstructor; eauto. + inv wfM1. simpl. + clear -H1. + unfold is_constructor in *. + destruct (nth_error args narg) eqn:Heq. + eapply nth_error_app_left in Heq. now rewrite -> Heq. discriminate. + + intros. rewrite mkApp_mkApps. now constructor. + + intros. simpl. + constructor. clear -X. induction X; constructor; auto. + + rewrite mkApp_tApp; auto. + now apply red1_tApp_mkApp. +Qed. + +Lemma red1_mkApps_l Σ Γ M1 N1 M2 : + Ast.wf M1 -> All Ast.wf M2 -> + red1 Σ Γ M1 N1 -> red1 Σ Γ (mkApps M1 M2) (mkApps N1 M2). +Proof. + induction M2 in M1, N1 |- *. simpl; auto. + intros. specialize (IHM2 (mkApp M1 a) (mkApp N1 a)). + inv X. + forward IHM2. apply wf_mkApp; auto. + forward IHM2. auto. + rewrite <- !mkApps_mkApp; auto. + apply IHM2. + apply red1_mkApp; auto. +Qed. + +Lemma red1_mkApps_r Σ Γ M1 M2 N2 : + Ast.wf M1 -> All Ast.wf M2 -> + OnOne2 (red1 Σ Γ) M2 N2 -> red1 Σ Γ (mkApps M1 M2) (mkApps M1 N2). +Proof. + intros. induction X0 in M1, H, X |- *. + inv X. + destruct (isApp M1) eqn:Heq. destruct M1; try discriminate. + simpl. constructor. apply OnOne2_app. constructor. auto. + rewrite mkApps_tApp; try congruence. + rewrite mkApps_tApp; try congruence. + constructor. constructor. auto. + inv X. + specialize (IHX0 (mkApp M1 hd)). forward IHX0. + apply wf_mkApp; auto. forward IHX0; auto. + now rewrite !mkApps_mkApp in IHX0. +Qed. diff --git a/template-coq/theories/TermEquality.v b/template-coq/theories/TermEquality.v index 00b539216..3b1484784 100644 --- a/template-coq/theories/TermEquality.v +++ b/template-coq/theories/TermEquality.v @@ -434,3 +434,69 @@ Proof. eapply All_impl; eauto. cbn. intros x [? ?] y [[[? ?] ?] ?]. repeat split; eauto. Qed. + + +Lemma eq_term_leq_term `{checker_flags} Σ φ t u : + eq_term Σ φ t u -> leq_term Σ φ t u. +Proof. + eapply eq_term_upto_univ_morphism. auto. + intros. + now apply eq_universe_leq_universe. +Qed. + +Lemma eq_term_upto_univ_App `{checker_flags} Σ Re Rle napp f f' : + eq_term_upto_univ_napp Σ Re Rle napp f f' -> + isApp f = isApp f'. +Proof. + inversion 1; reflexivity. +Qed. + +Lemma eq_term_App `{checker_flags} Σ φ f f' : + eq_term Σ φ f f' -> + isApp f = isApp f'. +Proof. + inversion 1; reflexivity. +Qed. + +Lemma eq_term_upto_univ_mkApps `{checker_flags} Σ Re Rle napp f l f' l' : + eq_term_upto_univ_napp Σ Re Rle (#|l| + napp) f f' -> + All2 (eq_term_upto_univ Σ Re Re) l l' -> + eq_term_upto_univ_napp Σ Re Rle napp (mkApps f l) (mkApps f' l'). +Proof. + induction l in f, f' |- *; intro e; inversion_clear 1. + - assumption. + - pose proof (eq_term_upto_univ_App _ _ _ _ _ _ e). + case_eq (isApp f). + + intro X; rewrite X in H0. + destruct f; try discriminate. + destruct f'; try discriminate. + cbn. inversion_clear e. constructor. + rewrite app_length /= -Nat.add_assoc //. + apply All2_app. assumption. + now constructor. + + intro X; rewrite X in H0. + rewrite !mkApps_tApp; eauto. + intro; discriminate. + intro; discriminate. + constructor. simpl. now simpl in e. + now constructor. +Qed. + +Lemma leq_term_mkApps `{checker_flags} Σ φ f l f' l' : + leq_term Σ φ f f' -> + All2 (eq_term Σ φ) l l' -> + leq_term Σ φ (mkApps f l) (mkApps f' l'). +Proof. + intros. + eapply eq_term_upto_univ_mkApps. + eapply eq_term_upto_univ_impl. 5:eauto. 4:auto with arith. + 1-3:typeclasses eauto. + apply X0. +Qed. + +Lemma leq_term_App `{checker_flags} Σ φ f f' : + leq_term Σ φ f f' -> + isApp f = isApp f'. +Proof. + inversion 1; reflexivity. +Qed. \ No newline at end of file diff --git a/template-coq/theories/TypingWf.v b/template-coq/theories/TypingWf.v index 29dcecfbd..c709f2cc3 100644 --- a/template-coq/theories/TypingWf.v +++ b/template-coq/theories/TypingWf.v @@ -1,6 +1,6 @@ (* Distributed under the terms of the MIT license. *) From MetaCoq.Template Require Import config utils Ast AstUtils Induction LiftSubst - UnivSubst Typing. + UnivSubst Reduction Typing. From Equations Require Import Equations. Require Import ssreflect. @@ -359,15 +359,6 @@ Proof. try red; simpl; intuition eauto. Qed. -Lemma subst_context_snoc s k Γ d : subst_context s k (d :: Γ) = subst_context s k Γ ,, map_decl (subst s (#|Γ| + k)) d. -Proof. - unfold subst_context, fold_context. - rewrite !rev_mapi !rev_involutive /mapi mapi_rec_eqn /snoc. - f_equal. now rewrite Nat.sub_0_r List.rev_length. - rewrite mapi_rec_Sk. simpl. apply mapi_rec_ext. intros. - rewrite app_length !List.rev_length. simpl. f_equal. f_equal. lia. -Qed. - Lemma wf_subst_context s k Γ : Forall wf_decl Γ -> Forall Ast.wf s -> Forall wf_decl (subst_context s k Γ). Proof. intros wfΓ. induction wfΓ in s |- *. From 903afe63dbaf69b61e4e8e25442c025e566c1da1 Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Thu, 10 Dec 2020 12:08:34 +0100 Subject: [PATCH 56/70] Make PCUIC -> Template parametric on checker_flags --- pcuic/theories/PCUICToTemplateCorrectness.v | 33 ++++++++++----------- 1 file changed, 16 insertions(+), 17 deletions(-) diff --git a/pcuic/theories/PCUICToTemplateCorrectness.v b/pcuic/theories/PCUICToTemplateCorrectness.v index bb78f8f41..59dba4cd0 100644 --- a/pcuic/theories/PCUICToTemplateCorrectness.v +++ b/pcuic/theories/PCUICToTemplateCorrectness.v @@ -11,6 +11,8 @@ Set Warnings "+notation_overridden". Require Import PCUICToTemplate. From Coq Require Import ssreflect. +Implicit Types cf : checker_flags. (* Use {cf} to parameterize by checker_flags where needed *) + (* from Checker Generation to avoid dependencies *) Derive Signature for Template.Typing.typing. @@ -25,8 +27,6 @@ Module ST := PCUICTyping. Module T := Template.Ast. Module TT := Template.Typing. -Local Existing Instance default_checker_flags. - Module SL := PCUICLiftSubst. Module TL := Template.LiftSubst. @@ -164,9 +164,9 @@ Proof. trivial. Qed. -Lemma trans_consistent_instance_ext Σ decl u: -ST.consistent_instance_ext Σ decl u -> -TT.consistent_instance_ext (trans_global Σ) decl u. +Lemma trans_consistent_instance_ext {cf} Σ decl u: + ST.consistent_instance_ext Σ decl u -> + TT.consistent_instance_ext (trans_global Σ) decl u. Proof. intros H. unfold consistent_instance_ext, ST.consistent_instance_ext in *. @@ -790,7 +790,7 @@ Proof. destruct Nat.leb => //. Qed. -Lemma trans_eq_term_upto_univ : +Lemma trans_eq_term_upto_univ {cf} : forall Σ Re Rle t u napp, PCUICEquality.eq_term_upto_univ_napp Σ Re Rle napp t u -> eq_term_upto_univ_napp (trans_global_decls Σ) Re Rle napp (trans t) (trans u). @@ -812,14 +812,14 @@ Proof. - destruct p as [? []]; constructor. Qed. -Lemma trans_leq_term Σ ϕ T U : +Lemma trans_leq_term {cf} Σ ϕ T U : PCUICEquality.leq_term Σ ϕ T U -> leq_term (trans_global_decls Σ) ϕ (trans T) (trans U). Proof. eapply trans_eq_term_upto_univ ; eauto. Qed. -Lemma trans_cumul Σ Γ T U : +Lemma trans_cumul {cf} Σ Γ T U : cumul Σ Γ T U -> TT.cumul (trans_global Σ) (trans_local Γ) (trans T) (trans U). Proof. @@ -873,9 +873,9 @@ Qed. -Definition TTwf_local Σ Γ := TT.All_local_env (TT.lift_typing TT.typing Σ) Γ. +Definition TTwf_local {cf} Σ Γ := TT.All_local_env (TT.lift_typing TT.typing Σ) Γ. -Lemma trans_wf_local': +Lemma trans_wf_local' {cf} : forall (Σ : PCUICAst.global_env_ext) Γ (wfΓ : wf_local Σ Γ), let P := (fun Σ0 Γ0 _ (t T : PCUICAst.term) _ => @@ -893,7 +893,7 @@ Proof. - simpl. constructor; auto. red. destruct tu. exists x. auto. Qed. -Lemma trans_wf_local_env Σ Γ : +Lemma trans_wf_local_env {cf} Σ Γ : ST.All_local_env (ST.lift_typing (fun (Σ : PCUICAst.global_env_ext) Γ b ty => @@ -911,7 +911,7 @@ Proof. red. red in t1. destruct t1. eapply t2. Qed. -Lemma trans_branches Σ Γ brs btys ps: +Lemma trans_branches {cf} Σ Γ brs btys ps: All2 (fun br bty : nat × PCUICAst.term => (((br.1 = bty.1 × ST.typing Σ Γ br.2 bty.2) @@ -935,7 +935,7 @@ Proof. + apply IHX. Qed. -Lemma trans_mfix_All Σ Γ mfix: +Lemma trans_mfix_All {cf} Σ Γ mfix: ST.All_local_env (ST.lift_typing (fun (Σ : PCUICEnvironment.global_env_ext) @@ -967,7 +967,7 @@ Proof. assumption. Qed. -Lemma trans_mfix_All2 Σ Γ mfix xfix: +Lemma trans_mfix_All2 {cf} Σ Γ mfix xfix: All (fun d : def PCUICAst.term => (ST.typing Σ (PCUICAst.app_context Γ (PCUICLiftSubst.fix_context xfix)) @@ -1001,7 +1001,7 @@ Proof. + auto. Qed. -Lemma All_over_All Σ Γ wfΓ : +Lemma All_over_All {cf} Σ Γ wfΓ : ST.All_local_env_over ST.typing (fun (Σ : PCUICAst.global_env_ext) (Γ : PCUICAst.context) (_ : wf_local Σ Γ) (t T : PCUICAst.term) @@ -1296,12 +1296,11 @@ Axiom cofix_guard_trans : ST.cofix_guard Σ Γ mfix -> TT.cofix_guard (trans_global Σ) (trans_local Γ) (map (map_def trans trans) mfix). -Theorem pcuic_to_template (Σ : S.global_env_ext) Γ t T : +Theorem pcuic_to_template {cf} (Σ : S.global_env_ext) Γ t T : ST.wf Σ -> ST.typing Σ Γ t T -> TT.typing (trans_global Σ) (trans_local Γ) (trans t) (trans T). Proof. - intros X X0. revert Σ X Γ t T X0. apply (ST.typing_ind_env (fun Σ Γ t T => From f9d81e97e99f2d915756af12ea035ac31c012681 Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Fri, 11 Dec 2020 14:46:56 +0100 Subject: [PATCH 57/70] Use strip_casts when checking fixpoints/cofixpoint types --- checker/theories/Checker.v | 6 + checker/theories/Generation.v | 6 +- checker/theories/Substitution.v | 86 ++- checker/theories/Weakening.v | 10 +- pcuic/theories/PCUICToTemplateCorrectness.v | 24 +- pcuic/theories/TemplateToPCUICCorrectness.v | 562 ++++++++++++-------- template-coq/theories/AstUtils.v | 22 + template-coq/theories/LiftSubst.v | 51 +- template-coq/theories/TermEquality.v | 2 +- template-coq/theories/Typing.v | 42 +- template-coq/theories/TypingWf.v | 160 +++++- 11 files changed, 674 insertions(+), 297 deletions(-) diff --git a/checker/theories/Checker.v b/checker/theories/Checker.v index 139a18def..969bf8dc5 100644 --- a/checker/theories/Checker.v +++ b/checker/theories/Checker.v @@ -31,6 +31,12 @@ Module RedFlags. Definition default := mk true true true true true true. End RedFlags. +Lemma congr_cumul_prod `{checker_flags} : forall Σ Γ na na' M1 M2 N1 N2, + cumul Σ Γ M1 N1 -> + cumul Σ (Γ ,, vass na M1) M2 N2 -> + cumul Σ Γ (tProd na M1 M2) (tProd na' N1 N2). +Proof. intros. todo "congr_cumul_prod". Defined. + Section Reduce. Context (flags : RedFlags.t) (Σ : global_env). diff --git a/checker/theories/Generation.v b/checker/theories/Generation.v index c1ae9ffd1..c4488683b 100644 --- a/checker/theories/Generation.v +++ b/checker/theories/Generation.v @@ -16,8 +16,10 @@ Proof. dependent induction Hty. - exists t_ty, t'. intuition. - destruct IHHty1 as [T' [U' [H' H'']]]. - exists T', U'. split; auto. - eapply cumul_trans; eauto. + exists T', A. split; auto. + destruct H' as [[[? ?] ?] ?]. + repeat split; auto. + eapply typing_spine_strengthen. Qed. Lemma type_mkApp `{checker_flags} Σ Γ f u T T' : diff --git a/checker/theories/Substitution.v b/checker/theories/Substitution.v index f2fd84fd8..444222361 100644 --- a/checker/theories/Substitution.v +++ b/checker/theories/Substitution.v @@ -1092,6 +1092,48 @@ Proof. rewrite !subst_context_length subst_instance_context_length. lia. now rewrite to_extended_list_k_subst. Qed. +(* +Lemma strip_casts_subst s k t : + Ast.wf t -> + strip_casts (subst s k t) = subst (map strip_casts s) k (strip_casts t). +Proof. + intros wf; revert s k. + induction wf using term_wf_forall_list_ind; simpl; intros; auto; + rewrite ?map_map_compose ?compose_on_snd ?compose_map_def ?map_length; + f_equal; solve_all; eauto. + - admit. + - rewrite subst_mkApps. + rewrite strip_casts_mkApps_wf; auto with wf. admit. admit. + rewrite IHwf. f_equal. rewrite !map_map_compose. solve_all. + + + pose proof (strip_casts_decompose_app (mkApps (subst s k t0) (map (subst s k) l))). + forward H1. auto with wf. admit. + destruct decompose_app eqn:eq. + specialize (H1 _ _ Logic.eq_refl). + rewrite map_map_compose. + rewrite -IHwf H1. + pose proof (strip_casts_decompose_app (mkApps (strip_casts t0) (map strip_casts l))). + forward H3. auto with wf. admit. + destruct (decompose_app (mkApps (strip_casts t0) _)) eqn:eq'. + specialize (H3 _ _ Logic.eq_refl). + + + + rewrite (strip_casts_mkApps_tApp t0) //. + simpl. rewrite subst_mkApps -IHwf. + rewrite map_map_compose. + + + rewrite IHwf. strip_casts_mkApps. map_map_compose. + f_equal; solve_all. +Qed. *) + +Lemma decompose_prod_assum_mkApps_nonnil ctx f a l : + decompose_prod_assum ctx (mkApps f (a :: l)) = (ctx, mkApps f (a :: l)). +Proof. + induction f; simpl; auto. +Qed. Hint Unfold subst1 : subst. @@ -1188,7 +1230,22 @@ Proof. subst c. rewrite app_context_assoc. unfold snoc. simpl. lia_f_equal. - - todo "applications". + - destruct args. + * simpl. specialize (IHt ctx k). destruct decompose_prod_assum eqn:da. + destruct IHt as [ctx' [t' [dec dec']]]. + rewrite decompose_prod_assum_ctx in dec'. + destruct (decompose_prod_assum [] (subst _ _ t)) eqn:da'. + noconf dec'. eexists _, _; split => //. + now rewrite decompose_prod_assum_ctx da'. + * specialize (IHt ctx k). destruct decompose_prod_assum eqn:da. + destruct IHt as [ctx' [t' [dec dec']]]. + rewrite decompose_prod_assum_ctx in dec'. + destruct (decompose_prod_assum [] (subst _ _ t)) eqn:da'. + noconf dec'. + cbn [map]. rewrite decompose_prod_assum_mkApps_nonnil. + eexists _, _; split => //. + rewrite decompose_prod_assum_ctx. + now rewrite decompose_prod_assum_mkApps_nonnil. Qed. Lemma map_option_out_impl {A B} (l : list A) (f g : A -> option B) x : @@ -1206,12 +1263,29 @@ Proof. * discriminate. - discriminate. Qed. + Lemma smash_context_app Δ Γ Γ' : smash_context Δ (Γ ++ Γ') = smash_context (smash_context Δ Γ) Γ'. Proof. revert Δ; induction Γ as [|[na [b|] ty]]; intros Δ; simpl; auto. Qed. + +Lemma strip_casts_decompose_app t : + Ast.wf t -> + forall f l, decompose_app t = (f, l) -> + strip_casts t = mkApps (strip_casts f) (map strip_casts l). +Proof. + intros wf. + induction wf using term_wf_forall_list_ind; simpl; intros; auto; noconf H; + try noconf H0; + rewrite ?map_map_compose ?compose_on_snd ?compose_map_def ?map_length; + f_equal; solve_all; eauto. + + - now noconf H3. + - now noconf H3. +Qed. + Lemma substitution_check_one_fix s k mfix inds : map_option_out (map check_one_fix mfix) = Some inds -> map_option_out (map (fun x : def term => @@ -1220,7 +1294,7 @@ Proof. apply map_option_out_impl. move=> [na ty def rarg] /=. rewrite decompose_prod_assum_ctx. - destruct (decompose_prod_assum _ ty) eqn:decomp. + destruct (decompose_prod_assum _ (strip_casts ty)) eqn:decomp. rewrite decompose_prod_assum_ctx in decomp. destruct (decompose_prod_assum [] ty) eqn:decty. noconf decomp. rewrite !app_context_nil_l. @@ -1228,10 +1302,10 @@ Proof. rewrite decty in X. destruct X as [ctx'' [t'' [dect decty']]]. rewrite -> subst_context_nil in decty'. simpl in decty'. - rewrite decty'. intros ind. - rewrite smash_context_app. Admitted. - (* rewrite (smash_context_acc _ (smash_context _ _)). + (*rewrite decty'. intros ind. + rewrite smash_context_app. + rewrite (smash_context_acc _ (smash_context _ _)). rewrite List.rev_app_distr. destruct (nth_error_spec (List.rev (smash_context [] c0)) rarg) => /= //; autorewrite with len in l; simpl in *. @@ -1268,7 +1342,6 @@ Proof. pose proof (subst_decompose_prod_assum_rec [] ty s k). rewrite decty in X. destruct X as [ctx'' [t'' [dect decty']]]. - rewrite decty'. Admitted. (* apply decompose_app_mkApps in eqapp. => //. subst t. @@ -1609,7 +1682,6 @@ Proof. now econstructor 3. Qed. - Lemma substitution_All_local_env_over `{cf : checker_flags} {Σ Γ Γ' Δ s} : wf Σ.1 -> forall wfΓ0 : wf_local Σ (Γ ,,, Γ' ,,, Δ), diff --git a/checker/theories/Weakening.v b/checker/theories/Weakening.v index ddd4d2bc3..d86bba66c 100644 --- a/checker/theories/Weakening.v +++ b/checker/theories/Weakening.v @@ -942,10 +942,11 @@ Lemma weakening_check_one_fix (Γ' Γ'' : context) mfix : Proof. apply map_ext. move=> [na ty def rarg] /=. rewrite decompose_prod_assum_ctx. - destruct (decompose_prod_assum _ ty) eqn:decomp. + rewrite strip_casts_lift. + destruct (decompose_prod_assum _ (strip_casts ty)) eqn:decomp. rewrite decompose_prod_assum_ctx in decomp. rewrite -lift_decompose_prod_assum. - destruct (decompose_prod_assum [] ty) eqn:decty. + destruct (decompose_prod_assum [] (strip_casts ty)) eqn:decty. noconf decomp. rewrite !app_context_nil_l (smash_context_lift []). destruct (nth_error_spec (List.rev (smash_context [] c0)) rarg). rewrite -> List.rev_length, ?smash_context_length in *; simpl in *. @@ -970,10 +971,11 @@ Lemma weakening_check_one_cofix (Γ' Γ'' : context) mfix : Proof. apply map_ext. move=> [na ty def rarg] /=. rewrite decompose_prod_assum_ctx. - destruct (decompose_prod_assum _ ty) eqn:decomp. + destruct (decompose_prod_assum _ (strip_casts ty)) eqn:decomp. rewrite decompose_prod_assum_ctx in decomp. + rewrite strip_casts_lift. rewrite -lift_decompose_prod_assum. - destruct (decompose_prod_assum [] ty) eqn:decty. + destruct (decompose_prod_assum [] (strip_casts ty)) eqn:decty. noconf decomp. destruct (decompose_app t) eqn:Happ. erewrite decompose_app_lift; eauto. diff --git a/pcuic/theories/PCUICToTemplateCorrectness.v b/pcuic/theories/PCUICToTemplateCorrectness.v index 59dba4cd0..dd2ccbf40 100644 --- a/pcuic/theories/PCUICToTemplateCorrectness.v +++ b/pcuic/theories/PCUICToTemplateCorrectness.v @@ -1070,11 +1070,6 @@ Proof. econstructor; eauto. Qed. -Lemma mkApp_ex t u : ∑ f args, mkApp t u = tApp f args. -Proof. - induction t; simpl; eexists _, _; reflexivity. -Qed. - Lemma trans_decompose_prod_assum : forall Γ t, let '(Δ, c) := decompose_prod_assum Γ t in @@ -1213,13 +1208,26 @@ Proof. now rewrite trans_to_extended_list trans_lift map_length. Qed. +Lemma strip_casts_trans t : AstUtils.strip_casts (trans t) = trans t. +Proof. + induction t using term_forall_list_ind; simpl; auto; + rewrite ?map_map_compose; + f_equal; solve_all. + + - rewrite strip_casts_mkApp_wf; auto with wf. + now rewrite IHt1 IHt2. + + - now destruct p as [? []]. +Qed. + Lemma trans_check_one_fix mfix : TT.check_one_fix (map_def trans trans mfix) = ST.check_one_fix mfix. Proof. unfold ST.check_one_fix, TT.check_one_fix. destruct mfix as [na ty arg rarg] => /=. move: (trans_decompose_prod_assum [] ty). - destruct decompose_prod_assum as [ctx p] => -> /=. + rewrite strip_casts_trans. + destruct decompose_prod_assum as [ctx p] => /= ->. rewrite -(trans_smash_context []) /trans_local. rewrite -List.map_rev nth_error_map. destruct nth_error => /= //. @@ -1236,13 +1244,13 @@ Proof. eapply map_ext => x. apply trans_check_one_fix. Qed. - Lemma trans_check_one_cofix mfix : TT.check_one_cofix (map_def trans trans mfix) = ST.check_one_cofix mfix. Proof. unfold ST.check_one_cofix, TT.check_one_cofix. destruct mfix as [na ty arg rarg] => /=. move: (trans_decompose_prod_assum [] ty). + rewrite strip_casts_trans. destruct decompose_prod_assum as [ctx p] => -> /=. move: (trans_decompose_app p). destruct decompose_app => /= ->. @@ -1420,3 +1428,5 @@ Proof. + eassumption. + now eapply trans_cumul. Qed. + +Print Assumptions trans_build_branches_type. \ No newline at end of file diff --git a/pcuic/theories/TemplateToPCUICCorrectness.v b/pcuic/theories/TemplateToPCUICCorrectness.v index 4661dc603..3b2c3b3a1 100644 --- a/pcuic/theories/TemplateToPCUICCorrectness.v +++ b/pcuic/theories/TemplateToPCUICCorrectness.v @@ -10,12 +10,11 @@ Set Warnings "+notation-overridden". From Equations.Prop Require Import DepElim. Implicit Types cf : checker_flags. -Module T := Template.Ast. -Module TEq := Template.TermEquality. -Module TTy := Template.Typing. -Module TEnv := Template.Ast.TemplateEnvironment. - -Module TL := Template.LiftSubst. +(* Source = Template, Target (unqualified) = Coq *) +Module S := Template.Ast. +Module SEq := Template.TermEquality. +Module STy := Template.Typing. +Module SL := Template.LiftSubst. Lemma mkApps_morphism (f : term -> term) u v : (forall x y, f (tApp x y) = tApp (f x) (f y)) -> @@ -33,7 +32,7 @@ Ltac solve_list := try solve_all; try typeclasses eauto with core. Lemma trans_lift n k t : - trans (TL.lift n k t) = lift n k (trans t). + trans (SL.lift n k t) = lift n k (trans t). Proof. revert k. induction t using Template.Induction.term_forall_list_ind; simpl; intros; try congruence. - f_equal. rewrite !map_map_compose. solve_all. @@ -50,7 +49,7 @@ Proof. revert f l'; induction l; simpl; trivial. Qed. -Lemma trans_mkApp u a : trans (T.mkApp u a) = tApp (trans u) (trans a). +Lemma trans_mkApp u a : trans (S.mkApp u a) = tApp (trans u) (trans a). Proof. induction u; simpl; try reflexivity. rewrite map_app. @@ -60,7 +59,7 @@ Proof. Qed. Lemma trans_mkApps u v : - trans (T.mkApps u v) = mkApps (trans u) (List.map trans v). + trans (S.mkApps u v) = mkApps (trans u) (List.map trans v). Proof. revert u; induction v. simpl; trivial. @@ -71,7 +70,7 @@ Proof. Qed. Lemma trans_subst t k u : - trans (TL.subst t k u) = subst (map trans t) k (trans u). + trans (SL.subst t k u) = subst (map trans t) k (trans u). Proof. revert k. induction u using Template.Induction.term_forall_list_ind; simpl; intros; try congruence. @@ -109,10 +108,10 @@ Qed. Require Import ssreflect. Lemma forall_decls_declared_constant Σ cst decl : - TTy.declared_constant Σ cst decl -> + STy.declared_constant Σ cst decl -> declared_constant (trans_global_decls Σ) cst (trans_constant_body decl). Proof. - unfold declared_constant, TTy.declared_constant. + unfold declared_constant, STy.declared_constant. induction Σ => //; try discriminate. case: a => // /= k b. unfold eq_kername; destruct kername_eq_dec; subst; auto. @@ -120,10 +119,10 @@ Proof. Qed. Lemma forall_decls_declared_minductive Σ cst decl : - TTy.declared_minductive Σ cst decl -> + STy.declared_minductive Σ cst decl -> declared_minductive (trans_global_decls Σ) cst (trans_minductive_body decl). Proof. - unfold declared_minductive, TTy.declared_minductive. + unfold declared_minductive, STy.declared_minductive. induction Σ => //; try discriminate. case: a => // /= k b. unfold eq_kername; destruct kername_eq_dec; subst; auto. @@ -131,10 +130,10 @@ Proof. Qed. Lemma forall_decls_declared_inductive Σ mdecl ind decl : - TTy.declared_inductive Σ mdecl ind decl -> + STy.declared_inductive Σ mdecl ind decl -> declared_inductive (trans_global_decls Σ) (trans_minductive_body mdecl) ind (trans_one_ind_body decl). Proof. - unfold declared_inductive, TTy.declared_inductive. + unfold declared_inductive, STy.declared_inductive. move=> [decl' Hnth]. pose proof (forall_decls_declared_minductive _ _ _ decl'). eexists. eauto. destruct decl'; simpl in *. @@ -143,11 +142,11 @@ Proof. Qed. Lemma forall_decls_declared_constructor Σ cst mdecl idecl decl : - TTy.declared_constructor Σ mdecl idecl cst decl -> + STy.declared_constructor Σ mdecl idecl cst decl -> declared_constructor (trans_global_decls Σ) (trans_minductive_body mdecl) (trans_one_ind_body idecl) cst ((fun '(x, y, z) => (x, trans y, z)) decl). Proof. - unfold declared_constructor, TTy.declared_constructor. + unfold declared_constructor, STy.declared_constructor. move=> [decl' Hnth]. pose proof (forall_decls_declared_inductive _ _ _ _ decl'). split; auto. destruct idecl; simpl. @@ -155,11 +154,11 @@ Proof. Qed. Lemma forall_decls_declared_projection Σ cst mdecl idecl decl : - TTy.declared_projection Σ mdecl idecl cst decl -> + STy.declared_projection Σ mdecl idecl cst decl -> declared_projection (trans_global_decls Σ) (trans_minductive_body mdecl) (trans_one_ind_body idecl) cst ((fun '(x, y) => (x, trans y)) decl). Proof. - unfold declared_constructor, TTy.declared_constructor. + unfold declared_constructor, STy.declared_constructor. move=> [decl' [Hnth Hnpar]]. pose proof (forall_decls_declared_inductive _ _ _ _ decl'). split; auto. destruct idecl; simpl. @@ -174,18 +173,20 @@ Proof. Qed. Lemma trans_destArity ctx t : - T.wf t -> + S.wf t -> match AstUtils.destArity ctx t with | Some (args, s) => destArity (trans_local ctx) (trans t) = Some (trans_local args, s) - | None => True + | None => destArity (trans_local ctx) (trans t) = None end. Proof. intros wf; revert ctx. induction wf using Template.Induction.term_wf_forall_list_ind; intros ctx; simpl; trivial. - apply (IHwf0 (T.vass n t :: ctx)). - apply (IHwf1 (T.vdef n t t0 :: ctx)). + apply (IHwf0 (S.vass n t :: ctx)). + apply (IHwf1 (S.vdef n t t0 :: ctx)). + destruct l. congruence. + now apply destArity_mkApps. Qed. (* TODO Duplicate? *) @@ -236,9 +237,9 @@ Qed. Definition on_pair {A B C D} (f : A -> B) (g : C -> D) (x : A * C) := (f (fst x), g (snd x)). -Lemma trans_inds kn u bodies : map trans (TTy.inds kn u bodies) = inds kn u (map trans_one_ind_body bodies). +Lemma trans_inds kn u bodies : map trans (STy.inds kn u bodies) = inds kn u (map trans_one_ind_body bodies). Proof. - unfold inds, TTy.inds. rewrite map_length. + unfold inds, STy.inds. rewrite map_length. induction bodies. simpl. reflexivity. simpl; f_equal. auto. Qed. @@ -246,7 +247,7 @@ Lemma trans_instantiate_params_subst params args s t : All TypingWf.wf_decl params -> All Ast.wf s -> All Ast.wf args -> forall s' t', - TTy.instantiate_params_subst params args s t = Some (s', t') -> + STy.instantiate_params_subst params args s t = Some (s', t') -> instantiate_params_subst (map trans_decl params) (map trans args) (map trans s) (trans t) = Some (map trans s', trans t'). @@ -273,18 +274,18 @@ Proof. Qed. Lemma trans_instantiate_params params args t : - T.wf t -> + S.wf t -> All TypingWf.wf_decl params -> All Ast.wf args -> forall t', - TTy.instantiate_params params args t = Some t' -> + STy.instantiate_params params args t = Some t' -> instantiate_params (map trans_decl params) (map trans args) (trans t) = Some (trans t'). Proof. intros wft wfpars wfargs t' eq. revert eq. - unfold TTy.instantiate_params. - case_eq (TTy.instantiate_params_subst (List.rev params) args [] t). + unfold STy.instantiate_params. + case_eq (STy.instantiate_params_subst (List.rev params) args [] t). all: try discriminate. intros [ctx u] e eq. inversion eq. subst. clear eq. assert (wfargs' : Forall Ast.wf args) by (apply All_Forall ; assumption). @@ -329,25 +330,43 @@ Proof. reflexivity. Qed. +Lemma decompose_prod_assum_mkApps_nonnil ctx f args : + args <> [] -> + decompose_prod_assum ctx (mkApps f args) = (ctx, mkApps f args). +Proof. + induction args => //. + intros. + rewrite mkApps_nonempty //. +Qed. + Lemma trans_decompose_prod_assum : forall Γ t, - let '(Δ, c) := AstUtils.decompose_prod_assum Γ t in - decompose_prod_assum (trans_local Γ) (trans t) = (trans_local Δ, trans c). + let '(Δ, c) := AstUtils.decompose_prod_assum (S.map_context STy.strip_casts Γ) (STy.strip_casts t) in + decompose_prod_assum (trans_local (S.map_context STy.strip_casts Γ)) (trans (STy.strip_casts t)) = + (trans_local Δ, trans c). Proof. intros Γ t. destruct AstUtils.decompose_prod_assum as [Δ c] eqn:e. induction t in Γ, Δ, c, e |- *. (* all: simpl in *. *) all: try solve [ inversion e ; subst ; reflexivity ]. - - eapply IHt1 in e as e'. give_up. - - eapply IHt2 in e as e'. assumption. - - eapply IHt3 in e as e'. assumption. - - simpl in *. give_up. -Abort. + - eapply IHt1 in e as e'. now simpl. + - simpl. simpl in e. eapply (IHt2 (Γ ,, Ast.vass na t1)) in e as e'. assumption. + - simpl. simpl in e. eapply (IHt3 (Γ ,, Ast.vdef na t1 t2)) in e as e'. assumption. + - simpl in *. rewrite trans_mkApps. + destruct args. + * simpl. now apply IHt. + * move: e. cbn [map]. + destruct (mkApps_ex (STy.strip_casts t) (STy.strip_casts t0) (map STy.strip_casts args)) as [f [? eq]]. + rewrite eq. intros [= <- <-]. rewrite -eq. + rewrite decompose_prod_assum_mkApps_nonnil //. + f_equal. + now rewrite trans_mkApps. +Qed. Lemma trans_build_branches_type : forall ind mdecl idecl args u p brtys, - map_option_out (TTy.build_branches_type ind mdecl idecl args u p) + map_option_out (STy.build_branches_type ind mdecl idecl args u p) = Some brtys -> map_option_out (build_branches_type ind (trans_minductive_body mdecl) @@ -359,28 +378,28 @@ Admitted. Lemma trans_build_case_predicate_type ind mdecl idecl params u ps : build_case_predicate_type ind (trans_minductive_body mdecl) (trans_one_ind_body idecl) (map trans params) u ps - = option_map trans (TTy.build_case_predicate_type ind mdecl idecl params u ps). + = option_map trans (STy.build_case_predicate_type ind mdecl idecl params u ps). Admitted. -(* Lemma trans_types_of_case (Σ : T.global_env) ind mdecl idecl args p u pty indctx pctx ps btys : *) -(* T.wf p -> T.wf pty -> T.wf (T.ind_type idecl) -> *) -(* All T.wf args -> *) -(* TTy.wf Σ -> *) -(* TTy.declared_inductive Σ mdecl ind idecl -> *) -(* TTy.types_of_case ind mdecl idecl args u p pty = Some (indctx, pctx, ps, btys) -> *) +(* Lemma trans_types_of_case (Σ : S.global_env) ind mdecl idecl args p u pty indctx pctx ps btys : *) +(* S.wf p -> S.wf pty -> S.wf (S.ind_type idecl) -> *) +(* All S.wf args -> *) +(* STy.wf Σ -> *) +(* STy.declared_inductive Σ mdecl ind idecl -> *) +(* STy.types_of_case ind mdecl idecl args u p pty = Some (indctx, pctx, ps, btys) -> *) (* types_of_case ind (trans_minductive_body mdecl) (trans_one_ind_body idecl) *) (* (map trans args) u (trans p) (trans pty) = *) (* Some (trans_local indctx, trans_local pctx, ps, map (on_snd trans) btys). *) (* Proof. *) (* intros wfp wfpty wfdecl wfargs wfΣ Hidecl. *) (* pose proof (on_declared_inductive wfΣ Hidecl) as [onmind onind]. *) -(* apply TTy.onParams in onmind as Hparams. *) +(* apply STy.onParams in onmind as Hparams. *) (* (* Maybe have a lemma for this we do it all the time *) *) -(* assert (wc : Forall wf_decl (UnivSubst.subst_instance_context u (T.ind_params mdecl))). *) -(* { assert (h : Forall wf_decl (T.ind_params mdecl)). *) +(* assert (wc : Forall wf_decl (UnivSubst.subst_instance_context u (S.ind_params mdecl))). *) +(* { assert (h : Forall wf_decl (S.ind_params mdecl)). *) (* { eapply typing_all_wf_decl ; revgoals. *) -(* - apply TTy.onParams in onmind. *) -(* unfold TTy.on_context in onmind. *) +(* - apply STy.onParams in onmind. *) +(* unfold STy.on_context in onmind. *) (* eassumption. *) (* - simpl. assumption. *) (* } *) @@ -394,11 +413,11 @@ Admitted. (* { eapply closed_wf_local ; eauto. eauto. } *) (* assert (wfparams : All wf_decl (Ast.ind_params mdecl)). *) (* { apply Forall_All. eapply typing_all_wf_decl ; eauto. simpl. eauto. } *) -(* unfold TTy.types_of_case, types_of_case. simpl. *) +(* unfold STy.types_of_case, types_of_case. simpl. *) (* match goal with *) -(* | |- context [ TTy.instantiate_params ?p ?a ?t ] => *) +(* | |- context [ STy.instantiate_params ?p ?a ?t ] => *) (* pose proof (trans_instantiate_params p a t) as ht ; *) -(* case_eq (TTy.instantiate_params p a t) *) +(* case_eq (STy.instantiate_params p a t) *) (* end. *) (* 2: discriminate. *) (* intros ity e. *) @@ -411,16 +430,16 @@ Admitted. (* apply wf_instantiate_params in e as wfity. *) (* all: auto with wf. *) (* pose proof (trans_destArity [] ity wfity) as e'. *) -(* destruct TTy.destArity as [[ctx s] | ]. 2: discriminate. *) +(* destruct STy.destArity as [[ctx s] | ]. 2: discriminate. *) (* rewrite e'. *) (* pose proof (trans_destArity [] pty wfpty) as e''. *) -(* destruct TTy.destArity as [[ctx' s'] | ]. 2: discriminate. *) +(* destruct STy.destArity as [[ctx' s'] | ]. 2: discriminate. *) (* simpl in e''. rewrite e''. *) -(* pose proof (TTy.onConstructors onind) as onc. *) +(* pose proof (STy.onConstructors onind) as onc. *) (* assert ( *) (* hb : *) (* forall brtys, *) -(* map_option_out (TTy.build_branches_type ind mdecl idecl args u p) *) +(* map_option_out (STy.build_branches_type ind mdecl idecl args u p) *) (* = Some brtys -> *) (* map_option_out *) (* (build_branches_type ind (trans_minductive_body mdecl) *) @@ -429,18 +448,18 @@ Admitted. (* = Some (map (on_snd trans) brtys) *) (* ). *) (* { intro brtys. *) -(* unfold TTy.build_branches_type, build_branches_type. *) +(* unfold STy.build_branches_type, build_branches_type. *) (* unfold trans_one_ind_body. simpl. rewrite -> mapi_map. *) -(* unfold TTy.on_constructors in onc. *) +(* unfold STy.on_constructors in onc. *) (* eapply All2_map_option_out_mapi_Some_spec. *) (* - eapply onc. *) (* - intros i [[id t] n] [t0 ar] z. *) (* unfold on_snd. simpl. *) (* intros [ont [cs ?]]. simpl in *. *) -(* unfold TTy.on_type in ont. simpl in ont. *) +(* unfold STy.on_type in ont. simpl in ont. *) (* destruct ont. *) -(* unfold TTy.instantiate_params, instantiate_params. *) -(* destruct TTy.instantiate_params_subst eqn:he. 2: discriminate. *) +(* unfold STy.instantiate_params, instantiate_params. *) +(* destruct STy.instantiate_params_subst eqn:he. 2: discriminate. *) (* destruct p0 as [s0 ty]. *) (* apply instantiate_params_subst_make_context_subst in he as he'. *) (* destruct he' as [ctx'' hctx'']. *) @@ -506,11 +525,11 @@ Admitted. (* reflexivity. *) (* Admitted. *) -Hint Constructors T.wf : wf. +Hint Constructors S.wf : wf. Hint Resolve Template.TypingWf.typing_wf : wf. -Lemma mkApps_trans_wf U l : T.wf (T.tApp U l) -> exists U' V', trans (T.tApp U l) = tApp U' V'. +Lemma mkApps_trans_wf U l : S.wf (S.tApp U l) -> exists U' V', trans (S.tApp U l) = tApp U' V'. Proof. simpl. induction l using rev_ind. intros. inv H. congruence. intros. rewrite map_app. simpl. exists (mkApps (trans U) (map trans l)), (trans x). @@ -519,7 +538,7 @@ Proof. rewrite mkApps_app. simpl. reflexivity. Qed. -Derive Signature for TEq.eq_term_upto_univ_napp. +Derive Signature for SEq.eq_term_upto_univ_napp. Lemma leq_term_mkApps {cf} Σ ϕ t u t' u' : eq_term Σ ϕ t t' -> All2 (eq_term Σ ϕ) u u' -> @@ -576,26 +595,49 @@ Proof. + now rewrite IHΣ. Qed. +Lemma context_assumptions_map ctx : context_assumptions (map trans_decl ctx) = Ast.context_assumptions ctx. +Proof. + induction ctx as [|[na [b|] ty] ctx]; simpl; auto. +Qed. + +Lemma typing_wf_wf {cf}: + forall (Σ : Template.Ast.global_env), + STy.wf Σ -> + STy.Forall_decls_typing + (fun (_ : Template.Ast.global_env_ext) (_ : Tcontext) (t T : Tterm) => Ast.wf t /\ Ast.wf T) Σ. +Proof. + intros Σ. + eapply on_global_env_impl. clear. + intros Σ Γ t S. + red. unfold STy.lift_typing. + intros ong. destruct S. + * intros ty. now eapply typing_wf. + * intros [s ty]. exists s. + now eapply typing_wf in ty. +Qed. + Lemma trans_R_global_instance {cf} Σ Re Rle gref napp u u' : - TTy.on_global_env (fun Σ => wf_decl_pred) Σ -> - TEq.R_global_instance Σ Re Rle gref napp u u' -> + STy.wf Σ -> + SEq.R_global_instance Σ Re Rle gref napp u u' -> R_global_instance (trans_global_decls Σ) Re Rle gref napp u u'. Proof. intros wfe. unfold PCUICEquality.R_global_instance, PCUICEquality.global_variance. - unfold TEq.R_global_instance, TEq.global_variance. + unfold SEq.R_global_instance, SEq.global_variance. destruct gref; simpl; auto. - unfold PCUICEquality.lookup_inductive, PCUICEquality.lookup_minductive. - unfold TEq.lookup_inductive, TEq.lookup_minductive. - rewrite trans_lookup. destruct Ast.lookup_env => //; simpl. - destruct g => /= //. rewrite nth_error_map. - destruct nth_error => /= //. - move: (trans_destArity [] (Ast.ind_type o)). - destruct AstUtils.destArity as [[ctx ps]|] => /= //. - admit. admit. - (* now rewrite context_assumptions_map. *) + unfold SEq.lookup_inductive, SEq.lookup_minductive. + rewrite trans_lookup. destruct Ast.lookup_env eqn:look => //; simpl. + destruct g => /= //. + rewrite nth_error_map. + destruct nth_error eqn:hnth => /= //. + assert (wfty : Ast.wf (Ast.ind_type o)). + { eapply declared_inductive_wf; eauto. eapply typing_wf_wf; eauto. split; eauto. } + move: (trans_destArity [] (Ast.ind_type o) wfty). + destruct AstUtils.destArity as [[ctx ps]|] eqn:eq => /= // -> //. + now rewrite context_assumptions_map. - unfold PCUICEquality.lookup_constructor, PCUICEquality.lookup_inductive, PCUICEquality.lookup_minductive. - unfold TEq.lookup_constructor, TEq.lookup_inductive, TEq.lookup_minductive. + unfold SEq.lookup_constructor, SEq.lookup_inductive, SEq.lookup_minductive. rewrite trans_lookup. destruct Ast.lookup_env => //; simpl. destruct g => /= //. rewrite nth_error_map. destruct nth_error => /= //. @@ -603,31 +645,33 @@ Proof. destruct nth_error => /= //. destruct p as [[id t] nargs]; simpl. destruct Nat.leb => //. -Admitted. +Qed. +Ltac tc := typeclasses eauto. (* TODO update Template Coq's eq_term to reflect PCUIC's cumulativity *) Lemma trans_eq_term_upto_univ {cf} : forall Σ Re Rle t u napp, - TTy.on_global_env (fun Σ => wf_decl_pred) Σ -> - T.wf t -> - T.wf u -> - TEq.eq_term_upto_univ_napp Σ Re Rle napp t u -> + RelationClasses.subrelation Re Rle -> + STy.wf Σ -> + S.wf t -> + S.wf u -> + SEq.eq_term_upto_univ_napp Σ Re Rle napp t u -> eq_term_upto_univ_napp (trans_global_decls Σ) Re Rle napp (trans t) (trans u). Proof. - intros Σ Re Rle t u napp wfΣ wt wu e. - induction t using Induction.term_forall_list_rect in Rle, napp, wt, u, wu, e |- *. + intros Σ Re Rle t u napp sub wfΣ wt wu e. + induction t using Induction.term_forall_list_rect in sub, Rle, napp, wt, u, wu, e |- *. all: invs e; cbn. all: try solve [ constructor ; auto ]. all: repeat (match goal with - | H : T.wf (_ _) |- _ => apply wf_inv in H; simpl in H + | H : S.wf (_ _) |- _ => apply wf_inv in H; simpl in H | H : _ /\ _ |- _ => destruct H end). all: try solve [ repeat constructor ; auto ; match goal with | ih : forall Rle (u : Tterm) (napp : nat), _ |- _ => - eapply ih ; eauto + now eapply ih end ]. - constructor. @@ -642,10 +686,7 @@ Proof. simpl. intros ? ? [[? [ih ?]] ?]. simpl in *. - eapply ih. all: auto. - - repeat constructor. - eapply eq_term_upto_univ_impl. 5:eauto. all:try typeclasses eauto. auto. - todo "update template". + eapply ih. all: auto. tc. - eapply eq_term_upto_univ_napp_mkApps. + rewrite map_length. now eapply IHt. + pose proof (All2_All_mix_left X X1) as h. @@ -659,17 +700,17 @@ Proof. eapply All2_impl. 1: exact h2. simpl. intros u v [[? [ih ?]] ?]. - eapply ih. all: auto. + eapply ih. all: auto; tc. - constructor. apply trans_R_global_instance; auto. - constructor. apply trans_R_global_instance; auto. - constructor. all: try solve [ match goal with | ih : forall Rle u, _ |- _ => - eapply ih ; auto + now eapply ih end ]. - assert (wl : All (T.wf ∘ snd) l) by solve_all. - assert (wbrs' : All (T.wf ∘ snd) brs') by solve_all. + assert (wl : All (S.wf ∘ snd) l) by solve_all. + assert (wbrs' : All (S.wf ∘ snd) brs') by solve_all. pose proof (All2_All_mix_left X X2) as h1. simpl in h1. pose proof (All2_All_mix_left wl h1) as h2. pose proof (All2_All_mix_right wbrs' h2) as h3. @@ -678,21 +719,21 @@ Proof. eapply All2_impl. 1: exact h3. simpl. intros [n u] [m v] [[? [ih [? ?]]] ?]. simpl in *. - intuition eauto. + intuition eauto. now apply ih. - constructor. assert ( w1 : All (fun def => - T.wf (dtype def) /\ - T.wf (dbody def) + S.wf (dtype def) /\ + S.wf (dbody def) ) m ). { solve_all. } assert ( w2 : All (fun def => - T.wf (dtype def) /\ - T.wf (dbody def)) mfix' + S.wf (dtype def) /\ + S.wf (dbody def)) mfix' ). { solve_all. } pose proof (All2_All_mix_left X X0) as h1. simpl in h1. @@ -704,16 +745,16 @@ Proof. simpl. intros [? ? ? ?] [? ? ? ?] [[[? ?] [[ih1 ih2] [? ?]]] [? ?]]. simpl in *. - intuition eauto. + intuition eauto. now eapply ih1. now eapply ih2. - constructor. assert ( w1 : - All (fun def => T.wf (dtype def) /\ T.wf (dbody def)) m + All (fun def => S.wf (dtype def) /\ S.wf (dbody def)) m ). { by eapply Forall_All. } assert ( w2 : - All (fun def => T.wf (dtype def) /\ T.wf (dbody def)) mfix' + All (fun def => S.wf (dtype def) /\ S.wf (dbody def)) mfix' ). { by eapply Forall_All. } pose proof (All2_All_mix_left X X0) as h1. simpl in h1. @@ -725,33 +766,33 @@ Proof. simpl. intros [? ? ? ?] [? ? ? ?] [[[? ?] [[ih1 ih2] [? ?]]] [? ?]]. simpl in *. - intuition eauto. + intuition eauto. now eapply ih1. now eapply ih2. Qed. Lemma trans_leq_term {cf} Σ ϕ T U : - TTy.on_global_env (fun Σ => wf_decl_pred) Σ -> - T.wf T -> T.wf U -> TEq.leq_term Σ ϕ T U -> + STy.wf Σ -> + S.wf T -> S.wf U -> SEq.leq_term Σ ϕ T U -> leq_term (trans_global_decls Σ) ϕ (trans T) (trans U). Proof. intros HT HU H. - eapply trans_eq_term_upto_univ ; eauto. + eapply trans_eq_term_upto_univ ; eauto. tc. Qed. Lemma trans_eq_term {cf} Σ φ t u : - TTy.on_global_env (fun Σ => wf_decl_pred) Σ -> - T.wf t -> T.wf u -> TEq.eq_term Σ φ t u -> + STy.wf Σ -> + S.wf t -> S.wf u -> SEq.eq_term Σ φ t u -> eq_term (trans_global_decls Σ) φ (trans t) (trans u). Proof. intros HT HU H. - eapply trans_eq_term_upto_univ ; eauto. + eapply trans_eq_term_upto_univ ; eauto. tc. Qed. Lemma trans_eq_term_list {cf}: forall Σ φ l l', - TTy.on_global_env (fun Σ => wf_decl_pred) Σ -> - List.Forall T.wf l -> - List.Forall T.wf l' -> - All2 (TEq.eq_term Σ φ) l l' -> + STy.wf Σ -> + List.Forall S.wf l -> + List.Forall S.wf l' -> + All2 (SEq.eq_term Σ φ) l l' -> All2 (eq_term (trans_global_decls Σ) φ) (List.map trans l) (List.map trans l'). Proof. intros Σ φ l l' wfΣ w w' h. @@ -764,12 +805,12 @@ Proof. intuition auto using trans_eq_term. Qed. -(* Lemma wf_mkApps t u : T.wf (T.mkApps t u) -> List.Forall T.wf u. *) +(* Lemma wf_mkApps t u : S.wf (S.mkApps t u) -> List.Forall S.wf u. *) (* Proof. *) (* induction u in t |- *; simpl. *) (* - intuition. *) (* - intros H; destruct t; try solve [inv H; intuition auto]. *) -(* specialize (IHu (T.tApp t (l ++ [a]))). *) +(* specialize (IHu (S.tApp t (l ++ [a]))). *) (* forward IHu. *) (* induction u; trivial. *) (* simpl. rewrite <- app_assoc. simpl. apply H. *) @@ -785,17 +826,17 @@ Proof. Qed. Lemma trans_iota_red pars c args brs : - trans (TTy.iota_red pars c args brs) = + trans (STy.iota_red pars c args brs) = iota_red pars c (List.map trans args) (List.map (on_snd trans) brs). Proof. - unfold TTy.iota_red, iota_red. + unfold STy.iota_red, iota_red. rewrite trans_mkApps. f_equal. induction brs in c |- *; simpl; destruct c; trivial. now rewrite map_skipn. Qed. Lemma trans_isLambda t : - T.wf t -> isLambda (trans t) = Ast.isLambda t. + S.wf t -> isLambda (trans t) = Ast.isLambda t. Proof. destruct 1; cbnr. destruct u; [contradiction|]. cbn. @@ -804,18 +845,18 @@ Proof. Qed. Lemma trans_unfold_fix mfix idx narg fn : - List.Forall (fun def : def Tterm => T.wf (dtype def) /\ T.wf (dbody def)) mfix -> - TTy.unfold_fix mfix idx = Some (narg, fn) -> + List.Forall (fun def : def Tterm => S.wf (dtype def) /\ S.wf (dbody def)) mfix -> + STy.unfold_fix mfix idx = Some (narg, fn) -> unfold_fix (map (map_def trans trans) mfix) idx = Some (narg, trans fn). Proof. - unfold TTy.unfold_fix, unfold_fix. intros wffix. + unfold STy.unfold_fix, unfold_fix. intros wffix. rewrite nth_error_map. destruct (nth_error mfix idx) eqn:Hdef => //. cbn. intros [= <- <-]. simpl. repeat f_equal. rewrite trans_subst. f_equal. clear Hdef. - unfold fix_subst, TTy.fix_subst. rewrite map_length. + unfold fix_subst, STy.fix_subst. rewrite map_length. generalize mfix at 1 3. induction wffix; trivial. simpl; intros mfix. f_equal. @@ -823,16 +864,16 @@ Proof. Qed. Lemma trans_unfold_cofix mfix idx narg fn : - List.Forall (fun def : def Tterm => T.wf (dtype def) /\ T.wf (dbody def)) mfix -> - TTy.unfold_cofix mfix idx = Some (narg, fn) -> + List.Forall (fun def : def Tterm => S.wf (dtype def) /\ S.wf (dbody def)) mfix -> + STy.unfold_cofix mfix idx = Some (narg, fn) -> unfold_cofix (map (map_def trans trans) mfix) idx = Some (narg, trans fn). Proof. - unfold TTy.unfold_cofix, unfold_cofix. intros wffix. + unfold STy.unfold_cofix, unfold_cofix. intros wffix. rewrite nth_error_map. destruct (nth_error mfix idx) eqn:Hdef. intros [= <- <-]. simpl. repeat f_equal. rewrite trans_subst. f_equal. clear Hdef. - unfold cofix_subst, TTy.cofix_subst. rewrite map_length. + unfold cofix_subst, STy.cofix_subst. rewrite map_length. generalize mfix at 1 3. induction wffix; trivial. simpl; intros mfix. f_equal. @@ -843,10 +884,10 @@ Definition isApp t := match t with tApp _ _ => true | _ => false end. Lemma trans_is_constructor: forall (args : list Tterm) (narg : nat), - TTy.is_constructor narg args = true -> is_constructor narg (map trans args) = true. + STy.is_constructor narg args = true -> is_constructor narg (map trans args) = true. Proof. intros args narg. - unfold TTy.is_constructor, is_constructor. + unfold STy.is_constructor, is_constructor. rewrite nth_error_map. destruct nth_error. simpl. intros. destruct t; try discriminate || reflexivity. simpl in H. destruct t; try discriminate || reflexivity. @@ -866,15 +907,26 @@ Proof. Qed. Ltac wf_inv H := try apply wf_inv in H; simpl in H; rdest. +Lemma wf_wf_decl_pred {cf} Σ : STy.wf Σ -> Typing.on_global_env (fun _ => wf_decl_pred) Σ. +Proof. + move/typing_wf_wf. + apply on_global_env_impl. + intros. + destruct T; simpl in *; auto. + destruct X0 as [s [Ht Hs]]. + red. split; auto. +Qed. +Hint Resolve wf_wf_decl_pred : wf. + Lemma trans_red1 {cf} Σ Γ T U : - TTy.on_global_env (fun Σ => wf_decl_pred) Σ -> + STy.wf Σ -> List.Forall wf_decl Γ -> - T.wf T -> - TTy.red1 Σ Γ T U -> + S.wf T -> + STy.red1 Σ Γ T U -> red1 (map (on_snd trans_global_decl) Σ) (trans_local Γ) (trans T) (trans U). Proof. intros wfΣ wfΓ Hwf. - induction 1 using TTy.red1_ind_all; wf_inv Hwf; simpl in *; + induction 1 using STy.red1_ind_all; wf_inv Hwf; simpl in *; try solve [econstructor; eauto]. - simpl. wf_inv H1. apply Forall_All in H2. inv H2. @@ -927,7 +979,7 @@ Proof. intuition eauto. apply b2. all: solve_all. - - rewrite !trans_mkApps; auto with wf. eapply wf_red1 in X; auto. + - rewrite !trans_mkApps; auto with wf. eapply wf_red1 in X; auto with wf. apply red1_mkApps_l. auto. - apply Forall_All in H2. clear H H0 H1. revert M1. induction X. @@ -935,7 +987,7 @@ Proof. apply red1_mkApps_l. apply app_red_r. auto. inv H2. specialize (IHX X0). simpl. intros. - eapply (IHX (T.tApp M1 [hd])). + eapply (IHX (S.tApp M1 [hd])). - constructor. apply IHX. constructor; hnf; simpl; auto. auto. - constructor. induction X; simpl; repeat constructor. apply p; auto. now inv Hwf. @@ -961,7 +1013,7 @@ Proof. red. rewrite <- !map_dtype. rewrite <- !map_dbody. intuition eauto. + unfold Template.Ast.app_context, trans_local in b. simpl in a. rewrite -> map_app in b. - unfold app_context. unfold TTy.fix_context in b. + unfold app_context. unfold STy.fix_context in b. rewrite map_rev map_mapi in b. simpl in b. unfold fix_context. rewrite mapi_map. simpl. forward b. @@ -996,7 +1048,7 @@ Proof. red. rewrite <- !map_dtype. rewrite <- !map_dbody. intuition eauto. + unfold Template.Ast.app_context, trans_local in b. simpl in a. rewrite -> map_app in b. - unfold app_context. unfold TTy.fix_context in b. + unfold app_context. unfold STy.fix_context in b. rewrite map_rev map_mapi in b. simpl in b. unfold fix_context. rewrite mapi_map. simpl. forward b. @@ -1016,7 +1068,7 @@ Proof. Qed. Lemma global_levels_trans Σ - : global_levels (trans_global_decls Σ) = TTy.global_levels Σ. + : global_levels (trans_global_decls Σ) = STy.global_levels Σ. Proof. induction Σ; simpl; auto. rewrite IHΣ. f_equal. clear. @@ -1024,19 +1076,19 @@ Proof. Qed. Lemma global_ext_levels_trans Σ - : global_ext_levels (trans_global Σ) = TTy.global_ext_levels Σ. + : global_ext_levels (trans_global Σ) = STy.global_ext_levels Σ. Proof. destruct Σ. - unfold trans_global, TTy.global_ext_levels, global_ext_levels; simpl. + unfold trans_global, STy.global_ext_levels, global_ext_levels; simpl. f_equal. clear u. now rewrite global_levels_trans. Qed. Lemma global_ext_constraints_trans Σ - : global_ext_constraints (trans_global Σ) = TTy.global_ext_constraints Σ. + : global_ext_constraints (trans_global Σ) = STy.global_ext_constraints Σ. Proof. destruct Σ. - unfold trans_global, TTy.global_ext_constraints, global_ext_constraints; simpl. + unfold trans_global, STy.global_ext_constraints, global_ext_constraints; simpl. f_equal. clear u. induction g. - reflexivity. @@ -1045,19 +1097,19 @@ Proof. Qed. Lemma trans_cumul {cf} (Σ : Ast.global_env_ext) Γ T U : - TTy.on_global_env (fun Σ => wf_decl_pred) Σ -> + STy.wf Σ -> List.Forall wf_decl Γ -> - T.wf T -> T.wf U -> TTy.cumul Σ Γ T U -> + S.wf T -> S.wf U -> STy.cumul Σ Γ T U -> trans_global Σ ;;; trans_local Γ |- trans T <= trans U. Proof. intros wfΣ wfΓ. induction 3. constructor; auto. eapply trans_leq_term in l; eauto. now rewrite global_ext_constraints_trans. - pose proof r as H3. apply wf_red1 in H3; auto. - apply trans_red1 in r; auto. econstructor 2; eauto. + pose proof r as H3. apply wf_red1 in H3; auto with wf. + apply trans_red1 in r; auto. econstructor 2; eauto with wf. econstructor 3. - apply IHX; auto. apply wf_red1 in r; auto. + apply IHX; auto. apply wf_red1 in r; auto with wf. apply trans_red1 in r; auto. Qed. @@ -1065,10 +1117,10 @@ Definition Tlift_typing (P : Template.Ast.global_env_ext -> Tcontext -> Tterm -> fun Σ Γ t T => match T with | Some T => P Σ Γ t T - | None => { s : Universe.t & P Σ Γ t (T.tSort s) } + | None => { s : Universe.t & P Σ Γ t (S.tSort s) } end. -Definition TTy_wf_local {cf : checker_flags} Σ Γ := TTy.All_local_env (TTy.lift_typing TTy.typing Σ) Γ. +Definition TTy_wf_local {cf : checker_flags} Σ Γ := STy.All_local_env (STy.lift_typing STy.typing Σ) Γ. Lemma trans_wf_local {cf}: forall (Σ : Template.Ast.global_env_ext) (Γ : Tcontext) (wfΓ : TTy_wf_local Σ Γ), @@ -1078,7 +1130,7 @@ Lemma trans_wf_local {cf}: trans_global Σ0;;; trans_local Γ0 |- trans t : trans T) in wf (trans_global Σ).1 -> - TTy.All_local_env_over TTy.typing P Σ Γ wfΓ -> + STy.All_local_env_over STy.typing P Σ Γ wfΓ -> wf_local (trans_global Σ) (trans_local Γ). Proof. intros. @@ -1092,10 +1144,10 @@ Proof. Qed. Lemma trans_wf_local_env {cf} Σ Γ : - TTy.All_local_env - (TTy.lift_typing + STy.All_local_env + (STy.lift_typing (fun (Σ : Ast.global_env_ext) (Γ : Tcontext) (b ty : Tterm) => - TTy.typing Σ Γ b ty × trans_global Σ;;; trans_local Γ |- trans b : trans ty) Σ) + STy.typing Σ Γ b ty × trans_global Σ;;; trans_local Γ |- trans b : trans ty) Σ) Γ -> wf_local (trans_global Σ) (trans_local Γ). Proof. @@ -1109,74 +1161,118 @@ Proof. red. red in t1. destruct t1. eapply t2. Qed. -Lemma typing_wf_wf {cf}: - forall (Σ : Template.Ast.global_env_ext), - TTy.wf Σ -> - TTy.Forall_decls_typing - (fun (_ : Template.Ast.global_env_ext) (_ : Tcontext) (t T : Tterm) => Ast.wf t /\ Ast.wf T) Σ. -Proof. - intros Σ wf. - red. unfold TTy.lift_typing. - induction wf. 1: constructor. - constructor. all: auto. - red. red in o0. - destruct d. - - hnf. destruct c as [ty [d|] ?] => /=. - + red in o0. simpl in *. eapply typing_wf. 2: eassumption. - simpl. auto. - + red. simpl in *. destruct o0 as [s ?]. - exists s. simpl in *. eapply typing_wf. 2: eassumption. auto. - - simpl in *. destruct o0. constructor. all: auto. - (* + eapply Alli_impl. 1: eassumption. - intros ? [? ? ? ? ?] []. simpl in *. - econstructor. all: eauto. *) - (* General implication lemma would be nicer: Simon *) -Admitted. - -(* eapply TTy.on_global_decls_impl. 2:eapply wf. eauto. intros * ongl ont. destruct t. *) +(* eapply STy.on_global_decls_impl. 2:eapply wf. eauto. intros * ongl ont. destruct t. *) (* red in ont. *) (* eapply typing_wf; eauto. destruct ont. exists x; eapply typing_wf; intuition eauto. *) (* Qed. *) Hint Resolve trans_wf_local : trans. -Lemma context_assumptions_map ctx : context_assumptions (map trans_decl ctx) = Ast.context_assumptions ctx. -Proof. - induction ctx as [|[na [b|] ty] ctx]; simpl; auto. -Qed. - Axiom fix_guard_trans : forall Σ Γ mfix, - TTy.fix_guard Σ Γ mfix -> + STy.fix_guard Σ Γ mfix -> fix_guard (trans_global Σ) (trans_local Γ) (map (map_def trans trans) mfix). Axiom cofix_guard_trans : forall Σ Γ mfix, - TTy.cofix_guard Σ Γ mfix -> + STy.cofix_guard Σ Γ mfix -> cofix_guard (trans_global Σ) (trans_local Γ) (map (map_def trans trans) mfix). - + +Lemma trans_check_one_fix mfix : + check_one_fix (map_def trans trans mfix) = STy.check_one_fix mfix. +Proof. + unfold STy.check_one_fix, check_one_fix. + destruct mfix as [na ty arg rarg] => /=. + move: (trans_decompose_prod_assum [] ty). simpl. + destruct decompose_prod_assum as [ctx p] => /=. + rewrite -(trans_smash_context []) /trans_local. + rewrite -List.map_rev nth_error_map. + destruct nth_error => /= //. + move: (trans_decompose_app (PCUICAst.decl_type c)). + destruct decompose_app => /=. + simpl. destruct c. simpl. intros ->. + now rewrite -trans_destInd. +Qed. + +Lemma map_option_out_check_one_fix mfix : + map (fun x => TS.check_one_fix (map_def trans trans x)) mfix = + map SS.check_one_fix mfix. +Proof. + eapply map_ext => x. apply trans_check_one_fix. +Qed. + + +Lemma trans_check_one_cofix mfix : + TS.check_one_cofix (map_def trans trans mfix) = SS.check_one_cofix mfix. +Proof. + unfold SS.check_one_cofix, TS.check_one_cofix. + destruct mfix as [na ty arg rarg] => /=. + move: (trans_decompose_prod_assum [] ty). + destruct decompose_prod_assum as [ctx p] => -> /=. + move: (trans_decompose_app p). + destruct decompose_app => /= ->. + now rewrite -trans_destInd. +Qed. + +Lemma map_option_out_check_one_cofix mfix : + map (fun x => TS.check_one_cofix (map_def trans trans x)) mfix = + map SS.check_one_cofix mfix. +Proof. + eapply map_ext => x. apply trans_check_one_cofix. +Qed. + +Lemma trans_check_rec_kind Σ k f : + SS.check_recursivity_kind Σ k f = TS.check_recursivity_kind (trans_global_decls Σ) k f. +Proof. + unfold SS.check_recursivity_kind, TS.check_recursivity_kind. + rewrite trans_lookup. + destruct S.lookup_env as [[]|] => //. +Qed. + +Lemma trans_wf_fixpoint Σ mfix : + TS.wf_fixpoint (trans_global_decls Σ) (map (map_def trans trans) mfix) = + SS.wf_fixpoint Σ mfix. +Proof. + unfold SS.wf_fixpoint, TS.wf_fixpoint. + rewrite map_map_compose. + rewrite map_option_out_check_one_fix. + destruct map_option_out as [[]|] => //. + now rewrite trans_check_rec_kind. +Qed. + +Lemma trans_wf_cofixpoint Σ mfix : + TS.wf_cofixpoint (trans_global_decls Σ) (map (map_def trans trans) mfix) = + SS.wf_cofixpoint Σ mfix. +Proof. + unfold SS.wf_cofixpoint, TS.wf_cofixpoint. + rewrite map_map_compose. + rewrite map_option_out_check_one_cofix. + destruct map_option_out as [[]|] => //. + now rewrite trans_check_rec_kind. +Qed. + Lemma trans_global_decl_universes d : - TTy.universes_decl_of_decl d = + STy.universes_decl_of_decl d = universes_decl_of_decl (trans_global_decl d). Proof. destruct d; reflexivity. Qed. Lemma trans_consistent_instance_ext {cf:checker_flags} Σ d u : - TTy.consistent_instance_ext Σ (TTy.universes_decl_of_decl d) u -> + STy.consistent_instance_ext Σ (STy.universes_decl_of_decl d) u -> consistent_instance_ext (trans_global Σ) (universes_decl_of_decl (trans_global_decl d)) u. Proof. - unfold TTy.consistent_instance_ext, consistent_instance_ext. + unfold STy.consistent_instance_ext, consistent_instance_ext. rewrite global_ext_levels_trans global_ext_constraints_trans trans_global_decl_universes. trivial. Qed. Theorem template_to_pcuic {cf} : - TTy.env_prop (fun Σ Γ t T => + STy.env_prop (fun Σ Γ t T => wf (trans_global Σ).1 -> typing (trans_global Σ) (trans_local Γ) (trans t) (trans T)). Proof. - apply (TTy.typing_ind_env (fun Σ Γ t T => + apply (STy.typing_ind_env (fun Σ Γ t T => wf (trans_global Σ).1 -> typing (trans_global Σ) (trans_local Γ) (trans t) (trans T) )%type). @@ -1219,12 +1315,11 @@ Proof. * econstructor; eauto. reflexivity. * simpl in p. destruct (TypingWf.typing_wf _ wfΣ _ _ _ typrod) as [wfAB _]. - intros wfT. + intros wfS. econstructor; eauto. + exists s; eauto. eapply p; eauto. - + change (tProd na (trans A) (trans B)) with (trans (T.tProd na A B)). + + change (tProd na (trans A) (trans B)) with (trans (S.tProd na A B)). apply trans_cumul; auto with trans. - apply TypingWf.typing_wf_sigma; auto. eapply Forall_impl. eapply TypingWf.typing_all_wf_decl; eauto. intros. auto. + eapply typing_wf in ty; eauto. destruct ty as [wfhd _]. @@ -1245,22 +1340,22 @@ Proof. replace (trans (Template.Ast.cst_type decl)) with (cst_type (trans_constant_body decl)) by (destruct decl; reflexivity). constructor; eauto with trans. - now apply (trans_consistent_instance_ext _ (T.ConstantDecl decl)). + now apply (trans_consistent_instance_ext _ (S.ConstantDecl decl)). - rewrite trans_subst_instance_constr. pose proof (forall_decls_declared_inductive _ _ _ _ isdecl). replace (trans (Template.Ast.ind_type idecl)) with (ind_type (trans_one_ind_body idecl)) by (destruct idecl; reflexivity). eapply type_Ind; eauto. eauto with trans. - now apply (trans_consistent_instance_ext _ (T.InductiveDecl mdecl)). + now apply (trans_consistent_instance_ext _ (S.InductiveDecl mdecl)). - pose proof (forall_decls_declared_constructor _ _ _ _ _ isdecl). - unfold TTy.type_of_constructor in *. + unfold STy.type_of_constructor in *. rewrite trans_subst. rewrite trans_subst_instance_constr. rewrite trans_inds. simpl. eapply refine_type. econstructor; eauto with trans. - now apply (trans_consistent_instance_ext _ (T.InductiveDecl mdecl)). + now apply (trans_consistent_instance_ext _ (S.InductiveDecl mdecl)). unfold type_of_constructor. simpl. f_equal. f_equal. destruct cdecl as [[id t] p]; simpl; auto. @@ -1294,8 +1389,8 @@ Proof. - eapply refine_type. assert (fix_context (map (map_def trans trans) mfix) = - trans_local (TTy.fix_context mfix)). - { unfold trans_local, TTy.fix_context. + trans_local (STy.fix_context mfix)). + { unfold trans_local, STy.fix_context. rewrite map_rev map_mapi /fix_context mapi_map. f_equal. apply mapi_ext; intros i x. simpl. rewrite trans_lift. reflexivity. } @@ -1316,8 +1411,8 @@ Proof. - eapply refine_type. assert (fix_context (map (map_def trans trans) mfix) = - trans_local (TTy.fix_context mfix)). - { unfold trans_local, TTy.fix_context. + trans_local (STy.fix_context mfix)). + { unfold trans_local, STy.fix_context. rewrite map_rev map_mapi /fix_context mapi_map. f_equal. apply mapi_ext => i x. simpl. rewrite trans_lift. reflexivity. } @@ -1336,11 +1431,10 @@ Proof. -- todo "wfcofix". -- destruct decl; reflexivity. - - assert (T.wf B). + - assert (S.wf B). { now apply typing_wf in X2. } eapply type_Cumul; eauto. eapply trans_cumul; eauto with trans. - eapply typing_wf_sigma; auto. clear X. apply typing_all_wf_decl in wfΓ; auto. eapply typing_wf in X0; eauto. destruct X0. auto. Qed. @@ -1352,10 +1446,10 @@ Proof. induction 1; constructor; auto. Qed. -Definition trans_constructor_shape (t : TTy.constructor_shape) : constructor_shape := - {| cshape_args := trans_local t.(TTy.cshape_args); - cshape_indices := map trans t.(TTy.cshape_indices); - cshape_sorts := t.(TTy.cshape_sorts) |}. +Definition trans_constructor_shape (t : STy.constructor_shape) : constructor_shape := + {| cshape_args := trans_local t.(STy.cshape_args); + cshape_indices := map trans t.(STy.cshape_indices); + cshape_sorts := t.(STy.cshape_sorts) |}. Lemma trans_reln l p Γ : map trans (TemplateEnvironment.reln l p Γ) = PCUICEnvironment.reln (map trans l) p (trans_local Γ). @@ -1392,10 +1486,10 @@ Proof. Qed. Lemma trans_on_global_env `{checker_flags} Σ P Q : - (forall Σ Γ t T, TTy.on_global_env P Σ.1 -> P Σ Γ t T -> + (forall Σ Γ t T, STy.on_global_env P Σ.1 -> P Σ Γ t T -> on_global_env Q (trans_global_decls Σ.1) -> Q (trans_global Σ) (trans_local Γ) (trans t) (option_map trans T)) -> - TTy.on_global_env P Σ -> on_global_env Q (trans_global_decls Σ). + STy.on_global_env P Σ -> on_global_env Q (trans_global_decls Σ). Proof. intros X X0. simpl in *. induction X0; simpl; constructor; auto. @@ -1424,20 +1518,20 @@ Proof. * destruct o0 as [onI onP onNP]. constructor; auto. -- eapply Alli_map. eapply Alli_impl. exact onI. eauto. intros. - unshelve refine {| ind_indices := trans_local X1.(TTy.ind_indices); - ind_sort := X1.(TTy.ind_sort); - ind_cshapes := map trans_constructor_shape X1.(TTy.ind_cshapes) |}. - --- simpl; rewrite X1.(TTy.ind_arity_eq). + unshelve refine {| ind_indices := trans_local X1.(STy.ind_indices); + ind_sort := X1.(STy.ind_sort); + ind_cshapes := map trans_constructor_shape X1.(STy.ind_cshapes) |}. + --- simpl; rewrite X1.(STy.ind_arity_eq). now rewrite !trans_it_mkProd_or_LetIn. - --- apply TTy.onArity in X1. unfold on_type in *; simpl in *. + --- apply STy.onArity in X1. unfold on_type in *; simpl in *. now apply (X (Σ, Ast.ind_universes m) [] (Ast.ind_type x) None). - --- pose proof X1.(TTy.onConstructors) as X11. red in X11. + --- pose proof X1.(STy.onConstructors) as X11. red in X11. red. eapply All2_map. eapply All2_impl; eauto. simpl. intros [[? ?] ?] cs onc. destruct onc; unshelve econstructor; eauto. + simpl. unfold trans_local. rewrite context_assumptions_map. now rewrite cstr_args_length. - + simpl; unfold cdecl_type, TTy.cdecl_type in cstr_eq |- *; simpl in *. + + simpl; unfold cdecl_type, STy.cdecl_type in cstr_eq |- *; simpl in *. rewrite cstr_eq. rewrite !trans_it_mkProd_or_LetIn. autorewrite with len. f_equal. f_equal. rewrite !trans_mkApps //. @@ -1447,12 +1541,12 @@ Proof. rewrite /trans_local !map_length. unfold TemplateEnvironment.to_extended_list_k. now rewrite trans_reln. - + unfold cdecl_type, TTy.cdecl_type in on_ctype |- *; simpl in *. + + unfold cdecl_type, STy.cdecl_type in on_ctype |- *; simpl in *. red. move: (X (Σ, Ast.ind_universes m) (Ast.arities_context (Ast.ind_bodies m)) t None). now rewrite trans_arities_context. + clear -X0 IHX0 X on_cargs. revert on_cargs. simpl. - generalize (TTy.cshape_args cs), (TTy.cshape_sorts cs). + generalize (STy.cshape_args cs), (STy.cshape_sorts cs). have foo := (X (Σ, udecl) _ _ _ X0). rewrite -trans_arities_context. induction c; destruct l; simpl; auto; @@ -1470,19 +1564,19 @@ Proof. revert on_cindices. rewrite trans_lift_context /trans_local -map_rev. simpl. rewrite {2}/trans_local map_length. - generalize (List.rev (LiftSubst.lift_context #|TTy.cshape_args cs| 0 (TTy.ind_indices X1))). - generalize (TTy.cshape_indices cs). + generalize (List.rev (LiftSubst.lift_context #|STy.cshape_args cs| 0 (STy.ind_indices X1))). + generalize (STy.cshape_indices cs). rewrite -trans_arities_context. induction 1; simpl; constructor; auto; have foo := (X (Σ, Ast.ind_universes m) _ _ _ X0); specialize (foo (Ast.app_context (Ast.app_context (Ast.arities_context (Ast.ind_bodies m)) - (Ast.ind_params m)) (TTy.cshape_args cs))). + (Ast.ind_params m)) (STy.cshape_args cs))). rewrite /trans_local !map_app in foo. now apply (foo i (Some t)). now rewrite (trans_subst_telescope [i] 0) in IHon_cindices. now rewrite (trans_subst_telescope [b] 0) in IHon_cindices. + clear -IHX0 on_ctype_positive. - unfold TTy.cdecl_type in *. unfold cdecl_type. simpl in *. + unfold STy.cdecl_type in *. unfold cdecl_type. simpl in *. change [] with (map trans_decl []). revert on_ctype_positive. generalize (@nil Ast.context_decl). induction 1; simpl. rewrite trans_mkApps. simpl. @@ -1499,11 +1593,11 @@ Proof. apply IHon_ctype_positive. + clear -on_ctype_variance. intros v indv. admit. - --- simpl; intros. have onp := X1.(TTy.onProjections). + --- simpl; intros. have onp := X1.(STy.onProjections). admit. - --- have inds := X1.(TTy.ind_sorts). + --- have inds := X1.(STy.ind_sorts). admit. - --- have inds := X1.(TTy.onIndices). + --- have inds := X1.(STy.onIndices). admit. -- red in onP. red. admit. @@ -1514,11 +1608,11 @@ Lemma template_to_pcuic_env {cf} Σ : Template.Typing.wf Σ -> wf (trans_global_ Proof. intros Hu. eapply trans_on_global_env; eauto. simpl; intros. - epose proof (TTy.env_prop_typing _ template_to_pcuic _ X Γ). + epose proof (STy.env_prop_typing _ template_to_pcuic _ X Γ). forward X2. - red in X0. destruct T. - now eapply TTy.typing_wf_local. - destruct X0 as [s Hs]. eapply TTy.typing_wf_local; eauto. + red in X0. destruct S. + now eapply STy.typing_wf_local. + destruct X0 as [s Hs]. eapply STy.typing_wf_local; eauto. destruct T; simpl in *. - eapply X2; eauto. - destruct X0 as [s Hs]. exists s. @@ -1538,12 +1632,12 @@ Proof. Qed. Theorem template_to_pcuic_typing {cf} Σ Γ t T : - TTy.wf Σ.1 -> - TTy.typing Σ Γ t T -> + STy.wf Σ.1 -> + STy.typing Σ Γ t T -> typing (trans_global Σ) (trans_local Γ) (trans t) (trans T). Proof. intros wf ty. - apply (TTy.env_prop_typing _ template_to_pcuic _ wf); auto. - now eapply TTy.typing_wf_local. + apply (STy.env_prop_typing _ template_to_pcuic _ wf); auto. + now eapply STy.typing_wf_local. now apply template_to_pcuic_env. Qed. diff --git a/template-coq/theories/AstUtils.v b/template-coq/theories/AstUtils.v index 317745221..3b87bc290 100644 --- a/template-coq/theories/AstUtils.v +++ b/template-coq/theories/AstUtils.v @@ -145,6 +145,28 @@ apply (List.firstn decl.(ind_npars)) in types. (snd (fst x))) ind_ctors). Defined. +Fixpoint strip_casts t := + match t with + | tEvar ev args => tEvar ev (List.map strip_casts args) + | tLambda na T M => tLambda na (strip_casts T) (strip_casts M) + | tApp u v => mkApps (strip_casts u) (List.map (strip_casts) v) + | tProd na A B => tProd na (strip_casts A) (strip_casts B) + | tCast c kind t => strip_casts c + | tLetIn na b t b' => tLetIn na (strip_casts b) (strip_casts t) (strip_casts b') + | tCase ind p c brs => + let brs' := List.map (on_snd (strip_casts)) brs in + tCase ind (strip_casts p) (strip_casts c) brs' + | tProj p c => tProj p (strip_casts c) + | tFix mfix idx => + let mfix' := List.map (map_def strip_casts strip_casts) mfix in + tFix mfix' idx + | tCoFix mfix idx => + let mfix' := List.map (map_def strip_casts strip_casts) mfix in + tCoFix mfix' idx + | tRel _ | tVar _ | tSort _ | tConst _ _ | tInd _ _ | tConstruct _ _ _ + | tInt _ | tFloat _ => t + end. + Fixpoint decompose_prod_assum (Γ : context) (t : term) : context * term := match t with | tProd n A B => decompose_prod_assum (Γ ,, vass n A) B diff --git a/template-coq/theories/LiftSubst.v b/template-coq/theories/LiftSubst.v index 4c45c9c29..3633858fe 100644 --- a/template-coq/theories/LiftSubst.v +++ b/template-coq/theories/LiftSubst.v @@ -1,6 +1,7 @@ (* Distributed under the terms of the MIT license. *) -From MetaCoq Require Import utils Ast AstUtils Induction. +From MetaCoq.Template Require Import utils Ast AstUtils Induction. From Coq Require Import ssreflect. +From Equations Require Import Equations. (** * Lifting and substitution for the AST @@ -742,3 +743,51 @@ Lemma noccur_between_subst k n t : noccur_between k n t -> Proof. Admitted. *) +Lemma strip_casts_lift n k t : + strip_casts (lift n k t) = lift n k (strip_casts t). +Proof. + induction t in k |- * using term_forall_list_ind; simpl; auto; + rewrite ?map_map_compose ?compose_on_snd ?compose_map_def ?map_length; + f_equal; solve_all; eauto. + + - rewrite lift_mkApps IHt map_map_compose. + f_equal; solve_all. +Qed. +Lemma mkApps_ex t u l : ∑ f args, Ast.mkApps t (u :: l) = Ast.tApp f args. +Proof. + induction t; simpl; eexists _, _; reflexivity. +Qed. +(* +Lemma mkApps_tApp' f l l' : mkApps (tApp f l) l' = mkApps f (l ++ l'). +Proof. + induction l'; simpl. rewrite app_nil_r. *) + +Lemma list_length_ind {A} (P : list A -> Type) (p0 : P []) + (pS : forall d Γ, (forall Γ', #|Γ'| <= #|Γ| -> P Γ') -> P (d :: Γ)) + Γ : P Γ. +Proof. + generalize (le_n #|Γ|). + generalize #|Γ| at 2. + induction n in Γ |- *. + destruct Γ; [|simpl; intros; elimtype False; lia]. + intros. apply p0. + intros. + destruct Γ; simpl in *. + apply p0. apply pS. intros. apply IHn. simpl. lia. +Qed. + +Lemma strip_casts_mkApps_tApp f l : + isApp f = false -> + strip_casts (mkApps f l) = strip_casts (tApp f l). +Proof. + induction l. simpl; auto. + intros. + rewrite mkApps_tApp //. +Qed. + +Lemma strip_casts_mkApps f l : + isApp f = false -> + strip_casts (mkApps f l) = mkApps (strip_casts f) (map strip_casts l). +Proof. + intros Hf. rewrite strip_casts_mkApps_tApp //. +Qed. \ No newline at end of file diff --git a/template-coq/theories/TermEquality.v b/template-coq/theories/TermEquality.v index 3b1484784..57dab3b9c 100644 --- a/template-coq/theories/TermEquality.v +++ b/template-coq/theories/TermEquality.v @@ -201,7 +201,7 @@ Inductive eq_term_upto_univ_napp Σ (Re Rle : Universe.t -> Universe.t -> Prop) eq_term_upto_univ_napp Σ Re Rle napp (tCoFix mfix idx) (tCoFix mfix' idx) | eq_Cast t1 c t2 t1' c' t2' : - eq_term_upto_univ_napp Σ Re Re napp t1 t1' -> + eq_term_upto_univ_napp Σ Re Re 0 t1 t1' -> eq_cast_kind c c' -> eq_term_upto_univ_napp Σ Re Re 0 t2 t2' -> eq_term_upto_univ_napp Σ Re Rle napp (tCast t1 c t2) (tCast t1' c' t2') diff --git a/template-coq/theories/Typing.v b/template-coq/theories/Typing.v index c1bfbe212..eb3a9909b 100644 --- a/template-coq/theories/Typing.v +++ b/template-coq/theories/Typing.v @@ -417,28 +417,6 @@ Inductive red Σ Γ M : term -> Type := We hence implement first an equality which considers casts and do a stripping phase of casts before checking equality. *) -Fixpoint strip_casts t := - match t with - | tEvar ev args => tEvar ev (List.map strip_casts args) - | tLambda na T M => tLambda na (strip_casts T) (strip_casts M) - | tApp u v => mkApps (strip_casts u) (List.map (strip_casts) v) - | tProd na A B => tProd na (strip_casts A) (strip_casts B) - | tCast c kind t => strip_casts c - | tLetIn na b t b' => tLetIn na (strip_casts b) (strip_casts t) (strip_casts b') - | tCase ind p c brs => - let brs' := List.map (on_snd (strip_casts)) brs in - tCase ind (strip_casts p) (strip_casts c) brs' - | tProj p c => tProj p (strip_casts c) - | tFix mfix idx => - let mfix' := List.map (map_def strip_casts strip_casts) mfix in - tFix mfix' idx - | tCoFix mfix idx => - let mfix' := List.map (map_def strip_casts strip_casts) mfix in - tCoFix mfix' idx - | tRel _ | tVar _ | tSort _ | tConst _ _ | tInd _ _ | tConstruct _ _ _ - | tInt _ | tFloat _ => t - end. - Definition eq_term_nocast `{checker_flags} (Σ : global_env) (φ : ConstraintSet.t) (t u : term) := eq_term Σ φ (strip_casts t) (strip_casts u). @@ -475,25 +453,15 @@ Inductive conv `{checker_flags} (Σ : global_env_ext) (Γ : context) : term -> t where " Σ ;;; Γ |- t = u " := (@conv _ Σ Γ t u) : type_scope. Lemma conv_refl' `{checker_flags} : forall Σ Γ t, Σ ;;; Γ |- t = t. - intros. todo "conv_refl". + intros. constructor. apply eq_term_refl. Defined. -Lemma cumul_refl' `{checker_flags} : forall Σ Γ t, Σ ;;; Γ |- t <= t. (* easy *) - intros. todo "cumul_refl'". -Defined. - -Lemma cumul_trans `{checker_flags} : forall Σ Γ t u v, Σ ;;; Γ |- t <= u -> Σ ;;; Γ |- u <= v -> Σ ;;; Γ |- t <= v. - intros. todo "cumul_trans". +Lemma cumul_refl' `{checker_flags} : forall Σ Γ t, Σ ;;; Γ |- t <= t. + intros. constructor. apply leq_term_refl. Defined. Hint Resolve conv_refl cumul_refl' : typecheck. -Lemma congr_cumul_prod `{checker_flags} : forall Σ Γ na na' M1 M2 N1 N2, - cumul Σ Γ M1 N1 -> - cumul Σ (Γ ,, vass na M1) M2 N2 -> - cumul Σ Γ (tProd na M1 M2) (tProd na' N1 N2). -Proof. intros. todo "congr_cumul_prod". Defined. - Definition eq_opt_term `{checker_flags} Σ φ (t u : option term) := match t, u with | Some t, Some u => eq_term Σ φ t u @@ -699,7 +667,7 @@ Definition check_one_fix d := dtype := ty; dbody := b; rarg := arg |} := d in - let '(ctx, ty) := decompose_prod_assum [] ty in + let '(ctx, ty) := decompose_prod_assum [] (strip_casts ty) in match nth_error (List.rev (smash_context [] ctx)) arg with | Some argd => let (hd, args) := decompose_app argd.(decl_type) in @@ -726,7 +694,7 @@ Definition check_one_cofix d := dtype := ty; dbody := b; rarg := arg |} := d in - let '(ctx, ty) := decompose_prod_assum [] ty in + let '(ctx, ty) := decompose_prod_assum [] (strip_casts ty) in let (hd, args) := decompose_app ty in match destInd hd with | Some (mkInd ind _, u) => Some ind diff --git a/template-coq/theories/TypingWf.v b/template-coq/theories/TypingWf.v index c709f2cc3..ade75bae3 100644 --- a/template-coq/theories/TypingWf.v +++ b/template-coq/theories/TypingWf.v @@ -1,8 +1,8 @@ (* Distributed under the terms of the MIT license. *) From MetaCoq.Template Require Import config utils Ast AstUtils Induction LiftSubst - UnivSubst Reduction Typing. + UnivSubst Reduction WfInv Typing. From Equations Require Import Equations. -Require Import ssreflect. +Require Import ssreflect ssrbool. (** * Well-formedness of terms and types in typing derivations @@ -60,7 +60,7 @@ Proof. simpl. intros H; now inv H. Qed. -Lemma wf_mkApps_napp t u : isApp t = false -> Ast.wf (mkApps t u) -> Ast.wf t /\ List.Forall Ast.wf u. +Lemma wf_mkApps_napp t u : ~~ isApp t -> Ast.wf (mkApps t u) -> Ast.wf t /\ List.Forall Ast.wf u. Proof. induction u in t |- *; simpl. - intuition. @@ -86,7 +86,7 @@ Qed. Hint Resolve wf_mkApps_inv : wf. Hint Constructors Ast.wf : wf. -Lemma isLambda_isApp t : isLambda t = true -> isApp t = false. +Lemma isLambda_isApp t : isLambda t = true -> ~~ isApp t. Proof. destruct t; simpl; congruence. Qed. Lemma unfold_fix_wf: @@ -718,3 +718,155 @@ Proof. eapply All_Forall, Alli_All; eauto. simpl; intros. eapply declared_projection_wf in H0; eauto. Qed. + +Lemma mkApp_ex_wf t u : Ast.wf (mkApp t u) -> + exists f args, mkApp t u = tApp f args /\ ~~ isApp f. +Proof. + induction t; simpl; try solve [eexists _, _; split; reflexivity]. + intros wf. + eapply wf_inv in wf as [appt [_ [wft wfargs]]]. + eapply Forall_app in wfargs as [wfargs wfu]. depelim wfu. + forward IHt. eapply wf_mkApp; intuition auto. + destruct IHt as [f [ar [eqf isap]]]. + eexists _, _; split; auto. rewrite appt //. +Qed. + +Lemma decompose_app_mkApp f u : + (decompose_app (mkApp f u)).2 <> []. +Proof. + induction f; simpl; auto; try congruence. + destruct args; simpl; congruence. +Qed. + +Lemma mkApps_tApp' f u f' u' : + ~~ isApp f' -> + mkApp f u = tApp f' u' -> mkApps f [u] = mkApps f' u'. +Proof. + intros. + rewrite -(mkApp_mkApps f u []). + simpl. rewrite H0. + rewrite -(mkApps_tApp f') // ?H //. + destruct u' => //. + eapply (f_equal decompose_app) in H0. + simpl in H0. pose proof (decompose_app_mkApp f u). + rewrite H0 /= in H1. congruence. +Qed. + +Lemma eq_decompose_app x y : + Ast.wf x -> Ast.wf y -> + decompose_app x = decompose_app y -> x = y. +Proof. + intros wfx; revert y. + induction wfx using term_wf_forall_list_ind; intros [] wfy; + eapply wf_inv in wfy; simpl in wfy; simpl; + intros [= ?]; try intuition congruence. +Qed. + +Lemma mkApp_ex t u : ∑ f args, mkApp t u = tApp f args. +Proof. + induction t; simpl; try solve [eexists _, _; reflexivity]. +Qed. + +Lemma strip_casts_decompose_app t : + Ast.wf t -> + forall f l, decompose_app t = (f, l) -> + strip_casts t = mkApps (strip_casts f) (map strip_casts l). +Proof. + intros wf. + induction wf using term_wf_forall_list_ind; simpl; intros; auto; noconf H; + try noconf H0; + rewrite ?map_map_compose ?compose_on_snd ?compose_map_def ?map_length; + f_equal; solve_all; eauto. + + - now noconf H3. + - now noconf H3. +Qed. + +Lemma mkApps_tApp f args : + ~~ isApp f -> + ~~ is_empty args -> + tApp f args = mkApps f args. +Proof. + intros. + destruct args, f; try discriminate; auto. +Qed. + +Lemma strip_casts_mkApps_napp_wf f u : + ~~ isApp f -> Ast.wf f -> Forall Ast.wf u -> + strip_casts (mkApps f u) = mkApps (strip_casts f) (map strip_casts u). +Proof. + intros nisapp wf wf'. + destruct u. + simpl. auto. + rewrite -(mkApps_tApp f (t :: u)) //. +Qed. + +Lemma mkApp_mkApps f u : mkApp f u = mkApps f [u]. +Proof. reflexivity. Qed. + +Lemma decompose_app_inv f l hd args : + Ast.wf f -> + decompose_app (mkApps f l) = (hd, args) -> + ∑ n, ~~ isApp hd /\ l = skipn n args /\ f = mkApps hd (firstn n args). +Proof. + destruct (isApp f) eqn:Heq. + revert l args hd. + induction f; try discriminate. intros. + simpl in H. + move/wf_inv: H => /= [isAppf [Hargs [wff wfargs]]]. + rewrite mkApps_tApp ?isAppf in H0 => //. destruct args => //. + rewrite mkApps_nested in H0. + rewrite decompose_app_mkApps ?isAppf in H0; auto. noconf H0. + exists #|args|; split; auto. now rewrite isAppf. + rewrite skipn_all_app. + rewrite firstn_app. rewrite firstn_all2. lia. + rewrite Nat.sub_diag firstn_O app_nil_r. split; auto. + rewrite mkApps_tApp ?isAppf //. now destruct args. + + intros wff fl. + rewrite decompose_app_mkApps in fl; auto. now apply negbT. + inversion fl. subst; exists 0. + split; auto. now eapply negbT. +Qed. + +Lemma eq_tip_skipn {A} (x : A) n l : [x] = skipn n l -> + exists l', l = l' ++ [x] /\ n = #|l'|. +Proof. + induction l in n |- *. rewrite skipn_nil //. + destruct n. simpl. destruct l => //. + intros eq. noconf eq. exists []; split; auto. + rewrite skipn_S. intros Hx. + destruct (IHl _ Hx) as [l' [-> ->]]. + exists (a :: l'); split; reflexivity. +Qed. + +Lemma strip_casts_mkApp_wf f u : + Ast.wf f -> Ast.wf u -> + strip_casts (mkApp f u) = mkApp (strip_casts f) (strip_casts u). +Proof. + intros wf wf'. + assert (wfa : Ast.wf (mkApp f u)). now apply wf_mkApp. + destruct (mkApp_ex_wf f u wfa) as [f' [args [eq isapp]]]. + eapply (f_equal decompose_app) in eq. simpl in eq. + epose proof (strip_casts_decompose_app _ wfa _ _ eq). + rewrite H. + rewrite mkApp_mkApps in eq. + destruct (decompose_app_inv _ _ _ _ wf eq) as [n [ng [stripeq stripf]]]. + apply eq_tip_skipn in stripeq. destruct stripeq as [l' [eqargs eqn]]. + subst n args. rewrite (firstn_app_left _ 0) // /= app_nil_r in stripf. subst f. + eapply wf_mkApps_napp in wf as [wff' wfl] => //. + rewrite strip_casts_mkApps_napp_wf //. + now rewrite mkApp_mkApps mkApps_nested map_app. +Qed. + +Lemma strip_casts_mkApps_wf f u : + Ast.wf f -> Forall Ast.wf u -> + strip_casts (mkApps f u) = mkApps (strip_casts f) (map strip_casts u). +Proof. + intros wf wf'. induction wf' in f, wf |- *. + simpl. auto. + rewrite -mkApps_mkApp IHwf'. + apply wf_mkApp; auto with wf. + rewrite strip_casts_mkApp_wf //. + now rewrite mkApps_mkApp. +Qed. From f363cd400236fd71316956b8c1d17d485fe7831b Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Fri, 11 Dec 2020 15:12:00 +0100 Subject: [PATCH 58/70] Remove entirely the checker folder, no longer needed --- Makefile | 19 +- checker/Makefile | 44 - checker/Makefile.coq.local | 4 - checker/Makefile.local | 3 - checker/Makefile.plugin.local | 16 - checker/_CoqProject.in | 17 - checker/_PluginProject.in | 99 - checker/demo.v | 9 - checker/src/.gitignore | 3 - checker/src/g_metacoq_checker.mlg | 36 - checker/src/metacoq_checker_plugin.mlpack | 14 - checker/src/to-lower.sh | 9 + checker/theories/All.v | 8 - checker/theories/Checker.v | 1166 ---------- checker/theories/Closed.v | 676 ------ checker/theories/Extraction.v | 46 - checker/theories/Generation.v | 55 - checker/theories/Loader.v | 6 - checker/theories/Retyping.v | 110 - checker/theories/Substitution.v | 1951 ----------------- checker/theories/Weakening.v | 1196 ---------- checker/theories/WeakeningEnv.v | 735 ------- checker/update_plugin.sh | 12 - pcuic/_CoqProject.in | 1 - pcuic/theories/PCUICConfluence.v | 2 +- pcuic/theories/PCUICCumulativity.v | 2 +- pcuic/theories/PCUICReduction.v | 3 +- pcuic/theories/PCUICRelations.v | 165 -- pcuic/theories/PCUICToTemplateCorrectness.v | 4 - template-coq/_CoqProject | 2 + {checker => template-coq}/theories/Normal.v | 0 template-coq/theories/Typing.v | 33 +- {checker => template-coq}/theories/WcbvEval.v | 0 template-coq/theories/utils/MCRelations.v | 160 ++ 34 files changed, 194 insertions(+), 6412 deletions(-) delete mode 100644 checker/Makefile delete mode 100644 checker/Makefile.coq.local delete mode 100644 checker/Makefile.local delete mode 100644 checker/Makefile.plugin.local delete mode 100644 checker/_CoqProject.in delete mode 100644 checker/_PluginProject.in delete mode 100644 checker/demo.v delete mode 100644 checker/src/.gitignore delete mode 100644 checker/src/g_metacoq_checker.mlg delete mode 100644 checker/src/metacoq_checker_plugin.mlpack create mode 100755 checker/src/to-lower.sh delete mode 100644 checker/theories/All.v delete mode 100644 checker/theories/Checker.v delete mode 100644 checker/theories/Closed.v delete mode 100644 checker/theories/Extraction.v delete mode 100644 checker/theories/Generation.v delete mode 100644 checker/theories/Loader.v delete mode 100644 checker/theories/Retyping.v delete mode 100644 checker/theories/Substitution.v delete mode 100644 checker/theories/Weakening.v delete mode 100644 checker/theories/WeakeningEnv.v delete mode 100755 checker/update_plugin.sh delete mode 100644 pcuic/theories/PCUICRelations.v rename {checker => template-coq}/theories/Normal.v (100%) rename {checker => template-coq}/theories/WcbvEval.v (100%) diff --git a/Makefile b/Makefile index f69fca98e..61343cfbb 100644 --- a/Makefile +++ b/Makefile @@ -1,12 +1,11 @@ TIMED ?= -all: template-coq checker pcuic safechecker erasure examples +all: template-coq pcuic safechecker erasure examples -.PHONY: all template-coq checker pcuic erasure install html clean mrproper .merlin test-suite translations +.PHONY: all template-coq pcuic erasure install html clean mrproper .merlin test-suite translations install: all $(MAKE) -C template-coq install - $(MAKE) -C checker install $(MAKE) -C pcuic install $(MAKE) -C safechecker install $(MAKE) -C erasure install @@ -14,7 +13,6 @@ install: all uninstall: all $(MAKE) -C template-coq uninstall - $(MAKE) -C checker uninstall $(MAKE) -C pcuic uninstall $(MAKE) -C safechecker uninstall $(MAKE) -C erasure uninstall @@ -23,7 +21,6 @@ uninstall: all html: all "coqdoc" -toc -utf8 -interpolate -l -html \ -R template-coq/theories MetaCoq.Template \ - -R checker/theories MetaCoq.Checker \ -R pcuic/theories MetaCoq.PCUIC \ -R safechecker/theories MetaCoq.SafeChecker \ -R erasure/theories MetaCoq.Erasure \ @@ -32,7 +29,6 @@ html: all clean: $(MAKE) -C template-coq clean - $(MAKE) -C checker clean $(MAKE) -C pcuic clean $(MAKE) -C safechecker clean $(MAKE) -C erasure clean @@ -45,7 +41,6 @@ mrproper: $(MAKE) -C pcuic mrproper $(MAKE) -C safechecker mrproper $(MAKE) -C erasure mrproper - $(MAKE) -C checker mrproper $(MAKE) -C examples mrproper $(MAKE) -C test-suite mrproper $(MAKE) -C translations mrproper @@ -55,7 +50,6 @@ mrproper: $(MAKE) -C pcuic .merlin $(MAKE) -C safechecker .merlin $(MAKE) -C erasure .merlin - $(MAKE) -C checker .merlin template-coq: $(MAKE) -C template-coq @@ -69,22 +63,17 @@ safechecker: template-coq pcuic erasure: template-coq safechecker pcuic $(MAKE) -C erasure -checker: template-coq - $(MAKE) -C checker - examples: checker safechecker erasure $(MAKE) -C examples -test-suite: template-coq checker safechecker erasure +test-suite: template-coq safechecker erasure $(MAKE) -C test-suite -translations: template-coq checker +translations: template-coq $(MAKE) -C translations cleanplugins: $(MAKE) -C template-coq cleanplugin - $(MAKE) -C pcuic cleanplugin - $(MAKE) -C checker cleanplugin $(MAKE) -C safechecker cleanplugin $(MAKE) -C erasure cleanplugin diff --git a/checker/Makefile b/checker/Makefile deleted file mode 100644 index d5ddec678..000000000 --- a/checker/Makefile +++ /dev/null @@ -1,44 +0,0 @@ -all: coq # plugin - -coq: Makefile.coq - $(MAKE) -f Makefile.coq - -_CoqProject: _CoqProject.in metacoq-config - cat metacoq-config > _CoqProject - cat _CoqProject.in >> _CoqProject - -_PluginProject: _PluginProject.in metacoq-config - cat metacoq-config > _PluginProject - cat _PluginProject.in >> _PluginProject - -Makefile.coq: _CoqProject - coq_makefile -f _CoqProject -o Makefile.coq - -Makefile.plugin: _PluginProject - coq_makefile -f _PluginProject -o Makefile.plugin - -plugin: Makefile.plugin coq - $(MAKE) -f Makefile.plugin - -install: coq # plugin - $(MAKE) -f Makefile.coq install - # $(MAKE) -f Makefile.plugin install - -uninstall: coq # plugin - $(MAKE) -f Makefile.coq uninstall - # $(MAKE) -f Makefile.plugin uninstall - -.PHONY: plugin - -clean: Makefile.coq Makefile.plugin - $(MAKE) -f Makefile.coq clean - $(MAKE) -f Makefile.plugin clean - -mrproper: - rm -f Makefile.coq Makefile.plugin _CoqProject _PluginProject - -.merlin: - make -f Makefile.plugin .merlin - -cleanplugin: Makefile.plugin - make -f Makefile.plugin clean diff --git a/checker/Makefile.coq.local b/checker/Makefile.coq.local deleted file mode 100644 index bb5386f49..000000000 --- a/checker/Makefile.coq.local +++ /dev/null @@ -1,4 +0,0 @@ -CAMLFLAGS+=-w -33 # Unused opens - -post-all:: - ./update_plugin.sh diff --git a/checker/Makefile.local b/checker/Makefile.local deleted file mode 100644 index 0ea15a69b..000000000 --- a/checker/Makefile.local +++ /dev/null @@ -1,3 +0,0 @@ -COQDOCFLAGS=--no-index --interpolate --parse-comments --utf8 $(COQLIBS_NOML) -INSTALLDEFAULTROOT=MetaCoq/Checker -CAMLFLAGS+=-w -33 # Unused opens \ No newline at end of file diff --git a/checker/Makefile.plugin.local b/checker/Makefile.plugin.local deleted file mode 100644 index c8b2e9962..000000000 --- a/checker/Makefile.plugin.local +++ /dev/null @@ -1,16 +0,0 @@ -CAMLFLAGS+=-open Metacoq_template_plugin # Loads the extractable monad -CAMLFLAGS+=-w -33 # Unused opens -CAMLFLAGS+=-w -32 # Unused value -CAMLFLAGS+=-w -39 # Unused rec flag -CAMLFLAGS+=-w -26 # Unused variable -CAMLFLAGS+=-w -34 # Unused type -CAMLFLAGS+=-w -20 # Unused argument -CAMLFLAGS+=-bin-annot # For merlin - -# Clean the source directory of all extracted filess -cleansrc: - rm -f src/*.ml src/*.mli src/*.d src/*.o src/*.cm* - -.PHONY: cleansrc - -theories/Loader.vo: src/metacoq_checker_plugin.cmxs diff --git a/checker/_CoqProject.in b/checker/_CoqProject.in deleted file mode 100644 index 4cc8ab28f..000000000 --- a/checker/_CoqProject.in +++ /dev/null @@ -1,17 +0,0 @@ --I ../template-coq/build --I src --R theories MetaCoq.Checker - -theories/Generation.v -theories/WeakeningEnv.v -theories/Closed.v -theories/Weakening.v -theories/Substitution.v -theories/Checker.v -theories/WcbvEval.v -theories/Retyping.v -theories/Normal.v -theories/All.v - -# Extraction -# theories/Extraction.v diff --git a/checker/_PluginProject.in b/checker/_PluginProject.in deleted file mode 100644 index 56a34318c..000000000 --- a/checker/_PluginProject.in +++ /dev/null @@ -1,99 +0,0 @@ --I src --Q src MetaCoq.Checker --R theories MetaCoq.Checker - -src/all_Forall.ml -src/all_Forall.mli -src/ascii.ml -src/ascii.mli -src/ast0.ml -src/ast0.mli -src/astUtils.ml -src/astUtils.mli -src/basicAst.ml -src/basicAst.mli -src/basics.ml -src/basics.mli -src/bool.ml -src/bool.mli -src/checker0.ml -src/checker0.mli -src/classes.ml -src/classes.mli -src/compare_dec.ml -src/compare_dec.mli -src/config0.ml -src/config0.mli -src/datatypes.ml -src/datatypes.mli -src/environment.ml -src/environment.mli -src/eqdepFacts.ml -src/eqdepFacts.mli -src/equalities.ml -src/equalities.mli -src/init.ml -src/init.mli -src/liftSubst.ml -src/liftSubst.mli -src/list0.ml -src/list0.mli -src/mCCompare.ml -src/mCCompare.mli -src/mCList.ml -src/mCList.mli -src/mCProd.ml -src/mCProd.mli -src/mSetDecide.ml -src/mSetDecide.mli -src/mSetFacts.ml -src/mSetFacts.mli -src/mSetInterface.ml -src/mSetInterface.mli -src/mSetList.ml -src/mSetList.mli -src/mSetProperties.ml -src/mSetProperties.mli -src/mSetWeakList.ml -src/mSetWeakList.mli -src/monad_utils.ml -src/monad_utils.mli -src/nat0.ml -src/nat0.mli -src/orders.ml -src/orders.mli -src/ordersFacts.ml -src/ordersFacts.mli -src/ordersLists.ml -src/ordersLists.mli -src/ordersTac.ml -src/ordersTac.mli -src/peanoNat.ml -src/peanoNat.mli -src/retyping0.ml -src/retyping0.mli -src/signature.ml -src/signature.mli -src/specif.ml -src/specif.mli -src/string0.ml -src/string0.mli -src/typing0.ml -src/typing0.mli -src/uGraph0.ml -src/uGraph0.mli -src/univSubst0.ml -src/univSubst0.mli -src/universes0.ml -src/universes0.mli -src/utils0.ml -src/utils0.mli -src/wGraph.ml -src/wGraph.mli -src/wf0.ml -src/wf0.mli - -src/g_metacoq_checker.mlg -src/metacoq_checker_plugin.mlpack - -theories/Loader.v diff --git a/checker/demo.v b/checker/demo.v deleted file mode 100644 index 59a75c78d..000000000 --- a/checker/demo.v +++ /dev/null @@ -1,9 +0,0 @@ -(* Distributed under the terms of the MIT license. *) -Require Import MetaCoq.Checker.Loader. - - -MetaCoq Check (3 + 9). - -Require Import Reals. - -MetaCoq Check Rplus. diff --git a/checker/src/.gitignore b/checker/src/.gitignore deleted file mode 100644 index bd41c435d..000000000 --- a/checker/src/.gitignore +++ /dev/null @@ -1,3 +0,0 @@ -*.mli -*.ml -to-lower.sh \ No newline at end of file diff --git a/checker/src/g_metacoq_checker.mlg b/checker/src/g_metacoq_checker.mlg deleted file mode 100644 index e2d1da052..000000000 --- a/checker/src/g_metacoq_checker.mlg +++ /dev/null @@ -1,36 +0,0 @@ - -DECLARE PLUGIN "metacoq_checker" - -{ - -open Stdarg -open Pp -open PeanoNat.Nat -open Checker0 -let pr_char c = str (Char.escaped c) - -let pr_char_list = prlist_with_sep mt pr_char - -let check env evm c = - (* Feedback.msg_debug (str"Quoting"); *) - let term = Ast_quoter.quote_term_rec env (EConstr.to_constr evm c) in - (* Feedback.msg_debug (str"Finished quoting.. checking."); *) - let fuel = pow two (pow two (pow two two)) in - let checker_flags = Config0.default_checker_flags in - match Checker0.typecheck_program checker_flags fuel term with - | CorrectDecl t -> - Feedback.msg_info (str "Successfully checked of type: " ++ pr_char_list (AstUtils.string_of_term t)) - | EnvError (AlreadyDeclared id) -> - CErrors.user_err ~hdr:"metacoq" (str "Already declared: " ++ pr_char_list id) - | EnvError (IllFormedDecl (id, e)) -> - CErrors.user_err ~hdr:"metacoq" (pr_char_list (Checker0.string_of_type_error e) ++ str ", while checking " ++ pr_char_list id) -} - -VERNAC COMMAND EXTEND MetaCoqCheck CLASSIFIED AS QUERY -| #[ poly = polymorphic ] [ "MetaCoq" "Check" constr(c) ] -> { - let env = Global.env () in - let evm = Evd.from_env env in - let (c, _) = Constrintern.interp_constr env evm c in - check env evm c - } -END diff --git a/checker/src/metacoq_checker_plugin.mlpack b/checker/src/metacoq_checker_plugin.mlpack deleted file mode 100644 index 34f9bd2fb..000000000 --- a/checker/src/metacoq_checker_plugin.mlpack +++ /dev/null @@ -1,14 +0,0 @@ -EqdepFacts -Wf -WGraph -Monad_utils -Utils -MSetWeakList -UGraph0 -EnvironmentTyping -Typing0 -Checker0 -Retyping0 -TypingWf - -G_metacoq_checker diff --git a/checker/src/to-lower.sh b/checker/src/to-lower.sh new file mode 100755 index 000000000..93bb3e362 --- /dev/null +++ b/checker/src/to-lower.sh @@ -0,0 +1,9 @@ +for i in *.ml* +do + newi=`echo $i | cut -b 1 | tr '[:upper:]' '[:lower:]'``echo $i | cut -b 2-`; + if [ $i != $newi ] + then + echo "Moving " $i "to" $newi; + mv $i $newi; + fi +done diff --git a/checker/theories/All.v b/checker/theories/All.v deleted file mode 100644 index 136a08cb0..000000000 --- a/checker/theories/All.v +++ /dev/null @@ -1,8 +0,0 @@ -(* Distributed under the terms of the MIT license. *) - -Require Export MetaCoq.Template.All. -From MetaCoq.Checker Require Export - Weakening (* Weakening lemmas *) - Substitution (* Weakening lemmas *) - Checker (* Partial typechecker implementation *) - Retyping (* Fast retyping judgment *). diff --git a/checker/theories/Checker.v b/checker/theories/Checker.v deleted file mode 100644 index 969bf8dc5..000000000 --- a/checker/theories/Checker.v +++ /dev/null @@ -1,1166 +0,0 @@ -(* Distributed under the terms of the MIT license. *) -From MetaCoq.Template Require Import config Ast AstUtils utils - LiftSubst UnivSubst uGraph Typing. - -(** * Coq type-checker for kernel terms - - Implemets [typecheck_program] which returns an error and - on success should guarantee that the term has the given type. - Currently uses fuel to implement reduction. - - Correctness and completeness proofs are a work-in-progress. - - This file implements reduction with a stack machine [reduce_stack], - conversion/cumulativity with the first-order fast-path heuristic [isconv] - that are used to type-check terms in reasonable time. *) - - -Local Notation " () " := Datatypes.unit : type_scope. -Local Notation " () " := tt. - -Module RedFlags. - - Record t := mk - { beta : bool; - iota : bool; - zeta : bool; - delta : bool; - fix_ : bool; - cofix_ : bool }. - - Definition default := mk true true true true true true. -End RedFlags. - -Lemma congr_cumul_prod `{checker_flags} : forall Σ Γ na na' M1 M2 N1 N2, - cumul Σ Γ M1 N1 -> - cumul Σ (Γ ,, vass na M1) M2 N2 -> - cumul Σ Γ (tProd na M1 M2) (tProd na' N1 N2). -Proof. intros. todo "congr_cumul_prod". Defined. - -Section Reduce. - Context (flags : RedFlags.t) (Σ : global_env). - - Definition zip (t : term * list term) := mkApps (fst t) (snd t). - - Fixpoint reduce_stack (Γ : context) (n : nat) (t : term) (stack : list term) - : option (term * list term) := - match n with 0 => None | S n => - match t with - - | tRel c => - if RedFlags.zeta flags then - d <- nth_error Γ c ;; - match d.(decl_body) with - | None => ret (t, stack) - | Some b => reduce_stack Γ n (lift0 (S c) b) stack - end - else ret (t, stack) - - | tLetIn _ b _ c => - if RedFlags.zeta flags then - reduce_stack Γ n (subst10 b c) stack - else ret (t, stack) - - | tConst c u => - if RedFlags.delta flags then - match lookup_env Σ c with - | Some (ConstantDecl {| cst_body := Some body |}) => - let body' := subst_instance_constr u body in - reduce_stack Γ n body' stack - | _ => ret (t, stack) - end - else ret (t, stack) - - | tApp f args => reduce_stack Γ n f (args ++ stack) - - | tLambda na ty b => - if RedFlags.beta flags then - match stack with - | a :: args' => - (** CBN reduction: we do not reduce arguments before substitution *) - (* a' <- reduce_stack Γ n a [] ;; *) - reduce_stack Γ n (subst10 a b) args' - | _ => ret (t, stack) - (* b' <- reduce_stack (Γ ,, vass na ty) n b stack ;; *) - (* ret (tLambda na ty (zip b'), stack) *) - end - else ret (t, stack) - - | tFix mfix idx => - if RedFlags.fix_ flags then - nf <- unfold_fix mfix idx ;; - let '(narg, fn) := nf in - match List.nth_error stack narg with - | Some c => - c' <- reduce_stack Γ n c [] ;; - match fst c' with - | tConstruct _ _ _ => reduce_stack Γ n fn stack - | _ => ret (t, stack) - end - | _ => ret (t, stack) - end - else ret (t, stack) - - | tProd _ _ _ => ret (t, stack) - - (* b' <- reduce_stack Γ n b [] ;; *) - (* t' <- reduce_stack (Γ ,, vass na (zip b')) n t [] ;; *) - (* ret (tProd na (zip b') (zip t'), stack) *) - - | tCast c _ _ => reduce_stack Γ n c stack - - | tCase ((ind, par), relevance) p c brs => - if RedFlags.iota flags then - c' <- reduce_stack Γ n c [] ;; - match c' with - | (tConstruct ind c _, args) => reduce_stack Γ n (iota_red par c args brs) stack - | _ => ret (tCase ((ind, par), relevance) p (zip c') brs, stack) - end - else ret (t, stack) - - | _ => ret (t, stack) - - end - end. - - Definition reduce_stack_term Γ n c := - res <- reduce_stack Γ n c [] ;; - ret (zip res). - - Definition fix_decls (l : mfixpoint term) := - let fix aux acc ds := - match ds with - | nil => acc - | d :: ds => aux (vass d.(dname) d.(dtype) :: acc) ds - end - in aux [] l. - - Definition map_constr_with_binders (f : context -> term -> term) Γ (t : term) : term := - match t with - | tRel i => t - | tEvar ev args => tEvar ev (List.map (f Γ) args) - | tLambda na T M => tLambda na (f Γ T) (f Γ M) - | tApp u v => tApp (f Γ u) (List.map (f Γ) v) - | tProd na A B => - let A' := f Γ A in - tProd na A' (f (Γ ,, vass na A') B) - | tCast c kind t => tCast (f Γ c) kind (f Γ t) - | tLetIn na b t c => - let b' := f Γ b in - let t' := f Γ t in - tLetIn na b' t' (f (Γ ,, vdef na b' t') c) - | tCase ind p c brs => - let brs' := List.map (on_snd (f Γ)) brs in - tCase ind (f Γ p) (f Γ c) brs' - | tProj p c => tProj p (f Γ c) - | tFix mfix idx => - let Γ' := fix_decls mfix ++ Γ in - let mfix' := List.map (map_def (f Γ) (f Γ')) mfix in - tFix mfix' idx - | tCoFix mfix k => - let Γ' := fix_decls mfix ++ Γ in - let mfix' := List.map (map_def (f Γ) (f Γ')) mfix in - tCoFix mfix' k - | x => x - end. - - Fixpoint reduce_opt Γ n c := - match n with - | 0 => None - | S n => - match reduce_stack_term Γ n c with - | Some c' => - Some (map_constr_with_binders - (fun Γ t => match reduce_opt Γ n t with - | Some t => t - | None => t end) Γ c') - | None => None - end - end. - -End Reduce. - -Definition isConstruct c := - match c with - | tConstruct _ _ _ => true - | tApp (tConstruct _ _ _) _ => true - | _ => false - end. - -Definition isCoFix c := - match c with - | tCoFix _ _ => true - | _ => false - end. - -Inductive conv_pb := -| Conv -| Cumul. - -Fixpoint eq_term `{checker_flags} (φ : universes_graph) (t u : term) {struct t} := - match t, u with - | tRel n, tRel n' => Nat.eqb n n' - | tEvar ev args, tEvar ev' args' => Nat.eqb ev ev' && forallb2 (eq_term φ) args args' - | tVar id, tVar id' => eq_string id id' - | tSort s, tSort s' => check_eqb_universe φ s s' - | tCast f k T, tCast f' k' T' => eq_term φ f f' && eq_term φ T T' - | tApp f args, tApp f' args' => eq_term φ f f' && forallb2 (eq_term φ) args args' - | tConst c u, tConst c' u' => eq_constant c c' && eqb_univ_instance φ u u' - | tInd i u, tInd i' u' => eq_inductive i i' && eqb_univ_instance φ u u' - | tConstruct i k u, tConstruct i' k' u' => eq_inductive i i' && Nat.eqb k k' - && eqb_univ_instance φ u u' - | tLambda _ b t, tLambda _ b' t' => eq_term φ b b' && eq_term φ t t' - | tProd _ b t, tProd _ b' t' => eq_term φ b b' && eq_term φ t t' - | tLetIn _ b t c, tLetIn _ b' t' c' => eq_term φ b b' && eq_term φ t t' && eq_term φ c c' - | tCase ((ind, par), rel) p c brs, - tCase ((ind',par'), rel') p' c' brs' => - eq_inductive ind ind' && Nat.eqb par par' && - eq_term φ p p' && eq_term φ c c' && forallb2 (fun '(a, b) '(a', b') => eq_term φ b b') brs brs' - | tProj p c, tProj p' c' => eq_projection p p' && eq_term φ c c' - | tFix mfix idx, tFix mfix' idx' => - forallb2 (fun x y => - eq_term φ x.(dtype) y.(dtype) && eq_term φ x.(dbody) y.(dbody)) mfix mfix' && - Nat.eqb idx idx' - | tCoFix mfix idx, tCoFix mfix' idx' => - forallb2 (fun x y => - eq_term φ x.(dtype) y.(dtype) && eq_term φ x.(dbody) y.(dbody)) mfix mfix' && - Nat.eqb idx idx' - | _, _ => false - end. - - -Fixpoint leq_term `{checker_flags} (φ : universes_graph) (t u : term) {struct t} := - match t, u with - | tRel n, tRel n' => Nat.eqb n n' - | tEvar ev args, tEvar ev' args' => Nat.eqb ev ev' && forallb2 (eq_term φ) args args' - | tVar id, tVar id' => eq_string id id' - | tSort s, tSort s' => check_leqb_universe φ s s' - | tApp f args, tApp f' args' => eq_term φ f f' && forallb2 (eq_term φ) args args' - | tCast f k T, tCast f' k' T' => eq_term φ f f' && eq_term φ T T' - | tConst c u, tConst c' u' => eq_constant c c' && eqb_univ_instance φ u u' - | tInd i u, tInd i' u' => eq_inductive i i' && eqb_univ_instance φ u u' - | tConstruct i k u, tConstruct i' k' u' => eq_inductive i i' && Nat.eqb k k' && - eqb_univ_instance φ u u' - | tLambda _ b t, tLambda _ b' t' => eq_term φ b b' && eq_term φ t t' - | tProd _ b t, tProd _ b' t' => eq_term φ b b' && leq_term φ t t' - | tLetIn _ b t c, tLetIn _ b' t' c' => eq_term φ b b' && eq_term φ t t' && leq_term φ c c' - | tCase ((ind, par), rel) p c brs, - tCase ((ind',par'), rel') p' c' brs' => - eq_inductive ind ind' && Nat.eqb par par' && - eq_term φ p p' && eq_term φ c c' && forallb2 (fun '(a, b) '(a', b') => eq_term φ b b') brs brs' - | tProj p c, tProj p' c' => eq_projection p p' && eq_term φ c c' - | tFix mfix idx, tFix mfix' idx' => - forallb2 (fun x y => - eq_term φ x.(dtype) y.(dtype) && eq_term φ x.(dbody) y.(dbody)) mfix mfix' && - Nat.eqb idx idx' - | tCoFix mfix idx, tCoFix mfix' idx' => - forallb2 (fun x y => - eq_term φ x.(dtype) y.(dtype) && eq_term φ x.(dbody) y.(dbody)) mfix mfix' && - Nat.eqb idx idx' - | _, _ => false - end. - -Section Conversion. - - Context `{checker_flags} (flags : RedFlags.t). - Context (Σ : global_env) (G : universes_graph). - - Definition nodelta_flags := RedFlags.mk true true true false true true. - - Definition unfold_one_fix n Γ mfix idx l := - unf <- unfold_fix mfix idx ;; - let '(arg, fn) := unf in - c <- nth_error l arg ;; - cred <- reduce_stack RedFlags.default Σ Γ n c [] ;; - let '(cred, _) := cred in - if negb (isConstruct cred) then None - else Some fn. - - Definition unfold_one_case n Γ c := - cred <- reduce_stack_term RedFlags.default Σ Γ n c ;; - if negb (isConstruct cred || isCoFix cred) then None - else Some cred. - - Definition reducible_head n Γ c l := - match c with - | tFix mfix idx => unfold_one_fix n Γ mfix idx l - | tCase ind' p' c' brs => - match unfold_one_case n Γ c' with - | None => None - | Some c' => Some (tCase ind' p' c' brs) - end - | tProj p c => - match unfold_one_case n Γ c with - | None => None - | Some c' => Some (tProj p c') - end - | tConst c _ => (* TODO Universes *) - match lookup_env Σ c with - | Some (ConstantDecl {| cst_body := Some body |}) => Some body - | _ => None - end - | _ => None - end. - - Definition lookup_env c := lookup_env Σ c. - - Definition opt_bool_to_bool (x : option bool) : bool := - match x with - | Some b => b - | None => false - end. - - - Fixpoint isconv (n : nat) (leq : conv_pb) (Γ : context) - (t1 : term) (l1 : list term) (t2 : term) (l2 : list term) {struct n} : option bool := - match n with 0 => None | S n => - red1 <- reduce_stack nodelta_flags Σ Γ n t1 l1 ;; - red2 <- reduce_stack nodelta_flags Σ Γ n t2 l2 ;; - let '(t1,l1) := red1 in - let '(t2,l2) := red2 in - isconv_prog n leq Γ t1 l1 t2 l2 - end - with isconv_prog (n : nat) (leq : conv_pb) (Γ : context) - (t1 : term) (l1 : list term) (t2 : term) (l2 : list term) - {struct n} : option bool := - match n with 0 => None | S n => - let isconv_stacks l1 l2 := - ret (forallb2 (fun x y => opt_bool_to_bool (isconv n Conv Γ x [] y [])) l1 l2) - in - let on_cond (b : bool) := if b then isconv_stacks l1 l2 else ret false in - (** Test equality at each step ?? *) - (* if eq_term t1 t2 && (match isconv_stacks l1 l2 with Some true => true | _ => false) *) - (* then ret true else *) - let fallback (x : unit) := - match reducible_head n Γ t1 l1 with - | Some t1 => - redt <- reduce_stack nodelta_flags Σ Γ n t1 l1 ;; - let '(t1, l1) := redt in - isconv_prog n leq Γ t1 l1 t2 l2 - | None => - match reducible_head n Γ t2 l2 with - | Some t2 => - redt <- reduce_stack nodelta_flags Σ Γ n t2 l2 ;; - let '(t2, l2) := redt in - isconv_prog n leq Γ t1 l1 t2 l2 - | None => - on_cond (match leq with - | Conv => eq_term G t1 t2 - | Cumul => leq_term G t1 t2 end) - end - end - in - match t1, t2 with - | tApp f args, tApp f' args' => - None (* Impossible *) - - | tCast t _ v, tCast u _ v' => None (* Impossible *) - - | tConst c u, tConst c' u' => (* TODO Universes *) - if eq_constant c c' then - b <- isconv_stacks l1 l2 ;; - if b then ret true (* FO optim *) - else - match lookup_env c with (* Unfold both bodies at once *) - | Some (ConstantDecl {| cst_body := Some body |}) => - isconv n leq Γ body l1 body l2 - | _ => ret false - end - else - match lookup_env c' with - | Some (ConstantDecl {| cst_body := Some body |}) => - isconv n leq Γ t1 l1 body l2 - | _ => - match lookup_env c with - | Some (ConstantDecl {| cst_body := Some body |}) => - isconv n leq Γ body l1 t2 l2 - | _ => ret false - end - end - - | tLambda na b t, tLambda _ b' t' => - cnv <- isconv n Conv Γ b [] b' [] ;; - if (cnv : bool) then - isconv n Conv (Γ ,, vass na b) t [] t' [] - else ret false - - | tProd na b t, tProd _ b' t' => - cnv <- isconv n Conv Γ b [] b' [] ;; - if (cnv : bool) then - isconv n leq (Γ ,, vass na b) t [] t' [] - else ret false - - | tCase (ind, par) p c brs, - tCase (ind',par') p' c' brs' => (* Hnf did not reduce, maybe delta needed in c *) - if eq_term G p p' && eq_term G c c' - && forallb2 (fun '(a, b) '(a', b') => eq_term G b b') brs brs' then - ret true - else - cred <- reduce_stack_term RedFlags.default Σ Γ n c ;; - c'red <- reduce_stack_term RedFlags.default Σ Γ n c' ;; - if eq_term G cred c && eq_term G c'red c' then ret true - else - isconv n leq Γ (tCase (ind, par) p cred brs) l1 (tCase (ind, par) p c'red brs') l2 - - | tProj p c, tProj p' c' => on_cond (eq_projection p p' && eq_term G c c') - - | tFix mfix idx, tFix mfix' idx' => - (* Hnf did not reduce, maybe delta needed *) - if eq_term G t1 t2 && opt_bool_to_bool (isconv_stacks l1 l2) then ret true - else - match unfold_one_fix n Γ mfix idx l1 with - | Some t1 => - redt <- reduce_stack nodelta_flags Σ Γ n t1 l1 ;; - let '(t1, l1) := redt in - isconv_prog n leq Γ t1 l1 t2 l2 - | None => - match unfold_one_fix n Γ mfix' idx' l2 with - | Some t2 => - redt <- reduce_stack nodelta_flags Σ Γ n t2 l2 ;; - let '(t2, l2) := redt in - isconv_prog n leq Γ t1 l1 t2 l2 - | None => ret false - end - end - - | tCoFix mfix idx, tCoFix mfix' idx' => - on_cond (eq_term G t1 t2) - - | _, _ => fallback () - end - end. -End Conversion. - -Definition try_reduce Σ Γ n t := - match reduce_opt RedFlags.default Σ Γ n t with - | Some t' => t' - | None => t - end. - - -Inductive type_error := -| UnboundRel (n : nat) -| UnboundVar (id : string) -| UnboundMeta (m : nat) -| UnboundEvar (ev : nat) -| UndeclaredConstant (c : kername) -| UndeclaredInductive (c : inductive) -| UndeclaredConstructor (c : inductive) (i : nat) -| NotConvertible (Γ : context) (t u t' u' : term) -| NotASort (t : term) -| NotAProduct (t t' : term) -| NotAnInductive (t : term) -| IllFormedFix (m : mfixpoint term) (i : nat) -| UnsatisfiedConstraints (c : ConstraintSet.t) -| UnsatisfiableConstraints (c : ConstraintSet.t) -| NotEnoughFuel (n : nat) -| NotSupported (s : string). - -Definition string_of_type_error (e : type_error) : string := - match e with - | UnboundRel n => "Unboound rel " ^ string_of_nat n - | UnboundVar id => "Unbound var " ^ id - | UnboundMeta m => "Unbound meta " ^ string_of_nat m - | UnboundEvar ev => "Unbound evar " ^ string_of_nat ev - | UndeclaredConstant c => "Undeclared constant " ^ string_of_kername c - | UndeclaredInductive c => "Undeclared inductive " ^ string_of_kername (inductive_mind c) - | UndeclaredConstructor c i => "Undeclared inductive " ^ string_of_kername (inductive_mind c) - | NotConvertible Γ t u t' u' => "Terms are not convertible: " ^ - string_of_term t ^ " " ^ string_of_term u ^ " after reduction: " ^ - string_of_term t' ^ " " ^ string_of_term u' - | NotASort t => "Not a sort" - | NotAProduct t t' => "Not a product" - | NotAnInductive t => "Not an inductive" - | IllFormedFix m i => "Ill-formed recursive definition" - | UnsatisfiedConstraints c => "Unsatisfied constraints" - | UnsatisfiableConstraints c => "Unsatisfiable constraints" - | NotEnoughFuel n => "Not enough fuel" - | NotSupported s => s ^ " are not supported" - end. - -Inductive typing_result (A : Type) := -| Checked (a : A) -| TypeError (t : type_error). -Global Arguments Checked {A} a. -Global Arguments TypeError {A} t. - -Instance typing_monad : Monad typing_result := - {| ret A a := Checked a ; - bind A B m f := - match m with - | Checked a => f a - | TypeError t => TypeError t - end - |}. - -Instance monad_exc : MonadExc type_error typing_result := - { raise A e := TypeError e; - catch A m f := - match m with - | Checked a => m - | TypeError t => f t - end - }. - -Definition check_conv_gen `{checker_flags} {F:Fuel} conv_pb Σ G Γ t u := - match isconv Σ G fuel conv_pb Γ t [] u [] with - | Some b => if b then ret () else raise (NotConvertible Γ t u t u) - | None => raise (NotEnoughFuel fuel) - end. - -Definition check_conv_leq `{checker_flags} {F:Fuel} := check_conv_gen Cumul. -Definition check_conv `{checker_flags} {F:Fuel} := check_conv_gen Conv. - - -Definition is_graph_of_global_env_ext `{checker_flags} Σ G := - is_graph_of_uctx G (global_ext_uctx Σ). - -Lemma conv_spec : forall `{checker_flags} {F:Fuel} Σ G Γ t u, - is_graph_of_global_env_ext Σ G -> - Σ ;;; Γ |- t = u <~> check_conv (fst Σ) G Γ t u = Checked (). -Proof. - intros. todo "Checker.conv_spec". -Defined. - -Lemma cumul_spec : forall `{checker_flags} {F:Fuel} Σ G Γ t u, - is_graph_of_global_env_ext Σ G -> - Σ ;;; Γ |- t <= u <~> check_conv_leq (fst Σ) G Γ t u = Checked (). -Proof. - intros. todo "Checker.cumul_spec". -Defined. - -Lemma reduce_cumul : - forall `{checker_flags} Σ Γ n t, Σ ;;; Γ |- try_reduce (fst Σ) Γ n t <= t. -Proof. intros. todo "Checker.reduce_cumul". Defined. - - -Section Typecheck. - Context {F : Fuel}. - Context (Σ : global_env). - - Definition hnf_stack Γ t := - match reduce_stack RedFlags.default Σ Γ fuel t [] with - | Some t' => ret t' - | None => raise (NotEnoughFuel fuel) - end. - - Definition reduce Γ t := - match reduce_opt RedFlags.default Σ Γ fuel t with - | Some t' => ret t' - | None => raise (NotEnoughFuel fuel) - end. - - Definition reduce_to_sort Γ (t : term) : typing_result Universe.t := - match t with - | tSort s => ret s - | _ => - t' <- hnf_stack Γ t ;; - match t' with - | (tSort s, []) => ret s - | _ => raise (NotASort t) - end - end. - - Definition reduce_to_prod Γ (t : term) : typing_result (term * term) := - match t with - | tProd _ a b => ret (a, b) - | _ => - t' <- hnf_stack Γ t ;; - match t' with - | (tProd _ a b,[]) => ret (a, b) - | _ => raise (NotAProduct t (zip t')) - end - end. - - Definition reduce_to_ind Γ (t : term) : - typing_result (inductive * list Level.t * list term) := - match decompose_app t with - | (tInd i u, l) => ret (i, u, l) - | _ => t' <- hnf_stack Γ t ;; - match t' with - | (tInd i u, l) => ret (i, u, l) - | _ => raise (NotAnInductive t) - end - end. -End Typecheck. - -Section Typecheck2. - Context {cf : checker_flags} {F : Fuel}. - Context (Σ : global_env) (G : universes_graph). - - Definition convert_leq Γ (t u : term) : typing_result unit := - if eq_term G t u then ret () - else - match isconv Σ G fuel Cumul Γ t [] u [] with - | Some b => - if b then ret () - else raise (NotConvertible Γ t u t u) - | None => (* fallback *) - t' <- reduce Σ Γ t ;; - u' <- reduce Σ Γ u ;; - if leq_term G t' u' then ret () - else raise (NotConvertible Γ t u t' u') - end. - - Section InferAux. - Variable (infer : context -> term -> typing_result term). - - Fixpoint infer_spine (Γ : context) (ty : term) (l : list term) - {struct l} : typing_result term := - match l with - | nil => ret ty - | cons x xs => - pi <- reduce_to_prod Σ Γ ty ;; - let '(a1, b1) := pi in - tx <- infer Γ x ;; - convert_leq Γ tx a1 ;; - infer_spine Γ (subst10 x b1) xs - end. - - Definition infer_type Γ t := - tx <- infer Γ t ;; - reduce_to_sort Σ Γ tx. - - Definition infer_cumul Γ t t' := - tx <- infer Γ t ;; - convert_leq Γ tx t'. - - End InferAux. - - Definition polymorphic_constraints u := - match u with - | Monomorphic_ctx _ => ConstraintSet.empty - | Polymorphic_ctx ctx => snd (AUContext.repr ctx) - end. - - Definition lookup_constant_type cst u := - match lookup_env Σ cst with - | Some (ConstantDecl {| cst_type := ty; cst_universes := uctx |}) => - ret (subst_instance_constr u ty) - | _ => raise (UndeclaredConstant cst) - end. - - Definition lookup_constant_type_cstrs cst u := - match lookup_env Σ cst with - | Some (ConstantDecl {| cst_type := ty; cst_universes := uctx |}) => - let cstrs := polymorphic_constraints uctx in - ret (subst_instance_constr u ty, subst_instance_cstrs u cstrs) - | _ => raise (UndeclaredConstant cst) - end. - - Definition lookup_ind_decl ind i := - match lookup_env Σ ind with - | Some (InductiveDecl {| ind_bodies := l; ind_universes := uctx |}) => - match nth_error l i with - | Some body => ret (l, uctx, body) - | None => raise (UndeclaredInductive (mkInd ind i)) - end - | _ => raise (UndeclaredInductive (mkInd ind i)) - end. - - Definition lookup_ind_type ind i (u : list Level.t) := - res <- lookup_ind_decl ind i ;; - ret (subst_instance_constr u (snd res).(ind_type)). - - Definition lookup_ind_type_cstrs ind i (u : list Level.t) := - res <- lookup_ind_decl ind i ;; - let '(l, uctx, body) := res in - let cstrs := polymorphic_constraints uctx in - ret (subst_instance_constr u body.(ind_type), subst_instance_cstrs u cstrs). - - Definition lookup_constructor_decl ind i k := - res <- lookup_ind_decl ind i;; - let '(l, uctx, body) := res in - match nth_error body.(ind_ctors) k with - | Some (_, ty, _) => ret (l, uctx, ty) - | None => raise (UndeclaredConstructor (mkInd ind i) k) - end. - - Definition lookup_constructor_type ind i k u := - res <- lookup_constructor_decl ind i k ;; - let '(l, uctx, ty) := res in - ret (subst0 (inds ind u l) (subst_instance_constr u ty)). - - Definition lookup_constructor_type_cstrs ind i k u := - res <- lookup_constructor_decl ind i k ;; - let '(l, uctx, ty) := res in - let cstrs := polymorphic_constraints uctx in - ret (subst0 (inds ind u l) (subst_instance_constr u ty), - subst_instance_cstrs u cstrs). - - Definition check_consistent_constraints cstrs := - if check_constraints G cstrs then ret tt - else raise (UnsatisfiedConstraints cstrs). - - Fixpoint infer (Γ : context) (t : term) : typing_result term := - match t with - | tRel n => - match nth_error Γ n with - | Some d => ret (lift0 (S n) d.(decl_type)) - | None => raise (UnboundRel n) - end - - | tVar n => raise (UnboundVar n) - | tEvar ev args => raise (UnboundEvar ev) - - | tSort s => ret (tSort (Universe.super s)) - - | tCast c k t => - infer_type infer Γ t ;; - infer_cumul infer Γ c t ;; - ret t - - | tProd n t b => - s1 <- infer_type infer Γ t ;; - s2 <- infer_type infer (Γ ,, vass n t) b ;; - ret (tSort (Universe.sort_of_product s1 s2)) - - | tLambda n t b => - infer_type infer Γ t ;; - t2 <- infer (Γ ,, vass n t) b ;; - ret (tProd n t t2) - - | tLetIn n b b_ty b' => - infer_type infer Γ b_ty ;; - infer_cumul infer Γ b b_ty ;; - b'_ty <- infer (Γ ,, vdef n b b_ty) b' ;; - ret (tLetIn n b b_ty b'_ty) - - | tApp t l => - t_ty <- infer Γ t ;; - infer_spine infer Γ t_ty l - - | tConst cst u => - tycstrs <- lookup_constant_type_cstrs cst u ;; - let '(ty, cstrs) := tycstrs in - check_consistent_constraints cstrs;; - ret ty - - | tInd (mkInd ind i) u => - tycstrs <- lookup_ind_type_cstrs ind i u;; - let '(ty, cstrs) := tycstrs in - check_consistent_constraints cstrs;; - ret ty - - | tConstruct (mkInd ind i) k u => - tycstrs <- lookup_constructor_type_cstrs ind i k u ;; - let '(ty, cstrs) := tycstrs in - check_consistent_constraints cstrs;; - ret ty - - | tCase ((ind, par), rel) p c brs => - ty <- infer Γ c ;; - indargs <- reduce_to_ind Σ Γ ty ;; - (** TODO check branches *) - let '(ind', u, args) := indargs in - if eq_inductive ind ind' then - ret (tApp p (List.skipn par args ++ [c])) - else - let ind1 := tInd ind u in - let ind2 := tInd ind' u in - raise (NotConvertible Γ ind1 ind2 ind1 ind2) - - | tProj p c => - ty <- infer Γ c ;; - indargs <- reduce_to_ind Σ Γ ty ;; - (* FIXME *) - ret ty - - | tFix mfix n => - match nth_error mfix n with - | Some f => ret f.(dtype) - | None => raise (IllFormedFix mfix n) - end - - | tCoFix mfix n => - match nth_error mfix n with - | Some f => ret f.(dtype) - | None => raise (IllFormedFix mfix n) - end - - | tInt _ | tFloat _ => raise (NotSupported "primitive types") - end. - - Definition check (Γ : context) (t : term) (ty : term) : typing_result unit := - infer Γ ty ;; - infer_cumul infer Γ t ty ;; - ret (). - - Definition typechecking (Γ : context) (t ty : term) := - match check Γ t ty with - | Checked _ => true - | TypeError _ => false - end. - -End Typecheck2. - -Lemma cumul_convert_leq : forall `{checker_flags} {F:Fuel} Σ G Γ t t', - is_graph_of_global_env_ext Σ G -> - Σ ;;; Γ |- t <= t' <~> convert_leq (fst Σ) G Γ t t' = Checked (). -Proof. intros. todo "Checker.cumul_convert_leq". Defined. - -Lemma cumul_reduce_to_sort : forall `{checker_flags} {F:Fuel} Σ G Γ t s', - is_graph_of_global_env_ext Σ G -> - Σ ;;; Γ |- t <= tSort s' <~> - { s'' & reduce_to_sort (fst Σ) Γ t = Checked s'' - /\ check_leqb_universe G s'' s' = true }. -Proof. intros. todo "Checker.cumul_reduce_to_sort". Defined. - -Lemma cumul_reduce_to_product : forall `{checker_flags} {F:Fuel} Σ Γ t na a b, - Σ ;;; Γ |- t <= tProd na a b -> - { a' & { b' & - ((reduce_to_prod (fst Σ) Γ t = Checked (a', b')) * - cumul Σ Γ (tProd na a' b') (tProd na a b))%type } }. -Proof. intros. todo "Checker.cumul_reduce_to_product". Defined. - -Lemma cumul_reduce_to_ind : forall `{checker_flags} {F:Fuel} Σ Γ t i u args, - Σ ;;; Γ |- t <= mkApps (tInd i u) args <~> - { args' & - ((reduce_to_ind (fst Σ) Γ t = Checked (i, u, args')) * - cumul Σ Γ (mkApps (tInd i u) args') (mkApps (tInd i u) args))%type }. -Proof. intros. todo "Checker.cumul_reduce_to_ind". Defined. - -Lemma lookup_constant_type_declared Σ cst u decl (isdecl : declared_constant Σ cst decl) : - lookup_constant_type_cstrs Σ cst u = - Checked (subst_instance_constr u decl.(cst_type), - subst_instance_cstrs u (polymorphic_constraints decl.(cst_universes))). -Proof. - unfold lookup_constant_type_cstrs, lookup_env. - red in isdecl. rewrite isdecl. destruct decl. reflexivity. -Qed. - -Lemma lookup_constant_type_is_declared Σ cst u T : - lookup_constant_type_cstrs Σ cst u = Checked T -> - { decl | declared_constant Σ cst decl /\ - subst_instance_constr u decl.(cst_type) = fst T }. -Proof. - unfold lookup_constant_type_cstrs, lookup_env, declared_constant. - destruct Ast.lookup_env eqn:Hlook; try discriminate. - destruct g eqn:Hg; intros; try discriminate. destruct c. - injection H as eq. subst T. simpl. - eexists. split; eauto. -Qed. - - -Arguments bind _ _ _ _ ! _. -Open Scope monad. - - -Section InferOk. - Context {cf : checker_flags} {F : Fuel}. - Context (Σ : global_env_ext) (G : universes_graph) - (HG : is_graph_of_global_env_ext Σ G). - - Ltac tc := eauto with typecheck. - -(* - Lemma infer_complete Γ t T : - Σ ;;; Γ |- t : T -> { T' & ((infer Γ t = Checked T') /\ squash (cumul Σ Γ T' T)) }. - Proof. - induction 1; unfold infer_type, infer_cumul in *; simpl; unfold infer_type, infer_cumul in *; - repeat match goal with - H : { T' & _ } |- _ => destruct H as [? [-> H]] - end; simpl; try (eexists; split; [ reflexivity | solve [ tc ] ]). - - - eexists. rewrite e. - split; [ reflexivity | constructor; tc ]. - - - eexists. split; [reflexivity | tc]. - constructor. simpl. unfold leq_universe. - admit. - - - eexists. - apply cumul_reduce_to_sort in IHX1 as [s'' [-> Hs'']]. - apply cumul_convert_leq in IHX2 as ->. - simpl. split; tc. - - - apply cumul_reduce_to_sort in IHX1 as [s'' [-> Hs'']]. - apply cumul_reduce_to_sort in IHX2 as [s''' [-> Hs''']]. - simpl. eexists; split; tc. - admit. - - - eexists. apply cumul_reduce_to_sort in IHX1 as [s'' [-> Hs'']]. - split. reflexivity. - apply congr_cumul_prod; tc. - - - apply cumul_convert_leq in IHX2 as ->; simpl. - eexists ; split; tc. - admit. - - - admit. - - - erewrite lookup_constant_type_declared; eauto. - eexists ; split; [ try reflexivity | tc ]. - simpl. unfold consistent_universe_context_instance in c. - destruct cst_universes. simpl. reflexivity. - simpl in *. destruct cst0. simpl in *. - destruct c. unfold check_consistent_constraints. rewrite H0. reflexivity. - admit. - - - admit. - - admit. - - - (* destruct indpar. *) - apply cumul_reduce_to_ind in IHX2 as [args' [-> Hcumul]]. - simpl in *. rewrite (proj2 (eq_ind_refl ind ind) eq_refl). - eexists ; split; [ reflexivity | tc ]. - admit. - - - admit. - - - eexists. rewrite e. - split; [ reflexivity | tc ]. - - - eexists. rewrite e. - split; [ reflexivity | tc ]. - - - eexists. - split; [ reflexivity | tc ]. - eapply cumul_trans; eauto. - Admitted. - *) - Ltac infers := - repeat - match goal with - | |- context [infer ?Γ ?t] => - destruct (infer Γ t) eqn:?; [ simpl | simpl; intro; discriminate ] - | |- context [infer_type ?Γ ?t] => - destruct (infer_type Γ t) eqn:?; [ simpl | simpl; intro; discriminate ] - | |- context [infer_cumul ?Γ ?t ?t2] => - destruct (infer_cumul Γ t t2) eqn:?; [ simpl | simpl; intro; discriminate ] - | |- context [convert_leq ?Γ ?t ?t2] => - destruct (convert_leq Γ t t2) eqn:?; [ simpl | simpl; intro; discriminate ] - end; try intros [= <-]. - - - Lemma infer_type_correct Γ t x : - (forall (Γ : context) (T : term), infer (fst Σ) G Γ t = Checked T -> Σ ;;; Γ |- t : T) -> - infer_type (fst Σ) (infer (fst Σ) G) Γ t = Checked x -> - Σ ;;; Γ |- t : tSort x. - Proof. - intros IH H. - unfold infer_type in H. - revert H; infers. - specialize (IH _ _ Heqt0). - intros. - eapply type_Conv. apply IH. - admit. - eapply cumul_reduce_to_sort. eassumption. - exists x. split; tc. - Admitted. - - - Lemma infer_cumul_correct Γ t u x x' : - (forall (Γ : context) (T : term), infer (fst Σ) G Γ u = Checked T -> Σ ;;; Γ |- u : T) -> - (forall (Γ : context) (T : term), infer (fst Σ) G Γ t = Checked T -> Σ ;;; Γ |- t : T) -> - infer_type (fst Σ) (infer (fst Σ) G) Γ u = Checked x' -> - infer_cumul (fst Σ) G (infer (fst Σ) G) Γ t u = Checked x -> - Σ ;;; Γ |- t : u. - Proof. - intros IH IH' H H'. - unfold infer_cumul in H'. - revert H'; infers. - specialize (IH' _ _ Heqt0). - intros. - eapply type_Conv. apply IH'. - apply infer_type_correct in H; eauto. - destruct a0. eapply cumul_convert_leq; eassumption. - Qed. - - Ltac infco := eauto using infer_cumul_correct, infer_type_correct. - - (* Axiom cheat : forall A, A. *) - (* Ltac admit := apply cheat. *) - - Lemma infer_correct Γ t T : wf_local Σ Γ -> - infer (fst Σ) G Γ t = Checked T -> Σ ;;; Γ |- t : T. - Proof. - (* induction t in Γ, T |- * ; simpl; intros; try discriminate; *) - (* revert H; infers; try solve [econstructor; infco]. *) - - (* - destruct nth_error eqn:Heq; try discriminate. *) - (* intros [= <-]. constructor; auto. *) - - (* - admit. *) - (* - admit. *) - - (* - admit. *) - (* intros. *) - (* destruct (lookup_constant_type) eqn:?. simpl in *. *) - (* apply (lookup_constant_type_is_declared k u) in Heqt. *) - (* destruct Heqt as [decl [Hdecl Heq]]. *) - (* destruct a eqn:eqa. simpl in *. *) - (* destruct check_consistent_constraints eqn:cons. *) - - (* simpl in *. injection H as ->. rewrite <- Heq. constructor. auto. *) - (* red in Hdecl. *) - (* unfold consistent_universe_context_instance. *) - (* unfold check_consistent_constraints in cons. *) - (* unfold check_constraints in cons. *) - (* destruct decl. simpl in *. *) - - (* destruct decl; simpl in *. destruct cst_universes; simpl in *. auto. *) - (* destruct cst. simpl. unfold check_consistent_constraints in cons. split; auto. *) - (* unfold lookup_constant_type in Heqt. *) - - (* pose (lookup_constant_type_is_declared k u). _ _ _ H) as [decl [Hdecl <-]]. *) - (* constructor. auto. *) - - (* - (* Ind *) admit. *) - - (* - (* Construct *) admit. *) - - (* - (* Case *) *) - (* (* match goal with H : inductive * nat |- _ => destruct H end. *) *) - (* (* infers. *) *) - (* (* destruct reduce_to_ind eqn:?; try discriminate. simpl. *) *) - (* (* destruct a0 as [[ind' u] args]. *) *) - (* (* destruct eq_ind eqn:?; try discriminate. *) *) - (* (* intros [= <-]. *) *) - (* admit. *) - (* (* eapply type_Case. simpl in *. *) *) - (* (* eapply type_Conv. eauto. *) *) - (* (* admit. *) *) - (* (* rewrite cumul_reduce_to_ind. *) *) - (* (* exists args. split; auto. *) *) - (* (* rewrite Heqt0. repeat f_equal. apply eq_ind_refl in Heqb. congruence. *) *) - (* (* tc. *) *) - - (* - (* Proj *) admit. *) - (* - admit. *) - (* - admit. *) - (* - admit. *) - (* - admit. *) - - (* - destruct nth_error eqn:?; intros [= <-]. *) - (* constructor; auto. admit. admit. *) - - (* - destruct nth_error eqn:?; intros [= <-]. *) - (* constructor; auto. admit. admit. *) - Admitted. - -End InferOk. - -Extract Constant infer_type_correct => "(fun f sigma ctx t x -> assert false)". -Extract Constant infer_correct => "(fun f sigma ctx t ty -> assert false)". - -Definition default_fuel : Fuel := Nat.pow 2 14. - -Fixpoint fresh id (env : global_env) : bool := - match env with - | nil => true - | cons g env => negb (eq_constant g.1 id) && fresh id env - end. - -Section Checker. - - Context {cf : checker_flags} {F : Fuel}. - - Inductive env_error := - | IllFormedDecl (e : string) (e : type_error) - | AlreadyDeclared (id : string). - - Inductive EnvCheck (A : Type) := - | CorrectDecl (a : A) - | EnvError (e : env_error). - Global Arguments EnvError {A} e. - Global Arguments CorrectDecl {A} a. - - Instance envcheck_monad : Monad EnvCheck := - {| ret A a := CorrectDecl a ; - bind A B m f := - match m with - | CorrectDecl a => f a - | EnvError e => EnvError e - end - |}. - - Definition wrap_error {A} (id : string) (check : typing_result A) : EnvCheck A := - match check with - | Checked a => CorrectDecl a - | TypeError e => EnvError (IllFormedDecl id e) - end. - - Definition check_wf_type id Σ G t := - wrap_error id (infer_type Σ (infer Σ G) [] t) ;; ret (). - - Definition check_wf_judgement id Σ G t ty := - wrap_error id (check Σ G [] t ty) ;; ret (). - - Definition infer_term Σ G t := - wrap_error "" (infer Σ G [] t). - - Definition check_wf_decl Σ G kn (g : global_decl) : EnvCheck () := - match g with - | ConstantDecl cst => - match cst.(cst_body) with - | Some term => check_wf_judgement (string_of_kername kn) Σ G term cst.(cst_type) - | None => check_wf_type (string_of_kername kn) Σ G cst.(cst_type) - end - | InductiveDecl inds => - List.fold_left (fun acc body => - acc ;; check_wf_type body.(ind_name) Σ G body.(ind_type)) - inds.(ind_bodies) (ret ()) - end. - - Fixpoint check_fresh id (env : global_env) : EnvCheck () := - match env with - | [] => ret () - | g :: env => - check_fresh id env;; - if eq_constant id g.1 then - EnvError (AlreadyDeclared (string_of_kername id)) - else ret () - end. - - Definition monomorphic_constraints u := - match u with - | Monomorphic_ctx ctx => snd ctx - | Polymorphic_ctx ctx => ConstraintSet.empty - end. - - (* FIXME : universe polym declarations *) - Definition global_decl_univs d := - match d with - | ConstantDecl cb => monomorphic_constraints cb.(cst_universes) - | InductiveDecl mb => monomorphic_constraints mb.(ind_universes) - end. - - Definition add_gc_constraints ctrs (G : universes_graph) : universes_graph - := (G.1.1, GoodConstraintSet.fold - (fun ctr => wGraph.EdgeSet.add (edge_of_constraint ctr)) ctrs G.1.2, - G.2). - - Fixpoint check_wf_env (g : global_env) - : EnvCheck universes_graph := - match g with - | [] => ret init_graph - | g :: env => - G <- check_wf_env env ;; - match gc_of_constraints (global_decl_univs g.2) with - | None => - EnvError (IllFormedDecl (string_of_kername g.1) - (UnsatisfiableConstraints (global_decl_univs g.2))) - | Some ctrs => - wrap_error "" (check_consistent_constraints G (global_decl_univs g.2)) ;; - let G' := add_gc_constraints ctrs G in - check_wf_decl env G' g.1 g.2 ;; - check_fresh g.1 env ;; - ret G' - end - end. - - Definition typecheck_program (p : program) : EnvCheck term := - let Σ := fst p in - G <- check_wf_env Σ ;; - infer_term Σ G (snd p). - -End Checker. - -(* for compatibility, will go away *) -Definition infer' `{checker_flags} `{Fuel} (Σ : global_env_ext) Γ t - := let uctx := (global_ext_uctx Σ) in - match gc_of_uctx uctx with - | None => raise (UnsatisfiableConstraints uctx.2) - | Some uctx => infer (fst Σ) (make_graph uctx) Γ t - end. diff --git a/checker/theories/Closed.v b/checker/theories/Closed.v deleted file mode 100644 index 9f0a98142..000000000 --- a/checker/theories/Closed.v +++ /dev/null @@ -1,676 +0,0 @@ -(* Distributed under the terms of the MIT license. *) -From MetaCoq.Template Require Import config utils Ast AstUtils Reflect Induction - LiftSubst UnivSubst Typing TypingWf. -From MetaCoq.Checker Require Import WeakeningEnv. - -Require Import ssreflect. -From Equations Require Import Equations. - -(** * Lemmas about the [closedn] predicate *) - -Definition closed_decl n d := - option_default (closedn n) d.(decl_body) true && closedn n d.(decl_type). - -Definition closedn_ctx n ctx := - forallb id (mapi (fun k d => closed_decl (n + k) d) (List.rev ctx)). - -Lemma closed_decl_upwards k d : closed_decl k d -> forall k', k <= k' -> closed_decl k' d. -Proof. - case: d => na [body|] ty; rewrite /closed_decl /=. - move/andb_and => [cb cty] k' lek'. do 2 rewrite (@closed_upwards k) //. - move=> cty k' lek'; rewrite (@closed_upwards k) //. -Qed. - -Notation closed_ctx ctx := (closedn_ctx 0 ctx). - -Lemma closedn_lift n k k' t : closedn k t -> closedn (k + n) (lift n k' t). -Proof. - revert k. - induction t in n, k' |- * using term_forall_list_ind; intros; - simpl in *; rewrite -> ?andb_and in *; - rewrite -> ?map_map_compose, ?compose_on_snd, ?compose_map_def, ?map_length, ?Nat.add_assoc; - simpl closed in *; solve_all; - unfold test_def, test_snd in *; - try solve [simpl lift; simpl closed; f_equal; auto; repeat (rtoProp; solve_all)]; try easy. - - - elim (Nat.leb_spec k' n0); intros. simpl. - elim (Nat.ltb_spec); auto. apply Nat.ltb_lt in H. lia. - simpl. elim (Nat.ltb_spec); auto. intros. - apply Nat.ltb_lt in H. lia. -Qed. - -Lemma closedn_lift_inv n k k' t : k <= k' -> - closedn (k' + n) (lift n k t) -> - closedn k' t. -Proof. - induction t in n, k, k' |- * using term_forall_list_ind; intros; - simpl in *; - rewrite -> ?map_map_compose, ?compose_on_snd, ?compose_map_def, ?map_length, ?Nat.add_assoc in *; - simpl closed in *; repeat (rtoProp; solve_all); try change_Sk; - unfold test_def, on_snd, test_snd in *; simpl in *; eauto with all. - - - revert H0. - elim (Nat.leb_spec k n0); intros. simpl in *. - elim (Nat.ltb_spec); auto. apply Nat.ltb_lt in H1. intros. lia. - revert H1. simpl. intro. repeat toProp. lia. - - specialize (IHt2 n (S k) (S k')). eauto with all. - - specialize (IHt2 n (S k) (S k')). eauto with all. - - specialize (IHt3 n (S k) (S k')). eauto with all. - - rtoProp. solve_all. specialize (b0 n (#|m| + k) (#|m| + k')). eauto with all. - - rtoProp. solve_all. specialize (b0 n (#|m| + k) (#|m| + k')). eauto with all. -Qed. - -Lemma closedn_mkApps k f u: - closedn k f -> forallb (closedn k) u -> - closedn k (mkApps f u). -Proof. - intros Hf Hu. - induction u; simpl; auto. - destruct f; simpl in *; try rewrite Hf Hu; auto. - rewrite forallb_app. simpl. rewrite Hu. - rewrite andb_assoc. now rewrite Hf. -Qed. - -Lemma closedn_mkApps_inv k f u: - closedn k (mkApps f u) -> - closedn k f && forallb (closedn k) u. -Proof. - induction u; simpl; auto. - - now rewrite andb_true_r. - - intros. destruct f; simpl in *; auto. - rewrite forallb_app in H. simpl in H. - now rewrite andb_assoc in H. -Qed. - -Lemma closedn_subst s k k' t : - forallb (closedn k) s -> closedn (k + k' + #|s|) t -> - closedn (k + k') (subst s k' t). -Proof. - intros Hs. solve_all. revert H. - induction t in k' |- * using term_forall_list_ind; intros; - simpl in *; - rewrite -> ?map_map_compose, ?compose_on_snd, ?compose_map_def, ?map_length; - simpl closed in *; try change_Sk; repeat (rtoProp; solve_all); - unfold test_def, on_snd, test_snd in *; simpl in *; eauto with all. - - - elim (Nat.leb_spec k' n); intros. simpl. - apply Nat.ltb_lt in H. - destruct nth_error eqn:Heq. - -- eapply closedn_lift. - now eapply nth_error_all in Heq; simpl; eauto; simpl in *. - -- simpl. elim (Nat.ltb_spec); auto. intros. - apply nth_error_None in Heq. lia. - -- simpl. apply Nat.ltb_lt in H0. - apply Nat.ltb_lt. apply Nat.ltb_lt in H0. lia. - - - specialize (IHt2 (S k')). - rewrite <- Nat.add_succ_comm in IHt2. eauto. - - specialize (IHt2 (S k')). - rewrite <- Nat.add_succ_comm in IHt2. eauto. - - specialize (IHt3 (S k')). - rewrite <- Nat.add_succ_comm in IHt3. eauto. - - rewrite closedn_mkApps; solve_all. - - rtoProp; solve_all. rewrite -> !Nat.add_assoc in *. - specialize (b0 (#|m| + k')). unfold is_true. rewrite <- b0. f_equal. lia. - unfold is_true. rewrite <- H0. f_equal. lia. - - rtoProp; solve_all. rewrite -> !Nat.add_assoc in *. - specialize (b0 (#|m| + k')). unfold is_true. rewrite <- b0. f_equal. lia. - unfold is_true. rewrite <- H0. f_equal. lia. -Qed. - -Lemma closedn_subst0 s k t : - forallb (closedn k) s -> closedn (k + #|s|) t -> - closedn k (subst0 s t). -Proof. - intros. - generalize (closedn_subst s k 0 t H). - rewrite Nat.add_0_r. eauto. -Qed. - -Lemma subst_closedn s k t : Ast.wf t -> - closedn k t -> subst s k t = t. -Proof. - intros Hcl. - pose proof (simpl_subst_rec _ Hcl s 0 k k). - intros. pose proof (lift_closed (#|s| + 0) _ _ H0). - do 2 (forward H; auto). rewrite H1 in H. - rewrite H. now apply lift_closed. -Qed. - -Lemma closedn_subst_instance_constr k t u : - closedn k (subst_instance_constr u t) = closedn k t. -Proof. - revert k. - induction t in |- * using term_forall_list_ind; intros; - simpl in *; rewrite -> ?andb_and in *; - rewrite -> ?map_map_compose, ?compose_on_snd, ?compose_map_def; - try solve [repeat (f_equal; eauto)]; simpl closed in *; - try rewrite ?map_length; intuition auto. - - - rewrite forallb_map; eapply Forall_forallb_eq_forallb; eauto. - - rewrite forallb_map. f_equal; eauto using Forall_forallb_eq_forallb. - - red in X. rewrite forallb_map. f_equal. - + f_equal; auto. - + eapply Forall_forallb_eq_forallb. - eapply All_Forall; tea. - intros [] XX; apply XX. - - red in X. rewrite forallb_map. - eapply Forall_forallb_eq_forallb. eapply All_Forall; eauto. - unfold test_def, map_def. simpl. - do 3 (f_equal; intuition eauto). - - red in X. rewrite forallb_map. - eapply Forall_forallb_eq_forallb. eapply All_Forall; eauto. - unfold test_def, map_def. simpl. - do 3 (f_equal; intuition eauto). -Qed. - - -Lemma destArity_spec ctx T : - match destArity ctx T with - | Some (ctx', s) => it_mkProd_or_LetIn ctx T = it_mkProd_or_LetIn ctx' (tSort s) - | None => True - end. -Proof. - induction T in ctx |- *; simpl; try easy. - specialize (IHT2 (ctx,, vass na T1)). now destruct destArity. - specialize (IHT3 (ctx,, vdef na T1 T2)). now destruct destArity. -Qed. - -Lemma closedn_All_local_closed: - forall (cf : checker_flags) (Σ : global_env_ext) (ctx : list context_decl) - (wfΓ' : wf_local Σ ctx), - All_local_env_over typing - (fun (Σ0 : global_env_ext) (Γ0 : context) (_ : wf_local Σ0 Γ0) (t T : term) (_ : Σ0;;; Γ0 |- t : T) => - closedn #|Γ0| t && closedn #|Γ0| T) Σ ctx wfΓ' -> - closedn_ctx 0 ctx. -Proof. - intros cf Σ Γ al. - induction 1. constructor. - rewrite /closedn_ctx /= mapi_app forallb_app /= [forallb _ _]IHX /id /closed_decl /=. - now rewrite Nat.add_0_r List.rev_length p. - rewrite /closedn_ctx /= mapi_app forallb_app /= [forallb _ _]IHX /id /closed_decl /=. - now rewrite Nat.add_0_r List.rev_length p. -Qed. - -Lemma closedn_ctx_cons n d Γ : closedn_ctx n (d :: Γ) -> closedn_ctx n Γ && closed_decl (n + #|Γ|) d. -Proof. - unfold closedn_ctx. - simpl. rewrite mapi_app. rewrite forallb_app. - move/andb_and => [] -> /=. now rewrite Nat.add_0_r List.rev_length andb_true_r. -Qed. - -Lemma closedn_ctx_app n Γ Γ' : - closedn_ctx n (Γ ,,, Γ') = - closedn_ctx n Γ && closedn_ctx (n + #|Γ|) Γ'. -Proof. - rewrite /closedn_ctx /app_context /= List.rev_app_distr mapi_app forallb_app /=. - f_equal. - rewrite List.rev_length. - f_equal. eapply mapi_ext. intros. - f_equal. lia. -Qed. - -Lemma closedn_mkProd_or_LetIn (Γ : context) d T : - closed_decl #|Γ| d -> - closedn (S #|Γ|) T -> closedn #|Γ| (mkProd_or_LetIn d T). -Proof. - destruct d as [na [b|] ty]; simpl in *. unfold closed_decl. - simpl. now move/andb_and => [] -> ->. - simpl. now move/andb_and => [] /= _ -> ->. -Qed. - -Lemma closedn_mkLambda_or_LetIn (Γ : context) d T : - closed_decl #|Γ| d -> - closedn (S #|Γ|) T -> closedn #|Γ| (mkLambda_or_LetIn d T). -Proof. - destruct d as [na [b|] ty]; simpl in *. unfold closed_decl. - simpl. now move/andb_and => [] -> ->. - simpl. now move/andb_and => [] /= _ -> ->. -Qed. - -Lemma closedn_it_mkProd_or_LetIn - (Γ : context) (ctx : list context_decl) T : - closedn_ctx #|Γ| ctx -> - closedn (#|Γ| + #|ctx|) T -> closedn #|Γ| (it_mkProd_or_LetIn ctx T). -Proof. - induction ctx in Γ, T |- *. simpl. - - now rewrite Nat.add_0_r. - - move/closedn_ctx_cons/andb_and => [] cctx ca cT. - apply (IHctx Γ (mkProd_or_LetIn a T) cctx). - simpl in cT. rewrite <- app_length. - eapply closedn_mkProd_or_LetIn; - now rewrite app_length // plus_n_Sm. -Qed. - -Lemma closedn_it_mkLambda_or_LetIn - (Γ : context) (ctx : list context_decl) T : - closedn_ctx #|Γ| ctx -> - closedn (#|Γ| + #|ctx|) T -> closedn #|Γ| (it_mkLambda_or_LetIn ctx T). -Proof. - induction ctx in Γ, T |- *. simpl. - - now rewrite Nat.add_0_r. - - move/closedn_ctx_cons/andb_and => [] cctx ca cT. - apply (IHctx Γ (mkLambda_or_LetIn a T) cctx). - simpl in cT. rewrite <- app_length. - eapply closedn_mkLambda_or_LetIn; - now rewrite app_length // plus_n_Sm. -Qed. - -Lemma type_local_ctx_All_local_env {cf:checker_flags} P Σ Γ Δ s : - All_local_env (lift_typing P Σ) Γ -> - type_local_ctx (lift_typing P) Σ Γ Δ s -> - All_local_env (lift_typing P Σ) (Γ ,,, Δ). -Proof. - induction Δ; simpl; auto. - destruct a as [na [b|] ty]; - intros wfΓ wfctx; constructor; intuition auto. - exists s; auto. -Qed. - -Definition Pclosed := - (fun (_ : global_env_ext) (Γ : context) (t T : term) => - closedn #|Γ| t && closedn #|Γ| T). - -Lemma type_local_ctx_Pclosed Σ Γ Δ s : - type_local_ctx (lift_typing Pclosed) Σ Γ Δ s -> - Alli (fun i d => closed_decl (#|Γ| + i) d) 0 (List.rev Δ). -Proof. - induction Δ; simpl; auto; try constructor. - destruct a as [? [] ?]; intuition auto. - - apply Alli_app_inv; auto. constructor. simpl. - rewrite List.rev_length. 2:constructor. - unfold closed_decl. unfold Pclosed in b0. simpl. - rewrite app_context_length in b0. now rewrite Nat.add_comm. - - apply Alli_app_inv; auto. constructor. simpl. - rewrite List.rev_length. 2:constructor. - unfold closed_decl. unfold Pclosed in b. simpl. - rewrite app_context_length in b. rewrite Nat.add_comm. - now rewrite andb_true_r in b. -Qed. - -Lemma sorts_local_ctx_Pclosed Σ Γ Δ s : - sorts_local_ctx (lift_typing Pclosed) Σ Γ Δ s -> - Alli (fun i d => closed_decl (#|Γ| + i) d) 0 (List.rev Δ). -Proof. - induction Δ in s |- *; simpl; auto; try constructor. - destruct a as [? [] ?]; intuition auto. - - apply Alli_app_inv; eauto. constructor. simpl. - rewrite List.rev_length. 2:constructor. - unfold closed_decl. unfold Pclosed in b0. simpl. - rewrite app_context_length in b0. now rewrite Nat.add_comm. - - destruct s; auto. destruct X. - apply Alli_app_inv; eauto. constructor. simpl. - rewrite List.rev_length. 2:constructor. - unfold closed_decl. unfold Pclosed in i. simpl. - rewrite app_context_length in i. rewrite Nat.add_comm. - now rewrite andb_true_r in i. -Qed. - -Lemma All_local_env_Pclosed Σ Γ : - All_local_env ( lift_typing Pclosed Σ) Γ -> - Alli (fun i d => closed_decl i d) 0 (List.rev Γ). -Proof. - induction Γ; simpl; auto; try constructor. - intros all; depelim all; intuition auto. - - apply Alli_app_inv; auto. constructor. simpl. - rewrite List.rev_length. 2:constructor. - unfold closed_decl. unfold Pclosed in l. simpl. red in l. - destruct l as [s H]. - now rewrite andb_true_r in H. - - apply Alli_app_inv; auto. constructor. simpl. - rewrite List.rev_length. 2:constructor. - unfold closed_decl. unfold Pclosed, lift_typing in *. now simpl. -Qed. - -Lemma closed_subst_context (Γ Δ Δ' : context) t : - closedn (#|Γ| + #|Δ|) t -> - Alli (fun i d => closed_decl (#|Γ| + S #|Δ| + i) d) 0 (List.rev Δ') -> - Alli (fun i d => closed_decl (#|Γ| + #|Δ| + i) d) 0 (List.rev (subst_context [t] 0 Δ')). -Proof. - induction Δ' in Δ |- *. - intros. simpl. auto. constructor. - destruct a as [? [] ?]; simpl. - - intros. eapply Alli_app in X as [X X']. - rewrite subst_context_snoc. simpl. eapply Alli_app_inv. - eapply IHΔ'; eauto. constructor; [|constructor]. - simpl. - rewrite /closed_decl /map_decl /= Nat.add_0_r List.rev_length subst_context_length. - inv X'. unfold closed_decl in H0. simpl in H0. - rewrite List.rev_length Nat.add_0_r in H0. - move/andb_and: H0 => [Hl Hr]. - rewrite !closedn_subst /= ?H //; eapply closed_upwards; eauto; try lia. - - intros. eapply Alli_app in X as [X X']. - rewrite subst_context_snoc. simpl. eapply Alli_app_inv. - eapply IHΔ'; eauto. constructor; [|constructor]. - simpl. - rewrite /closed_decl /map_decl /= Nat.add_0_r List.rev_length subst_context_length. - inv X'. unfold closed_decl in H0. simpl in H0. - rewrite List.rev_length Nat.add_0_r in H0. - rewrite !closedn_subst /= ?H //; eapply closed_upwards; eauto; try lia. -Qed. - -Lemma closed_smash_context_gen (Γ Δ Δ' : context) : - Alli (fun i d => closed_decl (#|Γ| + i) d) 0 (List.rev Δ) -> - Alli (fun i d => closed_decl (#|Γ| + #|Δ| + i) d) 0 (List.rev Δ') -> - Alli (fun i d => closed_decl (#|Γ| + i) d) 0 (List.rev (smash_context Δ' Δ)). -Proof. - induction Δ in Δ' |- *. - intros. simpl. auto. - simpl. eapply (Alli_impl _ X0). simpl. now rewrite Nat.add_0_r. - destruct a as [? [] ?]; simpl. - - intros. eapply Alli_app in X as [X X']. - eapply IHΔ; eauto. - inv X'. unfold closed_decl in H. simpl in H. - rewrite List.rev_length Nat.add_0_r in H. - clear X1. eapply closed_subst_context; auto. - now move/andb_and: H => []. - - intros. eapply Alli_app in X as [X X']. - eapply IHΔ; eauto. - inv X'. unfold closed_decl in H. simpl in H. - rewrite List.rev_length Nat.add_0_r in H. - clear X1. rewrite List.rev_app_distr. - eapply Alli_app_inv; repeat constructor. - now rewrite /closed_decl Nat.add_0_r /=. - rewrite List.rev_length /=. clear -X0. - apply Alli_shift, (Alli_impl _ X0). intros. - eapply closed_decl_upwards; eauto; lia. -Qed. - -Lemma closed_smash_context (Γ Δ : context) : - Alli (fun i d => closed_decl (#|Γ| + i) d) 0 (List.rev Δ) -> - Alli (fun i d => closed_decl (#|Γ| + i) d) 0 (List.rev (smash_context [] Δ)). -Proof. - intros; apply (closed_smash_context_gen Γ _ []); auto. constructor. -Qed. - -Lemma context_assumptions_app Γ Δ : context_assumptions (Γ ++ Δ) = - context_assumptions Γ + context_assumptions Δ. -Proof. - induction Γ as [|[? [] ?] ?]; simpl; auto. -Qed. - -Lemma weaken_env_prop_closed {cf:checker_flags} : - weaken_env_prop (lift_typing (fun (_ : global_env_ext) (Γ : context) (t T : term) => - closedn #|Γ| t && closedn #|Γ| T)). -Proof. repeat red. intros. destruct t; red in X0; eauto. Qed. - -Lemma declared_projection_closed_ind {cf:checker_flags} {Σ : global_env_ext} {mdecl idecl p pdecl} : - wf Σ.1 -> - declared_projection Σ.1 mdecl idecl p pdecl -> - Forall_decls_typing - (fun (_ : TemplateEnvironment.global_env_ext) (Γ : TemplateEnvironment.context) (t T : term) => - closedn #|Γ| t && closedn #|Γ| T) Σ.1 -> - closedn (S (ind_npars mdecl)) pdecl.2. -Proof. - intros wfΣ isdecl X0. - pose proof (declared_projection_inv weaken_env_prop_closed wfΣ X0 isdecl) as onp. - set (declared_inductive_inv _ wfΣ X0 isdecl.p1) as oib in *. - clearbody oib. - have onpars := onParams (declared_minductive_inv weaken_env_prop_closed wfΣ X0 isdecl.p1.p1). - have parslen := onNpars (declared_minductive_inv weaken_env_prop_closed wfΣ X0 isdecl.p1.p1). - simpl in onp. destruct (ind_cshapes oib) as [|? []] eqn:Heq; try contradiction. - red in onp. - destruct (nth_error (smash_context [] _) _) eqn:Heq'; try contradiction. - destruct onp as [onna onp]. - rewrite {}onp. - pose proof (onConstructors oib) as onc. - red in onc. rewrite Heq in onc. inv onc. clear X1. - eapply on_cargs in X. - simpl. - replace (S (ind_npars mdecl)) with (1 + ind_npars mdecl) by lia. - eapply (closedn_subst _ 0). - { clear. unfold inds. generalize (TemplateEnvironment.ind_bodies mdecl). - induction l; simpl; auto. } - rewrite inds_length. - eapply closedn_subst0. - { clear. unfold projs. induction p.2; simpl; auto. } - rewrite projs_length /=. - eapply (@closed_upwards (ind_npars mdecl + #|ind_bodies mdecl| + p.2 + 1)). - 2:lia. - eapply closedn_lift. - clear -parslen isdecl Heq' onpars X. - rename X into args. - apply sorts_local_ctx_Pclosed in args. - red in onpars. - eapply All_local_env_Pclosed in onpars. - eapply (Alli_impl (Q:=fun i d => closed_decl (#|ind_params mdecl| + i + #|arities_context (ind_bodies mdecl)|) d)) in args. - 2:{ intros n x. rewrite app_context_length. - intros H; eapply closed_decl_upwards; eauto. lia. } - eapply (Alli_shiftn (P:=fun i d => closed_decl (i + #|arities_context (ind_bodies mdecl)|) d)) in args. - rewrite Nat.add_0_r in args. - eapply (Alli_impl (Q:=fun i d => closed_decl (i + #|arities_context (ind_bodies mdecl)|) d)) in onpars. - 2:{ intros n x d. eapply closed_decl_upwards; eauto; lia. } - epose proof (Alli_app_inv onpars). rewrite List.rev_length /= in X. - specialize (X args). rewrite -List.rev_app_distr in X. - clear onpars args. - eapply (Alli_impl (Q:=fun i d => closed_decl (#|arities_context (ind_bodies mdecl)| + i) d)) in X. - 2:intros; eapply closed_decl_upwards; eauto; lia. - eapply closed_smash_context in X. - eapply Alli_rev_nth_error in X; eauto. - rewrite smash_context_length in X. simpl in X. - eapply nth_error_Some_length in Heq'. rewrite smash_context_length in Heq'. - simpl in Heq'. unfold closed_decl in X. - move/andb_and: X => [] _ cl. - eapply closed_upwards. eauto. rewrite arities_context_length. - rewrite context_assumptions_app parslen. - rewrite context_assumptions_app in Heq'. lia. -Qed. - -Lemma typecheck_closed `{cf : checker_flags} : - env_prop (fun Σ Γ t T => - closedn #|Γ| t && closedn #|Γ| T). -Proof. - assert (X := weaken_env_prop_closed). - apply typing_ind_env; intros; simpl; rewrite -> ?andb_and in *; try solve [intuition auto]. - - pose proof (nth_error_Some_length H). - elim (Nat.ltb_spec n #|Γ|); intuition. clear H0. - eapply (nth_error_All_local_env_over H) in X0 as [HΓ Hdecl]. - destruct lookup_wf_local_decl; cbn in *. - destruct decl as [na [b|] ty]; cbn in *. - -- move/andb_and: Hdecl => [] _. - rewrite skipn_length; try lia. - move/(closedn_lift (S n)). - now have->: #|Γ| - S n + S n = #|Γ| by lia. - -- rewrite andb_true_r in Hdecl. - move/(closedn_lift (S n)): Hdecl. - rewrite skipn_length; try lia. - now have->: #|Γ| - S n + S n = #|Γ| by lia. - - - destruct H. rewrite and_assoc. split. auto. - clear X0 H H0 H1. - induction X1; simpl. intuition auto. - rewrite -> andb_and in *. destruct p0. rewrite H. - rewrite <- andb_and. simpl. - apply IHX1. unfold subst. - pose proof (closedn_subst [hd] #|Γ| 0). rewrite Nat.add_0_r in H1. - apply H1. simpl. now rewrite H. - simpl. simpl in p. rewrite -> andb_and in p. intuition auto. - rewrite Nat.add_1_r. auto. - - - rewrite closedn_subst_instance_constr. - eapply lookup_on_global_env in H; eauto. - destruct H as [Σ' [HΣ' IH]]. - repeat red in IH. destruct decl, cst_body. simpl in *. - rewrite -> andb_and in IH. intuition. - eauto using closed_upwards with arith. - simpl in *. - repeat red in IH. destruct IH as [s Hs]. - rewrite -> andb_and in Hs. intuition. - eauto using closed_upwards with arith. - - - rewrite closedn_subst_instance_constr. - eapply declared_inductive_inv in X0; eauto. - apply onArity in X0. repeat red in X0. - destruct X0 as [s Hs]. rewrite -> andb_and in Hs. - intuition eauto using closed_upwards with arith. - - - destruct isdecl as [Hidecl Hcdecl]. - apply closedn_subst0. - + unfold inds. clear. simpl. induction #|ind_bodies mdecl|. constructor. - simpl. now rewrite IHn. - + rewrite inds_length. - rewrite closedn_subst_instance_constr. - eapply declared_inductive_inv in X0; eauto. - pose proof X0.(onConstructors) as XX. - eapply All2_nth_error_Some in Hcdecl; eauto. - destruct Hcdecl as [? [? ?]]. cbn in *. - destruct o.(on_ctype) as [s Hs]. rewrite -> andb_and in Hs. - apply proj1 in Hs. - unfold arities_context in Hs. - rewrite rev_map_length in Hs. - eauto using closed_upwards with arith. - - - intuition auto. solve_all. unfold test_snd. simpl in *. - rtoProp; eauto. - apply closedn_mkApps; auto. - rewrite forallb_app. simpl. rewrite H1. - rewrite forallb_skipn; auto. - now apply closedn_mkApps_inv in H8. - - - intuition auto. - apply closedn_subst0. - simpl. apply closedn_mkApps_inv in H2. - rewrite forallb_rev H1. apply H2. - simpl. rewrite List.rev_length. rewrite H0. - rewrite closedn_subst_instance_constr. - eapply closed_upwards. eapply declared_projection_closed_ind; eauto. - lia. - - - split. solve_all. - destruct x; simpl in *. - unfold test_def. simpl. rtoProp. - split. - rewrite -> app_context_length in *. rewrite -> Nat.add_comm in *. - eapply closedn_lift_inv in H3; eauto. lia. - subst types. - now rewrite app_context_length fix_context_length in H2. - eapply nth_error_all in H0; eauto. simpl in H0. intuition. rtoProp. - subst types. rewrite app_context_length in H2. - rewrite Nat.add_comm in H2. - now eapply closedn_lift_inv in H2. - - - split. solve_all. destruct x; simpl in *. - unfold test_def. simpl. rtoProp. - split. - rewrite -> app_context_length in *. rewrite -> Nat.add_comm in *. - eapply closedn_lift_inv in H3; eauto. lia. - subst types. - now rewrite -> app_context_length, fix_context_length in H2. - eapply (nth_error_all) in H0; eauto. simpl in *. - intuition. rtoProp. - subst types. rewrite app_context_length Nat.add_comm in H2. - now eapply closedn_lift_inv in H2. -Qed. - -Lemma declared_decl_closed `{checker_flags} {Σ : global_env} {cst decl} : - wf Σ -> - lookup_env Σ cst = Some decl -> - on_global_decl (fun Σ Γ b t => closedn #|Γ| b && option_default (closedn #|Γ|) t true) - (Σ, universes_decl_of_decl decl) cst decl. -Proof. - intros. - eapply weaken_lookup_on_global_env; try red; eauto. - eapply on_global_env_impl; cycle 1. - apply (env_prop_sigma _ typecheck_closed _ X). - red; intros. unfold lift_typing in *. destruct T; intuition auto with wf. - destruct X1 as [s0 Hs0]. simpl. rtoProp; intuition. -Qed. - -Definition closed_inductive_body mdecl idecl := - closedn 0 idecl.(ind_type) && - forallb (fun cdecl => - closedn (#|arities_context mdecl.(ind_bodies)|) (cdecl_type cdecl)) idecl.(ind_ctors) && - forallb (fun x => closedn (S (ind_npars mdecl)) x.2) idecl.(ind_projs). - -Definition closed_inductive_decl mdecl := - closed_ctx (ind_params mdecl) && - forallb (closed_inductive_body mdecl) (ind_bodies mdecl). - -Lemma closedn_All_local_env (ctx : list context_decl) : - All_local_env - (fun (Γ : context) (b : term) (t : option term) => - closedn #|Γ| b && option_default (closedn #|Γ|) t true) ctx -> - closedn_ctx 0 ctx. -Proof. - induction 1. constructor. - rewrite /closedn_ctx /= mapi_app forallb_app /= [forallb _ _]IHX /id /closed_decl /=. - now rewrite Nat.add_0_r List.rev_length t0. - rewrite /closedn_ctx /= mapi_app forallb_app /= [forallb _ _]IHX /id /closed_decl /=. - now rewrite Nat.add_0_r List.rev_length t1. -Qed. - -Lemma skipn_0 {A} (l : list A) : skipn 0 l = l. -Proof. reflexivity. Qed. - -Lemma declared_projection_closed {cf:checker_flags} {Σ : global_env_ext} {mdecl idecl p pdecl} : - wf Σ.1 -> - declared_projection Σ.1 mdecl idecl p pdecl -> - closedn (S (ind_npars mdecl)) pdecl.2. -Proof. - intros; eapply declared_projection_closed_ind; eauto. - eapply typecheck_closed; eauto. - constructor. eapply type_Prop. -Qed. - -Lemma declared_inductive_closed {cf:checker_flags} {Σ : global_env_ext} {mdecl mind} : - wf Σ.1 -> - declared_minductive Σ.1 mind mdecl -> - closed_inductive_decl mdecl. -Proof. - intros wfΣ decl. - pose proof (declared_decl_closed wfΣ decl) as decl'. - red in decl'. - unfold closed_inductive_decl. - apply andb_and. split. apply onParams in decl'. - now apply closedn_All_local_env in decl'; auto. - apply onInductives in decl'. - eapply All_forallb. - - assert (Alli (fun i => declared_inductive Σ.1 mdecl {| inductive_mind := mind; inductive_ind := i |}) - 0 (ind_bodies mdecl)). - { eapply forall_nth_error_Alli. intros. - split; auto. } - eapply Alli_mix in decl'; eauto. clear X. - clear decl. - eapply Alli_All; eauto. - intros n x [decli oib]. - rewrite /closed_inductive_body. - apply andb_and; split. apply andb_and. split. - - apply onArity in oib. hnf in oib. - now move/andb_and: oib => []. - - pose proof (onConstructors oib). - red in X. eapply All_forallb. eapply All2_All_left; eauto. - firstorder auto. - eapply on_ctype in X0. - now move/andb_and: X0 => []. - - eapply All_forallb. - pose proof (onProjections oib). - destruct (eq_dec (ind_projs x) []) as [->|eq]; try constructor. - specialize (X eq). clear eq. - destruct (ind_cshapes oib) as [|? []]; try contradiction. - apply on_projs in X. - assert (Alli (fun i pdecl => declared_projection Σ.1 mdecl x - (({| inductive_mind := mind; inductive_ind := n |}, mdecl.(ind_npars)), i) pdecl) - 0 (ind_projs x)). - { eapply forall_nth_error_Alli. - intros. split; auto. } - eapply (Alli_All X0). intros. - now eapply declared_projection_closed in H. -Qed. - -Lemma rev_subst_instance_context u Γ : - List.rev (subst_instance_context u Γ) = subst_instance_context u (List.rev Γ). -Proof. - unfold subst_instance_context, map_context. - now rewrite map_rev. -Qed. - -Lemma closedn_subst_instance_context k Γ u : - closedn_ctx k (subst_instance_context u Γ) = closedn_ctx k Γ. -Proof. - unfold closedn_ctx; f_equal. - rewrite rev_subst_instance_context. - rewrite mapi_map. apply mapi_ext. - intros n [? [] ?]; unfold closed_decl; cbn. - all: now rewrite !closedn_subst_instance_constr. -Qed. diff --git a/checker/theories/Extraction.v b/checker/theories/Extraction.v deleted file mode 100644 index c3dbe6211..000000000 --- a/checker/theories/Extraction.v +++ /dev/null @@ -1,46 +0,0 @@ -(* Distributed under the terms of the MIT license. *) -Require Import MetaCoq.Template.utils. -Require Import FSets ExtrOcamlBasic ExtrOcamlString ExtrOcamlZInt. - -(** * Extraction setup for template-coq. - - Any extracted code planning to link with the plugin's OCaml reifier - should use these same directives for consistency. -*) - - -(* Ignore [Decimal.int] before the extraction issue is solved: - https://github.com/coq/coq/issues/7017. *) -Extract Inductive Decimal.int => unit [ "(fun _ -> ())" "(fun _ -> ())" ] "(fun _ _ _ -> assert false)". - -Extract Constant ascii_compare => - "fun x y -> match Char.compare x y with 0 -> Eq | x when x < 0 -> Lt | _ -> Gt". - -Extraction Blacklist config uGraph Universes Ast String List Nat Int - UnivSubst Typing Checker Retyping OrderedType Logic Common Equality utils. -Set Warnings "-extraction-opaque-accessed". -Set Warnings "-extraction-reserved-identifier". - -Require Export MetaCoq.Template.Ast. -From MetaCoq.Checker Require All. - -Cd "src". - -From Equations Require Import Equations. - -(* Should be in Equations *) -Extraction Inline Equations.Prop.Classes.noConfusion. -Extraction Inline Equations.Prop.Logic.eq_elim. -Extraction Inline Equations.Prop.Logic.eq_elim_r. -Extraction Inline Equations.Prop.Logic.transport. -Extraction Inline Equations.Prop.Logic.transport_r. -Extraction Inline Equations.Prop.Logic.False_rect_dep. -Extraction Inline Equations.Prop.Logic.True_rect_dep. -Extraction Inline Equations.Init.pr1. -Extraction Inline Equations.Init.pr2. -Extraction Inline Equations.Init.hidebody. -Extraction Inline Equations.Prop.DepElim.solution_left. - -Separate Extraction Checker.typecheck_program Checker.infer' Retyping.sort_of. - -Cd "..". diff --git a/checker/theories/Generation.v b/checker/theories/Generation.v deleted file mode 100644 index c4488683b..000000000 --- a/checker/theories/Generation.v +++ /dev/null @@ -1,55 +0,0 @@ -(* Distributed under the terms of the MIT license. *) -From MetaCoq.Template Require Import config utils Ast AstUtils Reflect LiftSubst Typing. -Require Import Equations.Prop.DepElim. - -(** * Substitution lemmas for typing derivations. *) - -Derive Signature for typing. - -Lemma invert_type_App `{checker_flags} Σ Γ f u T : - Σ ;;; Γ |- tApp f u : T -> - { T' : term & { U' & ((Σ ;;; Γ |- f : T') * typing_spine Σ Γ T' u U' * - (isApp f = false) * (u <> []) * - (Σ ;;; Γ |- U' <= T))%type } }. -Proof. - intros Hty. - dependent induction Hty. - - exists t_ty, t'. intuition. - - destruct IHHty1 as [T' [U' [H' H'']]]. - exists T', A. split; auto. - destruct H' as [[[? ?] ?] ?]. - repeat split; auto. - eapply typing_spine_strengthen. -Qed. - -Lemma type_mkApp `{checker_flags} Σ Γ f u T T' : - Σ ;;; Γ |- f : T -> - typing_spine Σ Γ T [u] T' -> - Σ ;;; Γ |- mkApp f u : T'. -Proof. - intros Hf Hu. inv Hu. - simpl. destruct (isApp f) eqn:Happ. - destruct f; try discriminate. simpl. - eapply invert_type_App in Hf. - destruct Hf as (T'' & U' & (((Hf & HU) & Happf) & Hunil) & Hcumul). - eapply type_App; eauto. intro. destruct args; discriminate. - inv X2. clear Happ Hf Hunil. - induction HU. simpl. econstructor; eauto. - eapply cumul_trans; eauto. - econstructor. econstructor. eapply t. eauto. eauto. - apply IHHU; eauto. - rewrite -> mkApp_tApp; eauto. - econstructor; eauto. congruence. - econstructor; eauto. -Qed. - -Lemma type_mkApps `{checker_flags} Σ Γ f u T T' : - Σ ;;; Γ |- f : T -> - typing_spine Σ Γ T u T' -> - Σ ;;; Γ |- mkApps f u : T'. -Proof. - intros Hf Hu. induction Hu in f, Hf |- *. auto. - rewrite <- mkApps_mkApp. - eapply IHHu. eapply type_mkApp. eauto. - econstructor; eauto. constructor. -Qed. diff --git a/checker/theories/Loader.v b/checker/theories/Loader.v deleted file mode 100644 index 481ef62fc..000000000 --- a/checker/theories/Loader.v +++ /dev/null @@ -1,6 +0,0 @@ -(* Distributed under the terms of the MIT license. *) -Require Import String. -From MetaCoq.Template Require Import BasicAst Ast Loader. - -Declare ML Module "metacoq_template_plugin". -Declare ML Module "metacoq_checker_plugin". diff --git a/checker/theories/Retyping.v b/checker/theories/Retyping.v deleted file mode 100644 index 0a0db7b9d..000000000 --- a/checker/theories/Retyping.v +++ /dev/null @@ -1,110 +0,0 @@ -(* Distributed under the terms of the MIT license. *) -From MetaCoq.Template Require Import config utils Ast LiftSubst. -From MetaCoq.Checker Require Import Checker. - -(** * Retyping - - The [type_of] function provides a fast (and loose) type inference - function which assumes that the provided term is already well-typed in - the given context and recomputes its type. Only reduction (for - head-reducing types to uncover dependent products or inductives) and - substitution are costly here. No universe checking or conversion is done - in particular. *) - - -Local Existing Instance default_checker_flags. - -Section TypeOf. - Context `{F : Fuel}. - Context (Σ : global_env). - - Fixpoint infer_spine (Γ : context) (ty : term) (l : list term) - {struct l} : typing_result term := - match l with - | nil => ret ty - | cons x xs => - pi <- reduce_to_prod Σ Γ ty ;; - let '(a1, b1) := pi in - infer_spine Γ (subst10 x b1) xs - end. - - Section SortOf. - Context (type_of : context -> term -> typing_result term). - - Definition type_of_as_sort Γ t := - tx <- type_of Γ t ;; - reduce_to_sort Σ Γ tx. - - End SortOf. - - Fixpoint type_of (Γ : context) (t : term) : typing_result term := - match t with - | tRel n => - match nth_error Γ n with - | Some d => ret (lift0 (S n) d.(decl_type)) - | None => raise (UnboundRel n) - end - - | tVar n => raise (UnboundVar n) - | tEvar ev args => raise (UnboundEvar ev) - - | tSort s => ret (tSort (Universe.super s)) - - | tCast c k t => ret t - - | tProd n t b => - s1 <- type_of_as_sort type_of Γ t ;; - s2 <- type_of_as_sort type_of (Γ ,, vass n t) b ;; - ret (tSort (Universe.sort_of_product s1 s2)) - - | tLambda n t b => - t2 <- type_of (Γ ,, vass n t) b ;; - ret (tProd n t t2) - - | tLetIn n b b_ty b' => - b'_ty <- type_of (Γ ,, vdef n b b_ty) b' ;; - ret (tLetIn n b b_ty b'_ty) - - | tApp t l => - t_ty <- type_of Γ t ;; - infer_spine Γ t_ty l - - | tConst cst u => lookup_constant_type Σ cst u - - | tInd (mkInd ind i) u => lookup_ind_type Σ ind i u - - | tConstruct (mkInd ind i) k u => - lookup_constructor_type Σ ind i k u - - | tCase ((ind, par), rel) p c brs => - ty <- type_of Γ c ;; - indargs <- reduce_to_ind Σ Γ ty ;; - let '(ind', u, args) := indargs in - ret (tApp p (List.skipn par args ++ [c])) - - | tProj p c => - ty <- type_of Γ c ;; - indargs <- reduce_to_ind Σ Γ ty ;; - (* FIXME *) - ret ty - - | tFix mfix n => - match nth_error mfix n with - | Some f => ret f.(dtype) - | None => raise (IllFormedFix mfix n) - end - - | tCoFix mfix n => - match nth_error mfix n with - | Some f => ret f.(dtype) - | None => raise (IllFormedFix mfix n) - end - - | tInt _ | tFloat _ => raise (NotSupported "primitive types") - end. - - Definition sort_of (Γ : context) (t : term) : typing_result Universe.t := - ty <- type_of Γ t;; - type_of_as_sort type_of Γ ty. - -End TypeOf. diff --git a/checker/theories/Substitution.v b/checker/theories/Substitution.v deleted file mode 100644 index 444222361..000000000 --- a/checker/theories/Substitution.v +++ /dev/null @@ -1,1951 +0,0 @@ -(* Distributed under the terms of the MIT license. *) -From MetaCoq.Template Require Import config utils Ast AstUtils Induction LiftSubst - UnivSubst TermEquality Typing Reduction TypingWf. -From MetaCoq.Checker Require Import Generation Closed WeakeningEnv Weakening. - -From Equations Require Import Equations. -Require Import ssreflect. - -(** * Substitution lemmas for typing derivations. *) - - -Generalizable Variables Σ Γ t T. - -Derive Signature for Ast.wf. - -(** Well-typed substitution into a context with *no* let-ins *) - -Inductive subs `{cf : checker_flags} Σ (Γ : context) : list term -> context -> Type := -| emptys : subs Σ Γ [] [] -| cons_ass Δ s na t T : subs Σ Γ s Δ -> - Σ ;;; Γ |- t : subst0 s T -> - subs Σ Γ (t :: s) (Δ ,, vass na T). -(* | cons_let Δ s na t T : subs Σ Γ s Δ -> *) -(* Σ ;;; Γ |- subst0 s t : subst0 s T -> *) -(* subs Σ Γ (subst0 s t :: s) (Δ ,, vdef na t T). *) - -(** Linking a context (with let-ins), an instance (reversed substitution) - for its assumptions and a well-formed substitution for it. *) - -Inductive context_subst : context -> list term -> list term -> Type := -| context_subst_nil : context_subst [] [] [] -| context_subst_ass Γ args s na t a : - context_subst Γ args s -> - context_subst (vass na t :: Γ) (args ++ [a]) (a :: s) -| context_subst_def Γ args s na b t : - context_subst Γ args s -> - context_subst (vdef na b t :: Γ) args (subst s 0 b :: s). - -(** Promoting a substitution for the non-let declarations of ctx into a - substitution for the whole context *) - -Fixpoint make_context_subst ctx args s := - match ctx with - | [] => match args with - | [] => Some s - | a :: args => None - end - | d :: ctx => - match d.(decl_body) with - | Some body => make_context_subst ctx args (subst0 s body :: s) - | None => match args with - | a :: args => make_context_subst ctx args (a :: s) - | [] => None - end - end - end. - -Lemma subst_decl0 Γ k d : on_local_decl wf_decl_pred Γ d -> map_decl (subst [] k) d = d. -Proof. - unfold wf_decl_pred; intros Hd; destruct d; destruct decl_body; - unfold on_local_decl in Hd; unfold subst_decl, map_decl; simpl in *; - f_equal; simpl; rewrite subst_empty; intuition trivial. -Qed. - -Lemma subst0_context k Γ : All_local_env wf_decl_pred Γ -> subst_context [] k Γ = Γ. -Proof. - unfold subst_context, fold_context. - rewrite rev_mapi. rewrite List.rev_involutive. - unfold mapi. generalize 0. generalize #|List.rev Γ|. - induction Γ; intros; simpl; trivial. - eapply All_local_env_wf_decl_inv in X as [Ha HΓ]. - erewrite subst_decl0; f_equal; eauto. -Qed. - -Lemma fold_context_length f Γ : #|fold_context f Γ| = #|Γ|. -Proof. - unfold fold_context. now rewrite !List.rev_length mapi_length List.rev_length. -Qed. - -Hint Rewrite subst_context_length : subst. -Hint Rewrite subst_context_snoc : subst. - -Lemma subst_context_snoc0 s Γ d : subst_context s 0 (Γ ,, d) = subst_context s 0 Γ ,, subst_decl s #|Γ| d. -Proof. - unfold snoc. now rewrite subst_context_snoc Nat.add_0_r. -Qed. -Hint Rewrite subst_context_snoc : subst. - -Lemma subst_context_alt s k Γ : - subst_context s k Γ = - mapi (fun k' d => subst_decl s (Nat.pred #|Γ| - k' + k) d) Γ. -Proof. - unfold subst_context, fold_context. rewrite rev_mapi. rewrite List.rev_involutive. - apply mapi_ext. intros. f_equal. now rewrite List.rev_length. -Qed. - -Lemma subst_context_app s k Γ Δ : - subst_context s k (Γ ,,, Δ) = subst_context s k Γ ,,, subst_context s (#|Γ| + k) Δ. -Proof. - unfold subst_context, fold_context, app_context. - rewrite List.rev_app_distr. - rewrite mapi_app. rewrite <- List.rev_app_distr. f_equal. f_equal. - apply mapi_ext. intros. f_equal. rewrite List.rev_length. f_equal. lia. -Qed. - - -Lemma subst_decl_closed n k d : wf_decl d -> closed_decl k d -> subst_decl n k d = d. -Proof. - case: d => na [body|] ty; rewrite /closed_decl /subst_decl /map_decl /wf_decl /= => [[wfb wfty]]. - move/andb_and => [cb cty]. rewrite !subst_closedn //. - move=> cty; now rewrite !subst_closedn //. -Qed. - -Lemma closed_ctx_subst n k ctx : All wf_decl ctx -> closed_ctx ctx = true -> subst_context n k ctx = ctx. -Proof. - induction ctx in n, k |- *; auto. - unfold closed_ctx, id. intros wfctx. inv wfctx. - rewrite mapi_app forallb_app List.rev_length /= Nat.add_0_r. - move/andb_and => /= [Hctx /andb_and [Ha _]]. - rewrite subst_context_snoc /snoc /= IHctx // /map_decl subst_decl_closed //. - now apply: closed_decl_upwards. -Qed. - -Lemma map_vass_map_def g l n k : - (mapi (fun i (d : def term) => vass (dname d) (lift0 i (dtype d))) - (map (map_def (subst n k) g) l)) = - (mapi (fun i d => map_decl (subst n (i + k)) d) (mapi (fun i (d : def term) => vass (dname d) (lift0 i (dtype d))) l)). -Proof. - rewrite mapi_mapi mapi_map. apply mapi_ext. - intros. unfold map_decl, vass; simpl; f_equal. - rewrite commut_lift_subst_rec. lia. f_equal; lia. -Qed. - -Lemma All_local_env_subst (P Q : context -> term -> option term -> Type) c n k : - All_local_env Q c -> - (forall Γ t T, - Q Γ t T -> - P (subst_context n k Γ) (subst n (#|Γ| + k) t) - (option_map (subst n (#|Γ| + k)) T) - ) -> - All_local_env P (subst_context n k c). -Proof. - intros Hq Hf. - induction Hq in |- *; try econstructor; eauto; - simpl; unfold snoc; rewrite subst_context_snoc; econstructor; eauto. - - simpl. eapply (Hf _ _ None). eauto. - - simpl. eapply (Hf _ _ None). eauto. - - simpl. eapply (Hf _ _ (Some t)). eauto. -Qed. - -Lemma nth_error_subst_context (Γ' : context) s (v : nat) k : - nth_error (subst_context s k Γ') v = - option_map (subst_decl s (#|Γ'| - S v + k)) (nth_error Γ' v). -Proof. - induction Γ' in v |- *; intros. - - simpl. unfold subst_context, fold_context; simpl; rewrite nth_error_nil. easy. - - simpl. destruct v; rewrite subst_context_snoc. - + simpl. repeat f_equal; try lia. - + simpl. rewrite IHΓ'; simpl in *; (lia || congruence). -Qed. - -Lemma subst_length `{checker_flags} Σ Γ s Γ' : subs Σ Γ s Γ' -> #|s| = #|Γ'|. -Proof. - induction 1; simpl; auto with arith. -Qed. - -Hint Rewrite @app_context_length @subst_context_length : wf. - -Lemma subs_nth_error_ge `{checker_flags} Σ Γ Γ' Γ'' v s : - subs Σ Γ s Γ' -> - #|Γ' ,,, Γ''| <= v -> - nth_error (Γ ,,, Γ' ,,, Γ'') v = - nth_error (Γ ,,, subst_context s 0 Γ'') (v - #|Γ'|). -Proof. - simpl. - intros. rewrite app_context_length in H0. - rewrite !nth_error_app_ge; autorewrite with wf; f_equal; try lia. -Qed. - -Lemma subs_nth_error_lt `{checker_flags} Σ Γ Γ' Γ'' v s : - subs Σ Γ s Γ' -> - v < #|Γ''| -> - nth_error (Γ ,,, subst_context s 0 Γ'') v = - option_map (map_decl (subst s (#|Γ''| - S v))) (nth_error (Γ ,,, Γ' ,,, Γ'') v). -Proof. - simpl. intros Hs Hv. - rewrite !nth_error_app_lt; autorewrite with wf; f_equal; try lia. - erewrite nth_error_subst_context. f_equal. unfold subst_decl. rewrite Nat.add_0_r. reflexivity. -Qed. - -Lemma subst_iota_red s k pars c args brs : - subst s k (iota_red pars c args brs) = - iota_red pars c (List.map (subst s k) args) (List.map (on_snd (subst s k)) brs). -Proof. - unfold iota_red. rewrite !subst_mkApps. f_equal; auto using map_skipn. - rewrite nth_map; simpl; auto. -Qed. - -Lemma subst_unfold_fix n k mfix idx narg fn : - All Ast.wf n -> - unfold_fix mfix idx = Some (narg, fn) -> - unfold_fix (map (map_def (subst n k) (subst n (#|mfix| + k))) mfix) idx = Some (narg, subst n k fn). -Proof. - unfold unfold_fix. intros wfn. - rewrite nth_error_map. destruct (nth_error mfix idx) eqn:Hdef; try congruence. - move=> [= <- <-] /=. - f_equal. f_equal. - erewrite (distr_subst_rec _ _ _ wfn k 0). - rewrite fix_subst_length. simpl. f_equal. - unfold fix_subst. rewrite !map_length. - generalize #|mfix| at 2 3. induction n0; auto. simpl. - f_equal. apply IHn0. -Qed. -Hint Resolve subst_unfold_fix : core. - -Lemma subst_unfold_cofix n k mfix idx narg fn : - All Ast.wf n -> - unfold_cofix mfix idx = Some (narg, fn) -> - unfold_cofix (map (map_def (subst n k) (subst n (#|mfix| + k))) mfix) idx = Some (narg, subst n k fn). -Proof. - unfold unfold_cofix. intros wfn. - rewrite nth_error_map. destruct (nth_error mfix idx) eqn:Hdef; try congruence. - intros [= <- <-]. simpl. do 2 f_equal. solve_all. - erewrite (distr_subst_rec _ _ _ wfn k 0). - rewrite cofix_subst_length. simpl. f_equal. - unfold cofix_subst. rewrite !map_length. - generalize #|mfix| at 2 3. induction n0; auto. simpl. - f_equal. apply IHn0. -Qed. -Hint Resolve subst_unfold_cofix : core. - -Lemma subst_is_constructor: - forall (args : list term) (narg : nat) n k, - is_constructor narg args = true -> is_constructor narg (map (subst n k) args) = true. -Proof. - intros args narg. - unfold is_constructor; intros. - rewrite nth_error_map. destruct nth_error; try discriminate. simpl. intros. - destruct t; try discriminate || reflexivity. - destruct t; try discriminate || reflexivity. simpl. - destruct args0; auto. -Qed. -Hint Resolve subst_is_constructor : core. -Hint Constructors All_local_env : core. - -Lemma typed_subst `{checker_flags} Σ Γ t T n k : - wf Σ.1 -> k >= #|Γ| -> - Σ ;;; Γ |- t : T -> subst n k T = T /\ subst n k t = t. -Proof. - intros wfΣ Hk Hty. - pose proof (typing_wf_local Hty). - pose proof (typing_wf _ wfΣ _ _ _ Hty) as [wft wfT]. - apply typecheck_closed in Hty; eauto. - destruct Hty as [_ Hcl]. - rewrite -> andb_and in Hcl. destruct Hcl as [clb clty]. - pose proof (closed_upwards k clb). - simpl in *. forward H0 by lia. - pose proof (closed_upwards k clty). - simpl in *. forward H1 by lia. - apply (subst_closedn n) in H0; apply (subst_closedn n) in H1; auto. -Qed. - -Lemma subst_wf_local `{checker_flags} Σ Γ n k : - wf Σ.1 -> - wf_local Σ Γ -> - subst_context n k Γ = Γ. -Proof. - intros wfΣ. - induction 1; auto; unfold subst_context, snoc; rewrite fold_context_snoc0; - auto; unfold snoc; - f_equal; auto; unfold map_decl; simpl. - - destruct t0 as [s Hs]. unfold vass. simpl. f_equal. - eapply typed_subst; eauto. lia. - - unfold vdef. - f_equal. - + f_equal. eapply typed_subst; eauto. lia. - + eapply typed_subst in t1 as [Ht HT]; eauto. lia. -Qed. - -(* TODO MOVE *) -Lemma wf_Forall_decls_typing_wf `{checker_flags} : - forall Σ, - wf Σ -> - Forall_decls_typing (fun (_ : global_env_ext) (_ : context) (t T : term) => - Ast.wf t /\ Ast.wf T - ) Σ. -Proof. - intros Σ h. - apply typing_wf_sigma in h as ?. - eapply on_global_env_impl. 2: eassumption. - intros Σ' Γ t [T|] h1 h2. all: cbn in *. - - hnf in h2. assumption. - - hnf in h2. exists fresh_universe. intuition eauto. - constructor. -Qed. - -Lemma subst_declared_constant `{H:checker_flags} Σ cst decl n k u : - wf Σ -> - declared_constant Σ cst decl -> - map_constant_body (subst n k) (map_constant_body (subst_instance_constr u) decl) = - map_constant_body (subst_instance_constr u) decl. -Proof. - intros wΣ h. - apply declared_constant_wf in h as w. - 2: eapply wf_Forall_decls_typing_wf. 2: assumption. - destruct w as [wty wbo]. - eapply declared_decl_closed in h ; eauto. - unfold map_constant_body. - do 2 red in h. destruct decl as [ty [body|] univs]. all: simpl in *. - - rewrite -> andb_and in h. destruct h as [h1 h2]. - rewrite <- (closedn_subst_instance_constr 0 body u) in h1. - rewrite <- (closedn_subst_instance_constr 0 ty u) in h2. - f_equal. - + apply subst_closedn. - * apply wf_subst_instance_constr. assumption. - * eauto using closed_upwards with arith wf. - + f_equal. apply subst_closedn. - * apply wf_subst_instance_constr. assumption. - * eauto using closed_upwards with arith wf. - - red in h. f_equal. - simpl in *. - rewrite <- (closedn_subst_instance_constr 0 ty u) in h. - rewrite andb_true_r in h. - eapply subst_closedn. - + apply wf_subst_instance_constr. assumption. - + eauto using closed_upwards with arith wf. -Qed. - -Definition subst_mutual_inductive_body n k m := - map_mutual_inductive_body (fun k' => subst n (k' + k)) m. - -(* Damnit we also need Ast.wf arguments in Template-coq... to use closedness *) -Lemma subst_declared_minductive {cf:checker_flags} Σ cst decl n k : - wf Σ -> - declared_minductive Σ cst decl -> - subst_mutual_inductive_body n k decl = decl. -Proof. - intros wfΣ Hdecl. - pose proof (on_declared_minductive wfΣ Hdecl). apply onNpars in X. - unshelve epose proof (declared_inductive_closed (Σ:=(empty_ext Σ)) _ Hdecl). auto. - unshelve epose proof (declared_minductive_wf (Σ:=(empty_ext Σ)) _ Hdecl) as [wfpars wfbodies]. auto. - move: H. - rewrite /closed_inductive_decl /lift_mutual_inductive_body. - destruct decl; simpl in *. - move/andb_and => [clpar clbodies]. f_equal. - rewrite [fold_context _ _]closed_ctx_subst; try easy. - eapply Forall_All; eauto. - eapply forallb_All in clbodies. apply Forall_All in wfbodies. - eapply (All_mix wfbodies) in clbodies. clear wfbodies. - eapply Alli_mapi_id. - eapply (All_Alli clbodies). intros i oib [wfb clb]; eauto. - 2:{ intros. eapply X0. } - simpl. - move: clb. rewrite /closed_inductive_body. - destruct oib; simpl. move=> /andb_and[/andb_and [ci ct] cp]. - destruct wfb; simpl in *. - f_equal. rewrite subst_closedn; eauto. - eapply closed_upwards; eauto; lia. - eapply All_map_id. eapply forallb_All in ct. - eapply Forall_All in wf_ind_ctors. - eapply (All_mix wf_ind_ctors) in ct. - eapply (All_impl ct). intros x [wf cl]. - destruct x as [[id ty] arg]; unfold on_pi2; simpl; repeat f_equal. - apply subst_closedn. apply wf. unfold cdecl_type in cl; simpl in cl. - eapply closed_upwards; eauto; lia. - simpl in X. rewrite -X in cp. - eapply forallb_All in cp. - eapply Forall_All in wf_ind_projs. apply (All_mix wf_ind_projs) in cp. - eapply All_map_id; eauto. - eapply (All_impl cp); firstorder auto. - destruct x; unfold on_snd; simpl; f_equal. - apply subst_closedn; auto. rewrite context_assumptions_fold. - eapply closed_upwards; eauto; lia. -Qed. - -Lemma subst_declared_inductive `{checker_flags} Σ ind mdecl idecl n k : - wf Σ -> - declared_inductive Σ mdecl ind idecl -> - map_one_inductive_body (context_assumptions mdecl.(ind_params)) - (length (arities_context mdecl.(ind_bodies))) - (fun k' => subst n (k' + k)) (inductive_ind ind) idecl = idecl. -Proof. - unfold declared_inductive. intros wfΣ [Hmdecl Hidecl]. - eapply (subst_declared_minductive _ _ _ n k) in Hmdecl. - unfold subst_mutual_inductive_body in Hmdecl. - destruct mdecl. simpl in *. - injection Hmdecl. intros Heq. - clear Hmdecl. - pose proof Hidecl as Hidecl'. - rewrite <- Heq in Hidecl'. - rewrite nth_error_mapi in Hidecl'. - clear Heq. - unfold option_map in Hidecl'. rewrite Hidecl in Hidecl'. - congruence. auto. -Qed. - -Lemma subst0_inds_subst ind u mdecl n k t : - All Ast.wf n -> - (subst0 (inds (inductive_mind ind) u (ind_bodies mdecl)) - (subst n (#|arities_context (ind_bodies mdecl)| + k) t)) = - subst n k (subst0 (inds (inductive_mind ind) u (ind_bodies mdecl)) t). -Proof. - intros wfn. - pose proof (distr_subst_rec t (inds (inductive_mind ind) u (ind_bodies mdecl)) n wfn k 0). - simpl in H. rewrite H. - unfold arities_context. rewrite rev_map_length inds_length. - f_equal. generalize (ind_bodies mdecl). - clear. intros. - induction l; unfold inds; simpl; auto. f_equal. auto. -Qed. - -Lemma subst_declared_constructor `{cf:checker_flags} Σ c u mdecl idecl cdecl n k : - wf Σ -> All Ast.wf n -> - declared_constructor Σ mdecl idecl c cdecl -> - subst (map (UnivSubst.subst_instance_constr u) n) k (type_of_constructor mdecl cdecl c u) = (type_of_constructor mdecl cdecl c u). -Proof. - unfold declared_constructor. destruct c as [i ci]. - intros wfΣ wfn [Hidecl Hcdecl]. - eapply (subst_declared_inductive _ _ _ _ n k) in Hidecl; eauto. - unfold type_of_constructor. destruct cdecl as [[id t'] arity]. - destruct idecl; simpl in *. - injection Hidecl. intros. - pose Hcdecl as Hcdecl'. - rewrite <- H0 in Hcdecl'. - rewrite nth_error_map in Hcdecl'. rewrite Hcdecl in Hcdecl'. - simpl in Hcdecl'. injection Hcdecl'. - intros. - rewrite <- H2 at 2. - rewrite <- subst0_inds_subst. f_equal. - now rewrite <- subst_subst_instance_constr. - apply All_map. eapply All_impl; eauto. - intros. now apply wf_subst_instance_constr. -Qed. - -(* TODO MOVE *) -Lemma Forall_impl' : - forall A (P Q : A -> Prop) l, - @Forall A (fun x => P x -> Q x) l -> - Forall P l -> - Forall Q l. -Proof. - intros A P Q l h1 h2. - induction h2 in h1 |- *. - - constructor. - - inversion h1. subst. constructor. - + eauto. - + eauto. -Qed. - -Lemma subst_declared_projection {cf:checker_flags} Σ c mdecl idecl pdecl n k : - wf Σ -> - declared_projection Σ mdecl idecl c pdecl -> - on_snd (subst n (S (ind_npars mdecl + k))) pdecl = pdecl. -Proof. - intros wfΣ Hd. - eapply declared_projection_wf in Hd as w. - 2: eapply wf_Forall_decls_typing_wf. 2: assumption. - eapply (declared_projection_closed (Σ:=empty_ext Σ)) in Hd. 2:auto. - destruct pdecl; unfold on_snd; simpl; f_equal. apply subst_closedn; auto. - eapply closed_upwards; eauto. lia. -Qed. - -Lemma subst_fix_context: - forall (mfix : list (def term)) n (k : nat), - fix_context (map (map_def (subst n k) (subst n (#|mfix| + k))) mfix) = - subst_context n k (fix_context mfix). -Proof. - intros mfix n k. unfold fix_context. - rewrite map_vass_map_def rev_mapi. - fold (fix_context mfix). - rewrite (subst_context_alt n k (fix_context mfix)). - now rewrite /subst_decl mapi_length fix_context_length. -Qed. - -Lemma subst_destArity ctx t n k : - Ast.wf t -> - match destArity ctx t with - | Some (args, s) => - destArity (subst_context n k ctx) (subst n (#|ctx| + k) t) = Some (subst_context n k args, s) - | None => True - end. -Proof. - intros wf; revert ctx. - induction wf in n, k |- * using term_wf_forall_list_ind; intros ctx; simpl; trivial. - - - specialize (IHwf0 n k (ctx,, vass n0 t)). unfold snoc in IHwf0; rewrite subst_context_snoc in IHwf0. - simpl in IHwf0. unfold subst_decl, map_decl in IHwf0. unfold vass in *. simpl in IHwf0. - destruct destArity. destruct p. simpl in *. auto. exact I. - - specialize (IHwf1 n k (ctx,, vdef n0 t t0)). - unfold snoc in IHwf1; rewrite subst_context_snoc in IHwf1. - unfold vdef, subst_decl, map_decl in *. simpl in *. - destruct destArity as [[args s]|]. apply IHwf1. exact I. -Qed. - -Lemma decompose_prod_n_assum0 ctx t : decompose_prod_n_assum ctx 0 t = Some (ctx, t). -Proof. destruct t; simpl; reflexivity. Qed. - -Definition strip_outer_cast_tProd_tLetIn_morph f := - forall t k, - match strip_outer_cast t with - | tProd na A B => - strip_outer_cast (f k t) = tProd na (f k A) (f (S k) B) - | tLetIn na b ty b' => - strip_outer_cast (f k t) = tLetIn na (f k b) (f k ty) (f (S k) b') - | _ => True - end. - -Lemma strip_outer_cast_tProd_tLetIn_subst n : - strip_outer_cast_tProd_tLetIn_morph (subst n). -Proof. - unfold strip_outer_cast_tProd_tLetIn_morph. intros t k. - induction t; simpl in *; auto. -Qed. - -Lemma strip_outer_cast_subst_instance_constr u t : - strip_outer_cast (subst_instance_constr u t) = - subst_instance_constr u (strip_outer_cast t). -Proof. induction t; simpl; auto. Qed. - -Lemma strip_outer_cast_tProd_tLetIn_subst_instance_constr u : - strip_outer_cast_tProd_tLetIn_morph (fun _ => subst_instance_constr u). -Proof. - red. intros. - destruct (strip_outer_cast t) eqn:Heq; try auto. - rewrite strip_outer_cast_subst_instance_constr. now rewrite Heq. - rewrite strip_outer_cast_subst_instance_constr. now rewrite Heq. -Qed. - -Lemma subst_instantiate_params_subst n k params args s t : - All Ast.wf n -> forall s' t', - instantiate_params_subst params args s t = Some (s', t') -> - instantiate_params_subst - (mapi_rec (fun k' decl => subst_decl n (k' + k) decl) params #|s|) - (map (subst n k) args) (map (subst n k) s) (subst n (#|s| + k) t) = - Some (map (subst n k) s', subst n (#|s| + k + #|params|) t'). -Proof. - intros Hn. - induction params in args, t, n, Hn, k, s |- *; intros ctx' t'. - - destruct args; simpl; rewrite ?Nat.add_0_r; try congruence. - - simpl. - destruct a as [na [body|] ty]; simpl; try congruence; - destruct t; try congruence. - -- intros Ht'. - specialize (IHparams _ k _ _ _ Hn _ _ Ht'). - simpl in IHparams. - replace (#|s| + k + S #|params|) with (S (#|s| + k + #|params|)) by lia. - rewrite <- IHparams. f_equal. - now rewrite distr_subst. - -- intros Ht'. destruct args; try congruence. simpl. - specialize (IHparams _ k _ _ _ Hn _ _ Ht'). - simpl in IHparams. - replace (#|s| + k + S #|params|) with (S (#|s| + k + #|params|)) by lia. - now rewrite <- IHparams. -Qed. - -Lemma closed_tele_subst n k ctx : - All wf_decl ctx -> closed_ctx ctx -> - mapi (fun (k' : nat) (decl : context_decl) => subst_decl n (k' + k) decl) (List.rev ctx) = List.rev ctx. -Proof. - rewrite /closedn_ctx /mapi. simpl. generalize 0. - induction ctx using rev_ind; try easy. - move=> n0. - rewrite /closedn_ctx !rev_app_distr /id /=. - intro Hwf. move /andb_and => [closedx Hctx]. - apply All_app in Hwf as [? X]; inv X. - rewrite subst_decl_closed //. - rewrite (closed_decl_upwards n0) //; lia. - f_equal. now rewrite IHctx. -Qed. - -Lemma decompose_prod_n_assum_extend_ctx {ctx n t ctx' t'} ctx'' : - decompose_prod_n_assum ctx n t = Some (ctx', t') -> - decompose_prod_n_assum (ctx ++ ctx'') n t = Some (ctx' ++ ctx'', t'). -Proof. - induction n in ctx, t, ctx', t', ctx'' |- *. simpl. intros [= -> ->]. eauto. - simpl. - destruct (strip_outer_cast t); simpl; try congruence. - intros H. eapply (IHn _ _ _ _ ctx'' H). - intros H. eapply (IHn _ _ _ _ ctx'' H). -Qed. - -Lemma subst_it_mkProd_or_LetIn n k ctx t : - subst n k (it_mkProd_or_LetIn ctx t) = - it_mkProd_or_LetIn (subst_context n k ctx) (subst n (length ctx + k) t). -Proof. - induction ctx in n, k, t |- *; simpl; try congruence. - pose (subst_context_snoc n k ctx a). unfold snoc in e. rewrite e. clear e. - simpl. rewrite -> IHctx. - pose (subst_context_snoc n k ctx a). simpl. now destruct a as [na [b|] ty]. -Qed. - -Lemma to_extended_list_k_subst n k c k' : - to_extended_list_k (subst_context n k c) k' = to_extended_list_k c k'. -Proof. - unfold to_extended_list_k. revert k'. - generalize (@nil term) at 1 2. - induction c in n, k |- *; simpl; intros. reflexivity. - rewrite subst_context_snoc. unfold snoc. simpl. - destruct a. destruct decl_body. unfold subst_decl, map_decl. simpl. - now rewrite IHc. simpl. apply IHc. -Qed. - -Lemma to_extended_list_k_map_subst: - forall n (k : nat) (c : context) k', - #|c| + k' <= k -> - to_extended_list_k c k' = map (subst n k) (to_extended_list_k c k'). -Proof. - intros n k c k'. - pose proof (to_extended_list_k_spec c k'). - symmetry. solve_all. - destruct H as [x' [-> Hx']]. intuition. simpl. - destruct (leb_spec_Set k x'). lia. reflexivity. -Qed. - -Lemma subst_instantiate_params n k params args t ty : - All wf_decl params -> All Ast.wf n -> All Ast.wf args -> Ast.wf t -> - closed_ctx params -> - instantiate_params params args t = Some ty -> - instantiate_params params (map (subst n k) args) (subst n k t) = Some (subst n k ty). -Proof. - unfold instantiate_params. - move=> wfparams wfn wfargs wft. - move/(closed_tele_subst n k params)=> Heq. - rewrite -{2}Heq //. - specialize (subst_instantiate_params_subst n k (List.rev params) args [] t wfn). - move=> /= Heq'. - case E: (instantiate_params_subst (List.rev params) args)=> [[l' t']|] /= //. - specialize (Heq' _ _ E). rewrite Heq'. move=> [= <-]. f_equal. - rewrite distr_subst //. - move/instantiate_params_subst_length: E => -> /=. do 2 f_equal. lia. -Qed. -Hint Rewrite subst_instantiate_params : lift. - -Lemma wf_arities_context `{checker_flags} Σ mind mdecl : wf Σ -> - declared_minductive Σ mind mdecl -> wf_local (Σ, ind_universes mdecl) (arities_context mdecl.(ind_bodies)). -Proof. - intros wfΣ Hdecl. - eapply declared_minductive_inv in Hdecl. 2:apply weaken_env_prop_typing. all:eauto. - apply onInductives in Hdecl. - unfold arities_context. - revert Hdecl. - induction (ind_bodies mdecl) using rev_ind. constructor. - intros Ha. - rewrite rev_map_app. - simpl. apply Alli_app in Ha as [Hl Hx]. - inv Hx. clear X0. - apply onArity in X as [s Hs]. - specialize (IHl Hl). - econstructor; eauto. - fold (arities_context l) in *. - unshelve epose proof (weakening (Σ, ind_universes mdecl) [] (arities_context l) _ _ wfΣ _ Hs). - now rewrite app_context_nil_l. - simpl in X. - eapply (env_prop_typing _ typecheck_closed) in Hs; eauto. - rewrite -> andb_and in Hs. destruct Hs as [Hs Ht]. - simpl in Hs. apply (lift_closed #|arities_context l|) in Hs. - rewrite -> Hs, app_context_nil_l in X. simpl. exists s. - apply X. -Qed. - -Lemma on_constructor_closed_wf `{checker_flags} {Σ mind mdecl u idecl indices cdecl cs} : - wf Σ -> - on_constructor (lift_typing typing) (Σ, ind_universes mdecl) mdecl (inductive_ind mind) idecl indices cdecl cs -> - let cty := subst0 (inds (inductive_mind mind) u (ind_bodies mdecl)) - (subst_instance_constr u (snd (fst cdecl))) - in closed cty /\ Ast.wf cty. -Proof. - intros wfΣ [cs' ? Hparams [s Hs]]. - pose proof (typing_wf_local Hs). - apply typing_wf in Hs as w. 2: assumption. - destruct w as [w _]. - destruct cdecl as [[id cty] car]. - eapply (env_prop_typing _ typecheck_closed) in Hs; eauto. - rewrite arities_context_length in Hs. - rewrite -> andb_and in *. simpl in *. - destruct Hs as [Hs _]. split. - - eapply (closedn_subst _ 0 0). - + clear. unfold inds. - induction #|ind_bodies mdecl|; simpl; try constructor; auto. - + simpl. now rewrite -> inds_length, closedn_subst_instance_constr. - - apply wf_subst. - + auto with wf. - + apply wf_subst_instance_constr. assumption. -Qed. -(* -Lemma on_projection_closed_wf `{checker_flags} {Σ mind mdecl u i idecl pdecl} : - wf Σ -> mdecl.(ind_npars) = context_assumptions mdecl.(ind_params) -> - on_projection (lift_typing typing) (Σ, ind_universes mdecl) (inductive_mind mind) mdecl (inductive_ind mind) idecl i pdecl -> - let pty := subst_instance_constr u (snd pdecl) in - closedn (S (ind_npars mdecl)) pty = true /\ Ast.wf pty. -Proof. - intros wfΣ Hpar. - unfold on_projection. - intros [s Hs]. - pose proof (typing_wf_local Hs). - destruct pdecl as [id cty]. - eapply (env_prop_typing _ typing_wf_gen) in Hs as Hs'; eauto. - eapply (env_prop_typing _ typecheck_closed) in Hs; eauto. - rewrite -> andb_and in *. simpl in *. - destruct Hs as [Hs _]. - rewrite smash_context_length in Hs. simpl in *. - rewrite - Hpar in Hs. rewrite -> closedn_subst_instance_constr. - split; auto with wf. now apply wf_subst_instance_constr. -Qed. -*) -Lemma context_subst_length Γ a s : context_subst Γ a s -> #|Γ| = #|s|. -Proof. induction 1; simpl; congruence. Qed. - -Lemma context_subst_assumptions_length Γ a s : context_subst Γ a s -> context_assumptions Γ = #|a|. -Proof. induction 1; simpl; try congruence. rewrite app_length /=. lia. Qed. - -(* Lemma context_subst_app `{cf:checker_flags} Σ Γ Γ' a s : *) -(* All_local_env (fun _ _ t T => Ast.wf t /\ Ast.wf T) Σ Γ' -> *) -(* All Ast.wf a -> All Ast.wf s -> *) -(* context_subst (Γ' ++ Γ) a s -> *) -(* { a0 & { a1 & { s0 & { s1 & (context_subst Γ a0 s0 * context_subst (subst_context s0 0 Γ') a1 s1 *) -(* * (a = a0 ++ a1) * (s = s1 ++ s0))%type } } } }. *) -(* Proof. *) -(* induction Γ' in Γ, a, s |- *. simpl. *) -(* exists a, [], s, []. rewrite app_nil_r; intuition. *) - -(* simpl. intros wfΓ wfa wfs Hs. *) -(* revert wfΓ wfa wfs. inv Hs; intros wfΓ wfa wfs; inv wfΓ. *) -(* - eapply All_app in wfa as [Hargs Ha1]; *) -(* eapply (All_app (l:=[a1])) in wfs as [Ha'' Hs0]. *) -(* specialize (IHΓ' _ _ _ H0 Hargs Hs0 H). *) -(* destruct IHΓ' as (a0' & a1' & s1 & s2 & ((sa0 & sa1) & eqargs) & eqs0). *) -(* subst. exists a0', (a1' ++ [a1]), s1, (a1 :: s2). intuition eauto. *) -(* rewrite subst_context_snoc. constructor. auto. now rewrite app_assoc. *) -(* - eapply (All_app (l:=[subst0 s0 b])) in wfs as [Ha'' Hs0]. *) -(* specialize (IHΓ' _ _ _ H0 wfa Hs0 H). *) -(* destruct IHΓ' as (a0' & a1' & s1 & s2 & ((sa0 & sa1) & eqargs) & eqs0). *) -(* subst. exists a0', a1', s1, (subst s2 0 (subst s1 #|Γ'| b) :: s2). intuition eauto. *) -(* rewrite -> subst_context_snoc, Nat.add_0_r. *) -(* unfold subst_decl; simpl. unfold map_decl. simpl. *) -(* econstructor. auto. simpl. f_equal. *) -(* rewrite -> subst_app_simpl; auto. simpl. *) -(* pose proof(context_subst_length _ _ _ sa1) as Hs1. *) -(* rewrite subst_context_length in Hs1. rewrite -> Hs1. auto. auto. *) -(* apply All_app in Hs0. solve_all. *) -(* apply All_app in Hs0. solve_all. *) -(* Qed. *) - -Lemma make_context_subst_rec_spec ctx args s tele args' s' : - context_subst ctx args s -> - make_context_subst tele args' s = Some s' -> - context_subst (List.rev tele ++ ctx) (args ++ args') s'. -Proof. - induction tele in ctx, args, s, args', s' |- *. - - move=> /= Hc. case: args'. move => [= <-]. - now rewrite app_nil_r. - move=> a l //. - - move=> Hc /=. case: a => [na [body|] ty] /=. - -- specialize (IHtele (vdef na body ty :: ctx) args (subst0 s body :: s) args' s'). - move=> /=. rewrite <- app_assoc. - move/(IHtele _). move=> H /=. apply H. - constructor. auto. - -- case: args' => [|a args']; try congruence. - specialize (IHtele (vass na ty :: ctx) (args ++ [a]) (a :: s) args' s'). - move=> /=. rewrite <- app_assoc. - move/(IHtele _). move=> H /=. simpl in H. rewrite <- app_assoc in H. apply H. - constructor. auto. -Qed. - -Lemma make_context_subst_spec tele args s' : - make_context_subst tele args [] = Some s' -> - context_subst (List.rev tele) args s'. -Proof. - move/(make_context_subst_rec_spec [] [] [] _ _ _ context_subst_nil). - rewrite app_nil_r /= //. -Qed. - -Lemma instantiate_params_subst_make_context_subst ctx args s ty s' ty' : - instantiate_params_subst ctx args s ty = Some (s', ty') -> - exists ctx'', - make_context_subst ctx args s = Some s' /\ - decompose_prod_n_assum [] (length ctx) ty = Some (ctx'', ty'). -Proof. - induction ctx in args, s, ty, s' |- *; simpl. - case: args => [|a args'] // [= <- <-]. exists []; intuition congruence. - case: a => [na [body|] ty''] /=. - - destruct ty; try congruence. - intros. move: (IHctx _ _ _ _ H) => [ctx'' [Hmake Hdecomp]]. - eapply (decompose_prod_n_assum_extend_ctx [vdef na0 ty1 ty2]) in Hdecomp. - unfold snoc. eexists; intuition eauto. - - destruct ty; try congruence. - case: args => [|a args']; try congruence. - move=> H. move: (IHctx _ _ _ _ H) => [ctx'' [Hmake Hdecomp]]. - eapply (decompose_prod_n_assum_extend_ctx [vass na0 ty1]) in Hdecomp. - unfold snoc. eexists; intuition eauto. -Qed. - -Lemma instantiate_params_make_context_subst ctx args ty ty' : - instantiate_params ctx args ty = Some ty' -> - exists ctx' ty'' s', - decompose_prod_n_assum [] (length ctx) ty = Some (ctx', ty'') /\ - make_context_subst (List.rev ctx) args [] = Some s' /\ ty' = subst0 s' ty''. -Proof. - unfold instantiate_params. - case E: instantiate_params_subst => // [[s ty'']]. - move=> [= <-]. - eapply instantiate_params_subst_make_context_subst in E. - destruct E as [ctx'' [Hs Hty'']]. - exists ctx'', ty'', s. split; auto. - now rewrite -> List.rev_length in Hty''. -Qed. - -Lemma subst_cstr_concl_head ind u mdecl (arity : context) args : - let head := tRel (#|ind_bodies mdecl| - S (inductive_ind ind) + #|ind_params mdecl| + #|arity|) in - let s := (inds (inductive_mind ind) u (ind_bodies mdecl)) in - inductive_ind ind < #|ind_bodies mdecl| -> - subst s (#|arity| + #|ind_params mdecl|) - (subst_instance_constr u (mkApps head (to_extended_list_k (ind_params mdecl) #|arity| ++ args))) - = mkApps (tInd ind u) (to_extended_list_k (ind_params mdecl) #|arity| ++ - map (subst s (#|arity| + #|ind_params mdecl|)) (map (subst_instance_constr u) args)). -Proof. - intros. - rewrite subst_instance_constr_mkApps subst_mkApps. - f_equal. - - subst head. simpl subst_instance_constr. - rewrite (subst_rel_eq _ _ (#|ind_bodies mdecl| - S (inductive_ind ind)) (tInd ind u)) //; try lia. - subst s. rewrite inds_spec rev_mapi nth_error_mapi /=. - elim nth_error_spec. intros. simpl. - f_equal. destruct ind; simpl. f_equal. f_equal. simpl in H. lia. - rewrite List.rev_length. lia. - - rewrite !map_app. f_equal. - -- rewrite map_subst_instance_constr_to_extended_list_k. - erewrite to_extended_list_k_map_subst at 2. - now rewrite Nat.add_comm. lia. -Qed. - -Lemma subst_to_extended_list_k s k args ctx : - All Ast.wf s -> - make_context_subst (List.rev ctx) args [] = Some s -> - map (subst s k) (to_extended_list_k ctx k) = map (lift0 k) args. -Proof. - move=> wfs. - move/make_context_subst_spec. rewrite List.rev_involutive. - move=> H; induction H; simpl; auto. - - inv wfs. - rewrite map_app -IHcontext_subst //. - rewrite to_extended_list_k_cons /= !map_app; unf_term. - f_equal. - rewrite (lift_to_extended_list_k _ _ 1) map_map_compose. - pose proof (to_extended_list_k_spec Γ k); unf_term. - solve_all. destruct H2 as [n [-> Hn]]. - rewrite /lift (subst_app_decomp [a] s k); auto with wf. - rewrite subst_rel_gt. simpl; lia. - repeat (f_equal; simpl; try lia). - cbn -[subst]. f_equal. apply (subst_rel_eq _ _ 0 a); cbnr; lia. - - inv wfs. - rewrite -IHcontext_subst // to_extended_list_k_cons /=. - rewrite (lift_to_extended_list_k _ _ 1) map_map_compose. - pose proof (to_extended_list_k_spec Γ k). - solve_all. destruct H2 as [n [-> Hn]]. - rewrite /lift (subst_app_decomp [subst0 s b] s k); auto with wf. - rewrite subst_rel_gt. simpl; lia. - repeat (unf_term; f_equal; simpl; try lia). -Qed. - -Lemma wf_context_subst ctx args s : - All wf_decl ctx -> All Ast.wf args -> - context_subst ctx args s -> All Ast.wf s. -Proof. - move=> wfctx wfargs. - induction 1. constructor. - eapply All_app in wfargs as [wfargs wfa]. inv wfa. inv wfctx. - constructor; intuition auto. - inv wfctx. red in H. constructor; solve_all. apply wf_subst. solve_all. intuition auto with wf. -Qed. - -Lemma wf_make_context_subst ctx args s' : - All wf_decl ctx -> All Ast.wf args -> - make_context_subst (List.rev ctx) args [] = Some s' -> All Ast.wf s'. -Proof. - move=> wfctx wfargs. - move/make_context_subst_spec. rewrite rev_involutive. - eauto using wf_context_subst. -Qed. - -Hint Resolve All_Forall : wf. - -(* TODO Duplicate of PCUICSubstitution *) -Lemma Alli_map_option_out_mapi_Some_spec' {A B} (f g : nat -> A -> option B) h l t P : - All P l -> - (forall i x t, P x -> f i x = Some t -> g i x = Some (h t)) -> - map_option_out (mapi f l) = Some t -> - map_option_out (mapi g l) = Some (map h t). -Proof. - unfold mapi. generalize 0. - move => n Ha Hfg. move: t. - induction Ha in n |- *; try constructor; auto. - destruct t; cbnr; discriminate. - move=> t /=. case E: (f n x) => [b|]; try congruence. - rewrite (Hfg n _ _ p E). - case E' : map_option_out => [b'|]; try congruence. - move=> [= <-]. now rewrite (IHHa _ _ E'). -Qed. - -Lemma on_constructor_closed {cf:checker_flags} {Σ mind mdecl u idecl indices cdecl cs} : - wf Σ -> - on_constructor (lift_typing typing) (Σ, ind_universes mdecl) mdecl (inductive_ind mind) idecl indices cdecl cs -> - let cty := subst0 (inds (inductive_mind mind) u (ind_bodies mdecl)) - (subst_instance_constr u (snd (fst cdecl))) - in closed cty. -Proof. - intros wfΣ [cs' ? Hparams [s Hs] _]. - pose proof (typing_wf_local Hs). - destruct cdecl as [[id cty] car]. - eapply (env_prop_typing _ typecheck_closed) in Hs; eauto. - rewrite arities_context_length in Hs. - rewrite -> andb_and in *. simpl in *. - destruct Hs as [Hs _]. - eapply (closedn_subst _ 0 0). - clear. unfold inds. induction #|ind_bodies mdecl|; simpl; try constructor; auto. - simpl. now rewrite -> inds_length, closedn_subst_instance_constr. -Qed. - -(* TODO Duplicate of PCUICSubstitution? *) -Lemma map_subst_instance_constr_to_extended_list_k u ctx k : - to_extended_list_k (subst_instance_context u ctx) k - = to_extended_list_k ctx k. -Proof. - unfold to_extended_list_k. - cut (map (subst_instance_constr u) [] = []); [|reflexivity]. - generalize (@nil term); intros l Hl. - induction ctx in k, l, Hl |- *; cbnr. - destruct a as [? [] ?]; cbnr; eauto. apply IHctx. - simpl. now rewrite Hl. -Qed. - -Lemma subst_instance_context_assumptions u ctx : - context_assumptions (subst_instance_context u ctx) - = context_assumptions ctx. -Proof. - induction ctx; cbnr. - destruct (decl_body a); cbn; now rewrite IHctx. -Qed. - - -Lemma subst_build_case_predicate_type ind mdecl idecl u params ps pty n k : - closed_ctx (subst_instance_context u (ind_params mdecl)) -> - closed (ind_type idecl) -> - build_case_predicate_type ind mdecl idecl params u ps = Some pty -> - build_case_predicate_type ind mdecl - (map_one_inductive_body (context_assumptions mdecl.(ind_params)) - (length (arities_context (ind_bodies mdecl))) (fun k' => subst n (k' + k)) - (inductive_ind ind) idecl) - (map (subst n k) params) u ps - = Some (subst n k pty). -Proof. -(* intros closedparams closedtype. *) -(* unfold build_case_predicate_type; simpl. *) -(* case_eq (instantiate_params (subst_instance_context u (ind_params mdecl)) params *) -(* (subst_instance_constr u (ind_type idecl))); *) -(* [|discriminate ]. *) -(* intros ipars Hipars. *) -(* apply (subst_instantiate_params n k) in Hipars; tas. *) -(* rewrite ind_type_map. simpl. *) -(* rewrite subst_closedn in Hipars. *) -(* { rewrite closedn_subst_instance_constr; eapply closed_upwards; tea; lia. } *) -(* rewrite subst_closedn; [eapply closed_upwards; tea; lia|]. *) -(* rewrite Hipars. *) -(* specialize (subst_destArity [] ipars n k); *) -(* destruct (destArity [] ipars) as [[ctx s]|]; [|discriminate]. *) -(* simpl. cbn. move => -> /some_inj-HH. simpl. f_equal. *) -(* etransitivity. *) -(* 2: exact (f_equal (subst n k) HH). *) -(* rewrite subst_it_mkProd_or_LetIn. simpl. f_equal. f_equal. *) -(* { destruct idecl; reflexivity. } *) -(* rewrite subst_mkApps; simpl. f_equal. *) -(* rewrite map_app; f_equal. *) -(* - rewrite !map_map; apply map_ext; clear; intro. *) -(* rewrite subst_context_length. *) -(* rewrite commut_lift_subst_rec. lia. *) -(* f_equal. lia. *) -(* - rewrite /to_extended_list to_extended_list_k_subst. *) -(* rewrite <- to_extended_list_k_map_subst. reflexivity. lia. *) -(* Qed. *) -Admitted. - -Lemma subst_build_branches_type {cf:checker_flags} - n k Σ ind mdecl idecl indices args u p brs cs : - wf Σ -> - All Ast.wf args -> - Ast.wf (ind_type idecl) -> - All Ast.wf n -> - declared_inductive Σ mdecl ind idecl -> - closed_ctx (subst_instance_context u (ind_params mdecl)) -> - on_inductive (lift_typing typing) (Σ, ind_universes mdecl) - (inductive_mind ind) mdecl -> - on_constructors (lift_typing typing) (Σ, ind_universes mdecl) - mdecl (inductive_ind ind) idecl indices (ind_ctors idecl) cs -> - map_option_out (build_branches_type ind mdecl idecl args u p) = Some brs -> - map_option_out (build_branches_type ind mdecl - idecl (map (subst n k) args) u (subst n k p)) = - Some (map (on_snd (subst n k)) brs). -Proof. - intros wfΣ wargs widecl wn wfidecl closedparams onmind Honcs. - assert (wc : Forall wf_decl (subst_instance_context u (ind_params mdecl))). - { assert (h : Forall wf_decl (ind_params mdecl)). - { eapply typing_all_wf_decl ; revgoals. - - apply onParams in onmind. - unfold on_context in onmind. - change TemplateEnvironment.ind_params with ind_params in onmind. - eassumption. - - simpl. assumption. - } - clear - h. induction h. 1: constructor. - simpl. constructor. 2: assumption. - destruct x as [na [bo|] ty]. - all: unfold map_decl. all: unfold wf_decl in *. all: simpl in *. - all: intuition eauto with wf. - } - rewrite !build_branches_type_. cbn. - eapply Alli_map_option_out_mapi_Some_spec'. - eapply All2_All_left; tea. intros x y u'; exact (y; u'). - clear Honcs brs. - intros j [[id t] i] [t' k'] [cs' Honc]. - case_eq (instantiate_params (subst_instance_context u (ind_params mdecl)) args - (subst0 (inds (inductive_mind ind) u - (ind_bodies mdecl)) - (subst_instance_constr u t))); - [|discriminate]. - intros ty Heq; cbn. - pose proof (on_constructor_closed_wf wfΣ (u:=u) Honc) as [clt wt]. - cbn in clt. cbn in wt. - eapply (closed_upwards k) in clt; try lia. - remember (subst0 (inds (inductive_mind ind) u (ind_bodies mdecl)) - (subst_instance_constr u t)) as ty'. - apply (subst_instantiate_params n k) in Heq as Heq'. - all: auto using Forall_All with wf. - erewrite subst_closedn in Heq'; tas. - rewrite Heq'. - eapply instantiate_params_make_context_subst in Heq. - destruct Heq as [ctx' [ty'' [s' [Hty [Hsubst Ht0]]]]]. - subst ty; simpl. - rewrite Heqty' in Hty. - destruct Honc as [Hcshape_args ? cshape_eq Hty' _ _]; unfold cdecl_type in *; simpl in *. - rewrite cshape_eq in Hty. - rewrite -> !subst_instance_constr_it_mkProd_or_LetIn in Hty. - rewrite !subst_it_mkProd_or_LetIn in Hty. - assert (H0: #|subst_context (inds (inductive_mind ind) u (ind_bodies mdecl)) 0 - (subst_instance_context u (ind_params mdecl))| - = #|subst_instance_context u (ind_params mdecl)|). - { now rewrite subst_context_length. } - rewrite <- H0 in Hty. - rewrite decompose_prod_n_assum_it_mkProd in Hty. - injection Hty. clear Hty. - intros Heqty'' <-. revert Heqty''. - rewrite !subst_instance_context_length Nat.add_0_r. - rewrite subst_context_length subst_instance_context_length. - rewrite (subst_cstr_concl_head ind u mdecl cs'.(cshape_args) cs'.(cshape_indices)). - - destruct wfidecl as [Hmdecl Hnth]. - now apply nth_error_Some_length in Hnth. - - intros <-. rewrite !subst_it_mkProd_or_LetIn !subst_mkApps /=. - rewrite !decompose_prod_assum_it_mkProd /=; - try by rewrite is_ind_app_head_mkApps. - rewrite !decompose_app_mkApps; try by reflexivity. - simpl. rewrite !map_app !subst_context_length - !subst_instance_context_length Nat.add_0_r. - eapply subst_to_extended_list_k with (k:=#|cs'.(cshape_args)|) in Hsubst as XX. - 2:{ eapply wf_make_context_subst. 3: eassumption. - all: auto using Forall_All with wf. - } - rewrite map_subst_instance_constr_to_extended_list_k in XX. - rewrite !XX; clear XX. - apply make_context_subst_spec in Hsubst as Hsubst'. - rewrite rev_involutive in Hsubst'. - pose proof (context_subst_assumptions_length _ _ _ Hsubst') as H1. - case E: chop => [l l']. - have chopm := (chop_map _ _ _ _ _ E). - move: E chopm. - rewrite chop_n_app ?map_length. - { rewrite <- H1. apply onNpars in onmind. - now rewrite subst_instance_context_assumptions. - } - move=> [= <- <-] chopm. - move: {chopm}(chopm _ (subst n (#|cs'.(cshape_args)| + k))). - rewrite map_app. - move=> chopm; rewrite {}chopm /=. - inversion 1; subst. f_equal. unfold on_snd; cbn; f_equal. - rewrite !app_nil_r /on_snd /=. - rewrite subst_it_mkProd_or_LetIn !subst_context_length !subst_mkApps - !subst_instance_context_length !map_app. - f_equal. f_equal. - -- rewrite -> commut_lift_subst_rec. arith_congr. lia. - -- f_equal. simpl. f_equal. - rewrite !subst_mkApps /= !map_app. f_equal. - f_equal. - rewrite /to_extended_list -to_extended_list_k_map_subst. - rewrite !subst_context_length subst_instance_context_length. lia. - now rewrite to_extended_list_k_subst. -Qed. -(* -Lemma strip_casts_subst s k t : - Ast.wf t -> - strip_casts (subst s k t) = subst (map strip_casts s) k (strip_casts t). -Proof. - intros wf; revert s k. - induction wf using term_wf_forall_list_ind; simpl; intros; auto; - rewrite ?map_map_compose ?compose_on_snd ?compose_map_def ?map_length; - f_equal; solve_all; eauto. - - admit. - - rewrite subst_mkApps. - rewrite strip_casts_mkApps_wf; auto with wf. admit. admit. - rewrite IHwf. f_equal. rewrite !map_map_compose. solve_all. - - - pose proof (strip_casts_decompose_app (mkApps (subst s k t0) (map (subst s k) l))). - forward H1. auto with wf. admit. - destruct decompose_app eqn:eq. - specialize (H1 _ _ Logic.eq_refl). - rewrite map_map_compose. - rewrite -IHwf H1. - pose proof (strip_casts_decompose_app (mkApps (strip_casts t0) (map strip_casts l))). - forward H3. auto with wf. admit. - destruct (decompose_app (mkApps (strip_casts t0) _)) eqn:eq'. - specialize (H3 _ _ Logic.eq_refl). - - - - rewrite (strip_casts_mkApps_tApp t0) //. - simpl. rewrite subst_mkApps -IHwf. - rewrite map_map_compose. - - - rewrite IHwf. strip_casts_mkApps. map_map_compose. - f_equal; solve_all. -Qed. *) - -Lemma decompose_prod_assum_mkApps_nonnil ctx f a l : - decompose_prod_assum ctx (mkApps f (a :: l)) = (ctx, mkApps f (a :: l)). -Proof. - induction f; simpl; auto. -Qed. - - -Hint Unfold subst1 : subst. -Hint Rewrite subst_mkApps distr_subst: subst. - -Lemma subst_decompose_prod_assum_rec ctx t s k : - let (ctx', t') := decompose_prod_assum ctx t in - ∑ ctx'' t'', - (decompose_prod_assum [] (subst s (#|ctx'| + k) t') = (ctx'', t'')) * - (decompose_prod_assum (subst_context s k ctx) (subst s (length ctx + k) t) = - (subst_context s k ctx' ,,, ctx'', t'')). -Proof. - induction t in ctx, k |- *; simpl; try solve [ eexists _, _; firstorder eauto ]. - - elim: leb_spec_Set => comp. - + destruct (nth_error s (n - (#|ctx| + k))) eqn:Heq. - * destruct decompose_prod_assum eqn:Heq'. - eexists _, _; intuition eauto. - now rewrite decompose_prod_assum_ctx Heq'. - * eexists _,_; firstorder eauto. - + eexists _,_; firstorder eauto. - - destruct decompose_prod_assum eqn:Heq. - rewrite decompose_prod_assum_ctx in Heq. - destruct (decompose_prod_assum [] t1) eqn:Heq'. - noconf Heq. - specialize (IHt1 ctx k). - rewrite decompose_prod_assum_ctx in IHt1. - rewrite Heq' in IHt1. - destruct IHt1 as [ctx'' [t'' [eqt eqt1]]]. - exists ctx'', t''. rewrite -eqt. - split. - * unfold snoc; simpl. rewrite !app_context_length. - simpl. lia_f_equal. - * rewrite decompose_prod_assum_ctx in eqt1. - rewrite decompose_prod_assum_ctx. - destruct (decompose_prod_assum [] (subst s _ t1)) eqn:Heq''. - rewrite subst_context_app in eqt1. - rewrite !subst_context_app. - injection eqt1. intros <-. - intros eqctx. f_equal. - unfold app_context in eqctx. - rewrite app_assoc in eqctx. - apply app_inv_tail in eqctx. - subst c. rewrite app_context_assoc. - unfold snoc. simpl. lia_f_equal. - - destruct decompose_prod_assum eqn:Heq. - rewrite decompose_prod_assum_ctx in Heq. - destruct (decompose_prod_assum [] t2) eqn:Heq'. - noconf Heq. - specialize (IHt2 ctx (S k)). - rewrite decompose_prod_assum_ctx in IHt2. - rewrite Heq' in IHt2. - destruct IHt2 as [ctx'' [t'' [eqt eqt2]]]. - exists ctx'', t''. rewrite -eqt. - split. - * unfold snoc; simpl. rewrite !app_context_length. - simpl. lia_f_equal. - * rewrite decompose_prod_assum_ctx in eqt2. - rewrite decompose_prod_assum_ctx. - rewrite Nat.add_succ_r in eqt2. - destruct (decompose_prod_assum [] (subst s _ t2)) eqn:Heq''. - rewrite subst_context_app in eqt2. - rewrite !subst_context_app subst_context_snoc. - injection eqt2. intros <-. - intros eqctx. f_equal. - unfold app_context in eqctx. - rewrite app_assoc in eqctx. - apply app_inv_tail in eqctx. - subst c. rewrite app_context_assoc. - unfold snoc. simpl. lia_f_equal. - - - destruct decompose_prod_assum eqn:Heq. - rewrite decompose_prod_assum_ctx in Heq. - destruct (decompose_prod_assum [] t3) eqn:Heq'. - noconf Heq. - specialize (IHt3 ctx (S k)). - rewrite decompose_prod_assum_ctx in IHt3. - rewrite Heq' in IHt3. - destruct IHt3 as [ctx'' [t'' [eqt eqt3]]]. - exists ctx'', t''. rewrite -eqt. - split. - * unfold snoc; simpl. rewrite !app_context_length. - simpl. lia_f_equal. - * rewrite decompose_prod_assum_ctx in eqt3. - rewrite decompose_prod_assum_ctx. - rewrite Nat.add_succ_r in eqt3. - destruct (decompose_prod_assum [] (subst s _ t3)) eqn:Heq''. - rewrite subst_context_app in eqt3. - rewrite !subst_context_app subst_context_snoc. - injection eqt3. intros <-. - intros eqctx. f_equal. - unfold app_context in eqctx. - rewrite app_assoc in eqctx. - apply app_inv_tail in eqctx. - subst c. rewrite app_context_assoc. - unfold snoc. simpl. lia_f_equal. - - - destruct args. - * simpl. specialize (IHt ctx k). destruct decompose_prod_assum eqn:da. - destruct IHt as [ctx' [t' [dec dec']]]. - rewrite decompose_prod_assum_ctx in dec'. - destruct (decompose_prod_assum [] (subst _ _ t)) eqn:da'. - noconf dec'. eexists _, _; split => //. - now rewrite decompose_prod_assum_ctx da'. - * specialize (IHt ctx k). destruct decompose_prod_assum eqn:da. - destruct IHt as [ctx' [t' [dec dec']]]. - rewrite decompose_prod_assum_ctx in dec'. - destruct (decompose_prod_assum [] (subst _ _ t)) eqn:da'. - noconf dec'. - cbn [map]. rewrite decompose_prod_assum_mkApps_nonnil. - eexists _, _; split => //. - rewrite decompose_prod_assum_ctx. - now rewrite decompose_prod_assum_mkApps_nonnil. -Qed. - -Lemma map_option_out_impl {A B} (l : list A) (f g : A -> option B) x : - (forall x y, f x = Some y -> g x = Some y) -> - map_option_out (map f l) = Some x -> - map_option_out (map g l) = Some x. -Proof. - intros Hfg. - induction l in x |- *; simpl; auto. - destruct (f a) eqn:fa. - - rewrite (Hfg _ _ fa). - move: IHl; destruct map_option_out. - * move=> H'. specialize (H' _ eq_refl). - rewrite H'. congruence. - * discriminate. - - discriminate. -Qed. - -Lemma smash_context_app Δ Γ Γ' : - smash_context Δ (Γ ++ Γ') = smash_context (smash_context Δ Γ) Γ'. -Proof. - revert Δ; induction Γ as [|[na [b|] ty]]; intros Δ; simpl; auto. -Qed. - - -Lemma strip_casts_decompose_app t : - Ast.wf t -> - forall f l, decompose_app t = (f, l) -> - strip_casts t = mkApps (strip_casts f) (map strip_casts l). -Proof. - intros wf. - induction wf using term_wf_forall_list_ind; simpl; intros; auto; noconf H; - try noconf H0; - rewrite ?map_map_compose ?compose_on_snd ?compose_map_def ?map_length; - f_equal; solve_all; eauto. - - - now noconf H3. - - now noconf H3. -Qed. - -Lemma substitution_check_one_fix s k mfix inds : - map_option_out (map check_one_fix mfix) = Some inds -> - map_option_out (map (fun x : def term => - check_one_fix (map_def (subst s k) (subst s (#|mfix| + k)) x)) mfix) = Some inds. -Proof. - apply map_option_out_impl. - move=> [na ty def rarg] /=. - rewrite decompose_prod_assum_ctx. - destruct (decompose_prod_assum _ (strip_casts ty)) eqn:decomp. - rewrite decompose_prod_assum_ctx in decomp. - destruct (decompose_prod_assum [] ty) eqn:decty. - noconf decomp. rewrite !app_context_nil_l. - pose proof (subst_decompose_prod_assum_rec [] ty s k). - rewrite decty in X. - destruct X as [ctx'' [t'' [dect decty']]]. - rewrite -> subst_context_nil in decty'. simpl in decty'. -Admitted. - (*rewrite decty'. intros ind. - rewrite smash_context_app. - rewrite (smash_context_acc _ (smash_context _ _)). - rewrite List.rev_app_distr. - destruct (nth_error_spec (List.rev (smash_context [] c0)) rarg) => /= //; - autorewrite with len in l; simpl in *. - rewrite nth_error_app_lt; autorewrite with len; simpl; try lia. - rewrite (smash_context_subst []) /=. - rewrite nth_error_rev_inv; autorewrite with len; simpl; try lia. - rewrite nth_error_subst_context /=. - autorewrite with len. - rewrite nth_error_rev_inv in e; autorewrite with len; auto. - autorewrite with len in e. simpl in e. rewrite e. - simpl. - destruct (decompose_app (decl_type x)) eqn:Happ. - destruct t0; try discriminate. simpl in *. - erewrite decompose_app_subst; eauto. simpl. auto. -Qed. *) - -Lemma decompose_prod_assum_mkApps ctx ind u args : - decompose_prod_assum ctx (mkApps (tInd ind u) args) = (ctx, mkApps (tInd ind u) args). -Proof. - apply (decompose_prod_assum_it_mkProd ctx []). - now rewrite is_ind_app_head_mkApps. -Qed. - - -Lemma substitution_check_one_cofix s k mfix inds : - map_option_out (map check_one_cofix mfix) = Some inds -> - map_option_out (map (fun x : def term => - check_one_cofix (map_def (subst s k) (subst s (#|mfix| + k)) x)) mfix) = Some inds. -Proof. - apply map_option_out_impl. move=> [na ty def rarg] /= ind. - destruct (decompose_prod_assum [] ty) eqn:decty. - destruct (decompose_app t) eqn:eqapp. - destruct t0; try discriminate. simpl. - pose proof (subst_decompose_prod_assum_rec [] ty s k). - rewrite decty in X. - destruct X as [ctx'' [t'' [dect decty']]]. -Admitted. - (* apply decompose_app_mkApps in eqapp. => //. - subst t. - rewrite subst_mkApps /= in dect. - rewrite decompose_prod_assum_mkApps in dect. noconf dect. - rewrite decompose_app_mkApps //. -Qed. *) - - -Lemma subs_nth_error `{checker_flags} Σ Γ s Δ decl n t : - subs Σ Γ s Δ -> - nth_error Δ n = Some decl -> - nth_error s n = Some t -> - match decl_body decl return Type with - | Some t' => False - | None => - let ty := subst0 (skipn (S n) s) (decl_type decl) in - Σ ;;; Γ |- t : ty - end. -Proof. - induction 1 in n |- *; simpl; auto; destruct n; simpl; try congruence. - - intros [= <-]. intros [= ->]. - simpl. exact t1. - - apply IHX. -Qed. - -Lemma wf_fix : - forall (mfix : list (def term)) (k : nat), Ast.wf (tFix mfix k) -> - Forall - (fun def : def term => Ast.wf (dtype def) /\ Ast.wf (dbody def)) - mfix. -Proof. - intros. inv H. auto. -Defined. - -Lemma wf_cofix : - forall (mfix : list (def term)) (k : nat), Ast.wf (tCoFix mfix k) -> - Forall - (fun def : def term => Ast.wf (dtype def) /\ Ast.wf (dbody def)) - mfix. -Proof. - intros. inv H. auto. -Defined. - -Local Set Keyed Unification. - -Lemma substitution_red1 `{CF:checker_flags} Σ Γ Γ' Γ'' s M N : - wf Σ.1 -> All Ast.wf s -> subs Σ Γ s Γ' -> wf_local Σ Γ -> Ast.wf M -> - red1 (fst Σ) (Γ ,,, Γ' ,,, Γ'') M N -> - red1 (fst Σ) (Γ ,,, subst_context s 0 Γ'') (subst s #|Γ''| M) (subst s #|Γ''| N). -Proof. - intros wfΣ wfs Hs wfΓ wfM H. - remember (Γ ,,, Γ' ,,, Γ'') as Γ0. revert Γ Γ' Γ'' HeqΓ0 wfΓ Hs. - induction H using red1_ind_all in |- *; intros Γ0 Γ' Γ'' HeqΓ0 wfΓ Hs; try subst Γ; cbn -[iota_red]; - match goal with - |- context [iota_red _ _ _ _] => idtac - | |- _ => autorewrite with subst - end; auto; - try solve [ econstructor; ((forward IHred1; try inv wfM; eauto) || eauto) ]. - - (* remember (Γ ,,, Γ' ,,, Γ'') as Γ0. revert Γ Γ' Γ'' HeqΓ0 wfΓ Hs. *) - (* induction H using red1_ind_all in |- *; intros Γ0 Γ' Γ'' HeqΓ0 wfΓ Hs; try subst Γ; simpl; *) - (* autorewrite with subst; auto; *) - (* try solve [ econstructor; try eapply IHred1; try inv wfM; eauto; eauto ]. *) - (* - autorewrite with subst. rewrite distr_subst; auto. - eapply red_beta. - - - autorewrite with subst. rewrite distr_subst; auto. - eapply red_zeta. *) - - - pose proof (subst_length _ _ _ _ Hs). - elim (leb_spec_Set); intros Hn. - + destruct (nth_error s) eqn:Heq. - ++ pose proof (nth_error_Some_length Heq). - rewrite -> nth_error_app_context_ge in H by lia. - rewrite -> nth_error_app_context_lt in H by lia. - destruct nth_error eqn:HΓ'. - eapply subs_nth_error in Heq; eauto. - simpl in H. destruct decl_body; try contradiction. - discriminate. discriminate. - ++ apply nth_error_None in Heq. - assert(S i = #|s| + (S (i - #|s|))) by lia. - rewrite H1. rewrite -> simpl_subst; try lia. - econstructor. - rewrite nth_error_app_context_ge // in H. - rewrite nth_error_app_context_ge // in H. lia. - rewrite -> nth_error_app_context_ge. 2:(autorewrite with wf; lia). - rewrite <- H. f_equal. f_equal. autorewrite with wf. lia. - rewrite -> !nth_error_app_context_ge in H by lia. - destruct nth_error eqn:Hi. - eapply nth_error_All_local_env in wfΓ. red in wfΓ. - rewrite -> Hi in wfΓ. simpl in H. - destruct c; simpl in H; try discriminate. - injection H. intros ->. red in wfΓ. cbn in *. apply typing_wf in wfΓ. intuition eauto. eauto. - apply nth_error_Some_length in Hi. lia. discriminate. - + rewrite -> nth_error_app_context_lt in H by lia. - pose (commut_lift_subst_rec body s (S i) (#|Γ''| - S i) 0). - assert(eq:#|Γ''| - S i + S i = #|Γ''|) by lia. - rewrite -> eq in e. rewrite <- e by lia. - constructor. - rewrite -> nth_error_app_context_lt by (autorewrite with wf; lia). - rewrite -> nth_error_subst_context. - unfold subst_decl; now rewrite -> option_map_decl_body_map_decl, H, Nat.add_0_r. - - - rewrite subst_iota_red. - autorewrite with subst. - constructor. - - - rewrite mkApps_tApp; simpl; auto with wf. - inv wfM. auto with wf. - + eapply red_fix. erewrite subst_unfold_fix; eauto. - now apply subst_is_constructor. - - - pose proof (subst_declared_constant _ _ _ s #|Γ''| u wfΣ H). - apply (f_equal cst_body) in H1. - rewrite <- !map_cst_body in H1. rewrite H0 in H1. simpl in H1. - injection H1. intros ->. - econstructor. eauto. eauto. - - - simpl. constructor. - inv wfM. - now rewrite nth_error_map H. - - - constructor. - forward IHred1; try now inv wfM. - specialize (IHred1 Γ0 Γ' (Γ'' ,, _) eq_refl). - now rewrite subst_context_snoc0 in IHred1. - - - constructor. - forward IHred1; try now inv wfM. - specialize (IHred1 Γ0 Γ' (Γ'' ,, _) eq_refl). - now rewrite subst_context_snoc0 in IHred1. - - - constructor. - induction X. all: simpl. all: constructor. - + intuition auto. simpl. eapply b0. all: auto. - inversion wfM. subst. inversion H5. subst. auto. - + eapply IHX. inversion wfM. subst. - constructor. all: auto. - inversion H5. subst. assumption. - - - forward IHred1; try now inv wfM. - assert(All (Ast.wf ∘ subst s #|Γ''|) M2). - eapply (Forall_All (fun x => Ast.wf (subst s #|Γ''| x))). inv wfM; solve_all. - apply wf_subst; auto. solve_all. - specialize (IHred1 _ _ _ eq_refl). - specialize (IHred1 wfΓ Hs). - apply red1_mkApps_l; auto. inv wfM. apply wf_subst; auto. solve_all. - solve_all. - - - assert(Ast.wf (subst s #|Γ''| M1)). inv wfM. apply wf_subst; auto with wf. - assert(All (Ast.wf ∘ subst s #|Γ''|) M2). - { apply (Forall_All (fun x => Ast.wf (subst s #|Γ''| x))). - inv wfM. - eapply Forall_impl; eauto. simpl; eauto with wf. } - apply red1_mkApps_r; auto with wf. - now apply All_map. - assert(Ast.wf M1). now inv wfM. - assert(All Ast.wf M2). eapply Forall_All. now inv wfM. - clear -X H0 X1 wfΓ Hs. - induction X; constructor; auto. - intuition. - eapply b; eauto. now inv X1. - apply IHX. now inv X1. - - - forward IHred1. now inv wfM. - constructor. specialize (IHred1 _ _ (Γ'' ,, vass na M1) eq_refl). - now rewrite subst_context_snoc0 in IHred1. - - - constructor. - induction X; constructor; auto. - intuition. eapply b; eauto. - inv wfM. now inv H. - apply IHX. inv wfM. inv H; now constructor. - - - constructor. - rewrite -> (OnOne2_length X). generalize (#|mfix1|). - induction X. all: simpl. all: constructor. all: simpl. - + intuition eauto. - * eapply b0. all: eauto. - inv wfM. inv H. intuition eauto. - * inversion b. auto. - + eapply IHX. constructor. - apply wf_fix in wfM. inv wfM. assumption. - - - apply wf_fix in wfM. - apply fix_red_body. rewrite !subst_fix_context. - solve_all. apply (OnOne2_All_mix_left wfM) in X. (* clear wfM. *) - rewrite <- (OnOne2_length X). - eapply OnOne2_map. unfold on_Trel. solve_all. - + specialize (X Γ0 Γ' (Γ'' ,,, fix_context mfix0)). - rewrite app_context_assoc in X. specialize (X eq_refl). - rewrite -> app_context_length, fix_context_length in *. - rewrite -> subst_context_app in *. - rewrite -> app_context_assoc, Nat.add_0_r in *. - auto. - + inversion b0. auto. - - - constructor. - rewrite -> (OnOne2_length X). generalize (#|mfix1|). - induction X. all: simpl. all: constructor. all: simpl. - + intuition eauto. - * eapply b0. all: eauto. - inv wfM. inv H. intuition eauto. - * inversion b. auto. - + eapply IHX. constructor. - apply wf_cofix in wfM. inv wfM. assumption. - - - apply wf_cofix in wfM. - apply cofix_red_body. rewrite !subst_fix_context. - solve_all. apply (OnOne2_All_mix_left wfM) in X. (* clear wfM. *) - rewrite <- (OnOne2_length X). - eapply OnOne2_map. unfold on_Trel. solve_all. - + specialize (X Γ0 Γ' (Γ'' ,,, fix_context mfix0)). - rewrite app_context_assoc in X. specialize (X eq_refl). - rewrite -> app_context_length, fix_context_length in *. - rewrite -> subst_context_app in *. - rewrite -> app_context_assoc, Nat.add_0_r in *. - auto. - + inversion b0. auto. -Qed. - -Lemma subst_eq_term_upto_univ `{checker_flags} Σ Re Rle napp n k T U : - RelationClasses.Reflexive Re -> - RelationClasses.Reflexive Rle -> - eq_term_upto_univ_napp Σ Re Rle napp T U -> - eq_term_upto_univ_napp Σ Re Rle napp (subst n k T) (subst n k U). -Proof. - intros hRe hRle h. - induction T in napp, n, k, U, h, Rle, hRle |- * using term_forall_list_rect. - all: simpl ; inversion h ; simpl. - all: try (eapply eq_term_upto_univ_refl ; easy). - all: try (constructor ; easy). - - constructor. - eapply All2_map. eapply All2_impl' ; try eassumption. - eapply All_impl ; try eassumption. - cbn. intros x HH y HH'. now eapply HH. - - subst. eapply eq_term_upto_univ_mkApps. - rewrite map_length. eauto. - eapply All2_map. eapply All2_impl' ; try eassumption. - eapply All_impl ; try eassumption. - cbn. intros x HH y HH'. now eapply HH. - - constructor ; try easy. - eapply All2_map. - eapply All2_impl'. eassumption. - eapply All_impl. easy. - cbn. intros x HH y [? HH']. split ; [assumption | now apply HH]. - - constructor. - eapply All2_map. - eapply All2_impl'. eassumption. - eapply All_impl. eassumption. - cbn. apply All2_length in X0 as e. rewrite e. - intros x [] y []; now split. - - constructor. - eapply All2_map. - eapply All2_impl'. eassumption. - eapply All_impl. eassumption. - cbn. apply All2_length in X0 as e. rewrite e. - intros x [] y []; now split. -Qed. - -Lemma subst_eq_term `{checker_flags} Σ ϕ n k T U : - eq_term Σ ϕ T U -> - eq_term Σ ϕ (subst n k T) (subst n k U). -Proof. - intros Hleq. - eapply subst_eq_term_upto_univ. - - intro. eapply eq_universe_refl. - - intro. eapply eq_universe_refl. - - assumption. -Qed. - -Lemma subst_leq_term `{checker_flags} Σ ϕ n k T U : - leq_term Σ ϕ T U -> - leq_term Σ ϕ (subst n k T) (subst n k U). -Proof. - intros Hleq. - eapply subst_eq_term_upto_univ. - - intro. eapply eq_universe_refl. - - intro. eapply leq_universe_refl. - - assumption. -Qed. - - -Lemma subst_eq_decl `{checker_flags} Σ ϕ l k d d' : - eq_decl Σ ϕ d d' -> eq_decl Σ ϕ (subst_decl l k d) (subst_decl l k d'). -Proof. - destruct d, d', decl_body, decl_body0; - unfold eq_decl, map_decl; cbn; intuition auto using subst_eq_term. -Qed. - -Lemma subst_eq_context `{checker_flags} Σ φ l l' n k : - eq_context Σ φ l l' -> - eq_context Σ φ (subst_context n k l) (subst_context n k l'). -Proof. - induction l in l', n, k |- *; inversion 1. constructor. - rewrite !subst_context_snoc. constructor. - apply All2_length in X1 as e. rewrite e. - now apply subst_eq_decl. - now apply IHl. -Qed. - -Lemma subs_wf `{checker_flags} Σ Γ s Δ : wf Σ.1 -> subs Σ Γ s Δ -> All Ast.wf s. -Proof. - induction 2; constructor. - apply typing_wf in t0; intuition auto with wf. - eapply typing_wf_local in t0; eauto. -Qed. - -Lemma wf_red1_wf `{checker_flags} Σ Γ M N : wf Σ.1 -> wf_local Σ Γ -> Ast.wf M -> red1 (fst Σ) Γ M N -> Ast.wf N. -Proof. - intros wfΣ wfΓ wfM Hr. - apply wf_red1 in Hr; eauto. - apply typing_wf_sigma; auto. - apply typing_all_wf_decl in wfΓ; eauto. -Qed. - -(** The cumulativity relation is substitutive, yay! *) - -Lemma substitution_cumul `{CF:checker_flags} Σ Γ Γ' Γ'' s M N : - wf Σ.1 -> wf_local Σ (Γ ,,, Γ' ,,, Γ'') -> subs Σ Γ s Γ' -> Ast.wf M -> Ast.wf N -> - Σ ;;; Γ ,,, Γ' ,,, Γ'' |- M <= N -> - Σ ;;; Γ ,,, subst_context s 0 Γ'' |- subst s #|Γ''| M <= subst s #|Γ''| N. -Proof. - intros wfΣ wfΓ Hs wfM wfN. induction 1. - constructor. - - now apply subst_leq_term. - - pose proof r. - apply wf_red1_wf in X0; eauto. - eapply substitution_red1 in r. 4:eauto. all:auto. - econstructor 2; eauto. - eauto using subs_wf. - eauto with wf. - - pose proof r. - apply wf_red1_wf in X0; eauto. - eapply substitution_red1 in r. 4:eauto. - all:eauto using subs_wf with wf. - now econstructor 3. -Qed. - -Lemma substitution_All_local_env_over `{cf : checker_flags} {Σ Γ Γ' Δ s} : - wf Σ.1 -> - forall wfΓ0 : wf_local Σ (Γ ,,, Γ' ,,, Δ), - All_local_env_over typing - (fun (Σ : global_env_ext) (Γ : context) (_ : wf_local Σ Γ) - (t T : term) (_ : Σ;;; Γ |- t : T) => - forall (Γ0 Γ' Δ : context) (s : list term), - subs Σ Γ0 s Γ' -> - Γ = Γ0 ,,, Γ' ,,, Δ -> - Σ;;; Γ0 ,,, subst_context s 0 Δ |- subst s #|Δ| t : subst s #|Δ| T) Σ - (Γ ,,, Γ' ,,, Δ) wfΓ0 -> - subs Σ Γ s Γ' -> - wf_local Σ (Γ ,,, subst_context s 0 Δ). -Proof. - intros wfΣ wfΓ. - induction Δ; simpl; intros Hwf. - intros _. clear Hwf. simpl in wfΓ. now eapply All_local_env_app_inv in wfΓ. - depelim Hwf; - rewrite subst_context_snoc; simpl; constructor. - eapply IHΔ; eauto. red. exists (tu.π1). simpl. - rewrite Nat.add_0_r. eapply t0; eauto. - eapply IHΔ; eauto. red. exists (tu.π1). simpl. - rewrite Nat.add_0_r. eapply t1; eauto. - simpl. rewrite Nat.add_0_r. eapply t0; eauto. -Qed. - -Theorem substitution `{checker_flags} Σ Γ Γ' s Δ (t : term) T : - wf Σ.1 -> subs Σ Γ s Γ' -> - Σ ;;; Γ ,,, Γ' ,,, Δ |- t : T -> - Σ ;;; Γ ,,, subst_context s 0 Δ |- subst s #|Δ| t : subst s #|Δ| T. -Proof. - intros HΣ Hs Ht. - pose proof (typing_wf_local Ht). - generalize_eq Γ0 (Γ ,,, Γ' ,,, Δ). - revert Γ Γ' Δ s Hs. revert Σ HΣ Γ0 X t T Ht. - apply (typing_ind_env (fun Σ Γ0 t T => - forall (Γ Γ' Δ : context) (s : list term) - (sub : subs Σ Γ s Γ') (eqΓ0 : Γ0 = Γ ,,, Γ' ,,, Δ), - Σ ;;; Γ ,,, subst_context s 0 Δ |- subst s #|Δ| t : subst s #|Δ| T)); - intros Σ wfΣ Γ0 wfΓ0; intros; subst Γ0; simpl in *; - try ((epose proof (substitution_All_local_env_over wfΣ wfΓ0 X sub)) - || (epose proof (substitution_All_local_env_over wfΣ wfΓ0 X0 sub))); - try solve [econstructor; eauto]. - - - assert (wfcdecl : Ast.wf (decl_type decl)). - { clear X. apply typing_all_wf_decl in wfΓ0; eauto. - eapply (nth_error_forall) in wfΓ0; eauto. red in wfΓ0. intuition. } - elim (leb_spec_Set); intros Hn. - elim nth_error_spec. - + intros x Heq Hlt. - pose proof (subst_length _ _ _ _ sub). - rewrite -> nth_error_app_context_ge in H0 by lia. - rewrite -> nth_error_app_context_lt in H0 by lia. - eapply subs_nth_error in Heq; eauto. - destruct decl_body; try contradiction. - cbn -[skipn] in Heq. - eapply refine_type. - eapply (weakening _ _ (subst_context s 0 Δ)) in Heq; eauto with wf. - rewrite subst_context_length in Heq. eapply Heq. - rewrite -> commut_lift_subst_rec by lia. - rewrite <- (firstn_skipn (S (n - #|Δ|)) s) at 2. - rewrite -> subst_app_decomp. f_equal. - replace (S n) with ((S n - #|Δ|) + #|Δ|) by lia. - assert (eq:#|(map (lift0 #|skipn (S (n - #|Δ|)) s|) (firstn (S (n - #|Δ|)) s))| = S n - #|Δ|). - rewrite map_length. rewrite -> firstn_length by lia. lia. - rewrite <- eq. rewrite -> simpl_subst_rec; auto; try lia. - auto with wf. eapply subs_wf in sub; eauto. - now apply All_Forall, All_firstn. - - + intros Hs. - pose proof (subst_length _ _ _ _ sub). - rewrite H1 in Hs. - assert (S n = #|s| + (S (n - #|s|))) by lia. - rewrite H2. rewrite simpl_subst; auto; try lia. - constructor; auto. - rewrite -> nth_error_app_context_ge; try lia; rewrite subst_context_length. - rewrite -> 2!nth_error_app_context_ge in H0 by lia. - rewrite <- H0. f_equal. lia. - lia. - - + eapply subs_nth_error_lt in sub; eauto. - rewrite H0 in sub. simpl in sub. - eapply refine_type. constructor; eauto. - rewrite <- map_decl_type. - rewrite -> commut_lift_subst_rec by lia. - f_equal. lia. - - - econstructor; auto. eapply X1; eauto. - specialize (X1 Γ Γ' Δ s sub eq_refl). - specialize (X3 Γ Γ' (Δ,, vass n t) s sub eq_refl). - now rewrite subst_context_snoc0 in X3. - - - econstructor; auto. eapply X1; eauto. - specialize (X1 Γ Γ' Δ s sub eq_refl). - specialize (X3 Γ Γ' (Δ,, vass n t) s sub eq_refl). - now rewrite subst_context_snoc0 in X3. - - - specialize (X1 Γ Γ' Δ s sub eq_refl). - specialize (X3 Γ Γ' Δ s sub eq_refl). - specialize (X5 Γ Γ' (Δ,, vdef n b b_ty) s sub eq_refl). - rewrite subst_context_snoc0 in X5. - econstructor; eauto. - - - specialize (X0 Γ Γ' Δ s0 sub eq_refl). - eapply type_mkApps; eauto. - eapply typing_wf in X; eauto. destruct X. - clear X0 H2 H0 H1. - induction X1; try constructor; eauto. - specialize (p Γ Γ' Δ s0 sub eq_refl). - specialize (p0 Γ Γ' Δ s0 sub eq_refl). - simpl in *. econstructor; eauto. - change (tProd na (subst s0 #|Δ| A) (subst s0 (S #|Δ|) B)) - with (subst s0 #|Δ| (tProd na A B)). - eapply substitution_cumul; eauto. - eapply typing_wf in typrod; eauto. intuition. - unfold subst1 in IHX1 |- *. rewrite -> distr_subst in IHX1. - apply IHX1. - apply wf_subst. constructor; auto. - now apply typing_wf in ty. - apply typing_wf in typrod; eauto. - intuition. now inv H0. - eauto using subs_wf. - - - eapply refine_type. constructor; eauto. - rewrite !map_cst_type. eapply subst_declared_constant in H0 as ->; eauto. - - - eapply refine_type. econstructor; eauto. - eapply on_declared_inductive in isdecl as [on_mind on_ind]; auto. - apply onArity in on_ind as [s' Hindty]. - pose proof (typing_wf (Σ.1, ind_universes mdecl) wfΣ _ _ _ Hindty) as [clty _]. - apply typecheck_closed in Hindty as [_ Hindty]; eauto. symmetry. - move/andb_and/proj1: Hindty. rewrite -(closedn_subst_instance_constr _ _ u) => Hty. - apply: (subst_closedn s #|Δ|); auto with wf. - eapply closed_upwards. eauto. simpl; lia. - - - eapply refine_type. econstructor; eauto. - symmetry. - destruct (on_declared_constructor wfΣ isdecl) as [? [cs [? onc]]]. - eapply on_constructor_closed_wf in onc as [clty wty]; auto. - unfold type_of_constructor. - apply subst_closedn. 1: eauto with wf. - eapply closed_upwards; eauto. lia. - - - rewrite subst_mkApps map_app map_skipn. - specialize (X2 Γ Γ' Δ s sub eq_refl). - specialize (X4 Γ Γ' Δ s sub eq_refl). - assert (Hclos: closed_ctx (ind_params mdecl)). { - destruct isdecl as [Hmdecl Hidecl]. - eapply on_declared_minductive in Hmdecl; eauto. - eapply onParams in Hmdecl. - eapply closed_wf_local in Hmdecl; eauto. } - assert (Hclos': closed (ind_type idecl)). { - eapply on_declared_inductive in isdecl; eauto. - destruct isdecl as [_ oind]. clear -oind wfΣ. - apply onArity in oind; destruct oind as [s HH]; cbn in *. - apply typecheck_closed in HH; eauto. - apply snd in HH. apply andb_and in HH; apply HH. } - simpl. econstructor. all: eauto. - -- eapply subst_build_case_predicate_type in H1; tea. - simpl in *. subst params. rewrite firstn_map. - etransitivity; [|eapply H1; eauto]. f_equal. - now erewrite subst_declared_inductive. - now rewrite closedn_subst_instance_context. - -- now rewrite !subst_mkApps in X4. - -- simpl. - destruct (on_declared_inductive wfΣ isdecl) as [oind obod]. - pose obod.(onConstructors) as onc. - eapply (subst_build_branches_type s #|Δ|) in H4; eauto. - subst params. rewrite firstn_map. exact H4. - 4: now rewrite closedn_subst_instance_context. - all: eauto with wf. - subst params. eapply All_firstn. - eapply typing_wf in X3; auto. - destruct X3 as [wfc wfargs]. - eapply Forall_All. - now eapply wf_mkApps_inv in wfargs. - now eapply subs_wf in sub. - -- solve_all. - destruct b0 as [s' [Hs IHs]]; eauto. - - - specialize (X2 Γ Γ' Δ s sub eq_refl). - eapply refine_type. econstructor. - eauto. - rewrite subst_mkApps in X2. eauto. - rewrite map_length; eauto. - rewrite <- (Nat.add_0_l #|Δ|). - pose proof (subs_wf _ _ _ _ wfΣ sub). - erewrite distr_subst_rec. simpl. - rewrite map_rev. subst ty. - f_equal. - pose proof (declared_projection_closed wfΣ isdecl). - pose proof (declared_projection_wf _ _ _ _ _ isdecl). - pose proof (typing_wf_gen _ wfΣ _ localenv_nil _ _ (type_Prop _)) as [X' _]. - specialize (H2 X'). clear X'. - symmetry; apply subst_closedn; eauto. now apply wf_subst_instance_constr. - rewrite List.rev_length H0. rewrite closedn_subst_instance_constr. - eapply closed_upwards; eauto. lia. auto. - - - rewrite -> (map_dtype _ (subst s (#|mfix| + #|Δ|))). - eapply type_Fix; auto. - * eapply fix_guard_subst ; eauto. - * now rewrite -> nth_error_map, H1. - * eapply All_map. - eapply (All_impl X0); simpl. - intros x [u [Hs Hs']]; exists u. - now specialize (Hs' _ _ _ _ sub eq_refl). - * eapply All_map. - eapply (All_impl X1); simpl. - intros x [Hb IH]. - rewrite subst_fix_context. - specialize (IH Γ Γ' (Δ ,,, (fix_context mfix)) _ sub). - rewrite app_context_assoc in IH. specialize (IH eq_refl). - rewrite subst_context_app Nat.add_0_r app_context_assoc in IH. - rewrite app_context_length fix_context_length in IH. - rewrite subst_context_length fix_context_length. - rewrite commut_lift_subst_rec; try lia. now rewrite (Nat.add_comm #|Δ|). - * move: H2. - rewrite /wf_fixpoint. - pose proof (substitution_check_one_fix s #|Δ| mfix). - destruct map_option_out eqn:Heq => //. - specialize (H2 _ eq_refl). - rewrite map_map_compose. now rewrite H2. - - - rewrite -> (map_dtype _ (subst s (#|mfix| + #|Δ|))). - eapply type_CoFix; auto. - * eapply cofix_guard_subst; eauto. - * now rewrite -> nth_error_map, H1. - * eapply All_map. - eapply (All_impl X0); simpl. - intros x [u [Hs Hs']]; exists u. - now specialize (Hs' _ _ _ _ sub eq_refl). - * eapply All_map. - eapply (All_impl X1); simpl. - intros x [Hb IH]. - rewrite subst_fix_context. - specialize (IH Γ Γ' (Δ ,,, (fix_context mfix)) _ sub). - rewrite app_context_assoc in IH. specialize (IH eq_refl). - rewrite subst_context_app Nat.add_0_r app_context_assoc in IH. - rewrite app_context_length fix_context_length in IH. - rewrite subst_context_length fix_context_length. - rewrite commut_lift_subst_rec; try lia. now rewrite (Nat.add_comm #|Δ|). - * move: H2. - rewrite /wf_cofixpoint. - pose proof (substitution_check_one_cofix s #|Δ| mfix). - destruct map_option_out eqn:Heq => //. - specialize (H2 _ eq_refl). - rewrite map_map_compose. now rewrite H2. - - - econstructor; eauto. - eapply substitution_cumul; eauto. - now eapply typing_wf in X0. - now eapply typing_wf in X2. -Qed. - -Lemma substitution0 `{checker_flags} Σ Γ n u U (t : term) T : - wf Σ.1 -> - Σ ;;; Γ ,, vass n U |- t : T -> Σ ;;; Γ |- u : U -> - Σ ;;; Γ |- t {0 := u} : T {0 := u}. -Proof. - intros HΣ Ht Hu. - assert (wfΓ : wf_local Σ Γ). - apply typing_wf_local in Hu; eauto. - pose proof (substitution Σ Γ [vass n U] [u] [] t T HΣ) as thm. - forward thm. constructor. constructor. rewrite subst_empty; auto. - apply typing_wf in Hu; intuition. - now apply (thm Ht). -Qed. diff --git a/checker/theories/Weakening.v b/checker/theories/Weakening.v deleted file mode 100644 index d86bba66c..000000000 --- a/checker/theories/Weakening.v +++ /dev/null @@ -1,1196 +0,0 @@ -(* Distributed under the terms of the MIT license. *) -From MetaCoq.Template Require Import config utils Ast AstUtils Reflect Induction - LiftSubst UnivSubst TermEquality Typing TypingWf LibHypsNaming. -From MetaCoq.Checker Require Import WeakeningEnv Closed. - -Require Import ssreflect. -From Equations Require Import Equations. - -(** * Weakening lemmas for typing derivations. - - [weakening_*] proves weakening of typing, reduction etc... w.r.t. the *local* - environment. *) - - -Derive Signature for Ast.wf Forall. - -Generalizable Variables Σ Γ t T. - -Lemma typed_liftn `{checker_flags} Σ Γ t T n k : - wf Σ.1 -> wf_local Σ Γ -> k >= #|Γ| -> - Σ ;;; Γ |- t : T -> lift n k T = T /\ lift n k t = t. -Proof. - intros wfΣ wfΓ Hk Hty. - apply typecheck_closed in Hty; eauto. - destruct Hty as [_ Hcl]. - rewrite -> andb_and in Hcl. destruct Hcl as [clb clty]. - pose proof (closed_upwards k clb). - pose proof (closed_upwards k clty). - simpl in *. forward H0 by lia. - apply (lift_closed n) in H0. - simpl in *. forward H1 by lia. - now apply (lift_closed n) in H1. -Qed. - -Lemma lift_decl0 k d : map_decl (lift 0 k) d = d. -Proof. - destruct d; destruct decl_body; unfold map_decl; simpl; - f_equal; now rewrite ?lift0_id. -Qed. - -Lemma lift0_context k Γ : lift_context 0 k Γ = Γ. -Proof. - unfold lift_context, fold_context. - rewrite rev_mapi. rewrite List.rev_involutive. - unfold mapi. generalize 0 at 2. generalize #|List.rev Γ|. - induction Γ; intros; simpl; trivial. - rewrite lift_decl0; f_equal; auto. -Qed. - -Lemma lift_context_length n k Γ : #|lift_context n k Γ| = #|Γ|. -Proof. apply fold_context_length. Qed. -Hint Rewrite lift_context_length : lift. - -Definition lift_context_snoc0 n k Γ d : lift_context n k (d :: Γ) = lift_context n k Γ ,, lift_decl n (#|Γ| + k) d. -Proof. unfold lift_context. now rewrite fold_context_snoc0. Qed. -Hint Rewrite lift_context_snoc0 : lift. - -Lemma lift_context_snoc n k Γ d : lift_context n k (Γ ,, d) = lift_context n k Γ ,, lift_decl n (#|Γ| + k) d. -Proof. - unfold snoc. apply lift_context_snoc0. -Qed. -Hint Rewrite lift_context_snoc : lift. - -Lemma lift_context_app n k Γ Δ : - lift_context n k (Γ ,,, Δ) = lift_context n k Γ ,,, lift_context n (#|Γ| + k) Δ. -Proof. - unfold lift_context, fold_context, app_context. - rewrite List.rev_app_distr. - rewrite mapi_app. rewrite <- List.rev_app_distr. f_equal. f_equal. - apply mapi_ext. intros. f_equal. rewrite List.rev_length. f_equal. lia. -Qed. - -Lemma nth_error_lift_context: - forall (Γ' Γ'' : context) (v : nat), - v < #|Γ'| -> forall nth k, - nth_error Γ' v = Some nth -> - nth_error (lift_context #|Γ''| k Γ') v = Some (lift_decl #|Γ''| (#|Γ'| - S v + k) nth). -Proof. - induction Γ'; intros. - - easy. - - simpl. destruct v; rewrite lift_context_snoc0. - + simpl. repeat f_equal; try lia. simpl in *. congruence. - + simpl. apply IHΓ'; simpl in *; (lia || congruence). -Qed. - -Lemma nth_error_lift_context_eq: - forall (Γ' Γ'' : context) (v : nat) k, - nth_error (lift_context #|Γ''| k Γ') v = - option_map (lift_decl #|Γ''| (#|Γ'| - S v + k)) (nth_error Γ' v). -Proof. - induction Γ'; intros. - - simpl. unfold lift_context, fold_context; simpl. now rewrite nth_error_nil. - - simpl. destruct v; rewrite lift_context_snoc0. - + simpl. repeat f_equal; try lia. - + simpl. apply IHΓ'; simpl in *; (lia || congruence). -Qed. - -Lemma weaken_nth_error_ge {Γ Γ' v Γ''} : #|Γ'| <= v -> - nth_error (Γ ,,, Γ') v = - nth_error (Γ ,,, Γ'' ,,, lift_context #|Γ''| 0 Γ') (#|Γ''| + v). -Proof. - intros Hv. - rewrite -> !nth_error_app_context_ge, ?lift_context_length. f_equal. lia. - rewrite lift_context_length. lia. - rewrite lift_context_length. lia. auto. -Qed. - -Lemma weaken_nth_error_lt {Γ Γ' Γ'' v} : v < #|Γ'| -> - nth_error (Γ ,,, Γ'' ,,, lift_context #|Γ''| 0 Γ') v = - option_map (lift_decl #|Γ''| (#|Γ'| - S v)) (nth_error (Γ ,,, Γ') v). -Proof. - simpl. intros Hv. - rewrite -> !nth_error_app_context_lt. - rewrite nth_error_lift_context_eq. - do 2 f_equal. lia. lia. now rewrite lift_context_length. -Qed. - -Lemma lift_simpl {Γ'' Γ' : context} {i t} : i < #|Γ'| -> - lift0 (S i) (lift #|Γ''| (#|Γ'| - S i) t) = lift #|Γ''| #|Γ'| (lift0 (S i) t). -Proof. - intros. assert (#|Γ'| = S i + (#|Γ'| - S i)) by easy. - rewrite -> H0 at 2. - rewrite permute_lift; try easy. -Qed. - - -Lemma lift_decl_closed n k d : closed_decl k d -> lift_decl n k d = d. -Proof. - case: d => na [body|] ty; rewrite /closed_decl /lift_decl /map_decl /=. - move/andb_and => [cb cty]. now rewrite !lift_closed //. - move=> cty; now rewrite !lift_closed //. -Qed. - -Lemma closed_decl_upwards k d : closed_decl k d -> forall k', k <= k' -> closed_decl k' d. -Proof. - case: d => na [body|] ty; rewrite /closed_decl /=. - move/andb_and => [cb cty] k' lek'. do 2 rewrite (@closed_upwards k) //. - move=> cty k' lek'; rewrite (@closed_upwards k) //. -Qed. - -Lemma closed_ctx_lift n k ctx : closed_ctx ctx -> lift_context n k ctx = ctx. -Proof. - induction ctx in n, k |- *; auto. - unfold closed_ctx, id. simpl. - rewrite mapi_app forallb_app List.rev_length /= lift_context_snoc0 /snoc Nat.add_0_r. - move/andb_and => /= [Hctx /andb_and [Ha _]]. - rewrite IHctx // lift_decl_closed //. now apply: closed_decl_upwards. -Qed. - - -Lemma lift_iota_red n k pars c args brs : - lift n k (iota_red pars c args brs) = - iota_red pars c (List.map (lift n k) args) (List.map (on_snd (lift n k)) brs). -Proof. - unfold iota_red. rewrite !lift_mkApps. f_equal; auto using map_skipn. - rewrite nth_map; simpl; auto. -Qed. - -Lemma parsubst_empty k a : Ast.wf a -> subst [] k a = a. -Proof. - induction 1 in k |- * using term_wf_forall_list_ind; simpl; try congruence; - try solve [f_equal; eauto; solve_all; eauto]. - - - elim (Nat.compare_spec k n); destruct (Nat.leb_spec k n); intros; try easy. - subst. rewrite Nat.sub_diag. simpl. rewrite Nat.sub_0_r. reflexivity. - assert (n - k > 0) by lia. - assert (exists n', n - k = S n'). exists (Nat.pred (n - k)). lia. - destruct H2. rewrite H2. simpl. now rewrite Nat.sub_0_r. - - rewrite IHwf. rewrite mkApps_tApp; eauto with wf. - f_equal; solve_all. -Qed. - -Lemma lift_unfold_fix n k mfix idx narg fn : - unfold_fix mfix idx = Some (narg, fn) -> - unfold_fix (map (map_def (lift n k) (lift n (#|mfix| + k))) mfix) idx = Some (narg, lift n k fn). -Proof. - unfold unfold_fix. - rewrite nth_error_map. destruct (nth_error mfix idx) eqn:Hdef; try congruence. - intros [= <- <-]. simpl. - repeat f_equal. - rewrite (distr_lift_subst_rec _ _ n 0 k). - rewrite fix_subst_length. f_equal. - unfold fix_subst. rewrite !map_length. - generalize #|mfix| at 2 3. induction n0; auto. simpl. - f_equal. apply IHn0. -Qed. -Hint Resolve lift_unfold_fix : core. - -Lemma lift_unfold_cofix n k mfix idx narg fn : - unfold_cofix mfix idx = Some (narg, fn) -> - unfold_cofix (map (map_def (lift n k) (lift n (#|mfix| + k))) mfix) idx = Some (narg, lift n k fn). -Proof. - unfold unfold_cofix. - rewrite nth_error_map. destruct (nth_error mfix idx) eqn:Hdef; try congruence. - intros [= <- <-]. simpl. repeat f_equal. - rewrite (distr_lift_subst_rec _ _ n 0 k). - rewrite cofix_subst_length. f_equal. - unfold cofix_subst. rewrite !map_length. - generalize #|mfix| at 2 3. induction n0; auto. simpl. - f_equal. apply IHn0. -Qed. -Hint Resolve lift_unfold_cofix : core. - -Lemma lift_is_constructor: - forall (args : list term) (narg : nat) n k, - is_constructor narg args = true -> is_constructor narg (map (lift n k) args) = true. -Proof. - intros args narg. - unfold is_constructor; intros. - rewrite nth_error_map. destruct nth_error; try discriminate. simpl. intros. - destruct t; try discriminate || reflexivity. - destruct t; try discriminate || reflexivity. -Qed. -Hint Resolve lift_is_constructor : core. - -Hint Rewrite UnivSubst.lift_subst_instance_constr : lift. -Hint Rewrite lift_mkApps : lift. -Hint Rewrite distr_lift_subst distr_lift_subst10 : lift. -Hint Rewrite lift_iota_red : lift. - -Lemma lift_declared_constant `{checker_flags} Σ cst decl n k : - wf Σ -> - declared_constant Σ cst decl -> - decl = map_constant_body (lift n k) decl. -Proof. - unfold declared_constant. - intros. - eapply lookup_on_global_env in H0; eauto. - destruct H0 as [Σ' [wfΣ' decl']]. - red in decl'. red in decl'. - destruct decl. simpl in *. destruct cst_body. unfold map_constant_body. simpl. - pose proof decl' as declty. - apply typecheck_closed in declty; eauto. - destruct declty as [declty Hcl]. - rewrite -> andb_and in Hcl. destruct Hcl as [clb clty]. - pose proof (closed_upwards k clb). - pose proof (closed_upwards k clty). - simpl in *. forward H0 by lia. forward H1 by lia. - apply (lift_closed n k) in H0. - apply (lift_closed n k) in H1. rewrite H0 H1. reflexivity. - constructor. - red in decl'. - destruct decl'. - apply typecheck_closed in t. destruct t as [_ ccst]. - rewrite -> andb_and in ccst. destruct ccst as [ccst _]. - eapply closed_upwards in ccst; simpl. - apply (lift_closed n k) in ccst. unfold map_constant_body. simpl. - rewrite ccst. reflexivity. lia. apply wfΣ'. constructor. -Qed. - -Definition lift_mutual_inductive_body n k m := - map_mutual_inductive_body (fun k' => lift n (k' + k)) m. - -Lemma lift_wf_local `{checker_flags} Σ Γ n k : wf Σ.1 -> wf_local Σ Γ -> lift_context n k Γ = Γ. -Proof. - intros wfΣ. - induction 1; auto; unfold lift_context, snoc; rewrite fold_context_snoc0; auto; unfold snoc; - f_equal; auto; unfold map_decl; simpl. unfold vass. simpl. f_equal. - destruct t0. - eapply typed_liftn; eauto. lia. unfold vdef. - f_equal. f_equal. eapply typed_liftn; eauto. lia. - destruct t0. - eapply typed_liftn in t0 as [Ht HT]; eauto. lia. -Qed. - -Lemma closed_wf_local `{checker_flags} Σ Γ : - wf Σ.1 -> - wf_local Σ Γ -> - closed_ctx Γ. -Proof. - intros wfΣ. unfold closed_ctx, mapi. intros wf. generalize 0. - induction wf; intros n; auto; unfold closed_ctx, snoc; simpl; - rewrite mapi_rec_app forallb_app; unfold id, closed_decl. - - simpl. - destruct t0 as [s Hs]. - eapply typecheck_closed in Hs as [closedΓ tcl]; eauto. - rewrite -> andb_and in *. simpl in *; rewrite andb_true_r in tcl |- *. - simpl in *. intuition auto. apply IHwf. auto. - erewrite closed_upwards; eauto. rewrite List.rev_length. lia. - - simpl. eapply typecheck_closed in t1 as [closedΓ tcl]; eauto. - rewrite -> andb_and in *. intuition auto. apply IHwf. - erewrite closed_upwards; eauto. - * erewrite closed_upwards; eauto. - rewrite List.rev_length. lia. - * rewrite List.rev_length. lia. -Qed. - -Lemma lift_declared_minductive `{checker_flags} {Σ : global_env} cst decl n k : - wf Σ -> - declared_minductive Σ cst decl -> - lift_mutual_inductive_body n k decl = decl. -Proof. - intros wfΣ Hdecl. - pose proof (on_declared_minductive wfΣ Hdecl). apply onNpars in X. - apply (declared_inductive_closed (Σ:=(empty_ext Σ))) in Hdecl. auto. - move: Hdecl. - rewrite /closed_inductive_decl /lift_mutual_inductive_body. - destruct decl; simpl. - move/andb_and => [clpar clbodies]. f_equal. - now rewrite [fold_context _ _]closed_ctx_lift. - eapply forallb_All in clbodies. - eapply Alli_mapi_id. - eapply (All_Alli clbodies). intros; eauto. - 2:{ intros. eapply X0. } - simpl; intros. - move: H0. rewrite /closed_inductive_body. - destruct x; simpl. move=> /andb_and[/andb_and [ci ct] cp]. - f_equal. rewrite lift_closed; eauto. - eapply closed_upwards; eauto; lia. - eapply All_map_id. eapply forallb_All in ct. - eapply (All_impl ct). intros x. - destruct x as [[id ty] arg]; unfold on_pi2; intros c; simpl; repeat f_equal. - apply lift_closed. unfold cdecl_type in c; simpl in c. - eapply closed_upwards; eauto; lia. - simpl in X. rewrite -X in cp. - eapply forallb_All in cp. eapply All_map_id; eauto. - eapply (All_impl cp); firstorder auto. - destruct x; unfold on_snd; simpl; f_equal. - apply lift_closed. rewrite context_assumptions_fold. - eapply closed_upwards; eauto; lia. - simpl. auto. -Qed. - -Lemma lift_declared_inductive `{checker_flags} Σ ind mdecl idecl n k : - wf Σ -> - declared_inductive Σ mdecl ind idecl -> - map_one_inductive_body (context_assumptions mdecl.(ind_params)) - (length (arities_context mdecl.(ind_bodies))) - (fun k' => lift n (k' + k)) - (inductive_ind ind) idecl = idecl. -Proof. - unfold declared_inductive. intros wfΣ [Hmdecl Hidecl]. - eapply (lift_declared_minductive _ _ n k) in Hmdecl. - unfold lift_mutual_inductive_body in Hmdecl. - destruct mdecl. simpl in *. - injection Hmdecl. intros Heq. - clear Hmdecl. - pose proof Hidecl as Hidecl'. - rewrite <- Heq in Hidecl'. - rewrite nth_error_mapi in Hidecl'. - clear Heq. - unfold option_map in Hidecl'. rewrite Hidecl in Hidecl'. - congruence. auto. -Qed. - -Lemma subst0_inds_lift ind u mdecl n k t : - (subst0 (inds (inductive_mind ind) u (ind_bodies mdecl)) - (lift n (#|arities_context (ind_bodies mdecl)| + k) t)) = - lift n k (subst0 (inds (inductive_mind ind) u (ind_bodies mdecl)) t). -Proof. - rewrite (distr_lift_subst_rec _ _ n 0 k). simpl. - unfold arities_context. rewrite rev_map_length inds_length. - f_equal. generalize (ind_bodies mdecl). - clear. intros. - induction l; unfold inds; simpl; auto. f_equal. auto. -Qed. - -Lemma lift_declared_constructor `{checker_flags} Σ c u mdecl idecl cdecl n k : - wf Σ -> - declared_constructor Σ mdecl idecl c cdecl -> - lift n k (type_of_constructor mdecl cdecl c u) = (type_of_constructor mdecl cdecl c u). -Proof. - unfold declared_constructor. destruct c as [i ci]. intros wfΣ [Hidecl Hcdecl]. - eapply (lift_declared_inductive _ _ _ _ n k) in Hidecl; eauto. - unfold type_of_constructor. destruct cdecl as [[id t'] arity]. - destruct idecl; simpl in *. - injection Hidecl. - intros. - pose Hcdecl as Hcdecl'. - rewrite <- H1 in Hcdecl'. - rewrite nth_error_map in Hcdecl'. rewrite Hcdecl in Hcdecl'. - simpl in Hcdecl'. injection Hcdecl'. - intros. - rewrite <- H3 at 2. - rewrite <- lift_subst_instance_constr. - now rewrite subst0_inds_lift. -Qed. - -Lemma lift_declared_projection `{checker_flags} Σ c mdecl idecl pdecl n k : - wf Σ -> - declared_projection Σ mdecl idecl c pdecl -> - on_snd (lift n (S (ind_npars mdecl + k))) pdecl = pdecl. -Proof. - intros. - eapply (declared_projection_closed (Σ:=empty_ext Σ)) in H0; auto. - unfold on_snd. simpl. - rewrite lift_closed. eapply closed_upwards; eauto; try lia. - destruct pdecl; reflexivity. -Qed. - -Lemma lift_fix_context: - forall (mfix : list (def term)) (n k : nat), - fix_context (map (map_def (lift n k) (lift n (#|mfix| + k))) mfix) = lift_context n k (fix_context mfix). -Proof. - intros mfix n k. unfold fix_context. - rewrite map_vass_map_def rev_mapi. - fold (fix_context mfix). - rewrite (lift_context_alt n k (fix_context mfix)). - unfold lift_decl. now rewrite mapi_length fix_context_length. -Qed. - -Hint Rewrite <- lift_fix_context : lift. - -Lemma All_local_env_lift `{checker_flags} - (P Q : context -> term -> option term -> Type) c n k : - All_local_env Q c -> - (forall Γ t T, - Q Γ t T -> - P (lift_context n k Γ) (lift n (#|Γ| + k) t) - (option_map (lift n (#|Γ| + k)) T) - ) -> - All_local_env P (lift_context n k c). -Proof. - intros Hq Hf. - induction Hq in |- *; try econstructor; eauto; - simpl; rewrite lift_context_snoc; econstructor; eauto. - - simpl. eapply (Hf _ _ None). eauto. - - simpl. eapply (Hf _ _ None). eauto. - - simpl. eapply (Hf _ _ (Some t)). eauto. -Qed. - -Lemma lift_destArity ctx t n k : Ast.wf t -> - destArity (lift_context n k ctx) (lift n (#|ctx| + k) t) = - match destArity ctx t with - | Some (args, s) => Some (lift_context n k args, s) - | None => None - end. -Proof. - intros wf; revert ctx. - induction wf in n, k |- * using term_wf_forall_list_ind; intros ctx; simpl; trivial. - specialize (IHwf0 n k (ctx,, vass n0 t)). rewrite lift_context_snoc in IHwf0. - simpl in IHwf0. unfold lift_decl, map_decl in IHwf0. unfold vass. simpl in IHwf0. rewrite IHwf0. - reflexivity. - specialize (IHwf1 n k (ctx,, vdef n0 t t0)). rewrite lift_context_snoc in IHwf1. - unfold vdef, lift_decl, map_decl in *. simpl in *. rewrite IHwf1. reflexivity. -Qed. - -Lemma lift_strip_outer_cast n k t : lift n k (strip_outer_cast t) = strip_outer_cast (lift n k t). -Proof. - induction t; simpl; try reflexivity. - now rewrite IHt1. -Qed. - -Definition on_pair {A B C D} (f : A -> B) (g : C -> D) (x : A * C) := - (f (fst x), g (snd x)). - -Lemma lift_instantiate_params_subst n k params args s t : - instantiate_params_subst (mapi_rec (fun k' decl => lift_decl n (k' + k) decl) params #|s|) - (map (lift n k) args) (map (lift n k) s) (lift n (#|s| + k) t) = - option_map (on_pair (map (lift n k)) (lift n (#|s| + k + #|params|))) (instantiate_params_subst params args s t). -Proof. - induction params in args, t, n, k, s |- *. - - destruct args; simpl; rewrite ?Nat.add_0_r; reflexivity. - - simpl. simpl. - destruct a as [na [body|] ty]; simpl; try congruence. - destruct t; simpl; try congruence. - -- specialize (IHparams n k args (subst0 s body :: s) t3). - rewrite <- Nat.add_succ_r. simpl in IHparams. - rewrite Nat.add_succ_r. - replace (#|s| + k + S #|params|) with (S (#|s| + k + #|params|)) by lia. - rewrite <- IHparams. - rewrite distr_lift_subst. reflexivity. - -- destruct t; simpl; try congruence. - destruct args; simpl; try congruence. - specialize (IHparams n k args (t :: s) t2). simpl in IHparams. - replace (#|s| + k + S #|params|) with (S (#|s| + k + #|params|)) by lia. - rewrite <- IHparams. auto. -Qed. - -Lemma instantiate_params_subst_length params args s t ctx t' : - instantiate_params_subst params args s t = Some (ctx, t') -> - #|ctx| = #|s| + #|params|. -Proof. - induction params in args, s, t, ctx, t' |- * ; destruct args; simpl; auto; try congruence. - rewrite Nat.add_0_r. congruence. - destruct decl_body. simpl. - destruct t; simpl; try congruence. - intros. erewrite IHparams; eauto. simpl. lia. - destruct t; simpl; try congruence. - destruct decl_body. simpl. - destruct t; simpl; try congruence. - intros. erewrite IHparams; eauto. simpl. lia. - destruct t; simpl; try congruence. - intros. erewrite IHparams; eauto. simpl. lia. -Qed. - -Lemma closed_tele_lift n k ctx : - closed_ctx ctx -> - mapi (fun (k' : nat) (decl : context_decl) => lift_decl n (k' + k) decl) (List.rev ctx) = List.rev ctx. -Proof. - rewrite /closedn_ctx /mapi. simpl. generalize 0. - induction ctx using rev_ind. move=> //. - move=> n0. - rewrite /closedn_ctx !rev_app_distr /id /=. - move/andb_and => [closedx Hctx]. - rewrite lift_decl_closed. rewrite (@closed_decl_upwards n0) //; try lia. - f_equal. now rewrite IHctx. -Qed. - -Lemma lift_instantiate_params n k params args t : - closed_ctx params -> - option_map (lift n k) (instantiate_params params args t) = - instantiate_params params (map (lift n k) args) (lift n k t). -Proof. - unfold instantiate_params. - move/(closed_tele_lift n k params)=> Heq. - rewrite -{2}Heq. - specialize (lift_instantiate_params_subst n k (List.rev params) args [] t). - move=> /= Heq'; rewrite Heq'. - case E: (instantiate_params_subst (List.rev params) args)=> [[l' t']|] /= //. - rewrite distr_lift_subst. - move/instantiate_params_subst_length: E => -> /=. do 3 f_equal. lia. -Qed. -Hint Rewrite lift_instantiate_params : lift. - -Lemma decompose_prod_assum_ctx ctx t : decompose_prod_assum ctx t = - let (ctx', t') := decompose_prod_assum [] t in - (ctx ,,, ctx', t'). -Proof. - induction t in ctx |- *; simpl; auto. - - simpl. rewrite IHt2. - rewrite (IHt2 ([] ,, vass _ _)). - destruct (decompose_prod_assum [] t2). simpl. - unfold snoc. now rewrite app_context_assoc. - - simpl. rewrite IHt3. - rewrite (IHt3 ([] ,, vdef _ _ _)). - destruct (decompose_prod_assum [] t3). simpl. - unfold snoc. now rewrite app_context_assoc. -Qed. - -Lemma lift_decompose_prod_assum_rec ctx t n k : - (let (ctx', t') := decompose_prod_assum ctx t in - (lift_context n k ctx', lift n (length ctx' + k) t')) = - decompose_prod_assum (lift_context n k ctx) (lift n (length ctx + k) t). -Proof. - induction t in n, k, ctx |- *; simpl; - try rewrite -> Nat.sub_diag, Nat.add_0_r; try (eauto; congruence). - - specialize (IHt2 (ctx ,, vass na t1) n k). - destruct decompose_prod_assum. rewrite IHt2. simpl. - rewrite lift_context_snoc. reflexivity. - - specialize (IHt3 (ctx ,, vdef na t1 t2) n k). - destruct decompose_prod_assum. rewrite IHt3. simpl. - rewrite lift_context_snoc. reflexivity. -Qed. - -Lemma lift_decompose_prod_assum t n k : - (let (ctx', t') := decompose_prod_assum [] t in - (lift_context n k ctx', lift n (length ctx' + k) t')) = - decompose_prod_assum [] (lift n k t). -Proof. apply lift_decompose_prod_assum_rec. Qed. - -Lemma decompose_app_lift n k t f a : - decompose_app t = (f, a) -> decompose_app (lift n k t) = (lift n k f, map (lift n k) a). -Proof. destruct t; simpl; intros [= <- <-]; try reflexivity. Qed. -Hint Rewrite decompose_app_lift using auto : lift. - -Lemma lift_it_mkProd_or_LetIn n k ctx t : - lift n k (it_mkProd_or_LetIn ctx t) = - it_mkProd_or_LetIn (lift_context n k ctx) (lift n (length ctx + k) t). -Proof. - induction ctx in n, k, t |- *; simpl; try congruence. - pose (lift_context_snoc n k ctx a). unfold snoc in e. rewrite -> e. clear e. - simpl. rewrite -> IHctx. - pose (lift_context_snoc n k ctx a). - now destruct a as [na [b|] ty]. -Qed. -Hint Rewrite lift_it_mkProd_or_LetIn : lift. - -Lemma to_extended_list_lift n k c : - to_extended_list (lift_context n k c) = to_extended_list c. -Proof. - unfold to_extended_list, to_extended_list_k. generalize 0. - generalize (@nil term) at 1 2. - induction c in n, k |- *; simpl; intros. reflexivity. - rewrite -> lift_context_snoc0. unfold snoc. simpl. - destruct a. destruct decl_body. unfold lift_decl, map_decl. simpl. - now rewrite -> IHc. simpl. apply IHc. -Qed. - -Lemma to_extended_list_map_lift: - forall (n k : nat) (c : context), to_extended_list c = map (lift n (#|c| + k)) (to_extended_list c). -Proof. - intros n k c. - pose proof (to_extended_list_lift_above c). - symmetry. solve_all. - destruct H as [x' [-> Hx]]. simpl. - destruct (leb_spec_Set (#|c| + k) x'); unf_term. - f_equal. lia. reflexivity. -Qed. - -Lemma weakening_red1 `{CF:checker_flags} Σ Γ Γ' Γ'' M N : - wf Σ -> - red1 Σ (Γ ,,, Γ') M N -> - red1 Σ (Γ ,,, Γ'' ,,, lift_context #|Γ''| 0 Γ') (lift #|Γ''| #|Γ'| M) (lift #|Γ''| #|Γ'| N). -Proof. - intros wfΣ H. - remember (Γ ,,, Γ') as Γ0. revert Γ Γ' Γ'' HeqΓ0. - induction H using red1_ind_all in |- *; intros Γ0 Γ' Γ'' HeqΓ0; try subst Γ; simpl; - autorewrite with lift; - try solve [ econstructor; eauto ]. - - - elim (leb_spec_Set); intros Hn. - + rewrite -> simpl_lift; try lia. rewrite -> Nat.add_succ_r. - econstructor; eauto. - erewrite (weaken_nth_error_ge Hn) in H. eauto. - - + rewrite <- lift_simpl by easy. - econstructor. - rewrite -> (weaken_nth_error_lt Hn). - now unfold lift_decl; rewrite -> option_map_decl_body_map_decl, H. - - - econstructor; eauto. - rewrite H0. f_equal. - eapply (lookup_on_global_env _ _ _ _ wfΣ) in H. - destruct H as [Σ' [wfΣ' decl']]. - red in decl'. red in decl'. - rewrite -> H0 in decl'. - apply typecheck_closed in decl'; eauto. destruct decl'. - rewrite -> andb_and in i. destruct i as [Hclosed _]. - simpl in Hclosed. - pose proof (closed_upwards #|Γ'| Hclosed). - forward H by lia. - apply (lift_closed #|Γ''| #|Γ'|) in H. auto. constructor. - - - simpl. constructor. - now rewrite -> nth_error_map, H. - - - constructor. - specialize (IHred1 Γ0 (Γ' ,, vass na N) Γ'' eq_refl). - rewrite -> lift_context_snoc, Nat.add_0_r in IHred1. apply IHred1. - - - constructor. - specialize (IHred1 Γ0 (Γ' ,, vdef na b t) Γ'' eq_refl). - rewrite -> lift_context_snoc, Nat.add_0_r in IHred1. apply IHred1. - - - constructor. - induction X; constructor; auto. - intuition; eauto. - - - constructor. - induction X; constructor; auto. - intuition; eauto. - - - constructor. - specialize (IHred1 Γ0 (Γ' ,, vass na M1) Γ'' eq_refl). - rewrite -> lift_context_snoc, Nat.add_0_r in IHred1. apply IHred1. - - - constructor. - induction X; constructor; auto. - intuition; eauto. - - - constructor. - rewrite -> (OnOne2_length X). generalize (#|mfix1|). - induction X. all: simpl. all: constructor. 2: solve [ eauto ]. - simpl. intuition eauto. - inversion b. eauto. - - - apply fix_red_body. rewrite !lift_fix_context. - rewrite <- (OnOne2_length X). - eapply OnOne2_map. unfold on_Trel. solve_all. - + specialize (b0 Γ0 (Γ' ,,, fix_context mfix0)). - rewrite app_context_assoc in b0. specialize (b0 Γ'' eq_refl). - rewrite -> app_context_length, fix_context_length in *. - rewrite -> lift_context_app in *. - rewrite -> app_context_assoc, Nat.add_0_r in *. - auto. - + inversion b. eauto. - - - constructor. - rewrite -> (OnOne2_length X). generalize (#|mfix1|). - induction X. all: simpl. all: constructor. 2: solve [ eauto ]. - simpl. intuition eauto. - inversion b. eauto. - - - apply cofix_red_body. rewrite !lift_fix_context. - rewrite <- (OnOne2_length X). - eapply OnOne2_map. unfold on_Trel. solve_all. - + specialize (b0 Γ0 (Γ' ,,, fix_context mfix0)). - rewrite app_context_assoc in b0. specialize (b0 Γ'' eq_refl). - rewrite -> app_context_length, fix_context_length in *. - rewrite -> lift_context_app in *. - rewrite -> app_context_assoc, Nat.add_0_r in *. - auto. - + inversion b. eauto. -Qed. - -Lemma lift_eq_term_upto_univ Σ Re Rl n k T U napp : - eq_term_upto_univ_napp Σ Re Rl napp T U -> - eq_term_upto_univ_napp Σ Re Rl napp (lift n k T) (lift n k U). -Proof. - induction T in napp, n, k, U, Rl |- * using term_forall_list_rect; - inversion 1; simpl; try (now constructor). - - constructor. subst. clear - X X1. - induction l in X, args', X1 |- *. - + inversion X1; constructor. - + inversion X1. inversion X. subst. - simpl. constructor. all: easy. - - constructor. rewrite map_length; easy. clear - X X2. - induction l in X, u', X2 |- *. - + inversion X2; constructor. - + inversion X2; inversion X; subst. - now constructor. - - constructor; try easy. clear - X X3. - induction l in X, brs', X3 |- *. - + inversion X3; constructor. - + inversion X3; inversion X; subst. - constructor. cbn; easy. - easy. - - constructor; try easy. clear -napp X X1. - assert (XX:forall k k', All2 - (fun x y => ((eq_term_upto_univ Σ Re Re (dtype x) (dtype y) × - eq_term_upto_univ Σ Re Re (dbody x) (dbody y)) × - rarg x = rarg y) * eq_binder_annot (dname x) (dname y)) - (map (map_def (lift n k) (lift n (#|m| + k'))) m) - (map (map_def (lift n k) (lift n (#|mfix'| + k'))) mfix')); - [|now apply XX]. clear k. - induction m in X, mfix', X1 |- *. - + inversion X1; constructor. - + inversion X1; inversion X; subst. - simpl. constructor. split. split. split. cbn; easy. - cbn; erewrite All2_length by eassumption. - easy. easy. easy. - unfold tFixProp in IHm. cbn. - rewrite !plus_n_Sm. now apply IHm. - - constructor; try easy. clear - X X1. - assert (XX:forall k k', All2 - (fun x y => ((eq_term_upto_univ Σ Re Re (dtype x) (dtype y) × - eq_term_upto_univ Σ Re Re (dbody x) (dbody y)) × - rarg x = rarg y) * eq_binder_annot (dname x) (dname y)) - (map (map_def (lift n k) (lift n (#|m| + k'))) m) - (map (map_def (lift n k) (lift n (#|mfix'| + k'))) mfix')); - [|now apply XX]. clear k. - induction m in X, mfix', X1 |- *. - + inversion X1; constructor. - + inversion X1; inversion X; subst. - simpl. constructor. split. split. split. cbn; easy. - cbn; erewrite All2_length by eassumption. - easy. easy. easy. - unfold tFixProp in IHm. cbn. - rewrite !plus_n_Sm. now apply IHm. -Qed. - -Lemma lift_eq_term `{checker_flags} Σ ϕ n k T U : - eq_term Σ ϕ T U -> eq_term Σ ϕ (lift n k T) (lift n k U). -Proof. - apply lift_eq_term_upto_univ. -Qed. - -Lemma lift_leq_term `{checker_flags} Σ ϕ n k T U : - leq_term Σ ϕ T U -> leq_term Σ ϕ (lift n k T) (lift n k U). -Proof. - apply lift_eq_term_upto_univ. -Qed. - -Lemma weakening_cumul `{CF:checker_flags} Σ Γ Γ' Γ'' M N : - wf Σ.1 -> - Σ ;;; Γ ,,, Γ' |- M <= N -> - Σ ;;; Γ ,,, Γ'' ,,, lift_context #|Γ''| 0 Γ' |- lift #|Γ''| #|Γ'| M <= lift #|Γ''| #|Γ'| N. -Proof. - intros wfΣ. induction 1. - constructor. - - now apply lift_leq_term. - - eapply weakening_red1 in r; auto. - econstructor 2; eauto. - - eapply weakening_red1 in r; auto. - econstructor 3; eauto. -Qed. - -Lemma lift_eq_decl `{checker_flags} Σ ϕ n k d d' : - eq_decl Σ ϕ d d' -> eq_decl Σ ϕ (lift_decl n k d) (lift_decl n k d'). -Proof. - destruct d, d', decl_body, decl_body0; - unfold eq_decl, map_decl; cbn; intuition auto using lift_eq_term. -Qed. - -Lemma lift_eq_context `{checker_flags} Σ φ l l' n k : - eq_context Σ φ l l' -> - eq_context Σ φ (lift_context n k l) (lift_context n k l'). -Proof. - induction l in l', n, k |- *; intros; destruct l'; rewrite -> ?lift_context_snoc0. - - constructor. - - inversion X. - - inversion X. - - inversion X; subst. constructor. - + apply All2_length in X1. rewrite X1. - now apply lift_eq_decl. - + now apply IHl. -Qed. - - -Lemma lift_build_case_predicate_type ind mdecl idecl u params ps n k : - closed_ctx (subst_instance_context u (ind_params mdecl)) -> - build_case_predicate_type ind mdecl - (map_one_inductive_body (context_assumptions mdecl.(ind_params)) - (length (arities_context (ind_bodies mdecl))) (fun k' => lift n (k' + k)) - (inductive_ind ind) idecl) - (map (lift n k) params) u ps - = option_map (lift n k) (build_case_predicate_type ind mdecl idecl params u ps). -Proof. -(* intros closedpars. unfold build_case_predicate_type. *) -(* rewrite -> ind_type_map. simpl. *) -(* epose proof (lift_instantiate_params n k _ params (subst_instance_constr u (ind_type idecl))) as H. *) -(* rewrite <- lift_subst_instance_constr. *) -(* erewrite <- H; trivial. clear H. *) -(* case_eq (instantiate_params (subst_instance_context u (ind_params mdecl)) params (subst_instance_constr u (ind_type idecl))) ; cbnr. *) -(* intros ity eq. *) -(* pose proof (lift_destArity [] ity n k) as H; cbn in H. rewrite H; clear H. *) -(* destruct destArity as [[ctx s] | ]; [|reflexivity]. simpl. f_equal. *) -(* rewrite lift_it_mkProd_or_LetIn; cbn. f_equal. f_equal. *) -(* - destruct idecl; reflexivity. *) -(* - rewrite lift_mkApps; cbn; f_equal. rewrite map_app. f_equal. *) -(* + rewrite !map_map lift_context_length; apply map_ext. clear. *) -(* intro. now rewrite -> permute_lift by lia. *) -(* + now rewrite -> to_extended_list_lift, <- to_extended_list_map_lift. *) -(* Qed. *) -Admitted. - -Lemma lift_build_branches_type ind mdecl idecl u p params n k : - closed_ctx (subst_instance_context u (ind_params mdecl)) -> - build_branches_type ind mdecl - (map_one_inductive_body (context_assumptions mdecl.(ind_params)) - #|arities_context (ind_bodies mdecl)| (fun k' => lift n (k' + k)) - (inductive_ind ind) idecl) - (map (lift n k) params) u (lift n k p) - = map (option_map (on_snd (lift n k))) - (build_branches_type ind mdecl idecl params u p). -Proof. - intros closedpars. unfold build_branches_type. - rewrite -> ind_ctors_map. - rewrite -> mapi_map, map_mapi. eapply mapi_ext. intros i x. - destruct x as [[id t] arity]. simpl. - rewrite <- lift_subst_instance_constr. - rewrite subst0_inds_lift. - rewrite <- lift_instantiate_params ; trivial. - match goal with - | |- context [ option_map _ (instantiate_params ?x ?y ?z) ] => - destruct (instantiate_params x y z) eqn:Heqip; cbnr - end. - epose proof (lift_decompose_prod_assum t0 n k). - destruct (decompose_prod_assum [] t0). - rewrite <- H. - destruct (decompose_app t1) as [fn arg] eqn:?. - rewrite (decompose_app_lift _ _ _ fn arg); auto. simpl. - destruct (chop _ arg) eqn:Heqchop. - eapply chop_map in Heqchop. - rewrite -> Heqchop. clear Heqchop. - unfold on_snd. simpl. f_equal. - rewrite -> lift_it_mkProd_or_LetIn, !lift_mkApps, map_app; simpl. - rewrite -> !lift_mkApps, !map_app, lift_context_length. - rewrite -> permute_lift by lia. arith_congr. - now rewrite -> to_extended_list_lift, <- to_extended_list_map_lift. -Qed. - - -Lemma wf_ind_type `{checker_flags} Σ mdecl ind idecl : - wf Σ -> declared_inductive Σ mdecl ind idecl -> Ast.wf (ind_type idecl). -Proof. - intros wfΣ Hidecl. - eapply typing_wf_sigma in wfΣ. - destruct Hidecl. red in H0. - eapply (lookup_on_global_env _ _ _ _ wfΣ) in H0 as [Σ' [wfΣ' H0]]; eauto. - red in H0. apply onInductives in H0. - eapply (nth_error_alli H1) in H0. apply onArity in H0 as [Hs Hpars]. wf. -Qed. -Hint Resolve wf_ind_type : wf. - - -Lemma destArity_it_mkProd_or_LetIn ctx ctx' t : - destArity ctx (it_mkProd_or_LetIn ctx' t) = - destArity (ctx ,,, ctx') t. -Proof. - induction ctx' in ctx, t |- *; simpl; auto. - rewrite IHctx'. destruct a as [na [b|] ty]; reflexivity. -Qed. - -Derive Signature for All_local_env_over. - -Lemma weakening_All_local_env_over `{cf : checker_flags} {Σ Γ Γ' Γ''} : - wf Σ.1 -> - wf_local Σ (Γ ,,, Γ'') -> - forall wfΓ0 : wf_local Σ (Γ ,,, Γ'), - All_local_env_over typing - (fun (Σ : global_env_ext) (Γ : context) (_ : wf_local Σ Γ) - (t T : term) (_ : Σ;;; Γ |- t : T) => - forall Γ0 Γ' Γ'' : context, - wf_local Σ (Γ0 ,,, Γ'') -> - Γ = Γ0 ,,, Γ' -> - Σ;;; Γ0 ,,, Γ'' ,,, lift_context #|Γ''| 0 Γ' |- - lift #|Γ''| #|Γ'| t : lift #|Γ''| #|Γ'| T) Σ - (Γ ,,, Γ') wfΓ0 -> - wf_local Σ (Γ ,,, Γ'' ,,, lift_context #|Γ''| 0 Γ'). -Proof. - intros wfΣ wfΓ. - induction Γ'; simpl; intros wf Hwf. - induction Hwf; simpl; auto. - depelim Hwf; - rewrite lift_context_snoc; simpl; constructor. - eapply IHΓ'; eauto. red. exists (tu.π1). simpl. - rewrite Nat.add_0_r. apply t0; auto. - eapply IHΓ'; eauto. red. exists (tu.π1). simpl. - rewrite Nat.add_0_r. apply t1; auto. - simpl. rewrite Nat.add_0_r. apply t0; auto. -Qed. - -Lemma destInd_lift n k t : destInd (lift n k t) = destInd t. -Proof. - destruct t; simpl; try congruence. -Qed. - -Lemma smash_context_lift Δ k n Γ : - smash_context (lift_context n (k + #|Γ|) Δ) (lift_context n k Γ) = - lift_context n k (smash_context Δ Γ). -Proof. - revert Δ. induction Γ as [|[na [b|] ty]]; intros Δ; simpl; auto. - - now rewrite Nat.add_0_r. - - rewrite -IHΓ. - rewrite lift_context_snoc /=. f_equal. - rewrite !subst_context_alt !lift_context_alt !mapi_compose. - apply mapi_ext=> n' x. - destruct x as [na' [b'|] ty']; simpl. - * rewrite !mapi_length /lift_decl /subst_decl /= /map_decl /=; f_equal. - + f_equal. rewrite Nat.add_0_r distr_lift_subst_rec /=. - lia_f_equal. - + rewrite Nat.add_0_r distr_lift_subst_rec; simpl. lia_f_equal. - * rewrite !mapi_length /lift_decl /subst_decl /= /map_decl /=; f_equal. - rewrite Nat.add_0_r distr_lift_subst_rec /=. - repeat (lia || f_equal). - - rewrite -IHΓ. - rewrite lift_context_snoc /= // /lift_decl /subst_decl /map_decl /=. - f_equal. - rewrite lift_context_app. simpl. - rewrite /app_context; lia_f_equal. - rewrite /lift_context // /fold_context /= /map_decl /=. - now lia_f_equal. -Qed. - -Lemma weakening_check_one_fix (Γ' Γ'' : context) mfix : - map - (fun x : def term => - check_one_fix (map_def (lift #|Γ''| #|Γ'|) (lift #|Γ''| (#|mfix| + #|Γ'|)) x)) mfix = - map check_one_fix mfix. -Proof. - apply map_ext. move=> [na ty def rarg] /=. - rewrite decompose_prod_assum_ctx. - rewrite strip_casts_lift. - destruct (decompose_prod_assum _ (strip_casts ty)) eqn:decomp. - rewrite decompose_prod_assum_ctx in decomp. - rewrite -lift_decompose_prod_assum. - destruct (decompose_prod_assum [] (strip_casts ty)) eqn:decty. - noconf decomp. rewrite !app_context_nil_l (smash_context_lift []). - destruct (nth_error_spec (List.rev (smash_context [] c0)) rarg). - rewrite -> List.rev_length, ?smash_context_length in *; simpl in *. - - rewrite nth_error_rev_inv; rewrite !List.rev_length mapi_length List.rev_length smash_context_length; simpl; auto. - rewrite nth_error_lift_context_eq. - simpl. - rewrite nth_error_rev_inv ?List.rev_length smash_context_length in e; auto. - simpl in e. rewrite e. simpl. - destruct (decompose_app (decl_type x)) eqn:Happ. - erewrite decompose_app_lift; eauto. - rewrite destInd_lift. reflexivity. - - erewrite (proj2 (nth_error_None _ _)); auto. - rewrite List.rev_length lift_context_length. - now rewrite List.rev_length in l. -Qed. - -Lemma weakening_check_one_cofix (Γ' Γ'' : context) mfix : - map - (fun x : def term => - check_one_cofix (map_def (lift #|Γ''| #|Γ'|) (lift #|Γ''| (#|mfix| + #|Γ'|)) x)) mfix = - map check_one_cofix mfix. -Proof. - apply map_ext. move=> [na ty def rarg] /=. - rewrite decompose_prod_assum_ctx. - destruct (decompose_prod_assum _ (strip_casts ty)) eqn:decomp. - rewrite decompose_prod_assum_ctx in decomp. - rewrite strip_casts_lift. - rewrite -lift_decompose_prod_assum. - destruct (decompose_prod_assum [] (strip_casts ty)) eqn:decty. - noconf decomp. - destruct (decompose_app t) eqn:Happ. - erewrite decompose_app_lift; eauto. - rewrite destInd_lift. reflexivity. -Qed. - -Lemma weakening_typing `{cf : checker_flags} Σ Γ Γ' Γ'' (t : term) : - wf Σ.1 -> - wf_local Σ (Γ ,,, Γ') -> - wf_local Σ (Γ ,,, Γ'') -> - `(Σ ;;; Γ ,,, Γ' |- t : T -> - Σ ;;; Γ ,,, Γ'' ,,, lift_context #|Γ''| 0 Γ' |- - lift #|Γ''| #|Γ'| t : lift #|Γ''| #|Γ'| T). -Proof. - intros HΣ HΓΓ' HΓ'' * H. - generalize_eq Γ0 (Γ ,,, Γ'). intros eqw. - revert Γ Γ' Γ'' HΓ'' eqw. - revert Σ HΣ Γ0 HΓΓ' t T H. - apply (typing_ind_env (fun Σ Γ0 t T => forall Γ Γ' Γ'' : context, - wf_local Σ (Γ ,,, Γ'') -> - Γ0 = Γ ,,, Γ' -> - Σ;;; Γ ,,, Γ'' ,,, lift_context #|Γ''| 0 Γ' |- lift #|Γ''| #|Γ'| t : lift #|Γ''| #|Γ'| T)); - intros Σ wfΣ Γ0; !!intros; subst Γ0; simpl in *; - try ((epose proof (weakening_All_local_env_over wfΣ wf _ X); eauto) || - (epose proof (weakening_All_local_env_over wfΣ wf _ X0); eauto)); - try solve [econstructor; eauto]. - - - elim (leb_spec_Set); intros Hn. - + rewrite -> simpl_lift; try lia. rewrite -> Nat.add_succ_r. - constructor. auto. - now rewrite <- (weaken_nth_error_ge Hn). - + assert (forall t, lift0 (S n) (lift #|Γ''| (#|Γ'| - S n) t) = lift #|Γ''| #|Γ'| (lift0 (S n) t)). - intros. assert (H:#|Γ'| = S n + (#|Γ'| - S n)) by easy. - rewrite -> H at 2. - rewrite permute_lift; try easy. - rewrite <- H. - rewrite -> map_decl_type. constructor; auto. - now rewrite -> (weaken_nth_error_lt Hn), heq_nth_error. - - - econstructor; auto. - specialize (IHb Γ (Γ' ,, vass n t) Γ''). - forward IHb; auto. - rewrite -> lift_context_snoc, plus_0_r in IHb. - now eapply IHb. - - - econstructor; auto. - simpl. - specialize (IHb Γ (Γ' ,, vass n t) Γ''). - specialize (IHb wf eq_refl). - rewrite -> lift_context_snoc, plus_0_r in IHb. - eapply IHb. - - - econstructor; auto. - specialize (IHb Γ Γ' Γ'' wf eq_refl). simpl. - specialize (IHb' Γ (Γ' ,, vdef n b b_ty) Γ'' wf eq_refl). - rewrite -> lift_context_snoc, plus_0_r in IHb'. - apply IHb'. - - - econstructor; auto. - now apply lift_isApp. - now apply map_non_nil. - clear IHt heq_isApp hneq_l typet. - induction X1. econstructor; eauto. - eapply type_spine_cons. - simpl in p. apply p; auto. - change (tProd na (lift #|Γ''| #|Γ'| A) (lift #|Γ''| (S #|Γ'|) B)) - with (lift #|Γ''| #|Γ'| (tProd na A B)). - eapply weakening_cumul; eauto. auto. - rewrite -> distr_lift_subst10 in IHX1. apply IHX1. - - - autorewrite with lift. - rewrite -> map_cst_type. constructor; auto. - erewrite <- lift_declared_constant; eauto. - - - autorewrite with lift. - erewrite <- (ind_type_map (fun k' => lift #|Γ''| (k' + #|Γ'|))). - pose proof isdecl as isdecl'. - destruct isdecl. intuition auto. - eapply lift_declared_inductive in isdecl'. - rewrite -> isdecl'. - econstructor; try red; intuition eauto. - auto. - - - rewrite (lift_declared_constructor _ (ind, i) u mdecl idecl cdecl _ _ wfΣ isdecl). - econstructor; eauto. - - - rewrite -> lift_mkApps, map_app, map_skipn. - specialize (IHc _ _ _ wf eq_refl). - specialize (IHp _ _ _ wf eq_refl). - assert (Hclos: closed_ctx (subst_instance_context u (ind_params mdecl))). { - destruct isdecl as [Hmdecl Hidecl]. - eapply on_declared_minductive in Hmdecl; eauto. - eapply onParams in Hmdecl. - rewrite -> closedn_subst_instance_context. - eapply closed_wf_local in Hmdecl; eauto. } - simpl. econstructor. - 8:{ cbn. rewrite -> firstn_map. - erewrite lift_build_branches_type; tea. - rewrite map_option_out_map_option_map. - subst params. erewrite heq_map_option_out. reflexivity. } - all: eauto. - -- erewrite -> lift_declared_inductive; eauto. - -- simpl. erewrite firstn_map, lift_build_case_predicate_type; tea. - subst params. erewrite heq_build_case_predicate_type; reflexivity. - -- destruct idecl; simpl in *; auto. - -- now rewrite -> !lift_mkApps in IHc. - -- solve_all. - destruct b0 as [s [Hs IHs]]. exists s; eauto. - - - simpl. - erewrite (distr_lift_subst_rec _ _ _ 0 #|Γ'|). - simpl. rewrite -> map_rev. - subst ty. - rewrite -> List.rev_length, lift_subst_instance_constr. - replace (lift #|Γ''| (S (#|args| + #|Γ'|)) (snd pdecl)) - with (snd (on_snd (lift #|Γ''| (S (#|args| + #|Γ'|))) pdecl)) by now destruct pdecl. - econstructor. - red. split. apply (proj1 isdecl). - split. rewrite -> (proj1 (proj2 isdecl)). f_equal. - rewrite -> heq_length. - symmetry; eapply lift_declared_projection; eauto. - apply (proj2 (proj2 isdecl)). - specialize (IHc _ _ _ wf eq_refl). - rewrite -> lift_mkApps in *. eapply IHc. - now rewrite -> map_length. - - - rewrite -> (map_dtype _ (lift #|Γ''| (#|mfix| + #|Γ'|))). - eapply type_Fix; auto. - * eapply fix_guard_lift ; eauto. - * rewrite -> nth_error_map, heq_nth_error. reflexivity. - * eapply All_map. - eapply (All_impl X0); simpl. - intros x [s [Hs Hs']]; exists s. - now specialize (Hs' _ _ _ wf eq_refl). - * eapply All_map. - eapply (All_impl X1); simpl. - intros x [Hb IH]. - rewrite lift_fix_context. - specialize (IH Γ (Γ' ,,, (fix_context mfix)) Γ'' wf). - rewrite app_context_assoc in IH. specialize (IH eq_refl). - rewrite lift_context_app Nat.add_0_r app_context_assoc in IH. - rewrite app_context_length fix_context_length in IH. - rewrite lift_context_length fix_context_length. - rewrite permute_lift; try lia. now rewrite (Nat.add_comm #|Γ'|). - * red; rewrite <-H1. unfold wf_fixpoint. - rewrite map_map_compose. - now rewrite weakening_check_one_fix. - - - rewrite -> (map_dtype _ (lift #|Γ''| (#|mfix| + #|Γ'|))). - eapply type_CoFix; auto. - * eapply cofix_guard_lift; eauto. - * rewrite -> nth_error_map, heq_nth_error. reflexivity. - * eapply All_map. - eapply (All_impl X0); simpl. - intros x [s [Hs Hs']]; exists s. - now specialize (Hs' _ _ _ wf eq_refl). - * eapply All_map. - eapply (All_impl X1); simpl. - intros x [Hb IH]. - rewrite lift_fix_context. - specialize (IH Γ (Γ' ,,, (fix_context mfix)) Γ'' wf). - rewrite app_context_assoc in IH. specialize (IH eq_refl). - rewrite lift_context_app Nat.add_0_r app_context_assoc in IH. - rewrite app_context_length fix_context_length in IH. - rewrite lift_context_length fix_context_length. - rewrite permute_lift; try lia. now rewrite (Nat.add_comm #|Γ'|). - * red; rewrite <- H1. unfold wf_cofixpoint. - rewrite map_map_compose. - now rewrite weakening_check_one_cofix. - - - econstructor; eauto. - now eapply weakening_cumul. -Qed. - -Lemma weakening `{cf : checker_flags} Σ Γ Γ' (t : term) T : - wf Σ.1 -> wf_local Σ (Γ ,,, Γ') -> - Σ ;;; Γ |- t : T -> - Σ ;;; Γ ,,, Γ' |- lift0 #|Γ'| t : lift0 #|Γ'| T. -Proof. - intros HΣ HΓΓ' * H. - pose (weakening_typing Σ Γ [] Γ' t). - forward t0; eauto. - forward t0; eauto. now eapply wf_local_app_l in HΓΓ'. -Qed. - -Definition fix_context_gen k mfix := - (List.rev - (mapi_rec - (fun (i : nat) (d : def term) => - vass (dname d) (lift0 i (dtype d))) mfix k)). - -Corollary All_mfix_wf {cf:checker_flags} Σ Γ mfix : - wf Σ.1 -> wf_local Σ Γ -> - All (fun d : def term => isType Σ Γ (dtype d)) mfix -> - wf_local Σ (Γ ,,, fix_context mfix). -Proof. - move=> wfΣ wf a; move: wf. - change (fix_context mfix) with (fix_context_gen #|@nil context_decl| mfix). - change Γ with (Γ ,,, []). - generalize (@nil context_decl) as Δ. - rewrite /fix_context_gen. - intros Δ wfΔ. - eapply All_local_env_app. split; auto. - induction a in Δ, wfΔ |- *; simpl; auto. constructor. - simpl. - eapply All_local_env_app. split; auto. - constructor. constructor. simpl. - destruct p as [s Hs]. - exists s. eapply (weakening Σ Γ Δ _ (tSort s)); auto. - specialize (IHa (Δ ,,, [vass (dname x) (lift0 #|Δ| (dtype x))])). - rewrite app_length in IHa. simpl in IHa. - forward IHa. simpl. constructor; auto. - destruct p as [s Hs]. - exists s. eapply (weakening Σ Γ Δ _ (tSort s)); auto. - eapply All_local_env_impl; eauto. - simpl; intros. - rewrite app_context_assoc. apply X. -Qed. diff --git a/checker/theories/WeakeningEnv.v b/checker/theories/WeakeningEnv.v deleted file mode 100644 index 9e703f407..000000000 --- a/checker/theories/WeakeningEnv.v +++ /dev/null @@ -1,735 +0,0 @@ -(* Distributed under the terms of the MIT license. *) -From Coq Require Import RelationClasses. -From MetaCoq.Template Require Import config utils Ast AstUtils - LibHypsNaming TermEquality Typing. -Require Import ssreflect. - -(** * Weakening lemmas w.r.t. the global environment *) - -Generalizable Variables Σ Γ t T. - -Lemma weakening_env_global_ext_levels Σ Σ' φ (H : extends Σ Σ') l - : LevelSet.In l (global_ext_levels (Σ, φ)) - -> LevelSet.In l (global_ext_levels (Σ', φ)). -Proof. - unfold global_ext_levels; simpl. - intros Hl. apply LevelSet.union_spec in Hl. - apply LevelSet.union_spec. - destruct Hl as [Hl|Hl]; [now left|right]. clear φ. - destruct H as [Σ'' eq]; subst. - induction Σ'' in l, Hl |- *. - - now rewrite app_nil_l. - - simpl. apply LevelSet.union_spec. right; eauto. -Qed. -Hint Resolve weakening_env_global_ext_levels : extends. - -Lemma weakening_env_global_ext_levels' Σ Σ' φ (H : extends Σ Σ') l - : LevelSet.mem l (global_ext_levels (Σ, φ)) - -> LevelSet.mem l (global_ext_levels (Σ', φ)). -Proof. - intro HH. apply LevelSet.mem_spec in HH. - now eapply LevelSet.mem_spec, weakening_env_global_ext_levels. -Qed. - -Lemma lookup_env_Some_fresh Σ c decl : - lookup_env Σ c = Some decl -> ~ (fresh_global c Σ). -Proof. - induction Σ; cbn. congruence. - unfold eq_kername. destruct (kername_eq_dec c a.1). - - subst c. intros [= <-]. intros H2. inv H2. contradiction. - - intros H1 H2. apply IHΣ; tas. - now inv H2. -Qed. - -Lemma extends_lookup `{checker_flags} Σ Σ' c decl : - wf Σ' -> extends Σ Σ' -> lookup_env Σ c = Some decl -> lookup_env Σ' c = Some decl. -Proof. - intros wfΣ' [Σ'' ->]. simpl. - induction Σ'' in wfΣ', c, decl |- *. simpl. auto. - specialize (IHΣ'' c decl). forward IHΣ''. - inv wfΣ'. simpl in X0. apply X. - intros HΣ. specialize (IHΣ'' HΣ). - inv wfΣ'. simpl in *. - unfold eq_kername; destruct kername_eq_dec; subst. - eapply lookup_env_Some_fresh in IHΣ''; eauto. contradiction. - assumption. -Qed. -Hint Resolve extends_lookup : extends. - -Lemma extends_wf_local `{checker_flags} Σ Γ (wfΓ : wf_local Σ Γ) : - All_local_env_over typing - (fun Σ0 Γ0 wfΓ (t T : term) ty => - forall Σ' : global_env, - wf Σ' -> - extends Σ0 Σ' -> - (Σ', Σ0.2);;; Γ0 |- t : T - ) Σ Γ wfΓ -> - forall Σ' : global_env, wf Σ' -> extends Σ Σ' -> wf_local (Σ', Σ.2) Γ. -Proof. - intros X0 Σ' H0. - induction X0 in H0 |- *; try econstructor; simpl in *; intuition auto. - - destruct tu as [u Hu]; exists u; auto. - - destruct tu as [u Hu]; exists u; auto. -Qed. -Hint Resolve extends_wf_local : extends. - -Lemma weakening_env_red1 `{CF:checker_flags} Σ Σ' Γ M N : - wf Σ' -> - extends Σ Σ' -> - red1 Σ Γ M N -> - red1 Σ' Γ M N. -Proof. - induction 3 using red1_ind_all; - try solve [econstructor; eauto; - eapply (OnOne2_impl X1); simpl; intuition eauto]. - - eapply extends_lookup in X0; eauto. - econstructor; eauto. -Qed. - -Lemma global_ext_constraints_app Σ Σ' φ - : ConstraintSet.Subset (global_ext_constraints (Σ, φ)) - (global_ext_constraints (Σ' ++ Σ, φ)). -Proof. - unfold global_ext_constraints; simpl. - intros ctr Hc. apply ConstraintSet.union_spec in Hc. - apply ConstraintSet.union_spec. - destruct Hc as [Hc|Hc]; [now left|right]. clear φ. - induction Σ' in ctr, Hc |- *. - - now rewrite app_nil_l. - - simpl. apply ConstraintSet.union_spec. right; eauto. -Qed. - -Lemma satisfies_subset φ φ' val : - ConstraintSet.Subset φ φ' -> - satisfies val φ' -> - satisfies val φ. -Proof. - intros sub sat ? isin. - apply sat, sub; auto. -Qed. - -Lemma leq_universe_subset {cf:checker_flags} ctrs ctrs' t u - : ConstraintSet.Subset ctrs ctrs' - -> leq_universe ctrs t u -> leq_universe ctrs' t u. -Proof. - intros Hctrs H. unfold leq_universe in *. - destruct check_univs; [|trivial]. - intros v Hv. apply H. - eapply satisfies_subset; eauto. -Qed. - -Lemma eq_universe_subset {cf:checker_flags} ctrs ctrs' t u - : ConstraintSet.Subset ctrs ctrs' - -> eq_universe ctrs t u -> eq_universe ctrs' t u. -Proof. - intros Hctrs H. unfold eq_universe in *. - destruct check_univs; [|trivial]. - intros v Hv. apply H. - eapply satisfies_subset; eauto. -Qed. - -Lemma eq_term_subset {cf:checker_flags} Σ φ φ' t t' - : ConstraintSet.Subset φ φ' - -> eq_term Σ φ t t' -> eq_term Σ φ' t t'. -Proof. - intro H. apply eq_term_upto_univ_morphism. - all: intros u u'; eapply eq_universe_subset; assumption. -Qed. - -Lemma leq_term_subset {cf:checker_flags} Σ ctrs ctrs' t u - : ConstraintSet.Subset ctrs ctrs' -> leq_term Σ ctrs t u -> leq_term Σ ctrs' t u. -Proof. - intro H. apply eq_term_upto_univ_morphism. - intros t' u'; eapply eq_universe_subset; assumption. - intros t' u'; eapply leq_universe_subset; assumption. -Qed. - -Lemma global_variance_sigma_mon {cf:checker_flags} {Σ Σ' gr napp v} : - wf Σ' -> extends Σ Σ' -> - global_variance Σ gr napp = Some v -> - global_variance Σ' gr napp = Some v. -Proof. - intros wf ext. - rewrite /global_variance /lookup_constructor /lookup_inductive /lookup_minductive. - destruct gr as [|ind|[ind i]|] => /= //. - - destruct (lookup_env Σ ind) eqn:look => //. - eapply extends_lookup in look; eauto. rewrite look //. - - destruct (lookup_env Σ (inductive_mind i)) eqn:look => //. - eapply extends_lookup in look; eauto. rewrite look //. -Qed. - - -(** The definition of [R_global_instance] is defined so that it is weakenable. *) -Lemma R_global_instance_weaken_env {cf:checker_flags} Σ Σ' Re Re' Rle Rle' gr napp : - wf Σ' -> extends Σ Σ' -> - RelationClasses.subrelation Re Re' -> - RelationClasses.subrelation Rle Rle' -> - RelationClasses.subrelation Re Rle' -> - subrelation (R_global_instance Σ Re Rle gr napp) (R_global_instance Σ' Re' Rle' gr napp). -Proof. - intros wfΣ ext he hle hele t t'. - rewrite /R_global_instance /R_opt_variance. - destruct global_variance as [v|] eqn:look. - - rewrite (global_variance_sigma_mon wfΣ ext look). - induction t in v, t' |- *; destruct v, t'; simpl; auto. - intros []; split; auto. - destruct t0; simpl; auto. - - destruct (global_variance Σ' gr napp) => //. - * induction t in l, t' |- *; destruct l, t'; simpl; intros H; inv H; auto. - split; auto. destruct t0; simpl; auto. - * eauto using R_universe_instance_impl'. -Qed. - -Instance eq_term_upto_univ_weaken_env {cf:checker_flags} Σ Σ' Re Re' Rle Rle' napp : - wf Σ' -> extends Σ Σ' -> - RelationClasses.subrelation Re Re' -> - RelationClasses.subrelation Rle Rle' -> - RelationClasses.subrelation Re Rle' -> - CRelationClasses.subrelation (eq_term_upto_univ_napp Σ Re Rle napp) - (eq_term_upto_univ_napp Σ' Re' Rle' napp). -Proof. - intros wfΣ ext he hele hle t t'. - induction t in napp, t', Rle, Rle', hle, hele |- * using Induction.term_forall_list_rect; - try (inversion 1; subst; constructor; - eauto using R_universe_instance_impl'; fail). - - inversion 1; subst; constructor. - eapply All2_impl'; tea. - eapply All_impl; eauto. - - inversion 1; subst; constructor. - eapply IHt. 3:eauto. all:auto. - eapply All2_impl'; tea. - eapply All_impl; eauto. - - inversion 1; subst; constructor. - eapply R_global_instance_weaken_env. 6:eauto. all:eauto. - - inversion 1; subst; constructor. - eapply R_global_instance_weaken_env. 6:eauto. all:eauto. - - inversion 1; subst; constructor; eauto. - eapply All2_impl'; tea. - eapply All_impl; eauto. - cbn. intros x ? y [? ?]. split; eauto. - - inversion 1; subst; constructor. - eapply All2_impl'; tea. - eapply All_impl; eauto. - cbn. intros x [? ?] y [[[? ?] ?] ?]. repeat split; eauto. - - inversion 1; subst; constructor. - eapply All2_impl'; tea. - eapply All_impl; eauto. - cbn. intros x [? ?] y [[[? ?] ?] ?]. repeat split; eauto. -Qed. - - -Lemma weakening_env_conv `{CF:checker_flags} Σ Σ' φ Γ M N : - wf Σ' -> - extends Σ Σ' -> - conv (Σ, φ) Γ M N -> - conv (Σ', φ) Γ M N. -Proof. - intros wfΣ [Σ'' ->]. - induction 1; simpl. - - econstructor. eapply eq_term_subset. - + eapply global_ext_constraints_app. - + eapply eq_term_upto_univ_weaken_env; eauto. exists Σ''; eauto. - all:typeclasses eauto. - - econstructor 2; eauto. eapply weakening_env_red1; eauto. exists Σ''; eauto. - - econstructor 3; eauto. eapply weakening_env_red1; eauto. exists Σ''; eauto. -Qed. - -Lemma weakening_env_cumul `{CF:checker_flags} Σ Σ' φ Γ M N : - wf Σ' -> extends Σ Σ' -> - cumul (Σ, φ) Γ M N -> cumul (Σ', φ) Γ M N. -Proof. - intros wfΣ [Σ'' ->]. - induction 1; simpl. - - econstructor. eapply leq_term_subset. - + eapply global_ext_constraints_app. - + eapply eq_term_upto_univ_weaken_env; eauto. exists Σ''; eauto. - all:typeclasses eauto. - - econstructor 2; eauto. eapply weakening_env_red1; eauto. exists Σ''; eauto. - - econstructor 3; eauto. eapply weakening_env_red1; eauto. exists Σ''; eauto. -Qed. - -Lemma weakening_env_is_allowed_elimination `{CF:checker_flags} Σ Σ' φ u allowed : - wf Σ' -> extends Σ Σ' -> - is_allowed_elimination (global_ext_constraints (Σ, φ)) u allowed -> - is_allowed_elimination (global_ext_constraints (Σ', φ)) u allowed. -Proof. - intros wfΣ [Σ'' ->] al. - unfold is_allowed_elimination in *. - destruct check_univs; auto. - intros val sat. - unshelve epose proof (al val _) as al. - { eapply satisfies_subset; eauto. - apply global_ext_constraints_app. } - destruct allowed; auto; cbn in *; destruct ?; auto. -Qed. -Hint Resolve weakening_env_is_allowed_elimination : extends. - -Lemma weakening_env_declared_constant `{CF:checker_flags}: - forall (Σ : global_env) cst (decl : constant_body), - declared_constant Σ cst decl -> - forall Σ' : global_env, wf Σ' -> extends Σ Σ' -> declared_constant Σ' cst decl. -Proof. - intros Σ cst decl H0 Σ' X2 H2. - eapply extends_lookup; eauto. -Qed. -Hint Resolve weakening_env_declared_constant : extends. - -Lemma weakening_env_declared_minductive `{CF:checker_flags}: - forall (Σ : global_env) ind decl, - declared_minductive Σ ind decl -> - forall Σ' : global_env, wf Σ' -> extends Σ Σ' -> declared_minductive Σ' ind decl. -Proof. - intros Σ cst decl H0 Σ' X2 H2. - eapply extends_lookup; eauto. -Qed. -Hint Resolve weakening_env_declared_minductive : extends. - -Lemma weakening_env_declared_inductive: - forall (H : checker_flags) (Σ : global_env) ind mdecl decl, - declared_inductive Σ ind mdecl decl -> - forall Σ' : global_env, wf Σ' -> extends Σ Σ' -> declared_inductive Σ' ind mdecl decl. -Proof. - intros H Σ cst decl H0 [Hmdecl Hidecl] Σ' X2 H2. split; eauto with extends. -Qed. -Hint Resolve weakening_env_declared_inductive : extends. - -Lemma weakening_env_declared_constructor : - forall (H : checker_flags) (Σ : global_env) ind mdecl idecl decl, - declared_constructor Σ ind mdecl idecl decl -> - forall Σ' : global_env, wf Σ' -> extends Σ Σ' -> - declared_constructor Σ' ind mdecl idecl decl. -Proof. - intros H Σ cst mdecl idecl cdecl [Hidecl Hcdecl] Σ' X2 H2. - split; eauto with extends. -Qed. -Hint Resolve weakening_env_declared_constructor : extends. - -Lemma weakening_env_declared_projection : - forall (H : checker_flags) (Σ : global_env) ind mdecl idecl decl, - declared_projection Σ ind mdecl idecl decl -> - forall Σ' : global_env, wf Σ' -> extends Σ Σ' -> - declared_projection Σ' ind mdecl idecl decl. -Proof. - intros H Σ cst mdecl idecl cdecl [Hidecl Hcdecl] Σ' X2 H2. - split; eauto with extends. -Qed. -Hint Resolve weakening_env_declared_projection : extends. - -Lemma weakening_All_local_env_impl `{checker_flags} - (P Q : context -> term -> option term -> Type) l : - All_local_env P l -> - (forall Γ t T, P Γ t T -> Q Γ t T) -> - All_local_env Q l. -Proof. - induction 1; intros; simpl; econstructor; eauto. -Qed. - -Lemma weakening_env_global_ext_constraints Σ Σ' φ (H : extends Σ Σ') - : ConstraintSet.Subset (global_ext_constraints (Σ, φ)) - (global_ext_constraints (Σ', φ)). -Proof. - destruct H as [Σ'' eq]. subst. - apply global_ext_constraints_app. -Qed. - -Lemma eq_decl_subset {cf:checker_flags} Σ φ φ' d d' - : ConstraintSet.Subset φ φ' - -> eq_decl Σ φ d d' -> eq_decl Σ φ' d d'. -Proof. - intros Hφ [H1 H2]. split; [|eapply eq_term_subset; eauto]. - destruct d as [na [bd|] ty], d' as [na' [bd'|] ty']; cbn in *; trivial. - eapply eq_term_subset; eauto. -Qed. - -Lemma eq_context_subset {cf:checker_flags} Σ φ φ' Γ Γ' - : ConstraintSet.Subset φ φ' - -> eq_context Σ φ Γ Γ' -> eq_context Σ φ' Γ Γ'. -Proof. - intros Hφ. induction 1; constructor. - eapply eq_decl_subset; eassumption. assumption. -Qed. - -Lemma weakening_env_consistent_instance {cf:checker_flags} : - forall Σ Σ' φ ctrs u, - extends Σ Σ' -> - consistent_instance_ext (Σ, φ) ctrs u -> - consistent_instance_ext (Σ', φ) ctrs u. -Proof. - intros Σ Σ' φ ctrs u he. - unfold consistent_instance_ext, consistent_instance. - intros hc. - destruct ctrs=> //. - destruct cst as [nas cst]; simpl in *. - intuition auto. - eapply forallb_Forall in H. eapply forallb_Forall, Forall_impl; tea. - intros ? ? ; now eapply weakening_env_global_ext_levels'. - eapply valid_subset; tea; - now eapply weakening_env_global_ext_constraints. -Qed. -Hint Resolve weakening_env_consistent_instance : extends. - -Lemma extends_check_recursivity_kind {cf:checker_flags} Σ ind k Σ' : extends Σ Σ' -> wf Σ' -> - check_recursivity_kind Σ ind k -> check_recursivity_kind Σ' ind k. -Proof. - intros ext wfΣ'. - rewrite /check_recursivity_kind. - destruct lookup_env eqn:Heq => //. - eapply extends_lookup in Heq; eauto. - now rewrite Heq. -Qed. - -Lemma extends_wf_fixpoint {cf:checker_flags} Σ mfix Σ' : extends Σ Σ' -> wf Σ' -> - wf_fixpoint Σ mfix -> wf_fixpoint Σ' mfix. -Proof. - intros ext wfΣ'. - unfold wf_fixpoint. - destruct map_option_out as [[|ind inds]|]; auto. - move/andb_and => [->] /=. - now apply extends_check_recursivity_kind. -Qed. - -Lemma extends_wf_cofixpoint {cf:checker_flags} Σ mfix Σ' : extends Σ Σ' -> wf Σ' -> - wf_cofixpoint Σ mfix -> wf_cofixpoint Σ' mfix. -Proof. - intros ext wfΣ'. - unfold wf_cofixpoint. - destruct map_option_out as [[|ind inds]|]; auto. - move/andb_and => [->] /=. - now apply extends_check_recursivity_kind. -Qed. - -Hint Resolve extends_wf_fixpoint extends_wf_cofixpoint : extends. - -Lemma global_levels_Set Σ : - LevelSet.In Level.lSet (global_levels Σ). -Proof. - unfold global_levels. - induction Σ; simpl; auto. - - now apply LevelSet.singleton_spec. - - apply LevelSet.union_spec. right; auto. -Qed. - -Lemma global_levels_set Σ : - LevelSet.Equal (LevelSet.union (LevelSet.singleton Level.lSet) (global_levels Σ)) - (global_levels Σ). -Proof. - apply LevelSetProp.union_subset_equal. - intros x hin. eapply LevelSet.singleton_spec in hin; subst x. - apply global_levels_Set. -Qed. - -Lemma global_levels_ext {Σ Σ'} : - LevelSet.Equal (global_levels (Σ ++ Σ')) (LevelSet.union (global_levels Σ) (global_levels Σ')). -Proof. - unfold global_levels at 1. - induction Σ; simpl. - - rewrite global_levels_set. reflexivity. - - rewrite IHΣ. lsets. -Qed. - -Lemma extends_wf_universe {cf:checker_flags} {Σ : global_env_ext} Σ' u : extends Σ Σ' -> wf Σ' -> - wf_universe Σ u -> wf_universe (Σ', Σ.2) u. -Proof. - destruct Σ as [Σ univ]; cbn. - intros [Σ'' eq] wf. - destruct u; simpl; auto. - intros Hl. - intros l inl; specialize (Hl l inl). - cbn. rewrite eq /=. - unfold global_ext_levels. - eapply LevelSet.union_spec; simpl. - apply LevelSet.union_spec in Hl as [Hl|Hl]; cbn in Hl. - - simpl. simpl in Hl. now left. - - right. rewrite global_levels_ext. - eapply LevelSet.union_spec. right. - apply Hl. -Qed. - - -Ltac typing_my_rename_hyp h th := - match th with - | (wf ?E) => fresh "wf" E - | (typing _ _ ?t _) => fresh "type" t - | (@cumul _ _ _ ?t _) => fresh "cumul" t - | (conv _ _ ?t _) => fresh "conv" t - | (All_local_env (lift_typing (@typing _) _) ?G) => fresh "wf" G - | (All_local_env (lift_typing (@typing _) _) _) => fresh "wf" - | (All_local_env _ _ ?G) => fresh "H" G - | context [typing _ _ (_ ?t) _] => fresh "IH" t - end. - -Ltac my_rename_hyp h th := - match th with - | (extends ?t _) => fresh "ext" t - | (extends ?t.1 _) => fresh "ext" t - | (extends _ _) => fresh "ext" - | _ => typing_my_rename_hyp h th - end. - -Ltac rename_hyp h ht ::= my_rename_hyp h ht. - -Lemma weakening_env `{checker_flags} : - env_prop (fun Σ Γ t T => - forall Σ', wf Σ' -> extends Σ.1 Σ' -> (Σ', Σ.2) ;;; Γ |- t : T). -Proof. - apply typing_ind_env; intros; - rename_all_hyps; try solve [econstructor; eauto 2 with extends]. - - - econstructor; eauto 2 with extends. - intuition auto. eapply extends_wf_universe; eauto. - - econstructor; eauto 2 with extends. - destruct Σ as [Σ φ]. - clear typet heq_isApp forall_Σ' hneq_l. - induction X1. constructor. econstructor; eauto with extends. - eapply weakening_env_cumul in cumul; eauto. - - econstructor; eauto 2 with extends. - close_Forall. intros; intuition eauto with extends. - destruct b as [s [Hs IHs]]. exists s. eauto. - - econstructor; eauto with extends. - eapply fix_guard_extends; eauto. - eapply (All_impl X0); intuition eauto. - destruct X2 as [s Hs]; exists s; intuition eauto. - eapply All_impl; eauto; simpl; intuition eauto with extends. - - - econstructor; eauto with extends. auto. - eapply cofix_guard_extends; eauto. - eapply (All_impl X0); intuition eauto. - destruct X2 as [s Hs]; exists s; intuition eauto. - eapply All_impl; eauto; simpl; intuition eauto with extends. - - econstructor; eauto with extends. - destruct Σ as [Σ φ]. eapply weakening_env_cumul in cumulA; eauto. -Qed. - -Definition weaken_env_prop `{checker_flags} - (P : global_env_ext -> context -> term -> option term -> Type) := - forall Σ Σ' φ, wf Σ' -> extends Σ Σ' -> forall Γ t T, P (Σ, φ) Γ t T -> P (Σ', φ) Γ t T. - -Lemma weakening_on_global_decl `{checker_flags} P Σ Σ' φ kn decl : - weaken_env_prop P -> - wf Σ' -> extends Σ Σ' -> - on_global_decl P (Σ, φ) kn decl -> - on_global_decl P (Σ', φ) kn decl. -Proof. - unfold weaken_env_prop. - intros HPΣ wfΣ' Hext Hdecl. - destruct decl. destruct c. destruct cst_body. simpl in *. - red in Hdecl |- *. simpl in *. - eapply HPΣ; eauto. - eapply HPΣ; eauto. - simpl in *. - destruct Hdecl as [onI onP onnP]; constructor; eauto. - - eapply Alli_impl; eauto. intros. - destruct X. unshelve econstructor; eauto. - -- unfold on_type in *; intuition eauto. - -- unfold on_constructors in *. eapply All2_impl; eauto. - intros decl cs []. unshelve econstructor; eauto. - red in on_ctype |- *. eauto. - clear on_cindices cstr_eq cstr_args_length cstr_concl_head. - revert on_cargs. - generalize (cshape_sorts cs). - induction (cshape_args cs); destruct l; simpl in *; auto. - ** destruct a as [na [b|] ty]; simpl in *; intuition eauto. - ** destruct a as [na [b|] ty]; simpl in *; intuition eauto. - ** clear on_ctype on_cargs. - revert on_cindices. - generalize (List.rev (LiftSubst.lift_context #|cshape_args cs| 0 ind_indices)). - generalize (cshape_indices cs). induction 1; constructor; eauto. - ** simpl. - intros v indv. specialize (on_ctype_variance v indv). - simpl in *. move: on_ctype_variance. - unfold cstr_respects_variance. destruct variance_universes as [[[univs u] u']|]; auto. - intros [args idxs]. split. - eapply (context_relation_impl args); intros. - inversion X; constructor; auto. - eapply weakening_env_cumul; eauto. - eapply weakening_env_conv; eauto. - eapply weakening_env_cumul; eauto. - eapply (All2_impl idxs); intros. - eapply weakening_env_conv; eauto. - -- unfold check_ind_sorts in *. - destruct Universe.is_prop; auto. - destruct Universe.is_sprop; auto. - split; [apply fst in ind_sorts|apply snd in ind_sorts]. - eapply Forall_impl; tea; cbn. - intros. eapply Forall_impl; eauto; simpl. - intros; eapply leq_universe_subset; tea. - apply weakening_env_global_ext_constraints; tea. - destruct indices_matter; [|trivial]. clear -ind_sorts HPΣ wfΣ' Hext. - induction ind_indices; simpl in *; auto. - ** eapply (extends_wf_universe (Σ:=(Σ,φ)) Σ'); auto. - ** destruct a as [na [b|] ty]; simpl in *; intuition eauto. - -- intros v onv. - move: (onIndices v onv). unfold ind_respects_variance. - destruct variance_universes as [[[univs u] u']|] => //. - intros idx; eapply (context_relation_impl idx); simpl. - intros par par' t t'. - intros d. inv d; constructor; auto. - eapply weakening_env_cumul; eauto. - eapply weakening_env_conv; eauto. - eapply weakening_env_cumul; eauto. - - red in onP |- *. eapply All_local_env_impl; eauto. -Qed. - -Lemma weakening_env_lookup_on_global_env `{checker_flags} P Σ Σ' c decl : - weaken_env_prop P -> - wf Σ' -> extends Σ Σ' -> on_global_env P Σ -> - lookup_env Σ c = Some decl -> - on_global_decl P (Σ', universes_decl_of_decl decl) c decl. -Proof. - intros HP wfΣ Hext HΣ. - induction HΣ; simpl. congruence. - assert (HH: extends Σ Σ'). { - destruct Hext as [Σ'' HΣ'']. - exists (Σ'' ++ [(kn, d)]). now rewrite <- app_assoc. } - unfold eq_kername; destruct kername_eq_dec; subst. - - intros [= ->]. - clear Hext; eapply weakening_on_global_decl; eauto. - - now apply IHHΣ. -Qed. - -Lemma weaken_lookup_on_global_env `{checker_flags} P Σ c decl : - weaken_env_prop P -> - wf Σ -> on_global_env P Σ -> - lookup_env Σ c = Some decl -> - on_global_decl P (Σ, universes_decl_of_decl decl) c decl. -Proof. - intros. eapply weakening_env_lookup_on_global_env; eauto. - exists []; simpl; destruct Σ; eauto. -Qed. - -Lemma declared_minductive_inv `{checker_flags} {Σ P ind mdecl} : - weaken_env_prop (lift_typing P) -> - wf Σ -> Forall_decls_typing P Σ -> - declared_minductive Σ ind mdecl -> - on_inductive (lift_typing P) (Σ, ind_universes mdecl) ind mdecl. -Proof. - intros. - eapply weaken_lookup_on_global_env in X1; eauto. apply X1. -Qed. - -Lemma declared_inductive_inv `{checker_flags} {Σ P ind mdecl idecl} : - weaken_env_prop (lift_typing P) -> - wf Σ -> Forall_decls_typing P Σ -> - declared_inductive Σ mdecl ind idecl -> - on_ind_body (lift_typing P) (Σ, ind_universes mdecl) (inductive_mind ind) mdecl (inductive_ind ind) idecl. -Proof. - intros. - destruct H0 as [Hmdecl Hidecl]. - eapply declared_minductive_inv in Hmdecl; eauto. - apply onInductives in Hmdecl. - eapply nth_error_alli in Hidecl; eauto. - apply Hidecl. -Qed. - -Lemma declared_constructor_inv `{checker_flags} {Σ P mdecl idecl ref cdecl} - (HP : weaken_env_prop (lift_typing P)) - (wfΣ : wf Σ) - (HΣ : Forall_decls_typing P Σ) - (Hdecl : declared_constructor Σ mdecl idecl ref cdecl) : - ∑ cs, - let onib := declared_inductive_inv HP wfΣ HΣ (proj1 Hdecl) in - nth_error onib.(ind_cshapes) ref.2 = Some cs - × on_constructor (lift_typing P) (Σ, ind_universes mdecl) mdecl - (inductive_ind ref.1) idecl onib.(ind_indices) cdecl cs. -Proof. - intros. - destruct Hdecl as [Hidecl Hcdecl]. - set (declared_inductive_inv HP wfΣ HΣ (proj1 (conj Hidecl Hcdecl))) as HH. - clearbody HH. pose proof HH.(onConstructors) as HH'. - eapply All2_nth_error_Some in Hcdecl; tea. -Qed. - -Lemma declared_projection_inv `{checker_flags} {Σ P mdecl idecl ref pdecl} : - forall (HP : weaken_env_prop (lift_typing P)) - (wfΣ : wf Σ) - (HΣ : Forall_decls_typing P Σ) - (Hdecl : declared_projection Σ mdecl idecl ref pdecl), - let oib := declared_inductive_inv HP wfΣ HΣ (proj1 Hdecl) in - match oib.(ind_cshapes) return Type with - | [cs] => on_projection mdecl (inductive_mind ref.1.1) (inductive_ind ref.1.1) cs (snd ref) pdecl - | _ => False - end. -Proof. - intros. - destruct (declared_inductive_inv HP wfΣ HΣ (proj1 Hdecl)) in *. - destruct Hdecl as [Hidecl [Hcdecl Hnpar]]. simpl. clearbody oib. - forward onProjections. - { eapply nth_error_Some_length in Hcdecl. - destruct (ind_projs idecl); simpl in *. lia. congruence. } - destruct ind_cshapes as [|? []]; try contradiction. - destruct onProjections. - eapply nth_error_alli in Hcdecl; eauto. eapply Hcdecl. -Qed. - -Lemma wf_extends `{checker_flags} {Σ Σ'} : wf Σ' -> extends Σ Σ' -> wf Σ. -Proof. - intros HΣ' [Σ'' ->]. simpl in *. - induction Σ''. auto. - inv HΣ'. auto. -Qed. - -Lemma weaken_env_prop_typing `{checker_flags} : weaken_env_prop (lift_typing typing). -Proof. - red. intros * wfΣ' Hext *. - destruct T; simpl. - intros Ht. pose proof (wf_extends wfΣ' Hext). - eapply (weakening_env (_, _)); eauto. eapply typing_wf_local in Ht; eauto. - intros [s Ht]. pose proof (wf_extends wfΣ' Hext). exists s. - eapply (weakening_env (_, _)); eauto. eapply typing_wf_local in Ht; eauto. -Qed. - -Hint Unfold weaken_env_prop : pcuic. - -Lemma on_declared_minductive `{checker_flags} {Σ ref decl} : - wf Σ -> - declared_minductive Σ ref decl -> - on_inductive (lift_typing typing) (Σ, ind_universes decl) ref decl. -Proof. - intros wfΣ Hdecl. - apply (declared_minductive_inv weaken_env_prop_typing wfΣ wfΣ Hdecl). -Qed. - -Lemma on_declared_inductive `{checker_flags} {Σ ref mdecl idecl} : - wf Σ -> - declared_inductive Σ mdecl ref idecl -> - on_inductive (lift_typing typing) (Σ, ind_universes mdecl) (inductive_mind ref) mdecl * - on_ind_body (lift_typing typing) (Σ, ind_universes mdecl) (inductive_mind ref) mdecl (inductive_ind ref) idecl. -Proof. - intros wfΣ Hdecl. - split. destruct Hdecl as [Hmdecl _]. now apply on_declared_minductive in Hmdecl. - apply (declared_inductive_inv weaken_env_prop_typing wfΣ wfΣ Hdecl). -Qed. - -Lemma on_declared_constructor `{checker_flags} {Σ ref mdecl idecl cdecl} - (wfΣ : wf Σ) - (Hdecl : declared_constructor Σ mdecl idecl ref cdecl) : - on_inductive (lift_typing typing) (Σ, ind_universes mdecl) - (inductive_mind (fst ref)) mdecl * - on_ind_body (lift_typing typing) (Σ, ind_universes mdecl) - (inductive_mind (fst ref)) mdecl (inductive_ind (fst ref)) idecl * - ∑ ind_ctor_sort, - let onib := declared_inductive_inv weaken_env_prop_typing wfΣ wfΣ (proj1 Hdecl) in - nth_error (ind_cshapes onib) ref.2 = Some ind_ctor_sort - × on_constructor (lift_typing typing) (Σ, ind_universes mdecl) - mdecl (inductive_ind (fst ref)) - idecl onib.(ind_indices) cdecl ind_ctor_sort. -Proof. - split. destruct Hdecl as [Hidecl Hcdecl]. - now apply on_declared_inductive in Hidecl. - apply (declared_constructor_inv weaken_env_prop_typing wfΣ wfΣ Hdecl). -Qed. - -Lemma on_declared_projection `{checker_flags} {Σ ref mdecl idecl pdecl} : - forall (wfΣ : wf Σ) (Hdecl : declared_projection Σ mdecl idecl ref pdecl), - on_inductive (lift_typing typing) (Σ, ind_universes mdecl) (inductive_mind (fst (fst ref))) mdecl * - let oib := declared_inductive_inv weaken_env_prop_typing wfΣ wfΣ (proj1 Hdecl) in - match oib.(ind_cshapes) return Type with - | [cs] => on_projection mdecl (inductive_mind ref.1.1) (inductive_ind ref.1.1) cs (snd ref) pdecl - | _ => False - end. -Proof. - intros wfΣ Hdecl. - split. destruct Hdecl as [Hidecl Hcdecl]. now apply on_declared_inductive in Hidecl. - apply (declared_projection_inv weaken_env_prop_typing wfΣ wfΣ Hdecl). -Qed. diff --git a/checker/update_plugin.sh b/checker/update_plugin.sh deleted file mode 100755 index 305d6dcb4..000000000 --- a/checker/update_plugin.sh +++ /dev/null @@ -1,12 +0,0 @@ -#!/bin/bash -TEMPLATE_LIB=../template-coq - -if [[ "src" -ot "${TEMPLATE_LIB}/gen-src" || ! -f "src/metacoq_checker_plugin.cmxa" \ - || "src/metacoq_checker_plugin.cmxa" -ot "gen-src/Extract.v" ]] -then - echo "Renaming extracted files" - cp -r ${TEMPLATE_LIB}/gen-src/to-lower.sh src - (cd src; ./to-lower.sh) -else - echo "Extracted code is up-to-date" -fi \ No newline at end of file diff --git a/pcuic/_CoqProject.in b/pcuic/_CoqProject.in index 38dd47169..a78d52b8f 100644 --- a/pcuic/_CoqProject.in +++ b/pcuic/_CoqProject.in @@ -1,7 +1,6 @@ -R theories MetaCoq.PCUIC theories/PCUICUtils.v -theories/PCUICRelations.v theories/PCUICPrimitive.v theories/PCUICAst.v theories/PCUICSize.v diff --git a/pcuic/theories/PCUICConfluence.v b/pcuic/theories/PCUICConfluence.v index 2c70b6d6d..01a2e7fee 100644 --- a/pcuic/theories/PCUICConfluence.v +++ b/pcuic/theories/PCUICConfluence.v @@ -1,6 +1,6 @@ (* Distributed under the terms of the MIT license. *) From MetaCoq.Template Require Import config utils. -From MetaCoq.PCUIC Require Import PCUICRelations PCUICAst PCUICLiftSubst PCUICTyping +From MetaCoq.PCUIC Require Import PCUICAst PCUICLiftSubst PCUICTyping PCUICReduction PCUICWeakening PCUICEquality PCUICUnivSubstitution PCUICParallelReduction PCUICParallelReductionConfluence. diff --git a/pcuic/theories/PCUICCumulativity.v b/pcuic/theories/PCUICCumulativity.v index 9d453ce23..df651c893 100644 --- a/pcuic/theories/PCUICCumulativity.v +++ b/pcuic/theories/PCUICCumulativity.v @@ -1,6 +1,6 @@ (* Distributed under the terms of the MIT license. *) From MetaCoq.Template Require Import config utils BasicAst. -From MetaCoq.PCUIC Require Import PCUICRelations PCUICAst PCUICAstUtils +From MetaCoq.PCUIC Require Import PCUICAst PCUICAstUtils PCUICLiftSubst PCUICEquality PCUICUnivSubst PCUICReduction. Set Default Goal Selector "!". diff --git a/pcuic/theories/PCUICReduction.v b/pcuic/theories/PCUICReduction.v index 7fa6b58f5..28f0353cb 100644 --- a/pcuic/theories/PCUICReduction.v +++ b/pcuic/theories/PCUICReduction.v @@ -1,13 +1,12 @@ (* Distributed under the terms of the MIT license. *) From MetaCoq.Template Require Import config utils. -From MetaCoq.PCUIC Require Import PCUICRelations PCUICAst PCUICAstUtils +From MetaCoq.PCUIC Require Import PCUICAst PCUICAstUtils PCUICLiftSubst PCUICEquality PCUICUnivSubst PCUICInduction. Require Import ssreflect. Require Import Equations.Prop.DepElim. From Equations Require Import Equations. - Set Default Goal Selector "!". Definition tDummy := tVar String.EmptyString. diff --git a/pcuic/theories/PCUICRelations.v b/pcuic/theories/PCUICRelations.v deleted file mode 100644 index 029b0d8af..000000000 --- a/pcuic/theories/PCUICRelations.v +++ /dev/null @@ -1,165 +0,0 @@ -(* Distributed under the terms of the MIT license. *) -Require Import ssreflect. -Require Export CRelationClasses. -Require Export Equations.Type.Relation Equations.Type.Relation_Properties. - - -Section Flip. - Local Set Universe Polymorphism. - Context {A : Type} (R : crelation A). - - Lemma flip_Reflexive : Reflexive R -> Reflexive (flip R). - Proof. - intros HR x. unfold flip. apply reflexivity. - Qed. - - Lemma flip_Symmetric : Symmetric R -> Symmetric (flip R). - Proof. - intros HR x y. unfold flip. apply symmetry. - Qed. - - Lemma flip_Transitive : Transitive R -> Transitive (flip R). - Proof. - intros HR x y z xy yz. - unfold flip in *. eapply HR; eassumption. - Qed. - -End Flip. - - - - -Definition commutes {A} (R S : relation A) := - forall x y z, R x y -> S x z -> { w & S y w * R z w}%type. - - -Lemma clos_t_rt {A} {R : A -> A -> Type} x y : trans_clos R x y -> clos_refl_trans R x y. -Proof. - induction 1; try solve [econstructor; eauto]. -Qed. - - -Arguments rt_step {A} {R} {x y}. -Polymorphic Hint Resolve rt_refl rt_step : core. - - -Definition clos_rt_monotone {A} (R S : relation A) : - inclusion R S -> inclusion (clos_refl_trans R) (clos_refl_trans S). -Proof. - move => incls x y. - induction 1; solve [econstructor; eauto]. -Qed. - -Lemma relation_equivalence_inclusion {A} (R S : relation A) : - inclusion R S -> inclusion S R -> relation_equivalence R S. -Proof. firstorder. Qed. - -Lemma clos_rt_disjunction_left {A} (R S : relation A) : - inclusion (clos_refl_trans R) - (clos_refl_trans (relation_disjunction R S)). -Proof. - apply clos_rt_monotone. - intros x y H; left; exact H. -Qed. - -Lemma clos_rt_disjunction_right {A} (R S : relation A) : - inclusion (clos_refl_trans S) - (clos_refl_trans (relation_disjunction R S)). -Proof. - apply clos_rt_monotone. - intros x y H; right; exact H. -Qed. - -Global Instance clos_rt_trans A R : Transitive (@clos_refl_trans A R). -Proof. - intros x y z H H'. econstructor 3; eauto. -Qed. - -Global Instance clos_rt_refl A R : Reflexive (@clos_refl_trans A R). -Proof. intros x. constructor 2. Qed. - -Lemma clos_refl_trans_prod_l {A B} (R : relation A) (S : relation (A * B)) : - (forall x y b, R x y -> S (x, b) (y, b)) -> - forall (x y : A) b, - clos_refl_trans R x y -> - clos_refl_trans S (x, b) (y, b). -Proof. - intros. induction X0; try solve [econstructor; eauto]. -Qed. - -Lemma clos_refl_trans_prod_r {A B} (R : relation B) (S : relation (A * B)) a : - (forall x y, R x y -> S (a, x) (a, y)) -> - forall (x y : B), - clos_refl_trans R x y -> - clos_refl_trans S (a, x) (a, y). -Proof. - intros. induction X0; try solve [econstructor; eauto]. -Qed. - -Lemma clos_rt_t_incl {A} {R : relation A} `{Reflexive A R} : - inclusion (clos_refl_trans R) (trans_clos R). -Proof. - intros x y. induction 1; try solve [econstructor; eauto]. -Qed. - -Lemma clos_t_rt_incl {A} {R : relation A} `{Reflexive A R} : - inclusion (trans_clos R) (clos_refl_trans R). -Proof. - intros x y. induction 1; try solve [econstructor; eauto]. -Qed. - -Lemma clos_t_rt_equiv {A} {R} `{Reflexive A R} : - relation_equivalence (trans_clos R) (clos_refl_trans R). -Proof. - apply relation_equivalence_inclusion. - apply clos_t_rt_incl. - apply clos_rt_t_incl. -Qed. - -Global Instance relation_disjunction_refl_l {A} {R S : relation A} : - Reflexive R -> Reflexive (relation_disjunction R S). -Proof. - intros HR x. left; auto. -Qed. - -Global Instance relation_disjunction_refl_r {A} {R S : relation A} : - Reflexive S -> Reflexive (relation_disjunction R S). -Proof. - intros HR x. right; auto. -Qed. - -Global Instance clos_rt_trans_Symmetric A R : - Symmetric R -> Symmetric (@clos_refl_trans A R). -Proof. - intros X x y H. induction H; eauto. - eapply clos_rt_trans; eassumption. -Qed. - -Definition clos_sym {A} (R : relation A) := relation_disjunction R (flip R). - -Global Instance clos_sym_Symmetric A R : - Symmetric (@clos_sym A R). -Proof. - intros x y []; [right|left]; assumption. -Qed. - -Global Instance clos_refl_sym_trans_Symmetric A R : - Symmetric (@clos_refl_sym_trans A R) - := rst_sym R. - -Global Instance clos_refl_sym_trans_Reflexive A R : - Reflexive (@clos_refl_sym_trans A R) - := rst_refl R. - -Global Instance clos_refl_sym_trans_Transitive A R : - Transitive (@clos_refl_sym_trans A R) - := rst_trans R. - -Global Instance relation_disjunction_Symmetric {A} {R S : relation A} : - Symmetric R -> Symmetric S -> Symmetric (relation_disjunction R S). -Proof. - intros HR HS x y [X|X]; [left|right]; eauto. -Qed. - -Ltac rst_induction h := - induction h; [constructor|reflexivity|etransitivity]. diff --git a/pcuic/theories/PCUICToTemplateCorrectness.v b/pcuic/theories/PCUICToTemplateCorrectness.v index dd2ccbf40..685c869b3 100644 --- a/pcuic/theories/PCUICToTemplateCorrectness.v +++ b/pcuic/theories/PCUICToTemplateCorrectness.v @@ -1031,10 +1031,6 @@ Proof. split;eassumption. Qed. - - - - Lemma invert_type_App `{checker_flags} Σ Γ f u T : TT.typing Σ Γ (tApp f u) T -> { T' : term & { U' & ((TT.typing Σ Γ f T') * TT.typing_spine Σ Γ T' u U' * diff --git a/template-coq/_CoqProject b/template-coq/_CoqProject index edc5cf783..fa2e539e5 100644 --- a/template-coq/_CoqProject +++ b/template-coq/_CoqProject @@ -41,6 +41,8 @@ theories/TermEquality.v theories/Typing.v theories/Reduction.v theories/TypingWf.v +theories/Normal.v +theories/WcbvEval.v # The Template monad theories/TemplateMonad.v diff --git a/checker/theories/Normal.v b/template-coq/theories/Normal.v similarity index 100% rename from checker/theories/Normal.v rename to template-coq/theories/Normal.v diff --git a/template-coq/theories/Typing.v b/template-coq/theories/Typing.v index eb3a9909b..f80caa02a 100644 --- a/template-coq/theories/Typing.v +++ b/template-coq/theories/Typing.v @@ -1,5 +1,7 @@ (* Distributed under the terms of the MIT license. *) -From Coq Require Import ssreflect Wellfounded Relation_Operators. +(** This defines relation operators in Type *) +From Equations.Type Require Import Relation. +From Coq Require Import ssreflect Wellfounded Relation_Operators CRelationClasses. From MetaCoq.Template Require Import config utils Ast AstUtils LiftSubst UnivSubst EnvironmentTyping Reflect TermEquality. @@ -431,36 +433,33 @@ Reserved Notation " Σ ;;; Γ |- t : T " (at level 50, Γ, t, T at next level). Reserved Notation " Σ ;;; Γ |- t <= u " (at level 50, Γ, t, u at next level). Reserved Notation " Σ ;;; Γ |- t = u " (at level 50, Γ, t, u at next level). -(** ** Cumulativity *) +(** ** Cumulativity: -Inductive cumul `{checker_flags} (Σ : global_env_ext) (Γ : context) : term -> term -> Type := -| cumul_refl t u : leq_term Σ (global_ext_constraints Σ) t u -> Σ ;;; Γ |- t <= u -| cumul_red_l t u v : red1 Σ.1 Γ t v -> Σ ;;; Γ |- v <= u -> Σ ;;; Γ |- t <= u -| cumul_red_r t u v : Σ ;;; Γ |- t <= v -> red1 Σ.1 Γ u v -> Σ ;;; Γ |- t <= u + The reflexive-transitive closure of reduction, expansion and term comparison up-to universes. +*) -where " Σ ;;; Γ |- t <= u " := (cumul Σ Γ t u) : type_scope. +Definition cumul `{checker_flags} (Σ : global_env_ext) (Γ : context) : term -> term -> Type := + Relation.clos_refl_trans (relation_disjunction (clos_sym (red1 Σ Γ)) (leq_term Σ Σ)). +Notation " Σ ;;; Γ |- t <= u " := (cumul Σ Γ t u) : type_scope. (** *** Conversion - Defined as cumulativity in both directions. + The reflexive-symmetric-transitive closure of reduction, expansion and term comparison up-to universes. *) -Inductive conv `{checker_flags} (Σ : global_env_ext) (Γ : context) : term -> term -> Type := - | conv_refl t u : eq_term Σ (global_ext_constraints Σ) t u -> Σ ;;; Γ |- t = u - | conv_red_l t u v : red1 Σ.1 Γ t v -> Σ ;;; Γ |- v = u -> Σ ;;; Γ |- t = u - | conv_red_r t u v : Σ ;;; Γ |- t = v -> red1 Σ.1 Γ u v -> Σ ;;; Γ |- t = u - - where " Σ ;;; Γ |- t = u " := (@conv _ Σ Γ t u) : type_scope. +Definition conv `{checker_flags} (Σ : global_env_ext) (Γ : context) : term -> term -> Type := + Relation.clos_refl_sym_trans (relation_disjunction (red1 Σ Γ) (eq_term Σ Σ)). +Notation " Σ ;;; Γ |- t = u " := (@conv _ Σ Γ t u) : type_scope. Lemma conv_refl' `{checker_flags} : forall Σ Γ t, Σ ;;; Γ |- t = t. - intros. constructor. apply eq_term_refl. + intros. constructor. right. apply eq_term_refl. Defined. Lemma cumul_refl' `{checker_flags} : forall Σ Γ t, Σ ;;; Γ |- t <= t. - intros. constructor. apply leq_term_refl. + intros. constructor. right. apply leq_term_refl. Defined. -Hint Resolve conv_refl cumul_refl' : typecheck. +Hint Resolve conv_refl' cumul_refl' : typecheck. Definition eq_opt_term `{checker_flags} Σ φ (t u : option term) := match t, u with diff --git a/checker/theories/WcbvEval.v b/template-coq/theories/WcbvEval.v similarity index 100% rename from checker/theories/WcbvEval.v rename to template-coq/theories/WcbvEval.v diff --git a/template-coq/theories/utils/MCRelations.v b/template-coq/theories/utils/MCRelations.v index 00f5877b4..ecfd3bbf9 100644 --- a/template-coq/theories/utils/MCRelations.v +++ b/template-coq/theories/utils/MCRelations.v @@ -1,4 +1,7 @@ +(* Distributed under the terms of the MIT license. *) +Require Import ssreflect. Require Import CRelationClasses. +Require Import Equations.Type.Relation Equations.Type.Relation_Properties. Infix "<~>" := iffT (at level 90). @@ -16,6 +19,163 @@ Notation Trel_conj R S := Notation on_Trel_eq R f g := (fun x y => (R (f x) (f y) * (g x = g y)))%type. +Section Flip. + Local Set Universe Polymorphism. + Context {A : Type} (R : crelation A). + + Lemma flip_Reflexive : Reflexive R -> Reflexive (flip R). + Proof. + intros HR x. unfold flip. apply reflexivity. + Qed. + + Lemma flip_Symmetric : Symmetric R -> Symmetric (flip R). + Proof. + intros HR x y. unfold flip. apply symmetry. + Qed. + + Lemma flip_Transitive : Transitive R -> Transitive (flip R). + Proof. + intros HR x y z xy yz. + unfold flip in *. eapply HR; eassumption. + Qed. + +End Flip. + +Definition commutes {A} (R S : relation A) := + forall x y z, R x y -> S x z -> { w & S y w * R z w}%type. + +Lemma clos_t_rt {A} {R : A -> A -> Type} x y : trans_clos R x y -> clos_refl_trans R x y. +Proof. + induction 1; try solve [econstructor; eauto]. +Qed. + + +Arguments rt_step {A} {R} {x y}. +Polymorphic Hint Resolve rt_refl rt_step : core. + + +Definition clos_rt_monotone {A} (R S : relation A) : + inclusion R S -> inclusion (clos_refl_trans R) (clos_refl_trans S). +Proof. + move => incls x y. + induction 1; solve [econstructor; eauto]. +Qed. + +Lemma relation_equivalence_inclusion {A} (R S : relation A) : + inclusion R S -> inclusion S R -> relation_equivalence R S. +Proof. firstorder. Qed. + +Lemma clos_rt_disjunction_left {A} (R S : relation A) : + inclusion (clos_refl_trans R) + (clos_refl_trans (relation_disjunction R S)). +Proof. + apply clos_rt_monotone. + intros x y H; left; exact H. +Qed. + +Lemma clos_rt_disjunction_right {A} (R S : relation A) : + inclusion (clos_refl_trans S) + (clos_refl_trans (relation_disjunction R S)). +Proof. + apply clos_rt_monotone. + intros x y H; right; exact H. +Qed. + +Global Instance clos_rt_trans A R : Transitive (@clos_refl_trans A R). +Proof. + intros x y z H H'. econstructor 3; eauto. +Qed. + +Global Instance clos_rt_refl A R : Reflexive (@clos_refl_trans A R). +Proof. intros x. constructor 2. Qed. + +Lemma clos_refl_trans_prod_l {A B} (R : relation A) (S : relation (A * B)) : + (forall x y b, R x y -> S (x, b) (y, b)) -> + forall (x y : A) b, + clos_refl_trans R x y -> + clos_refl_trans S (x, b) (y, b). +Proof. + intros. induction X0; try solve [econstructor; eauto]. +Qed. + +Lemma clos_refl_trans_prod_r {A B} (R : relation B) (S : relation (A * B)) a : + (forall x y, R x y -> S (a, x) (a, y)) -> + forall (x y : B), + clos_refl_trans R x y -> + clos_refl_trans S (a, x) (a, y). +Proof. + intros. induction X0; try solve [econstructor; eauto]. +Qed. + +Lemma clos_rt_t_incl {A} {R : relation A} `{Reflexive A R} : + inclusion (clos_refl_trans R) (trans_clos R). +Proof. + intros x y. induction 1; try solve [econstructor; eauto]. +Qed. + +Lemma clos_t_rt_incl {A} {R : relation A} `{Reflexive A R} : + inclusion (trans_clos R) (clos_refl_trans R). +Proof. + intros x y. induction 1; try solve [econstructor; eauto]. +Qed. + +Lemma clos_t_rt_equiv {A} {R} `{Reflexive A R} : + relation_equivalence (trans_clos R) (clos_refl_trans R). +Proof. + apply relation_equivalence_inclusion. + apply clos_t_rt_incl. + apply clos_rt_t_incl. +Qed. + +Global Instance relation_disjunction_refl_l {A} {R S : relation A} : + Reflexive R -> Reflexive (relation_disjunction R S). +Proof. + intros HR x. left; auto. +Qed. + +Global Instance relation_disjunction_refl_r {A} {R S : relation A} : + Reflexive S -> Reflexive (relation_disjunction R S). +Proof. + intros HR x. right; auto. +Qed. + +Global Instance clos_rt_trans_Symmetric A R : + Symmetric R -> Symmetric (@clos_refl_trans A R). +Proof. + intros X x y H. induction H; eauto. + eapply clos_rt_trans; eassumption. +Qed. + +Definition clos_sym {A} (R : relation A) := relation_disjunction R (flip R). + +Global Instance clos_sym_Symmetric A R : + Symmetric (@clos_sym A R). +Proof. + intros x y []; [right|left]; assumption. +Qed. + +Global Instance clos_refl_sym_trans_Symmetric A R : + Symmetric (@clos_refl_sym_trans A R) + := rst_sym R. + +Global Instance clos_refl_sym_trans_Reflexive A R : + Reflexive (@clos_refl_sym_trans A R) + := rst_refl R. + +Global Instance clos_refl_sym_trans_Transitive A R : + Transitive (@clos_refl_sym_trans A R) + := rst_trans R. + +Global Instance relation_disjunction_Symmetric {A} {R S : relation A} : + Symmetric R -> Symmetric S -> Symmetric (relation_disjunction R S). +Proof. + intros HR HS x y [X|X]; [left|right]; eauto. +Qed. + +Ltac rst_induction h := + induction h; [constructor|reflexivity|etransitivity]. + + (* Definition MR {T M} (R : M -> M -> Prop) (m : T -> M) (x y: T): Prop := R (m x) (m y). *) (* From measure_wf of Program.Wf *) From f4b79ff87fa89cf2da5c792a71d10e341877ca94 Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Fri, 11 Dec 2020 20:56:07 +0100 Subject: [PATCH 59/70] Finished PCUICToTemplate correctness proof.This is much less trivial than anticipated: one really has to do surgeryon the binary applications derivation to produce onewhere applications are n-ary *without* relying on transitivity of cumulativityanywhere. This requires to use induction on the size of derivations (includingnon-principal/paranoid hypotheses). --- pcuic/theories/PCUICConversion.v | 2 +- pcuic/theories/PCUICCumulativity.v | 2 + pcuic/theories/PCUICReduction.v | 11 +- pcuic/theories/PCUICSpine.v | 2 +- pcuic/theories/PCUICTemplateEquiv.v | 34 + pcuic/theories/PCUICToTemplateCorrectness.v | 380 +++++++++-- pcuic/theories/PCUICTyping.v | 714 ++++++++++++-------- pcuic/theories/TemplateToPCUICCorrectness.v | 251 +++++-- template-coq/theories/Ast.v | 1 + template-coq/theories/AstUtils.v | 1 - template-coq/theories/Typing.v | 29 +- template-coq/theories/utils/MCRelations.v | 2 +- 12 files changed, 1007 insertions(+), 422 deletions(-) create mode 100644 pcuic/theories/PCUICTemplateEquiv.v diff --git a/pcuic/theories/PCUICConversion.v b/pcuic/theories/PCUICConversion.v index 41adb575b..527ce3503 100644 --- a/pcuic/theories/PCUICConversion.v +++ b/pcuic/theories/PCUICConversion.v @@ -58,7 +58,7 @@ Proof. eapply cumul_alt in X0 as [w [w' [[redl' redr'] eq']]]. destruct (red_confluence wfΣ redr redl') as [nf [nfl nfr]]. eapply cumul_alt. - eapply red_eq_term_upto_univ_r in eq; tc;eauto with pcuic. + eapply red_eq_term_upto_univ_r in eq. all:tc;eauto with pcuic. destruct eq as [v'0 [red'0 eq2]]. eapply red_eq_term_upto_univ_l in eq'; tc;eauto with pcuic. destruct eq' as [v'1 [red'1 eq1]]. diff --git a/pcuic/theories/PCUICCumulativity.v b/pcuic/theories/PCUICCumulativity.v index df651c893..346361e62 100644 --- a/pcuic/theories/PCUICCumulativity.v +++ b/pcuic/theories/PCUICCumulativity.v @@ -1,4 +1,6 @@ (* Distributed under the terms of the MIT license. *) +From Coq Require Import CRelationClasses. +From Equations.Type Require Import Relation Relation_Properties. From MetaCoq.Template Require Import config utils BasicAst. From MetaCoq.PCUIC Require Import PCUICAst PCUICAstUtils PCUICLiftSubst PCUICEquality PCUICUnivSubst PCUICReduction. diff --git a/pcuic/theories/PCUICReduction.v b/pcuic/theories/PCUICReduction.v index 28f0353cb..a63e073c1 100644 --- a/pcuic/theories/PCUICReduction.v +++ b/pcuic/theories/PCUICReduction.v @@ -5,6 +5,7 @@ From MetaCoq.PCUIC Require Import PCUICAst PCUICAstUtils Require Import ssreflect. Require Import Equations.Prop.DepElim. +From Equations.Type Require Import Relation Relation_Properties. From Equations Require Import Equations. Set Default Goal Selector "!". @@ -14,7 +15,6 @@ Definition tDummy := tVar String.EmptyString. Definition iota_red npar c args brs := (mkApps (snd (List.nth c brs (0, tDummy))) (List.skipn npar args)). - (** ** Reduction *) (** *** Helper functions for reduction *) @@ -319,7 +319,6 @@ Hint Constructors red1 : pcuic. Definition red Σ Γ := clos_refl_trans (red1 Σ Γ). - Lemma refl_red Σ Γ t : red Σ Γ t t. Proof. reflexivity. @@ -712,7 +711,7 @@ Section ReductionCongruence. red Σ Γ M M' -> red Σ (Γ ,, vass na M') N N' -> red Σ Γ (tLambda na M N) (tLambda na M' N'). Proof. - intros. eapply (transitivity (y := tLambda na M' N)). + intros. transitivity (tLambda na M' N). - now apply (red_ctx (tCtxLambda_l _ tCtxHole _)). - now eapply (red_ctx (tCtxLambda_r _ _ tCtxHole)). Qed. @@ -729,7 +728,7 @@ Section ReductionCongruence. red Σ Γ N0 N1 -> red Σ Γ (tApp M0 N0) (tApp M1 N1). Proof. - intros; eapply (transitivity (y := tApp M1 N0)). + intros; transitivity (tApp M1 N0). - now apply (red_ctx (tCtxApp_l tCtxHole _)). - now eapply (red_ctx (tCtxApp_r _ tCtxHole)). Qed. @@ -785,9 +784,9 @@ Section ReductionCongruence. red Σ Γ d0 d1 -> red Σ Γ t0 t1 -> red Σ (Γ ,, vdef na d1 t1) b0 b1 -> red Σ Γ (tLetIn na d0 t0 b0) (tLetIn na d1 t1 b1). Proof. - intros; eapply (transitivity (y := tLetIn na d1 t0 b0)). + intros; transitivity (tLetIn na d1 t0 b0). - now apply (red_ctx (tCtxLetIn_l _ tCtxHole _ _)). - - eapply (transitivity (y := tLetIn na d1 t1 b0)). + - transitivity (tLetIn na d1 t1 b0). + now eapply (red_ctx (tCtxLetIn_b _ _ tCtxHole _)). + now eapply (red_ctx (tCtxLetIn_r _ _ _ tCtxHole)). Qed. diff --git a/pcuic/theories/PCUICSpine.v b/pcuic/theories/PCUICSpine.v index c412a2dd1..b116d3b3a 100644 --- a/pcuic/theories/PCUICSpine.v +++ b/pcuic/theories/PCUICSpine.v @@ -1783,7 +1783,7 @@ Lemma typing_spine_app {cf:checker_flags} Σ Γ ty args na A B arg : Proof. intros wfΣ H; revert arg. dependent induction H. - - intros arg Harg. simpl. econstructor; eauto. + - intros arg Harg. simpl. econstructor; eauto. constructor. 2:reflexivity. eapply isType_tProd in i as [watd wat]. eapply (isType_subst wfΣ (Δ:=[vass na A])); eauto. diff --git a/pcuic/theories/PCUICTemplateEquiv.v b/pcuic/theories/PCUICTemplateEquiv.v new file mode 100644 index 000000000..60b3b0edd --- /dev/null +++ b/pcuic/theories/PCUICTemplateEquiv.v @@ -0,0 +1,34 @@ + +Lemma T_cumul_trans {cf} (Σ : PCUICAst.global_env_ext) Γ T U V : + STy.wf (trans_global Σ) -> + PCUICTyping.wf (TemplateToPCUIC.trans_global (trans_global Σ)).1 -> + wf T -> wf U -> wf V -> + TT.cumul (trans_global Σ) (trans_local Γ) T U -> + TT.cumul (trans_global Σ) (trans_local Γ) U V -> + TT.cumul (trans_global Σ) (trans_local Γ) T V. +Proof. + intros wftΣ wftΣ' wfT wfU wfV. + assert (wfΓ : Forall wf_decl (trans_local Γ)). admit. + intros TU UV. + pose proof (TemplateToPCUICCorrectness.trans_cumul (trans_global Σ) (trans_local Γ) _ _ wftΣ wfΓ wfT wfU TU). + pose proof (TemplateToPCUICCorrectness.trans_cumul (trans_global Σ) (trans_local Γ) _ _ wftΣ wfΓ wfU wfV UV). + pose proof (PCUICConversion.cumul_trans _ _ _ _ _ _ X X0). + apply trans_cumul in X1. +Admitted. + +Lemma T_cumul_trans' {cf} (Σ : global_env_ext) Γ T U V : + STy.wf Σ -> + PCUICTyping.wf (TemplateToPCUIC.trans_global_decls Σ) -> + wf T -> wf U -> wf V -> + TT.cumul Σ Γ T U -> + TT.cumul Σ Γ U V -> + TT.cumul Σ Γ T V. +Proof. + intros wftΣ wftransb wfT wfU wfV. + assert (wfΓ : Forall wf_decl Γ). admit. + intros TU UV. + pose proof (TemplateToPCUICCorrectness.trans_cumul Σ Γ _ _ wftΣ wfΓ wfT wfU TU). + pose proof (TemplateToPCUICCorrectness.trans_cumul Σ Γ _ _ wftΣ wfΓ wfU wfV UV). + unshelve epose proof (PCUICConversion.cumul_trans _ _ _ _ _ _ X X0). + apply trans_cumul in X1. +Admitted. diff --git a/pcuic/theories/PCUICToTemplateCorrectness.v b/pcuic/theories/PCUICToTemplateCorrectness.v index 685c869b3..047abc51f 100644 --- a/pcuic/theories/PCUICToTemplateCorrectness.v +++ b/pcuic/theories/PCUICToTemplateCorrectness.v @@ -1,6 +1,9 @@ (* Distributed under the terms of the MIT license. *) +From Coq Require Import ssreflect ssrbool CRelationClasses. +From Equations.Type Require Import Relation Relation_Properties. From MetaCoq.PCUIC Require Import PCUICAst PCUICAstUtils PCUICInduction - PCUICLiftSubst PCUICEquality PCUICReduction PCUICUnivSubst PCUICTyping PCUICGeneration. + PCUICLiftSubst PCUICEquality PCUICReduction PCUICUnivSubst PCUICTyping PCUICGeneration + TemplateToPCUICCorrectness. (* We use the back and forth to show transitivity of cumulativity *) Set Warnings "-notation-overridden". From MetaCoq.Template Require Import config utils Ast TypingWf WfInv UnivSubst @@ -9,7 +12,6 @@ From MetaCoq.Template Require Import config utils Ast TypingWf WfInv UnivSubst Set Warnings "+notation_overridden". Require Import PCUICToTemplate. -From Coq Require Import ssreflect. Implicit Types cf : checker_flags. (* Use {cf} to parameterize by checker_flags where needed *) @@ -619,8 +621,6 @@ Proof. eapply IHmfix. Qed. -Definition isApp t := match t with tApp _ _ => true | _ => false end. - Lemma trans_is_constructor: forall (args : list S.term) (narg : nat), is_constructor narg args = true -> TT.is_constructor narg (map trans args) = true. @@ -1031,41 +1031,6 @@ Proof. split;eassumption. Qed. -Lemma invert_type_App `{checker_flags} Σ Γ f u T : - TT.typing Σ Γ (tApp f u) T -> - { T' : term & { U' & ((TT.typing Σ Γ f T') * TT.typing_spine Σ Γ T' u U' * - (isApp f = false) * (u <> []) * - (TT.cumul Σ Γ U' T))%type } }. -Proof. - intros Hty. - dependent induction Hty. - - exists t_ty, t'. intuition. - - edestruct IHHty1 as [T' [U' [H' H'']]]. - exists T', U'. split; auto. - eapply TT.cumul_trans; eauto. -Qed. - -Lemma type_mkApp `{checker_flags} Σ Γ f u T T' : - TT.typing Σ Γ f T -> - TT.typing_spine Σ Γ T [u] T' -> - TT.typing Σ Γ (mkApp f u) T'. -Proof. - intros Hf Hu. inv Hu. - simpl. destruct (isApp f) eqn:Happ. - destruct f; try discriminate. simpl. - eapply invert_type_App in Hf. - destruct Hf as (T'' & U' & (((Hf & HU) & Happf) & Hunil) & Hcumul). - eapply TT.type_App; eauto. intro. destruct args; discriminate. - inv X2. clear Happ Hf Hunil. - induction HU. simpl. econstructor; eauto. - eapply TT.cumul_trans; eauto. - econstructor. econstructor. eapply t. eauto. eauto. - apply IHHU; eauto. - rewrite -> AstUtils.mkApp_tApp; eauto. - econstructor; eauto. congruence. - econstructor; eauto. -Qed. - Lemma trans_decompose_prod_assum : forall Γ t, let '(Δ, c) := decompose_prod_assum Γ t in @@ -1110,6 +1075,12 @@ Proof. now destruct prim as [? []]. Qed. +Lemma trans_nisApp t : ~~ PCUICAst.isApp t -> ~~ Ast.isApp (trans t). +Proof. + destruct t => //. + now destruct prim as [? []]. +Qed. + Lemma trans_destInd t : ST.destInd t = TT.destInd (trans t). Proof. destruct t => //. simpl. @@ -1129,7 +1100,6 @@ Proof. now rewrite trans_isApp. Qed. - Lemma All2_map_option_out_mapi_Some_spec : forall {A B B'} (f : nat -> A -> option B) (g' : B -> B') (g : nat -> A -> option B') l t, @@ -1222,7 +1192,6 @@ Proof. unfold ST.check_one_fix, TT.check_one_fix. destruct mfix as [na ty arg rarg] => /=. move: (trans_decompose_prod_assum [] ty). - rewrite strip_casts_trans. destruct decompose_prod_assum as [ctx p] => /= ->. rewrite -(trans_smash_context []) /trans_local. rewrite -List.map_rev nth_error_map. @@ -1246,7 +1215,6 @@ Proof. unfold ST.check_one_cofix, TT.check_one_cofix. destruct mfix as [na ty arg rarg] => /=. move: (trans_decompose_prod_assum [] ty). - rewrite strip_casts_trans. destruct decompose_prod_assum as [ctx p] => -> /=. move: (trans_decompose_app p). destruct decompose_app => /= ->. @@ -1290,6 +1258,21 @@ Proof. now rewrite trans_check_rec_kind. Qed. +Lemma type_mkApps_napp `{checker_flags} Σ Γ f u T T' : + ~~ isApp f -> + TT.typing Σ Γ f T -> + TT.typing_spine Σ Γ T u T' -> + TT.typing Σ Γ (mkApps f u) T'. +Proof. + intros hf hty hsp. + depelim hsp. simpl; auto. + rewrite mkApps_tApp. + destruct f => //. congruence. + econstructor; eauto. + destruct f => //. congruence. + econstructor; eauto. +Qed. + Axiom fix_guard_trans : forall Σ Γ mfix, ST.fix_guard Σ Γ mfix -> @@ -1299,7 +1282,265 @@ Axiom cofix_guard_trans : forall Σ Γ mfix, ST.cofix_guard Σ Γ mfix -> TT.cofix_guard (trans_global Σ) (trans_local Γ) (map (map_def trans trans) mfix). + +(* This version of typing spine allows to not require [isType] assumptions at the end of the + application chain, which is crucial to be able to build an application spine *) +Inductive typing_spine {cf} (Σ : global_env_ext) (Γ : context) : term -> list term -> term -> Type := +| type_spine_eq ty : typing_spine Σ Γ ty [] ty + +| type_spine_nil ty ty' : + isType Σ Γ ty' -> + Σ ;;; Γ |- ty <= ty' -> + typing_spine Σ Γ ty [] ty' + +| type_spine_cons hd tl na A B T B' : + isType Σ Γ (tProd na A B) -> + Σ ;;; Γ |- T <= tProd na A B -> + Σ ;;; Γ |- hd : A -> + typing_spine Σ Γ (subst10 hd B) tl B' -> + typing_spine Σ Γ T (hd :: tl) B'. + +Section Typing_Spine_size. + Context `{checker_flags}. + Context {Σ : global_env_ext} {Γ : context}. + + Fixpoint typing_spine_size {t T U} (s : typing_spine Σ Γ t T U) : size := + match s with + | type_spine_eq ty => 0 + | type_spine_nil ty ty' ist cum => typing_size ist.π2 + | type_spine_cons hd tl na A B T B' typrod cumul ty s' => + (max (typing_size typrod.π2) (max (typing_size ty) (typing_spine_size s')))%nat + end. +End Typing_Spine_size. + +Require Import PCUICArities. + +Require Import PCUICSpine. +Lemma typing_spine_weaken_concl {cf:checker_flags} {Σ Γ T args S S'} : + wf Σ.1 -> + typing_spine Σ Γ T args S -> + Σ ;;; Γ |- S <= S' -> + isType Σ Γ S' -> + typing_spine Σ Γ T args S'. +Proof. + intros wfΣ sp. + induction sp in S' => cum. constructor; auto. constructor; auto. + now transitivity ty'. + intros isType. econstructor. eauto. eauto. eauto. + eauto. +Defined. + +Lemma typing_spine_weaken_concl_size {cf:checker_flags} {Σ Γ T args S S'} + (wf : wf Σ.1) + (sp :typing_spine Σ Γ T args S) + (Hs : Σ ;;; Γ |- S <= S') + (ist : isType Σ Γ S') : + typing_spine_size (typing_spine_weaken_concl wf sp Hs ist) <= + max (typing_spine_size sp) (typing_size ist.π2). +Proof. + induction sp; simpl; auto. lia. + rewrite - !Nat.max_assoc. specialize (IHsp Hs). lia. +Qed. + +Lemma typing_spine_strengthen {cf:checker_flags} Σ Γ T args U : + wf Σ.1 -> + typing_spine Σ Γ T args U -> + forall T', Σ ;;; Γ |- T' <= T -> + isType Σ Γ T -> + typing_spine Σ Γ T' args U. +Proof. + induction 2 in |- *; intros T' (*WAT*)redT. + - intros. econstructor 2. eauto. eauto. + - intros. econstructor 2. eauto. transitivity ty; auto. + - specialize (IHX0 (B {0 := hd})). + forward IHX0. { reflexivity. } + intros. eapply type_spine_cons with na A B; auto. + etransitivity; eauto. +Qed. +(* +Lemma typing_spine_app {cf:checker_flags} Σ Γ ty args na A B arg : + wf Σ.1 -> + isType Σ Γ (tProd na A B) -> + typing_spine Σ Γ ty args (tProd na A B) -> + Σ ;;; Γ |- arg : A -> + typing_spine Σ Γ ty (args ++ [arg]) (B {0 := arg}). +Proof. + intros wfΣ isty H; revert arg. + remember (tProd na A B) as prod. + revert na A B Heqprod. + induction H. + - intros na A B eq arg Harg. simpl. econstructor; eauto. now rewrite <-eq. now rewrite <-eq. + constructor. + - intros na A B eq arg Harg. simpl. + econstructor; eauto. rewrite <- eq. exact i. now rewrite <- eq. constructor. + - intros na' A' B'' eq arg Harg. simpl. + econstructor. apply i. auto. auto. + eapply IHtyping_spine. now rewrite eq. exact eq. apply Harg. +Defined. + *) + +Ltac sig := unshelve eexists. + +Lemma typing_spine_app {cf:checker_flags} Σ Γ ty args na A B arg + (wf : wf Σ.1) + (isty : isType Σ Γ (tProd na A B)) + (sp : typing_spine Σ Γ ty args (tProd na A B)) + (argd : Σ ;;; Γ |- arg : A) : + ∑ sp' : typing_spine Σ Γ ty (args ++ [arg]) (B {0 := arg}), + typing_spine_size sp' <= max (typing_size isty.π2) (max (typing_spine_size sp) (typing_size argd)). +Proof. + revert arg argd. + remember (tProd na A B) as prod. symmetry in Heqprod. + revert na A B Heqprod. + induction sp. + - intros na A B eq arg Harg. simpl. + sig. + * econstructor; eauto. now rewrite -> eq. now rewrite -> eq. + constructor. + * destruct eq => /=. unfold eq_rect_r. simpl. lia. + - intros na A B eq arg Harg. simpl. + sig. + * econstructor; eauto. rewrite -> eq. exact i. + now rewrite -> eq. constructor. + * simpl. destruct eq. unfold eq_rect_r. simpl. lia. + - intros na' A' B'' eq arg Harg. simpl. + specialize (IHsp isty _ _ _ eq _ Harg) as [sp' Hsp']. + sig. + * econstructor. apply i. auto. auto. exact sp'. + * destruct eq. simpl. lia. +Qed. + +Lemma TT_typing_spine_app {cf:checker_flags} Σ Γ ty T' args na A B arg s : + TT.typing Σ Γ (T.tProd na A B) (T.tSort s) -> + TT.typing_spine Σ Γ ty args T' -> + TT.cumul Σ Γ T' (T.tProd na A B) -> + TT.typing Σ Γ arg A -> + TT.typing_spine Σ Γ ty (args ++ [arg]) (TL.subst1 arg 0 B). +Proof. + intros isty H; revert arg. + remember (T.tProd na A B) as prod. + revert na A B Heqprod. + induction H. + - intros na A B eq arg Harg. simpl. econstructor; eauto. now rewrite <-eq. rewrite <-eq. + apply Harg. + constructor. + - intros na' A' B'' eq arg Harg. simpl. + econstructor. apply t. auto. auto. + eapply IHtyping_spine. now rewrite eq. exact eq. apply Harg. apply X. +Defined. + + +Lemma destrb (b : bool) : b + ~~ b. +Proof. + destruct b. left; auto. right; auto. +Defined. + +Lemma decompose_app_napp_nonnil t f l : + isApp t -> + decompose_app t = (f, l) -> + ~~ is_empty l. +Proof. + intros isApp. + destruct t; simpl => //. + intros da. + pose proof (decompose_app_notApp _ _ _ da). + apply decompose_app_inv in da. + destruct l using rev_ind. + unfold decompose_app => /=. + destruct f => //. + destruct l => //. +Qed. + +Lemma type_app {cf} {Σ Γ t T} (d : Σ ;;; Γ |- t : T) : + wf Σ.1 -> + if isApp t then + let (f, l) := decompose_app t in + ∑ fty (d' : Σ ;;; Γ |- f : fty), + ((typing_size d' <= typing_size d) * + ∑ (sp : typing_spine Σ Γ fty l T), + (typing_spine_size sp <= typing_size d))%type + else True. +Proof. + intros wfΣ. + induction d; simpl; auto. + - destruct (isApp t) eqn:isapp. + destruct (decompose_app (tApp t u)) eqn:da. + unfold decompose_app in da. + simpl in da. + apply decompose_app_rec_inv' in da as [n [napp [equ eqt]]]. + subst t. clear IHd1 IHd3. + rewrite decompose_app_mkApps // in IHd2. + destruct IHd2 as [fty [d' [sp hd']]]. + exists fty, d'. + split. lia. + destruct hd' as [sp' Hsp]. + destruct (typing_spine_app _ _ _ _ _ _ _ _ wfΣ (s; d1) sp' d3) as [appsp Happ]. + simpl in Happ. + move: appsp Happ. rewrite equ firstn_skipn. + intros app happ. exists app. lia. + + unfold decompose_app. simpl. + rewrite atom_decompose_app. destruct t => /= //. + exists _, d2. split. lia. + unshelve eexists. + econstructor. exists s; eauto. reflexivity. assumption. constructor. + simpl. lia. + + - destruct (isApp t) eqn:isapp => //. + destruct (decompose_app t) eqn:da. + assert (l <> []). + { eapply decompose_app_napp_nonnil in da => //. destruct l => //. } + destruct IHd1 as [fty [d' [? ?]]]. + exists fty, d'. split. lia. + destruct s0 as [sp Hsp]. + unshelve eexists. eapply typing_spine_weaken_concl; eauto. now exists s. + epose proof (typing_spine_weaken_concl_size wfΣ sp c (s; d2)). simpl in H0. lia. +Qed. + +Lemma make_typing_spine {cf} {Σ Γ fty l T} + (sp : typing_spine Σ Γ fty l T) n + (IH : forall t' T' (Ht' : Σ ;;; Γ |- t' : T'), + typing_size Ht' <= n -> + TT.typing (trans_global Σ) (trans_local Γ) (trans t') (trans T')) : + typing_spine_size sp <= n -> + ∑ T', TT.typing_spine (trans_global Σ) (trans_local Γ) (trans fty) (map trans l) T' * + ((T' = trans T) + + (TT.cumul (trans_global Σ) (trans_local Γ) T' (trans T) * + ∑ s, TT.typing (trans_global Σ) (trans_local Γ) (trans T) (T.tSort s)))%type. +Proof. + induction sp; simpl; intros. + - exists (trans ty); split. + * constructor. + * left; auto. + - exists (trans ty). + split. constructor. right. + split. + now eapply trans_cumul in c. + specialize (IH _ _ i.π2 H). now exists i.π1. + + - simpl; intros. + forward IHsp by lia. + specialize (IH _ _ t) as IHt. + forward IHt by lia. + apply trans_cumul in c. + specialize (IH _ _ i.π2) as IHi. + forward IHi by lia. + simpl in IHi. + destruct IHsp as [T' [Hsp eq]]. + destruct eq. subst T'. + exists (trans B'). split; auto. + econstructor. + eauto. + apply c. + apply IHt. + now rewrite trans_subst in Hsp. + exists T'. split; auto. + econstructor. + eauto. apply c. apply IHt. + now rewrite trans_subst in Hsp. +Qed. + Theorem pcuic_to_template {cf} (Σ : S.global_env_ext) Γ t T : ST.wf Σ -> ST.typing Σ Γ t T -> @@ -1307,7 +1548,7 @@ Theorem pcuic_to_template {cf} (Σ : S.global_env_ext) Γ t T : Proof. intros X X0. revert Σ X Γ t T X0. - apply (ST.typing_ind_env (fun Σ Γ t T => + apply (typing_ind_env (fun Σ Γ t T => TT.typing (trans_global Σ) (trans_local Γ) (trans t) (trans T) )%type (fun Σ Γ wfΓ => @@ -1324,19 +1565,40 @@ Proof. - eapply TT.type_Prod;assumption. - eapply TT.type_Lambda;eassumption. - eapply TT.type_LetIn;eassumption. - - eapply type_mkApp. - + eassumption. - + econstructor. - 3: eassumption. - 3: { - rewrite trans_subst10. - constructor. - } - 2: { - cbn. constructor. - apply leq_term_refl. - } - eapply X1. + - simpl. rewrite trans_subst10. + destruct (isApp t) eqn:isapp. + move: (type_app Ht wfΣ). rewrite isapp. + destruct (decompose_app t) eqn:da. + intros [fty [d' [hd' [sp hsp]]]]. + assert (IHt := X3 _ _ d' hd'). + epose proof (make_typing_spine sp (typing_size Ht) X3 hsp) as [T' [IH []]]. + * subst T'. rewrite (decompose_app_inv da). + rewrite trans_mkApps mkApp_mkApps AstUtils.mkApps_nested. + pose proof (AstUtils.mkApps_nested (trans t0) (map trans l) [trans u]). + apply decompose_app_notApp in da. + apply trans_isApp in da. + eapply type_mkApps_napp. rewrite da //. + eassumption. + eapply TT_typing_spine_app. simpl in X1. eapply X1. + apply IH. apply TT.cumul_refl'. + apply X5. + * destruct p as [hcum _]. + rewrite (decompose_app_inv da). + rewrite trans_mkApps mkApp_mkApps AstUtils.mkApps_nested. + pose proof (AstUtils.mkApps_nested (trans t0) (map trans l) [trans u]). + apply decompose_app_notApp in da. + apply trans_isApp in da. + eapply type_mkApps_napp. rewrite da //. + eassumption. + eapply TT_typing_spine_app. simpl in X1. eapply X1. + apply IH. apply hcum. + apply X5. + * rewrite mkApp_mkApps. + eapply type_mkApps_napp. + apply trans_isApp in isapp. rewrite isapp //. + now simpl in X2. + econstructor. simpl in X1. eapply X1. + apply TT.cumul_refl'. assumption. constructor. - rewrite trans_subst_instance_constr. rewrite trans_cst_type. eapply TT.type_Const; eauto. @@ -1354,8 +1616,8 @@ Proof. * now apply trans_declared_inductive. * now apply map_nth_error. + now apply trans_consistent_instance_ext. - - replace (trans (PCUICAst.mkApps p (skipn npar args ++ [c]))) - with (mkApps (trans p) (skipn npar (map trans args) ++ [trans c])). + - replace (trans (mkApps p (skipn npar args ++ [c]))) + with (Ast.mkApps (trans p) (skipn npar (map trans args) ++ [trans c])). 2: { rewrite trans_mkApps. rewrite map_app. @@ -1425,4 +1687,4 @@ Proof. + now eapply trans_cumul. Qed. -Print Assumptions trans_build_branches_type. \ No newline at end of file +Print Assumptions pcuic_to_template. \ No newline at end of file diff --git a/pcuic/theories/PCUICTyping.v b/pcuic/theories/PCUICTyping.v index 4ee74367d..e3bde6629 100644 --- a/pcuic/theories/PCUICTyping.v +++ b/pcuic/theories/PCUICTyping.v @@ -686,10 +686,439 @@ Qed. (** *** An induction principle ensuring the Σ declarations enjoy the same properties. Also theads the well-formedness of the local context and the induction principle for it, - and gives the right induction hypothesis - on typing judgments in application spines, fix and cofix blocks. + and gives the right induction hypothesis on typing judgments in application spines, + fix and cofix blocks. This general version allows to get the induction hypothesis on + any subderivation of the head of applications. + + The specialized version `typing_ind_env` below is the one used in general, with + no special case for applications. *) +Lemma typing_ind_env_app_size `{cf : checker_flags} : + forall (P : global_env_ext -> context -> term -> term -> Type) + (Pdecl := fun Σ Γ wfΓ t T tyT => P Σ Γ t T) + (PΓ : forall Σ Γ, wf_local Σ Γ -> Type), + + (forall Σ (wfΣ : wf Σ.1) (Γ : context) (wfΓ : wf_local Σ Γ), + All_local_env_over typing Pdecl Σ Γ wfΓ -> PΓ Σ Γ wfΓ) -> + + (forall Σ (wfΣ : wf Σ.1) (Γ : context) (wfΓ : wf_local Σ Γ) (n : nat) decl, + nth_error Γ n = Some decl -> + PΓ Σ Γ wfΓ -> + P Σ Γ (tRel n) (lift0 (S n) decl.(decl_type))) -> + + (forall Σ (wfΣ : wf Σ.1) (Γ : context) (wfΓ : wf_local Σ Γ) (u : Universe.t), + PΓ Σ Γ wfΓ -> + wf_universe Σ u -> + P Σ Γ (tSort u) (tSort (Universe.super u))) -> + + (forall Σ (wfΣ : wf Σ.1) (Γ : context) (wfΓ : wf_local Σ Γ) (n : aname) (t b : term) (s1 s2 : Universe.t), + PΓ Σ Γ wfΓ -> + Σ ;;; Γ |- t : tSort s1 -> + P Σ Γ t (tSort s1) -> + Σ ;;; Γ,, vass n t |- b : tSort s2 -> + P Σ (Γ,, vass n t) b (tSort s2) -> P Σ Γ (tProd n t b) (tSort (Universe.sort_of_product s1 s2))) -> + + (forall Σ (wfΣ : wf Σ.1) (Γ : context) (wfΓ : wf_local Σ Γ) (n : aname) (t b : term) + (s1 : Universe.t) (bty : term), + PΓ Σ Γ wfΓ -> + Σ ;;; Γ |- t : tSort s1 -> + P Σ Γ t (tSort s1) -> + Σ ;;; Γ,, vass n t |- b : bty -> P Σ (Γ,, vass n t) b bty -> P Σ Γ (tLambda n t b) (tProd n t bty)) -> + + (forall Σ (wfΣ : wf Σ.1) (Γ : context) (wfΓ : wf_local Σ Γ) (n : aname) (b b_ty b' : term) + (s1 : Universe.t) (b'_ty : term), + PΓ Σ Γ wfΓ -> + Σ ;;; Γ |- b_ty : tSort s1 -> + P Σ Γ b_ty (tSort s1) -> + Σ ;;; Γ |- b : b_ty -> + P Σ Γ b b_ty -> + Σ ;;; Γ,, vdef n b b_ty |- b' : b'_ty -> + P Σ (Γ,, vdef n b b_ty) b' b'_ty -> P Σ Γ (tLetIn n b b_ty b') (tLetIn n b b_ty b'_ty)) -> + + (forall Σ (wfΣ : wf Σ.1) (Γ : context) (wfΓ : wf_local Σ Γ) (t : term) na A B u s, + PΓ Σ Γ wfΓ -> + + + Σ ;;; Γ |- tProd na A B : tSort s -> P Σ Γ (tProd na A B) (tSort s) -> + forall (Ht : Σ ;;; Γ |- t : tProd na A B), P Σ Γ t (tProd na A B) -> + + (* Give a stronger induction hypothesis allowing to crawl under applications *) + (forall t' T' (Ht' : Σ ;;; Γ |- t' : T'), typing_size Ht' <= typing_size Ht -> P Σ Γ t' T') -> + + Σ ;;; Γ |- u : A -> P Σ Γ u A -> + P Σ Γ (tApp t u) (B{0 := u})) -> + + (forall Σ (wfΣ : wf Σ.1) (Γ : context) (wfΓ : wf_local Σ Γ) cst u (decl : constant_body), + Forall_decls_typing P Σ.1 -> + PΓ Σ Γ wfΓ -> + declared_constant Σ.1 cst decl -> + consistent_instance_ext Σ decl.(cst_universes) u -> + P Σ Γ (tConst cst u) (subst_instance_constr u (cst_type decl))) -> + + (forall Σ (wfΣ : wf Σ.1) (Γ : context) (wfΓ : wf_local Σ Γ) (ind : inductive) u + mdecl idecl (isdecl : declared_inductive Σ.1 mdecl ind idecl), + Forall_decls_typing P Σ.1 -> + PΓ Σ Γ wfΓ -> + consistent_instance_ext Σ mdecl.(ind_universes) u -> + P Σ Γ (tInd ind u) (subst_instance_constr u (ind_type idecl))) -> + + (forall Σ (wfΣ : wf Σ.1) (Γ : context) (wfΓ : wf_local Σ Γ) (ind : inductive) (i : nat) u + mdecl idecl cdecl (isdecl : declared_constructor Σ.1 mdecl idecl (ind, i) cdecl), + Forall_decls_typing P Σ.1 -> + PΓ Σ Γ wfΓ -> + consistent_instance_ext Σ mdecl.(ind_universes) u -> + P Σ Γ (tConstruct ind i u) (type_of_constructor mdecl cdecl (ind, i) u)) -> + + (forall Σ (wfΣ : wf Σ.1) (Γ : context) (wfΓ : wf_local Σ Γ) (ind : inductive) u (npar : nat) + (p c : term) (brs : list (nat * term)) + (args : list term) (mdecl : mutual_inductive_body) (idecl : one_inductive_body) + (isdecl : declared_inductive (fst Σ) mdecl ind idecl), + Forall_decls_typing P Σ.1 -> PΓ Σ Γ wfΓ -> + ind_npars mdecl = npar -> + let params := firstn npar args in + forall ps pty, build_case_predicate_type ind mdecl idecl params u ps = Some pty -> + Σ ;;; Γ |- p : pty -> + P Σ Γ p pty -> + is_allowed_elimination (global_ext_constraints Σ) ps idecl.(ind_kelim) -> + Σ ;;; Γ |- c : mkApps (tInd ind u) args -> + isCoFinite mdecl.(ind_finite) = false -> + P Σ Γ c (mkApps (tInd ind u) args) -> + forall btys, map_option_out (build_branches_type ind mdecl idecl params u p) = Some btys -> + All2 (fun br bty => (br.1 = bty.1) * + (Σ ;;; Γ |- br.2 : bty.2) * P Σ Γ br.2 bty.2 * + ∑ s, (Σ ;;; Γ |- bty.2 : tSort s) * P Σ Γ bty.2 (tSort s)) + brs btys -> + P Σ Γ (tCase (ind, npar) p c brs) (mkApps p (skipn npar args ++ [c]))) -> + + (forall Σ (wfΣ : wf Σ.1) (Γ : context) (wfΓ : wf_local Σ Γ) (p : projection) (c : term) u + mdecl idecl pdecl (isdecl : declared_projection Σ.1 mdecl idecl p pdecl) args, + Forall_decls_typing P Σ.1 -> PΓ Σ Γ wfΓ -> + Σ ;;; Γ |- c : mkApps (tInd (fst (fst p)) u) args -> + P Σ Γ c (mkApps (tInd (fst (fst p)) u) args) -> + #|args| = ind_npars mdecl -> + let ty := snd pdecl in P Σ Γ (tProj p c) (subst0 (c :: List.rev args) (subst_instance_constr u ty))) -> + + (forall Σ (wfΣ : wf Σ.1) (Γ : context) (wfΓ : wf_local Σ Γ) (mfix : list (def term)) (n : nat) decl, + let types := fix_context mfix in + fix_guard Σ Γ mfix -> + nth_error mfix n = Some decl -> + PΓ Σ Γ wfΓ -> + All (fun d => {s & (Σ ;;; Γ |- d.(dtype) : tSort s)%type * P Σ Γ d.(dtype) (tSort s)})%type mfix -> + All (fun d => (Σ ;;; Γ ,,, types |- d.(dbody) : lift0 #|types| d.(dtype))%type * + P Σ (Γ ,,, types) d.(dbody) (lift0 #|types| d.(dtype)))%type mfix -> + wf_fixpoint Σ.1 mfix -> + P Σ Γ (tFix mfix n) decl.(dtype)) -> + + (forall Σ (wfΣ : wf Σ.1) (Γ : context) (wfΓ : wf_local Σ Γ) (mfix : list (def term)) (n : nat) decl, + let types := fix_context mfix in + cofix_guard Σ Γ mfix -> + nth_error mfix n = Some decl -> + PΓ Σ Γ wfΓ -> + All (fun d => {s & (Σ ;;; Γ |- d.(dtype) : tSort s)%type * P Σ Γ d.(dtype) (tSort s)})%type mfix -> + All (fun d => (Σ ;;; Γ ,,, types |- d.(dbody) : lift0 #|types| d.(dtype))%type * + P Σ (Γ ,,, types) d.(dbody) (lift0 #|types| d.(dtype)))%type mfix -> + wf_cofixpoint Σ.1 mfix -> + P Σ Γ (tCoFix mfix n) decl.(dtype)) -> + + (forall Σ (wfΣ : wf Σ.1) (Γ : context) (wfΓ : wf_local Σ Γ) (t A B : term) s, + PΓ Σ Γ wfΓ -> + Σ ;;; Γ |- t : A -> + P Σ Γ t A -> + Σ ;;; Γ |- B : tSort s -> + P Σ Γ B (tSort s) -> + Σ ;;; Γ |- A <= B -> + P Σ Γ t B) -> + + env_prop P PΓ. +Proof. + intros P Pdecl PΓ; unfold env_prop. + intros XΓ X X0 X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 Σ wfΣ Γ t T H. + (* NOTE (Danil): while porting to 8.9, I had to split original "pose" into 2 pieces, + otherwise it takes forever to execure the "pose", for some reason *) + pose (@Fix_F ({ Σ : _ & { wfΣ : wf Σ.1 & { Γ : context & + { t : term & { T : term & Σ ;;; Γ |- t : T }}}}})) as p0. + specialize (p0 (PCUICUtils.dlexprod (precompose lt (fun Σ => globenv_size (fst Σ))) + (fun Σ => precompose lt (fun x => typing_size (projT2 (projT2 (projT2 (projT2 x)))))))) as p. + set(foo := existT _ Σ (existT _ wfΣ (existT _ Γ (existT _ t (existT _ _ H)))) : { Σ : _ & { wfΣ : wf Σ.1 & { Γ : context & { t : term & { T : term & Σ ;;; Γ |- t : T }}}}}). + change Σ with (projT1 foo). + change Γ with (projT1 (projT2 (projT2 foo))). + change t with (projT1 (projT2 (projT2 (projT2 foo)))). + change T with (projT1 (projT2 (projT2 (projT2 (projT2 foo))))). + change H with (projT2 (projT2 (projT2 (projT2 (projT2 foo))))). + revert foo. + match goal with + |- let foo := _ in @?P foo => specialize (p (fun x => P x)) + end. + forward p; [ | apply p; apply PCUICUtils.wf_dlexprod; intros; apply wf_precompose; apply lt_wf]. + clear p. + clear Σ wfΣ Γ t T H. + intros (Σ & wfΣ & Γ & t & t0 & H). simpl. + intros IH. simpl in IH. + split. split. + destruct Σ as [Σ φ]. destruct Σ. + constructor. + cbn in wfΣ; inversion_clear wfΣ. auto. + inv wfΣ. + rename X14 into Xg. + constructor; auto. unfold Forall_decls_typing in IH. + - simple refine (let IH' := IH ((Σ, udecl); (X13; []; (tSort Universe.lProp); _; _)) in _). + shelve. simpl. apply type_Prop. + forward IH'. constructor 1; cbn. lia. + apply IH'; auto. + - simpl. simpl in *. + destruct d; simpl. + + destruct c; simpl in *. + destruct cst_body; simpl in *. + simpl. + intros. red in Xg. simpl in Xg. + specialize (IH (existT _ (Σ, udecl) (existT _ X13 (existT _ [] (existT _ _ (existT _ _ Xg)))))). + simpl in IH. + forward IH. constructor 1. simpl; lia. + apply IH. + red. simpl. red in Xg; simpl in Xg. + destruct Xg as [s Hs]. red. simpl. + specialize (IH (existT _ (Σ, udecl) (existT _ X13 (existT _ [] (existT _ _ (existT _ _ Hs)))))). + simpl in IH. + forward IH. constructor 1. simpl; lia. exists s. eapply IH. + + red in Xg. + destruct Xg as [onI onP onnp]; constructor; eauto. + eapply Alli_impl; eauto. clear onI onP onnp; intros n x Xg. + refine {| ind_indices := Xg.(ind_indices); + ind_arity_eq := Xg.(ind_arity_eq); + ind_cshapes := Xg.(ind_cshapes) |}. + + ++ apply onArity in Xg. destruct Xg as [s Hs]. exists s; auto. + specialize (IH (existT _ (Σ, udecl) (existT _ X13 (existT _ [] (existT _ _ (existT _ _ Hs)))))). + simpl in IH. simpl. apply IH; constructor 1; simpl; lia. + ++ pose proof Xg.(onConstructors) as Xg'. + eapply All2_impl; eauto. intros. + destruct X14 as [cass chead tyeq onctyp oncargs oncind]. + unshelve econstructor; eauto. + destruct onctyp as [s Hs]. + simpl in Hs. + specialize (IH (existT _ (Σ, udecl) (existT _ X13 (existT _ _ (existT _ _ (existT _ _ Hs)))))). + simpl in IH. simpl. exists s. simpl. apply IH; constructor 1; simpl; auto with arith. + eapply sorts_local_ctx_impl; eauto. simpl. intros. red in X14. + destruct T. + specialize (IH ((Σ, udecl); (X13; _; _; _; X14))). + apply IH. simpl. constructor 1. simpl. auto with arith. + destruct X14 as [u Hu]. exists u. + specialize (IH (existT _ (Σ, udecl) (existT _ X13 (existT _ _ (existT _ _ (existT _ _ Hu)))))). + apply IH. simpl. constructor 1. simpl. auto with arith. + clear -X13 IH oncind. + revert oncind. + generalize (List.rev (lift_context #|cshape_args y| 0 (ind_indices Xg))). + generalize (cshape_indices y). induction 1; constructor; auto. + red in p0 |- *. + specialize (IH (existT _ (Σ, udecl) (existT _ X13 (existT _ _ (existT _ _ (existT _ _ p0)))))). + apply IH. simpl. constructor 1. simpl. auto with arith. + ++ intros Hprojs; pose proof (onProjections Xg Hprojs); auto. + ++ destruct Xg. simpl. unfold check_ind_sorts in *. + destruct Universe.is_prop; auto. + destruct Universe.is_sprop; auto. + split. apply ind_sorts0. destruct indices_matter; auto. + eapply type_local_ctx_impl. eapply ind_sorts0. + intros. red in X14. + destruct T. + specialize (IH ((Σ, udecl); (X13; _; _; _; X14))). + apply IH. simpl. constructor 1. simpl. auto with arith. + destruct X14 as [u Hu]. exists u. + specialize (IH (existT _ (Σ, udecl) (existT _ X13 (existT _ _ (existT _ _ (existT _ _ Hu)))))). + apply IH. simpl. constructor 1. simpl. auto with arith. + ++ apply onIndices. + ++ red in onP |- *. + eapply All_local_env_impl; eauto. + intros. destruct T; simpl in X14. + specialize (IH (existT _ (Σ, udecl) (existT _ X13 (existT _ _ (existT _ _ (existT _ _ X14)))))). + simpl in IH. apply IH. constructor 1. simpl. lia. + destruct X14 as [u Hu]. + specialize (IH (existT _ (Σ, udecl) (existT _ X13 (existT _ _ (existT _ _ (existT _ _ Hu)))))). + simpl in IH. simpl. exists u. apply IH. constructor 1. simpl. lia. + + - assert (forall Γ t T (Hty : Σ ;;; Γ |- t : T), + typing_size Hty < typing_size H -> + Forall_decls_typing P Σ.1 * P Σ Γ t T). + intros. + specialize (IH (existT _ Σ (existT _ wfΣ (existT _ _ (existT _ _ (existT _ _ Hty)))))). + simpl in IH. + forward IH. + constructor 2. simpl. apply H0. + split; apply IH. clear IH. + rename X13 into X14. + + assert (All_local_env_over typing Pdecl Σ Γ (typing_wf_local H)). + { clear -Pdecl wfΣ X14. + pose proof (typing_wf_local_size H). + set (foo := typing_wf_local H) in *. + clearbody foo. + revert foo H0. generalize Γ at 1 2 4. + induction foo; simpl in *; try destruct t2 as [u Hu]; simpl in *; constructor. + - simpl in *. apply IHfoo. lia. + - red. eapply (X14 _ _ _ Hu). lia. + - simpl in *. apply IHfoo. lia. + - red. apply (X14 _ _ _ t3). lia. + - red. apply (X14 _ _ _ Hu). lia. } + eapply XΓ; eauto. + + - assert (forall Γ t T (Hty : Σ ;;; Γ |- t : T), + typing_size Hty < typing_size H -> + Forall_decls_typing P Σ.1 * P Σ Γ t T). + intros. + specialize (IH (existT _ Σ (existT _ wfΣ (existT _ _ (existT _ _ (existT _ _ Hty)))))). + simpl in IH. + forward IH. + constructor 2. simpl. apply H0. + split; apply IH. clear IH. + rename X13 into X14. + + assert (Hdecls: typing_size H > 1 -> Forall_decls_typing P Σ.1). + { specialize (X14 _ _ _ (type_Prop _)). + simpl in X14. intros Hle. apply X14. lia. } + + assert (All_local_env_over typing Pdecl Σ Γ (typing_wf_local H)). + { clear -Pdecl wfΣ X14. + pose proof (typing_wf_local_size H). + set (foo := typing_wf_local H) in *. + clearbody foo. + revert foo H0. generalize Γ at 1 2 4. + induction foo; simpl in *; try destruct t2 as [u Hu]; simpl in *; constructor. + - simpl in *. apply IHfoo. lia. + - red. eapply (X14 _ _ _ Hu). lia. + - simpl in *. apply IHfoo. lia. + - red. apply (X14 _ _ _ t3). lia. + - red. apply (X14 _ _ _ Hu). lia. } + apply XΓ in X13. all:auto. + + destruct H; + try solve [ match reverse goal with + H : _ |- _ => eapply H + end; eauto; + unshelve eapply X14; simpl; auto with arith]. + + -- match reverse goal with + H : _ |- _ => eapply H + end; eauto; + unshelve eapply X14; simpl; eauto with arith wf. + + -- match reverse goal with + H : _ |- _ => eapply H + end; eauto. all:try unshelve eapply X14; simpl; auto; try lia. + Unshelve. 2:exact H0. + simpl. intros. + eapply X14. instantiate (1 := Ht'). + simpl. lia. + + -- match reverse goal with + H : _ |- _ => eapply H + end; eauto. + simpl in Hdecls. apply Hdecls; lia. + + -- eapply X6; eauto. + apply Hdecls; simpl; lia. + + -- eapply X7; eauto. apply Hdecls; simpl; lia. + + -- destruct indnpar as [ind' npar']; + cbn in ind; cbn in npar; subst ind; subst npar. + eapply X8; eauto. + ++ eapply (X14 _ _ _ H); eauto. simpl; auto with arith. + ++ eapply (X14 _ _ _ H); eauto. simpl; auto with arith. + ++ simpl in *. + eapply (X14 _ _ _ H0); eauto. clear. lia. + ++ clear X13 Hdecls. revert a X14. simpl. clear. intros. + induction a; simpl in *. + ** constructor. + ** destruct r as [[? ?] ?]. constructor. + --- intuition eauto. + +++ eapply (X14 _ _ _ t); eauto. simpl; auto with arith. + lia. + +++ destruct s as [s Hs]. exists s; split; [auto|]. + eapply (X14 _ _ _ Hs); eauto. simpl; auto with arith. + lia. + --- apply IHa. auto. intros. + eapply (X14 _ _ _ Hty). lia. + + -- eapply X9; eauto. apply Hdecls; simpl. + pose proof (typing_size_pos H). lia. + eapply (X14 _ _ _ H). simpl. lia. + + -- clear X X0 X1 X2 X3 X4 X5 X6 X7 X8 X9 X11 X12. + eapply X10; eauto; clear X10. simpl in *. + * assert(forall (t T : term) (Hty : Σ;;; Γ |- t : T), + typing_size Hty < + S (all_size (fun x : def term => + ∑ s : Universe.t, Σ;;; Γ |- dtype x : tSort s) + (fun (x : def term) + (p : ∑ s : Universe.t, Σ;;; Γ |- dtype x : tSort s) => + typing_size p.π2) a0) -> + Forall_decls_typing P Σ.1 * P Σ Γ t T). + intros; eauto. eapply (X14 _ _ _ Hty); eauto. lia. + clear X13 X14 a Hdecls. + clear -a0 X. + induction a0; constructor. + destruct p as [s Hs]. exists s; split; auto. + apply (X (dtype x) (tSort s) Hs). simpl. lia. + apply IHa0. intros. eapply (X _ _ Hty); eauto. + simpl. lia. + * simpl in X14. + assert(forall Γ0 : context, + wf_local Σ Γ0 -> + forall (t T : term) (Hty : Σ;;; Γ0 |- t : T), + typing_size Hty < + S + (all_size _ (fun (x : def term) p => typing_size p) a1) -> + Forall_decls_typing P Σ.1 * P Σ Γ0 t T). + {intros. eapply (X14 _ _ _ Hty); eauto. lia. } + clear X14 X13. + clear e decl i a0 Hdecls i0. + remember (fix_context mfix) as mfixcontext. clear Heqmfixcontext. + + induction a1; econstructor; eauto. + ++ split; auto. + eapply (X _ (typing_wf_local p) _ _ p). simpl. lia. + ++ eapply IHa1. intros. + eapply (X _ X0 _ _ Hty). simpl; lia. + + -- clear X X0 X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X12. + eapply X11; eauto; clear X11. simpl in *. + * assert(forall (t T : term) (Hty : Σ;;; Γ |- t : T), + typing_size Hty < + S (all_size (fun x : def term => + ∑ s : Universe.t, Σ;;; Γ |- dtype x : tSort s) + (fun (x : def term) + (p : ∑ s : Universe.t, Σ;;; Γ |- dtype x : tSort s) => + typing_size p.π2) a0) -> + Forall_decls_typing P Σ.1 * P Σ Γ t T). + intros; eauto. eapply (X14 _ _ _ Hty); eauto. lia. + clear X13 X14 a Hdecls. + clear -a0 X. + induction a0; constructor. + destruct p as [s Hs]. exists s; split; auto. + apply (X (dtype x) (tSort s) Hs). simpl. lia. + apply IHa0. intros. eapply (X _ _ Hty); eauto. + simpl. lia. + * simpl in X14. + assert(forall Γ0 : context, + wf_local Σ Γ0 -> + forall (t T : term) (Hty : Σ;;; Γ0 |- t : T), + typing_size Hty < + S + (all_size (fun x : def term => (Σ;;; Γ ,,, fix_context mfix |- dbody x : lift0 #|fix_context mfix| (dtype x))%type) + (fun (x : def term) p => typing_size p) a1) -> + Forall_decls_typing P Σ.1 * P Σ Γ0 t T). + {intros. eapply (X14 _ _ _ Hty); eauto. lia. } + clear X14 X13. + clear e decl i a0 Hdecls i0. + remember (fix_context mfix) as mfixcontext. clear Heqmfixcontext. + + induction a1; econstructor; eauto. + ++ split; auto. + eapply (X _ (typing_wf_local p) _ _ p). simpl. lia. + ++ eapply IHa1. intros. + eapply (X _ X0 _ _ Hty). simpl; lia. +Qed. + Lemma typing_ind_env `{cf : checker_flags} : forall (P : global_env_ext -> context -> term -> term -> Type) (Pdecl := fun Σ Γ wfΓ t T tyT => P Σ Γ t T) @@ -824,287 +1253,8 @@ Lemma typing_ind_env `{cf : checker_flags} : Proof. intros P Pdecl PΓ; unfold env_prop. intros XΓ X X0 X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 Σ wfΣ Γ t T H. - (* NOTE (Danil): while porting to 8.9, I had to split original "pose" into 2 pieces, - otherwise it takes forever to execure the "pose", for some reason *) - pose (@Fix_F ({ Σ : _ & { wfΣ : wf Σ.1 & { Γ : context & - { t : term & { T : term & Σ ;;; Γ |- t : T }}}}})) as p0. - specialize (p0 (dlexprod (precompose lt (fun Σ => globenv_size (fst Σ))) - (fun Σ => precompose lt (fun x => typing_size (projT2 (projT2 (projT2 (projT2 x)))))))) as p. - set(foo := existT _ Σ (existT _ wfΣ (existT _ Γ (existT _ t (existT _ _ H)))) : { Σ : _ & { wfΣ : wf Σ.1 & { Γ : context & { t : term & { T : term & Σ ;;; Γ |- t : T }}}}}). - change Σ with (projT1 foo). - change Γ with (projT1 (projT2 (projT2 foo))). - change t with (projT1 (projT2 (projT2 (projT2 foo)))). - change T with (projT1 (projT2 (projT2 (projT2 (projT2 foo))))). - change H with (projT2 (projT2 (projT2 (projT2 (projT2 foo))))). - revert foo. - match goal with - |- let foo := _ in @?P foo => specialize (p (fun x => P x)) - end. - forward p; [ | apply p; apply wf_dlexprod; intros; apply wf_precompose; apply lt_wf]. - clear p. - clear Σ wfΣ Γ t T H. - intros (Σ & wfΣ & Γ & t & t0 & H). simpl. - intros IH. simpl in IH. - split. split. - destruct Σ as [Σ φ]. destruct Σ. - constructor. - cbn in wfΣ; inversion_clear wfΣ. auto. - inv wfΣ. - rename X14 into Xg. - constructor; auto. unfold Forall_decls_typing in IH. - - simple refine (let IH' := IH ((Σ, udecl); (X13; []; (tSort Universe.lProp); _; _)) in _). - shelve. simpl. apply type_Prop. - forward IH'. constructor 1; cbn. lia. - apply IH'; auto. - - simpl. simpl in *. - destruct d; simpl. - + destruct c; simpl in *. - destruct cst_body; simpl in *. - simpl. - intros. red in Xg. simpl in Xg. - specialize (IH (existT _ (Σ, udecl) (existT _ X13 (existT _ [] (existT _ _ (existT _ _ Xg)))))). - simpl in IH. - forward IH. constructor 1. simpl; lia. - apply IH. - red. simpl. red in Xg; simpl in Xg. - destruct Xg as [s Hs]. red. simpl. - specialize (IH (existT _ (Σ, udecl) (existT _ X13 (existT _ [] (existT _ _ (existT _ _ Hs)))))). - simpl in IH. - forward IH. constructor 1. simpl; lia. exists s. eapply IH. - + red in Xg. - destruct Xg as [onI onP onnp]; constructor; eauto. - eapply Alli_impl; eauto. clear onI onP onnp; intros n x Xg. - refine {| ind_indices := Xg.(ind_indices); - ind_arity_eq := Xg.(ind_arity_eq); - ind_cshapes := Xg.(ind_cshapes) |}. - - ++ apply onArity in Xg. destruct Xg as [s Hs]. exists s; auto. - specialize (IH (existT _ (Σ, udecl) (existT _ X13 (existT _ [] (existT _ _ (existT _ _ Hs)))))). - simpl in IH. simpl. apply IH; constructor 1; simpl; lia. - ++ pose proof Xg.(onConstructors) as Xg'. - eapply All2_impl; eauto. intros. - destruct X14 as [cass chead tyeq onctyp oncargs oncind]. - unshelve econstructor; eauto. - destruct onctyp as [s Hs]. - simpl in Hs. - specialize (IH (existT _ (Σ, udecl) (existT _ X13 (existT _ _ (existT _ _ (existT _ _ Hs)))))). - simpl in IH. simpl. exists s. simpl. apply IH; constructor 1; simpl; auto with arith. - eapply sorts_local_ctx_impl; eauto. simpl. intros. red in X14. - destruct T. - specialize (IH ((Σ, udecl); (X13; _; _; _; X14))). - apply IH. simpl. constructor 1. simpl. auto with arith. - destruct X14 as [u Hu]. exists u. - specialize (IH (existT _ (Σ, udecl) (existT _ X13 (existT _ _ (existT _ _ (existT _ _ Hu)))))). - apply IH. simpl. constructor 1. simpl. auto with arith. - clear -X13 IH oncind. - revert oncind. - generalize (List.rev (lift_context #|cshape_args y| 0 (ind_indices Xg))). - generalize (cshape_indices y). induction 1; constructor; auto. - red in p0 |- *. - specialize (IH (existT _ (Σ, udecl) (existT _ X13 (existT _ _ (existT _ _ (existT _ _ p0)))))). - apply IH. simpl. constructor 1. simpl. auto with arith. - ++ intros Hprojs; pose proof (onProjections Xg Hprojs); auto. - ++ destruct Xg. simpl. unfold check_ind_sorts in *. - destruct Universe.is_prop; auto. - destruct Universe.is_sprop; auto. - split. apply ind_sorts0. destruct indices_matter; auto. - eapply type_local_ctx_impl. eapply ind_sorts0. - intros. red in X14. - destruct T. - specialize (IH ((Σ, udecl); (X13; _; _; _; X14))). - apply IH. simpl. constructor 1. simpl. auto with arith. - destruct X14 as [u Hu]. exists u. - specialize (IH (existT _ (Σ, udecl) (existT _ X13 (existT _ _ (existT _ _ (existT _ _ Hu)))))). - apply IH. simpl. constructor 1. simpl. auto with arith. - ++ apply onIndices. - ++ red in onP |- *. - eapply All_local_env_impl; eauto. - intros. destruct T; simpl in X14. - specialize (IH (existT _ (Σ, udecl) (existT _ X13 (existT _ _ (existT _ _ (existT _ _ X14)))))). - simpl in IH. apply IH. constructor 1. simpl. lia. - destruct X14 as [u Hu]. - specialize (IH (existT _ (Σ, udecl) (existT _ X13 (existT _ _ (existT _ _ (existT _ _ Hu)))))). - simpl in IH. simpl. exists u. apply IH. constructor 1. simpl. lia. - - - assert (forall Γ t T (Hty : Σ ;;; Γ |- t : T), - typing_size Hty < typing_size H -> - Forall_decls_typing P Σ.1 * P Σ Γ t T). - intros. - specialize (IH (existT _ Σ (existT _ wfΣ (existT _ _ (existT _ _ (existT _ _ Hty)))))). - simpl in IH. - forward IH. - constructor 2. simpl. apply H0. - split; apply IH. clear IH. - rename X13 into X14. - - assert (All_local_env_over typing Pdecl Σ Γ (typing_wf_local H)). - { clear -Pdecl wfΣ X14. - pose proof (typing_wf_local_size H). - set (foo := typing_wf_local H) in *. - clearbody foo. - revert foo H0. generalize Γ at 1 2 4. - induction foo; simpl in *; try destruct t2 as [u Hu]; simpl in *; constructor. - - simpl in *. apply IHfoo. lia. - - red. eapply (X14 _ _ _ Hu). lia. - - simpl in *. apply IHfoo. lia. - - red. apply (X14 _ _ _ t3). lia. - - red. apply (X14 _ _ _ Hu). lia. } - eapply XΓ; eauto. - - - assert (forall Γ t T (Hty : Σ ;;; Γ |- t : T), - typing_size Hty < typing_size H -> - Forall_decls_typing P Σ.1 * P Σ Γ t T). - intros. - specialize (IH (existT _ Σ (existT _ wfΣ (existT _ _ (existT _ _ (existT _ _ Hty)))))). - simpl in IH. - forward IH. - constructor 2. simpl. apply H0. - split; apply IH. clear IH. - rename X13 into X14. - - assert (Hdecls: typing_size H > 1 -> Forall_decls_typing P Σ.1). - { specialize (X14 _ _ _ (type_Prop _)). - simpl in X14. intros Hle. apply X14. lia. } - - assert (All_local_env_over typing Pdecl Σ Γ (typing_wf_local H)). - { clear -Pdecl wfΣ X14. - pose proof (typing_wf_local_size H). - set (foo := typing_wf_local H) in *. - clearbody foo. - revert foo H0. generalize Γ at 1 2 4. - induction foo; simpl in *; try destruct t2 as [u Hu]; simpl in *; constructor. - - simpl in *. apply IHfoo. lia. - - red. eapply (X14 _ _ _ Hu). lia. - - simpl in *. apply IHfoo. lia. - - red. apply (X14 _ _ _ t3). lia. - - red. apply (X14 _ _ _ Hu). lia. } - apply XΓ in X13. all:auto. - - destruct H; - try solve [ match reverse goal with - H : _ |- _ => eapply H - end; eauto; - unshelve eapply X14; simpl; auto with arith]. - - -- match reverse goal with - H : _ |- _ => eapply H - end; eauto; - unshelve eapply X14; simpl; eauto with arith wf. - - -- match reverse goal with - H : _ |- _ => eapply H - end; eauto; unshelve eapply X14; simpl; auto; try lia. - - -- match reverse goal with - H : _ |- _ => eapply H - end; eauto. - simpl in Hdecls. apply Hdecls; lia. - - -- eapply X6; eauto. - apply Hdecls; simpl; lia. - - -- eapply X7; eauto. apply Hdecls; simpl; lia. - - -- destruct indnpar as [ind' npar']; - cbn in ind; cbn in npar; subst ind; subst npar. - eapply X8; eauto. - ++ eapply (X14 _ _ _ H); eauto. simpl; auto with arith. - ++ eapply (X14 _ _ _ H); eauto. simpl; auto with arith. - ++ simpl in *. - eapply (X14 _ _ _ H0); eauto. clear. lia. - ++ clear X13 Hdecls. revert a X14. simpl. clear. intros. - induction a; simpl in *. - ** constructor. - ** destruct r as [[? ?] ?]. constructor. - --- intuition eauto. - +++ eapply (X14 _ _ _ t); eauto. simpl; auto with arith. - lia. - +++ destruct s as [s Hs]. exists s; split; [auto|]. - eapply (X14 _ _ _ Hs); eauto. simpl; auto with arith. - lia. - --- apply IHa. auto. intros. - eapply (X14 _ _ _ Hty). lia. - - -- eapply X9; eauto. apply Hdecls; simpl. - pose proof (typing_size_pos H). lia. - eapply (X14 _ _ _ H). simpl. lia. - - -- clear X X0 X1 X2 X3 X4 X5 X6 X7 X8 X9 X11 X12. - eapply X10; eauto; clear X10. simpl in *. - * assert(forall (t T : term) (Hty : Σ;;; Γ |- t : T), - typing_size Hty < - S (all_size (fun x : def term => - ∑ s : Universe.t, Σ;;; Γ |- dtype x : tSort s) - (fun (x : def term) - (p : ∑ s : Universe.t, Σ;;; Γ |- dtype x : tSort s) => - typing_size p.π2) a0) -> - Forall_decls_typing P Σ.1 * P Σ Γ t T). - intros; eauto. eapply (X14 _ _ _ Hty); eauto. lia. - clear X13 X14 a Hdecls. - clear -a0 X. - induction a0; constructor. - destruct p as [s Hs]. exists s; split; auto. - apply (X (dtype x) (tSort s) Hs). simpl. lia. - apply IHa0. intros. eapply (X _ _ Hty); eauto. - simpl. lia. - * simpl in X14. - assert(forall Γ0 : context, - wf_local Σ Γ0 -> - forall (t T : term) (Hty : Σ;;; Γ0 |- t : T), - typing_size Hty < - S - (all_size _ (fun (x : def term) p => typing_size p) a1) -> - Forall_decls_typing P Σ.1 * P Σ Γ0 t T). - {intros. eapply (X14 _ _ _ Hty); eauto. lia. } - clear X14 X13. - clear e decl i a0 Hdecls i0. - remember (fix_context mfix) as mfixcontext. clear Heqmfixcontext. - - induction a1; econstructor; eauto. - ++ split; auto. - eapply (X _ (typing_wf_local p) _ _ p). simpl. lia. - ++ eapply IHa1. intros. - eapply (X _ X0 _ _ Hty). simpl; lia. - - -- clear X X0 X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X12. - eapply X11; eauto; clear X11. simpl in *. - * assert(forall (t T : term) (Hty : Σ;;; Γ |- t : T), - typing_size Hty < - S (all_size (fun x : def term => - ∑ s : Universe.t, Σ;;; Γ |- dtype x : tSort s) - (fun (x : def term) - (p : ∑ s : Universe.t, Σ;;; Γ |- dtype x : tSort s) => - typing_size p.π2) a0) -> - Forall_decls_typing P Σ.1 * P Σ Γ t T). - intros; eauto. eapply (X14 _ _ _ Hty); eauto. lia. - clear X13 X14 a Hdecls. - clear -a0 X. - induction a0; constructor. - destruct p as [s Hs]. exists s; split; auto. - apply (X (dtype x) (tSort s) Hs). simpl. lia. - apply IHa0. intros. eapply (X _ _ Hty); eauto. - simpl. lia. - * simpl in X14. - assert(forall Γ0 : context, - wf_local Σ Γ0 -> - forall (t T : term) (Hty : Σ;;; Γ0 |- t : T), - typing_size Hty < - S - (all_size (fun x : def term => (Σ;;; Γ ,,, fix_context mfix |- dbody x : lift0 #|fix_context mfix| (dtype x))%type) - (fun (x : def term) p => typing_size p) a1) -> - Forall_decls_typing P Σ.1 * P Σ Γ0 t T). - {intros. eapply (X14 _ _ _ Hty); eauto. lia. } - clear X14 X13. - clear e decl i a0 Hdecls i0. - remember (fix_context mfix) as mfixcontext. clear Heqmfixcontext. - - induction a1; econstructor; eauto. - ++ split; auto. - eapply (X _ (typing_wf_local p) _ _ p). simpl. lia. - ++ eapply IHa1. intros. - eapply (X _ X0 _ _ Hty). simpl; lia. + apply typing_ind_env_app_size; eauto. Qed. -Print Assumptions typing_ind_env. Ltac my_rename_hyp h th := match th with diff --git a/pcuic/theories/TemplateToPCUICCorrectness.v b/pcuic/theories/TemplateToPCUICCorrectness.v index 3b2c3b3a1..1e19bf359 100644 --- a/pcuic/theories/TemplateToPCUICCorrectness.v +++ b/pcuic/theories/TemplateToPCUICCorrectness.v @@ -339,10 +339,15 @@ Proof. rewrite mkApps_nonempty //. Qed. -Lemma trans_decompose_prod_assum : +(* This is if Template's decompose_prod_assum handled casts. This does not work unless the specs + use a stronger decompose_prod_assum in PCUIC, as decompose_prod_assum is used to check fixpoints types. + Would be fixed having contexts instead of lambda abstractions in the Ast for fixpoints, where casts + cannot be introduced. +*) +(*Lemma trans_decompose_prod_assum : forall Γ t, - let '(Δ, c) := AstUtils.decompose_prod_assum (S.map_context STy.strip_casts Γ) (STy.strip_casts t) in - decompose_prod_assum (trans_local (S.map_context STy.strip_casts Γ)) (trans (STy.strip_casts t)) = + let '(Δ, c) := AstUtils.decompose_prod_assum (S.map_context AstUtils.strip_casts Γ) (AstUtils.strip_casts t) in + decompose_prod_assum (trans_local (S.map_context AstUtils.strip_casts Γ)) (trans (AstUtils.strip_casts t)) = (trans_local Δ, trans c). Proof. intros Γ t. @@ -357,12 +362,32 @@ Proof. destruct args. * simpl. now apply IHt. * move: e. cbn [map]. - destruct (mkApps_ex (STy.strip_casts t) (STy.strip_casts t0) (map STy.strip_casts args)) as [f [? eq]]. + destruct (SL.mkApps_ex (AstUtils.strip_casts t) (AstUtils.strip_casts t0) (map AstUtils.strip_casts args)) as [f [? eq]]. rewrite eq. intros [= <- <-]. rewrite -eq. rewrite decompose_prod_assum_mkApps_nonnil //. f_equal. now rewrite trans_mkApps. Qed. +*) + +Lemma trans_decompose_prod_assum : + forall Γ t, + S.wf t -> + let '(Δ, c) := AstUtils.decompose_prod_assum Γ t in + decompose_prod_assum (trans_local Γ) (trans t) = (trans_local Δ, trans c). +Proof. + intros Γ t wf. + destruct AstUtils.decompose_prod_assum as [Δ c] eqn:e. + revert Γ Δ c e. + induction wf using Template.Induction.term_wf_forall_list_ind; intros. + all: try solve [ inversion e ; subst ; reflexivity ]. + - simpl in e. eapply IHwf0 in e as e'. now simpl. + - simpl. simpl in e. eapply (IHwf1 (Γ ,, Ast.vdef n t t0)) in e as e'. assumption. + - simpl in *. noconf e. simpl. + destruct l => //. + cbn [map]. + rewrite decompose_prod_assum_mkApps_nonnil //. +Qed. Lemma trans_build_branches_type : forall ind mdecl idecl args u p brtys, @@ -1102,15 +1127,16 @@ Lemma trans_cumul {cf} (Σ : Ast.global_env_ext) Γ T U : S.wf T -> S.wf U -> STy.cumul Σ Γ T U -> trans_global Σ ;;; trans_local Γ |- trans T <= trans U. Proof. - intros wfΣ wfΓ. - induction 3. constructor; auto. - eapply trans_leq_term in l; eauto. - now rewrite global_ext_constraints_trans. - pose proof r as H3. apply wf_red1 in H3; auto with wf. - apply trans_red1 in r; auto. econstructor 2; eauto with wf. - econstructor 3. - apply IHX; auto. apply wf_red1 in r; auto with wf. - apply trans_red1 in r; auto. + intros wfΣ. + induction 4. + - constructor; auto. + eapply trans_leq_term in l; eauto. + now rewrite global_ext_constraints_trans. + - pose proof r as H3. apply wf_red1 in H3; auto with wf. + apply trans_red1 in r; auto. econstructor 2; eauto with wf. + - econstructor 3. + apply IHX; auto. apply wf_red1 in r; auto with wf. + apply trans_red1 in r; auto. Qed. Definition Tlift_typing (P : Template.Ast.global_env_ext -> Tcontext -> Tterm -> Tterm -> Type) := @@ -1178,77 +1204,178 @@ Axiom cofix_guard_trans : STy.cofix_guard Σ Γ mfix -> cofix_guard (trans_global Σ) (trans_local Γ) (map (map_def trans trans) mfix). -Lemma trans_check_one_fix mfix : - check_one_fix (map_def trans trans mfix) = STy.check_one_fix mfix. +Notation Swf_fix def := (S.wf (dtype def) /\ S.wf (dbody def)). + +Lemma trans_subst_context s k Γ : + trans_local (SL.subst_context s k Γ) = subst_context (map trans s) k (trans_local Γ). +Proof. + induction Γ as [|[na [b|] ty] Γ]; simpl; auto. + - rewrite SL.subst_context_snoc /=. rewrite [subst_context _ _ _ ]subst_context_snoc. + f_equal; auto. rewrite IHΓ /snoc /subst_decl /map_decl /=; f_equal. + now rewrite !trans_subst map_length. + - rewrite SL.subst_context_snoc /=. rewrite [subst_context _ _ _ ]subst_context_snoc. + f_equal; auto. rewrite IHΓ /snoc /subst_decl /map_decl /=; f_equal. + now rewrite !trans_subst map_length. +Qed. + +Lemma trans_smash_context Γ Δ : trans_local (STy.smash_context Γ Δ) = smash_context (trans_local Γ) (trans_local Δ). +Proof. + induction Δ in Γ |- *; simpl; auto. + destruct a as [na [b|] ty] => /=. + rewrite IHΔ. f_equal. + now rewrite (trans_subst_context [_]). + rewrite IHΔ. f_equal. rewrite /trans_local map_app //. +Qed. + +Lemma trans_decompose_app {t ind u l} : + S.wf t -> + AstUtils.decompose_app t = (Ast.tInd ind u, l) -> + ∑ l', decompose_app (trans t) = (tInd ind u, l'). +Proof. + intros wft. destruct (AstUtils.decompose_app t) eqn:da. + pose proof (TypingWf.decompose_app_inv _ [] _ _ wft da) as [n [napp [eqsk ->]]]. + rewrite trans_mkApps. + intros [= -> ->]. + rewrite decompose_app_mkApps //. eexists _; eauto. +Qed. + +Lemma decompose_prod_assum_it_mkProd_or_LetIn ctx t ctx' t' : + AstUtils.decompose_prod_assum ctx t = (ctx', t') -> + Ast.it_mkProd_or_LetIn ctx t = Ast.it_mkProd_or_LetIn ctx' t'. +Proof. + induction t in ctx, ctx', t' |- *; simpl; try intros [= -> <-]; auto. + - intros H. now apply IHt2 in H. + - intros H. now apply IHt3 in H. +Qed. + +Lemma it_mkProd_or_LetIn_wf Γ t + : Ast.wf (Ast.it_mkProd_or_LetIn Γ t) <-> Forall wf_decl Γ /\ Ast.wf t . +Proof. + revert t. induction Γ. + - intros t. simpl. split => //; try split => //; trivial. now intros []. + - intros t. + destruct a as [na [b|] ty]; simpl in *. rewrite /Ast.mkProd_or_LetIn /=. + * rewrite IHΓ /=. split; intros []. + depelim H0. intuition constructor; auto. split; auto. + depelim H. red in H. simpl in H. split; auto with wf. constructor; intuition auto. + * rewrite IHΓ /=. split; intros []. + depelim H0. simpl in H0_. split; [constructor|];auto. + split; simpl; auto. + depelim H. destruct H as [_ wfty]. simpl in wfty. + split; auto. constructor; simpl; auto. +Qed. + +Lemma trans_check_one_fix mfix ind : + Swf_fix mfix -> + STy.check_one_fix mfix = Some ind -> + check_one_fix (map_def trans trans mfix) = Some ind. Proof. unfold STy.check_one_fix, check_one_fix. - destruct mfix as [na ty arg rarg] => /=. - move: (trans_decompose_prod_assum [] ty). simpl. - destruct decompose_prod_assum as [ctx p] => /=. + case: mfix => [na ty arg rarg] /= [wfty wfarg]. + move: (trans_decompose_prod_assum [] ty wfty) => /=. + destruct AstUtils.decompose_prod_assum as [ctx p] eqn:dp => /= // ->. rewrite -(trans_smash_context []) /trans_local. rewrite -List.map_rev nth_error_map. - destruct nth_error => /= //. - move: (trans_decompose_app (PCUICAst.decl_type c)). - destruct decompose_app => /=. - simpl. destruct c. simpl. intros ->. - now rewrite -trans_destInd. + destruct nth_error eqn:hnth => /= //. + destruct AstUtils.decompose_app eqn:da. + destruct t => //. + have [| l' eq] := (trans_decompose_app _ da). + { eapply decompose_prod_assum_it_mkProd_or_LetIn in dp. + simpl in dp; subst ty. + eapply it_mkProd_or_LetIn_wf in wfty as [wfctx _]. + eapply (nth_error_forall (P:=wf_decl)) in hnth; cycle 1. + eapply rev_Forall. + pose proof (nth_error_Some_length hnth). + rewrite nth_error_rev // List.rev_involutive in hnth. + now apply wf_smash_context. apply hnth. } + destruct c => /=. rewrite eq /= //. +Qed. + +Lemma Forall_map_option_out_map_Some_spec {A B} {f g : A -> option B} {P : A -> Prop} {l} : + (forall x t, P x -> f x = Some t -> g x = Some t) -> + Forall P l -> + forall t, + map_option_out (map f l) = Some t -> + map_option_out (map g l) = Some t. +Proof. + move => Hfg Hl. move: Hl. + induction 1; try constructor; auto. + simpl. move=> //. + case E: (f x) => [b|] //. + rewrite (Hfg _ _ H E). + case E' : map_option_out => [b'|] //. + move=> t [= <-]. now rewrite (IHHl _ E'). Qed. -Lemma map_option_out_check_one_fix mfix : - map (fun x => TS.check_one_fix (map_def trans trans x)) mfix = - map SS.check_one_fix mfix. +Lemma map_option_out_check_one_fix {mfix} : + Forall (fun def => (S.wf (dtype def) /\ S.wf (dbody def))) mfix -> + forall l, + map_option_out (map (fun x => STy.check_one_fix x) mfix) = Some l -> + map_option_out (map (fun x => check_one_fix (map_def trans trans x)) mfix) = Some l. Proof. - eapply map_ext => x. apply trans_check_one_fix. + eapply Forall_map_option_out_map_Some_spec => x kn. + apply trans_check_one_fix. Qed. - -Lemma trans_check_one_cofix mfix : - TS.check_one_cofix (map_def trans trans mfix) = SS.check_one_cofix mfix. +Lemma trans_check_one_cofix mfix ind : + Swf_fix mfix -> + STy.check_one_cofix mfix = Some ind -> + check_one_cofix (map_def trans trans mfix) = Some ind. Proof. - unfold SS.check_one_cofix, TS.check_one_cofix. - destruct mfix as [na ty arg rarg] => /=. - move: (trans_decompose_prod_assum [] ty). - destruct decompose_prod_assum as [ctx p] => -> /=. - move: (trans_decompose_app p). - destruct decompose_app => /= ->. - now rewrite -trans_destInd. + unfold STy.check_one_cofix, check_one_cofix. + case: mfix => [na ty arg rarg] /= [wfty wfarg]. + move: (trans_decompose_prod_assum [] ty wfty) => /=. + destruct AstUtils.decompose_prod_assum as [ctx p] eqn:dp => /= // ->. + destruct AstUtils.decompose_app eqn:da. + destruct t => //. + have [| l' ->] := (trans_decompose_app _ da) => //. + { eapply decompose_prod_assum_it_mkProd_or_LetIn in dp. + simpl in dp; subst ty. + now eapply it_mkProd_or_LetIn_wf in wfty as [_ wfp]. } Qed. -Lemma map_option_out_check_one_cofix mfix : - map (fun x => TS.check_one_cofix (map_def trans trans x)) mfix = - map SS.check_one_cofix mfix. +Lemma map_option_out_check_one_cofix {mfix} : + Forall (fun def => (S.wf (dtype def) /\ S.wf (dbody def))) mfix -> + forall l, + map_option_out (map (fun x => STy.check_one_cofix x) mfix) = Some l -> + map_option_out (map (fun x => check_one_cofix (map_def trans trans x)) mfix) = Some l. Proof. - eapply map_ext => x. apply trans_check_one_cofix. + apply Forall_map_option_out_map_Some_spec => x kn. + apply trans_check_one_cofix. Qed. -Lemma trans_check_rec_kind Σ k f : - SS.check_recursivity_kind Σ k f = TS.check_recursivity_kind (trans_global_decls Σ) k f. +Lemma trans_check_rec_kind {Σ k f} : + STy.check_recursivity_kind Σ k f = check_recursivity_kind (trans_global_decls Σ) k f. Proof. - unfold SS.check_recursivity_kind, TS.check_recursivity_kind. + unfold STy.check_recursivity_kind, check_recursivity_kind. rewrite trans_lookup. destruct S.lookup_env as [[]|] => //. Qed. Lemma trans_wf_fixpoint Σ mfix : - TS.wf_fixpoint (trans_global_decls Σ) (map (map_def trans trans) mfix) = - SS.wf_fixpoint Σ mfix. + Forall (fun def => (S.wf (dtype def) /\ S.wf (dbody def))) mfix -> + STy.wf_fixpoint Σ mfix -> + wf_fixpoint (trans_global_decls Σ) (map (map_def trans trans) mfix). Proof. - unfold SS.wf_fixpoint, TS.wf_fixpoint. + unfold STy.wf_fixpoint, wf_fixpoint. rewrite map_map_compose. - rewrite map_option_out_check_one_fix. - destruct map_option_out as [[]|] => //. - now rewrite trans_check_rec_kind. + intros wf. + destruct map_option_out eqn:ma => //. + rewrite (map_option_out_check_one_fix wf _ ma). + destruct l; auto. now rewrite -trans_check_rec_kind. Qed. Lemma trans_wf_cofixpoint Σ mfix : - TS.wf_cofixpoint (trans_global_decls Σ) (map (map_def trans trans) mfix) = - SS.wf_cofixpoint Σ mfix. + Forall (fun def => (S.wf (dtype def) /\ S.wf (dbody def))) mfix -> + STy.wf_cofixpoint Σ mfix -> + wf_cofixpoint (trans_global_decls Σ) (map (map_def trans trans) mfix). Proof. - unfold SS.wf_cofixpoint, TS.wf_cofixpoint. + unfold STy.wf_cofixpoint, wf_cofixpoint. rewrite map_map_compose. - rewrite map_option_out_check_one_cofix. - destruct map_option_out as [[]|] => //. - now rewrite trans_check_rec_kind. + intros wf. + destruct map_option_out eqn:ma => //. + rewrite (map_option_out_check_one_cofix wf _ ma). + destruct l; auto. now rewrite -trans_check_rec_kind. Qed. Lemma trans_global_decl_universes d : @@ -1406,7 +1533,10 @@ Proof. rewrite H2. rewrite /trans_local map_length. rewrite /trans_local map_app in X3. rewrite <- trans_lift. apply X3; auto. - -- todo "wffix". + -- eapply trans_wf_fixpoint => //. + solve_all. destruct a as [s [Hs IH]]. + now eapply TypingWf.typing_wf in Hs. + now eapply TypingWf.typing_wf in a0. -- destruct decl; reflexivity. - eapply refine_type. @@ -1428,7 +1558,10 @@ Proof. unfold Template.Ast.app_context in X3. rewrite /trans_local map_app in X3. cbn. rewrite <- trans_lift. now apply X3. - -- todo "wfcofix". + -- eapply trans_wf_cofixpoint => //. + solve_all. destruct a as [s [Hs IH]]. + now eapply TypingWf.typing_wf in Hs. + now eapply TypingWf.typing_wf in a0. -- destruct decl; reflexivity. - assert (S.wf B). @@ -1610,7 +1743,7 @@ Proof. eapply trans_on_global_env; eauto. simpl; intros. epose proof (STy.env_prop_typing _ template_to_pcuic _ X Γ). forward X2. - red in X0. destruct S. + red in X0. destruct T. now eapply STy.typing_wf_local. destruct X0 as [s Hs]. eapply STy.typing_wf_local; eauto. destruct T; simpl in *. diff --git a/template-coq/theories/Ast.v b/template-coq/theories/Ast.v index 8efdd5707..4b8a0dfc1 100644 --- a/template-coq/theories/Ast.v +++ b/template-coq/theories/Ast.v @@ -129,6 +129,7 @@ Inductive wf : term -> Prop := | wf_tCoFix mfix k : Forall (fun def => wf def.(dtype) /\ wf def.(dbody)) mfix -> wf (tCoFix mfix k) | wf_tInt i : wf (tInt i) | wf_tFloat f : wf (tFloat f). +Derive Signature for wf. (** ** Entries diff --git a/template-coq/theories/AstUtils.v b/template-coq/theories/AstUtils.v index 3b87bc290..37bf10920 100644 --- a/template-coq/theories/AstUtils.v +++ b/template-coq/theories/AstUtils.v @@ -171,7 +171,6 @@ Fixpoint decompose_prod_assum (Γ : context) (t : term) : context * term := match t with | tProd n A B => decompose_prod_assum (Γ ,, vass n A) B | tLetIn na b bty b' => decompose_prod_assum (Γ ,, vdef na b bty) b' - | tCast t _ _ => decompose_prod_assum Γ t | _ => (Γ, t) end. diff --git a/template-coq/theories/Typing.v b/template-coq/theories/Typing.v index f80caa02a..ba8633dfb 100644 --- a/template-coq/theories/Typing.v +++ b/template-coq/theories/Typing.v @@ -435,28 +435,33 @@ Reserved Notation " Σ ;;; Γ |- t = u " (at level 50, Γ, t, u at next level). (** ** Cumulativity: - The reflexive-transitive closure of reduction, expansion and term comparison up-to universes. + Reduction to terms in the leq_term relation. *) -Definition cumul `{checker_flags} (Σ : global_env_ext) (Γ : context) : term -> term -> Type := - Relation.clos_refl_trans (relation_disjunction (clos_sym (red1 Σ Γ)) (leq_term Σ Σ)). -Notation " Σ ;;; Γ |- t <= u " := (cumul Σ Γ t u) : type_scope. +Inductive cumul `{checker_flags} (Σ : global_env_ext) (Γ : context) : term -> term -> Type := +| cumul_refl t u : leq_term Σ (global_ext_constraints Σ) t u -> Σ ;;; Γ |- t <= u +| cumul_red_l t u v : red1 Σ.1 Γ t v -> Σ ;;; Γ |- v <= u -> Σ ;;; Γ |- t <= u +| cumul_red_r t u v : Σ ;;; Γ |- t <= v -> red1 Σ.1 Γ u v -> Σ ;;; Γ |- t <= u +where " Σ ;;; Γ |- t <= u " := (cumul Σ Γ t u) : type_scope. (** *** Conversion - The reflexive-symmetric-transitive closure of reduction, expansion and term comparison up-to universes. + Reduction to terms in the eq_term relation *) -Definition conv `{checker_flags} (Σ : global_env_ext) (Γ : context) : term -> term -> Type := - Relation.clos_refl_sym_trans (relation_disjunction (red1 Σ Γ) (eq_term Σ Σ)). -Notation " Σ ;;; Γ |- t = u " := (@conv _ Σ Γ t u) : type_scope. + Inductive conv `{checker_flags} (Σ : global_env_ext) (Γ : context) : term -> term -> Type := + | conv_refl t u : eq_term Σ (global_ext_constraints Σ) t u -> Σ ;;; Γ |- t = u + | conv_red_l t u v : red1 Σ.1 Γ t v -> Σ ;;; Γ |- v = u -> Σ ;;; Γ |- t = u + | conv_red_r t u v : Σ ;;; Γ |- t = v -> red1 Σ.1 Γ u v -> Σ ;;; Γ |- t = u + + where " Σ ;;; Γ |- t = u " := (@conv _ Σ Γ t u) : type_scope. Lemma conv_refl' `{checker_flags} : forall Σ Γ t, Σ ;;; Γ |- t = t. - intros. constructor. right. apply eq_term_refl. + intros. constructor. apply eq_term_refl. Defined. Lemma cumul_refl' `{checker_flags} : forall Σ Γ t, Σ ;;; Γ |- t <= t. - intros. constructor. right. apply leq_term_refl. + intros. constructor. apply leq_term_refl. Defined. Hint Resolve conv_refl' cumul_refl' : typecheck. @@ -666,7 +671,7 @@ Definition check_one_fix d := dtype := ty; dbody := b; rarg := arg |} := d in - let '(ctx, ty) := decompose_prod_assum [] (strip_casts ty) in + let '(ctx, ty) := decompose_prod_assum [] ty in match nth_error (List.rev (smash_context [] ctx)) arg with | Some argd => let (hd, args) := decompose_app argd.(decl_type) in @@ -693,7 +698,7 @@ Definition check_one_cofix d := dtype := ty; dbody := b; rarg := arg |} := d in - let '(ctx, ty) := decompose_prod_assum [] (strip_casts ty) in + let '(ctx, ty) := decompose_prod_assum [] ty in let (hd, args) := decompose_app ty in match destInd hd with | Some (mkInd ind _, u) => Some ind diff --git a/template-coq/theories/utils/MCRelations.v b/template-coq/theories/utils/MCRelations.v index ecfd3bbf9..f24839fc0 100644 --- a/template-coq/theories/utils/MCRelations.v +++ b/template-coq/theories/utils/MCRelations.v @@ -1,7 +1,7 @@ (* Distributed under the terms of the MIT license. *) Require Import ssreflect. -Require Import CRelationClasses. Require Import Equations.Type.Relation Equations.Type.Relation_Properties. +Require Import CRelationClasses. Infix "<~>" := iffT (at level 90). From 2ec7fe18a46158b1aaadeb9e6e04b0bfeb2004bb Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Sat, 12 Dec 2020 03:01:59 +0100 Subject: [PATCH 60/70] Cleaned up and documented PCUICToTemplateCorrectness --- pcuic/theories/PCUICAstUtils.v | 40 ++-- pcuic/theories/PCUICToTemplateCorrectness.v | 224 ++++++++------------ template-coq/theories/AstUtils.v | 4 + template-coq/theories/utils/All_Forall.v | 12 ++ 4 files changed, 128 insertions(+), 152 deletions(-) diff --git a/pcuic/theories/PCUICAstUtils.v b/pcuic/theories/PCUICAstUtils.v index 4c4754bad..f6afefa10 100644 --- a/pcuic/theories/PCUICAstUtils.v +++ b/pcuic/theories/PCUICAstUtils.v @@ -376,6 +376,34 @@ Proof. eapply decompose_app_rec_notApp. eassumption. Qed. + +Lemma decompose_app_rec_inv {t l' f l} : + decompose_app_rec t l' = (f, l) -> + mkApps t l' = mkApps f l. +Proof. + induction t in f, l', l |- *; try intros [= <- <-]; try reflexivity. + simpl. apply/IHt1. +Qed. + +Lemma decompose_app_inv {t f l} : + decompose_app t = (f, l) -> t = mkApps f l. +Proof. by apply/decompose_app_rec_inv. Qed. + +Lemma decompose_app_nonnil t f l : + isApp t -> + decompose_app t = (f, l) -> l <> []. +Proof. + intros isApp. + destruct t; simpl => //. + intros da. + pose proof (decompose_app_notApp _ _ _ da). + apply decompose_app_inv in da. + destruct l using rev_ind. + unfold decompose_app => /=. + destruct f => //. + destruct l => //. +Qed. + Fixpoint nApp t := match t with | tApp u _ => S (nApp u) @@ -450,18 +478,6 @@ Proof. - assumption. Qed. -Lemma decompose_app_rec_inv {t l' f l} : - decompose_app_rec t l' = (f, l) -> - mkApps t l' = mkApps f l. -Proof. - induction t in f, l', l |- *; try intros [= <- <-]; try reflexivity. - simpl. apply/IHt1. -Qed. - -Lemma decompose_app_inv {t f l} : - decompose_app t = (f, l) -> t = mkApps f l. -Proof. by apply/decompose_app_rec_inv. Qed. - Lemma mkApps_Fix_spec mfix idx args t : mkApps (tFix mfix idx) args = t -> match decompose_app t with | (tFix mfix idx, args') => args' = args diff --git a/pcuic/theories/PCUICToTemplateCorrectness.v b/pcuic/theories/PCUICToTemplateCorrectness.v index 047abc51f..5bdd399ab 100644 --- a/pcuic/theories/PCUICToTemplateCorrectness.v +++ b/pcuic/theories/PCUICToTemplateCorrectness.v @@ -38,13 +38,6 @@ Ltac solve_list := try rewrite !map_length; try solve_all; try typeclasses eauto with core. -Lemma mkAppMkApps s t: - mkApp s t = mkApps s [t]. -Proof. - cbn. unfold mkApp. - reflexivity. -Qed. - Lemma mapOne {X Y} (f:X->Y) x: map f [x] = [f x]. Proof. @@ -57,7 +50,7 @@ Proof. revert k. induction t using PCUICInduction.term_forall_list_ind; simpl; intros; try congruence. - f_equal. rewrite !map_map_compose. solve_all. - rewrite IHt1 IHt2. - rewrite mkAppMkApps. + rewrite AstUtils.mkAppMkApps. rewrite <- mapOne. rewrite <- TL.lift_mkApps. f_equal. @@ -118,8 +111,8 @@ Proof. Qed. Lemma trans_mem_level_set l Σ: -LevelSet.mem l (ST.global_ext_levels Σ) -> -LevelSet.mem l (TT.global_ext_levels (trans_global Σ)). + LevelSet.mem l (ST.global_ext_levels Σ) -> + LevelSet.mem l (TT.global_ext_levels (trans_global Σ)). Proof. intros. rewrite <- trans_global_ext_levels. @@ -127,8 +120,8 @@ Proof. Qed. Lemma trans_in_level_set l Σ: -LevelSet.In l (ST.global_ext_levels Σ) -> -LevelSet.In l (TT.global_ext_levels (trans_global Σ)). + LevelSet.In l (ST.global_ext_levels Σ) -> + LevelSet.In l (TT.global_ext_levels (trans_global Σ)). Proof. intros. rewrite <- trans_global_ext_levels. @@ -159,8 +152,8 @@ Proof. Qed. Lemma trans_constraintSet_in x Σ: -ConstraintSet.In x (ST.global_ext_constraints Σ) -> -ConstraintSet.In x (TT.global_ext_constraints (trans_global Σ)). + ConstraintSet.In x (ST.global_ext_constraints Σ) -> + ConstraintSet.In x (TT.global_ext_constraints (trans_global Σ)). Proof. rewrite trans_global_ext_constraints. trivial. @@ -217,28 +210,14 @@ Proof. reflexivity. Qed. - Lemma trans_decl_type decl: -trans (PCUICAst.decl_type decl) = -decl_type (trans_decl decl). + trans (PCUICAst.decl_type decl) = + decl_type (trans_decl decl). Proof. destruct decl. reflexivity. Qed. -Lemma All_forall {X Y} (f:X->Y->Prop) xs: - All (fun a => forall b, f a b) xs -> - (forall b, All (fun a => f a b) xs). -Proof. - intros. - induction X0. - - constructor. - - constructor. - + apply p. - + apply IHX0. -Qed. - - Lemma trans_subst xs k t: trans (SL.subst xs k t) = TL.subst (map trans xs) k (trans t). @@ -302,8 +281,8 @@ Qed. Lemma trans_subst10 u B: -trans (SL.subst1 u 0 B)= -TL.subst10 (trans u) (trans B). + trans (SL.subst1 u 0 B) = + TL.subst10 (trans u) (trans B). Proof. unfold SL.subst1. rewrite trans_subst. @@ -311,8 +290,8 @@ Proof. Qed. Lemma trans_subst_instance_constr u t: -trans (PCUICUnivSubst.subst_instance_constr u t) = -Template.UnivSubst.subst_instance_constr u (trans t). + trans (PCUICUnivSubst.subst_instance_constr u t) = + Template.UnivSubst.subst_instance_constr u (trans t). Proof. induction t using PCUICInduction.term_forall_list_ind;cbn;auto;try congruence. - do 2 rewrite map_map. @@ -320,7 +299,7 @@ Proof. apply All_map_eq. apply X. - rewrite IHt1 IHt2. - do 2 rewrite mkAppMkApps. + do 2 rewrite AstUtils.mkAppMkApps. rewrite subst_instance_constr_mkApps. cbn. reflexivity. @@ -361,26 +340,26 @@ Proof. Qed. Lemma trans_cst_type decl: -trans (PCUICAst.cst_type decl) = -cst_type (trans_constant_body decl). + trans (PCUICAst.cst_type decl) = + cst_type (trans_constant_body decl). Proof. reflexivity. Qed. Lemma trans_ind_type idecl: -trans (PCUICAst.ind_type idecl) = -ind_type (trans_one_ind_body idecl). + trans (PCUICAst.ind_type idecl) = + ind_type (trans_one_ind_body idecl). Proof. reflexivity. Qed. Lemma trans_type_of_constructor mdecl cdecl ind i u: -trans (ST.type_of_constructor mdecl cdecl (ind, i) u) = -TT.type_of_constructor - (trans_minductive_body mdecl) - (trans_ctor cdecl) - (ind,i) - u. + trans (ST.type_of_constructor mdecl cdecl (ind, i) u) = + TT.type_of_constructor + (trans_minductive_body mdecl) + (trans_ctor cdecl) + (ind,i) + u. Proof. unfold ST.type_of_constructor. rewrite trans_subst. @@ -407,24 +386,24 @@ Proof. Qed. Lemma trans_dtype decl: -trans (dtype decl) = -dtype (trans_def decl). + trans (dtype decl) = + dtype (trans_def decl). Proof. destruct decl. reflexivity. Qed. Lemma trans_dbody decl: -trans (dbody decl) = -dbody (trans_def decl). + trans (dbody decl) = + dbody (trans_def decl). Proof. destruct decl. reflexivity. Qed. Lemma trans_declared_projection Σ mdecl idecl p pdecl : -ST.declared_projection Σ.1 mdecl idecl p pdecl -> -TT.declared_projection (trans_global Σ).1 (trans_minductive_body mdecl) (trans_one_ind_body idecl) p (on_snd trans pdecl). + ST.declared_projection Σ.1 mdecl idecl p pdecl -> + TT.declared_projection (trans_global Σ).1 (trans_minductive_body mdecl) (trans_one_ind_body idecl) p (on_snd trans pdecl). Proof. intros (?&?&?). split;[|split]. @@ -452,7 +431,6 @@ Proof. repeat split;eassumption. Qed. - Lemma trans_instantiate_params params pars ty: option_map trans (ST.instantiate_params @@ -487,7 +465,7 @@ Proof. Qed. Lemma trans_instantiate_params' u mdecl args npar x ty : -ST.instantiate_params + ST.instantiate_params (PCUICUnivSubst.subst_instance_context u (PCUICAst.ind_params mdecl)) (firstn npar args) ty = @@ -529,8 +507,8 @@ Proof. Qed. Lemma trans_destr_arity x: - AstUtils.destArity [] (trans x) - = option_map (fun '(xs,u) => (map trans_decl xs,u)) (PCUICAstUtils.destArity [] x). + AstUtils.destArity [] (trans x) = + option_map (fun '(xs,u) => (map trans_decl xs,u)) (PCUICAstUtils.destArity [] x). Proof. remember (@nil PCUICAst.context_decl) as xs. replace (@nil context_decl) with (map trans_decl xs) by (now subst). @@ -871,8 +849,6 @@ Proof. now destruct a as [? [] ?];rewrite <- IHl;cbn. Qed. - - Definition TTwf_local {cf} Σ Γ := TT.All_local_env (TT.lift_typing TT.typing Σ) Γ. Lemma trans_wf_local' {cf} : @@ -1284,10 +1260,21 @@ Axiom cofix_guard_trans : TT.cofix_guard (trans_global Σ) (trans_local Γ) (map (map_def trans trans) mfix). (* This version of typing spine allows to not require [isType] assumptions at the end of the - application chain, which is crucial to be able to build an application spine *) - + application chain, which is crucial to be able to build a spine that both encompasses PCUIC's + applications and mimicks the typing rule of Template. Otherwise we would only model: + + |- tProd na A B : s + |- f : tProd na A B + |- u : A + *** |- B [0 := u] : s *** <- this last hypothesis is problematic, it's not present in PCUIC + ------------------------ derivations for example. + |- tApp f u : B [0 := u] + +*) + +Import PCUICAst PCUICLiftSubst PCUICTyping. Inductive typing_spine {cf} (Σ : global_env_ext) (Γ : context) : term -> list term -> term -> Type := -| type_spine_eq ty : typing_spine Σ Γ ty [] ty +| type_spine_eq ty : typing_spine Σ Γ ty [] ty | type_spine_nil ty ty' : isType Σ Γ ty' -> @@ -1300,7 +1287,9 @@ Inductive typing_spine {cf} (Σ : global_env_ext) (Γ : context) : term -> list Σ ;;; Γ |- hd : A -> typing_spine Σ Γ (subst10 hd B) tl B' -> typing_spine Σ Γ T (hd :: tl) B'. +Derive Signature for typing_spine. +(* The size of a spine is the maximal depth of any typing derivation appearing in it *) Section Typing_Spine_size. Context `{checker_flags}. Context {Σ : global_env_ext} {Γ : context}. @@ -1314,9 +1303,7 @@ Section Typing_Spine_size. end. End Typing_Spine_size. -Require Import PCUICArities. - -Require Import PCUICSpine. +(* We can weaken a spine by cumulativity, using the type_spine_nil *) Lemma typing_spine_weaken_concl {cf:checker_flags} {Σ Γ T args S S'} : wf Σ.1 -> typing_spine Σ Γ T args S -> @@ -1331,6 +1318,7 @@ Proof. eauto. Defined. +(* The size includes the new [isType] hypothesis *) Lemma typing_spine_weaken_concl_size {cf:checker_flags} {Σ Γ T args S S'} (wf : wf Σ.1) (sp :typing_spine Σ Γ T args S) @@ -1343,45 +1331,12 @@ Proof. rewrite - !Nat.max_assoc. specialize (IHsp Hs). lia. Qed. -Lemma typing_spine_strengthen {cf:checker_flags} Σ Γ T args U : - wf Σ.1 -> - typing_spine Σ Γ T args U -> - forall T', Σ ;;; Γ |- T' <= T -> - isType Σ Γ T -> - typing_spine Σ Γ T' args U. -Proof. - induction 2 in |- *; intros T' (*WAT*)redT. - - intros. econstructor 2. eauto. eauto. - - intros. econstructor 2. eauto. transitivity ty; auto. - - specialize (IHX0 (B {0 := hd})). - forward IHX0. { reflexivity. } - intros. eapply type_spine_cons with na A B; auto. - etransitivity; eauto. -Qed. -(* -Lemma typing_spine_app {cf:checker_flags} Σ Γ ty args na A B arg : - wf Σ.1 -> - isType Σ Γ (tProd na A B) -> - typing_spine Σ Γ ty args (tProd na A B) -> - Σ ;;; Γ |- arg : A -> - typing_spine Σ Γ ty (args ++ [arg]) (B {0 := arg}). -Proof. - intros wfΣ isty H; revert arg. - remember (tProd na A B) as prod. - revert na A B Heqprod. - induction H. - - intros na A B eq arg Harg. simpl. econstructor; eauto. now rewrite <-eq. now rewrite <-eq. - constructor. - - intros na A B eq arg Harg. simpl. - econstructor; eauto. rewrite <- eq. exact i. now rewrite <- eq. constructor. - - intros na' A' B'' eq arg Harg. simpl. - econstructor. apply i. auto. auto. - eapply IHtyping_spine. now rewrite eq. exact eq. apply Harg. -Defined. - *) - Ltac sig := unshelve eexists. +(** We can also append an argument to a spine *without* requiring a typing for the new conclusion type. + This would be a derivation for a substitution of [B], hence incomparable in depth to the arguments. + The invariant is witnessed by the spine size being lower than the arguments. +*) Lemma typing_spine_app {cf:checker_flags} Σ Γ ty args na A B arg (wf : wf Σ.1) (isty : isType Σ Γ (tProd na A B)) @@ -1391,26 +1346,24 @@ Lemma typing_spine_app {cf:checker_flags} Σ Γ ty args na A B arg typing_spine_size sp' <= max (typing_size isty.π2) (max (typing_spine_size sp) (typing_size argd)). Proof. revert arg argd. - remember (tProd na A B) as prod. symmetry in Heqprod. - revert na A B Heqprod. - induction sp. - - intros na A B eq arg Harg. simpl. + depind sp. + - intros arg Harg. simpl. sig. - * econstructor; eauto. now rewrite -> eq. now rewrite -> eq. + * econstructor; eauto. apply cumul_refl'. constructor. - * destruct eq => /=. unfold eq_rect_r. simpl. lia. - - intros na A B eq arg Harg. simpl. + * simpl. lia. + - intros arg Harg. simpl. sig. - * econstructor; eauto. rewrite -> eq. exact i. - now rewrite -> eq. constructor. - * simpl. destruct eq. unfold eq_rect_r. simpl. lia. - - intros na' A' B'' eq arg Harg. simpl. - specialize (IHsp isty _ _ _ eq _ Harg) as [sp' Hsp']. + * econstructor; eauto. constructor. + * simpl. lia. + - intros arg Harg. simpl. + specialize (IHsp wf isty _ Harg) as [sp' Hsp']. sig. * econstructor. apply i. auto. auto. exact sp'. - * destruct eq. simpl. lia. + * simpl. lia. Qed. +(** Likewise, in Template-Coq, we can append without re-typing the result *) Lemma TT_typing_spine_app {cf:checker_flags} Σ Γ ty T' args na A B arg s : TT.typing Σ Γ (T.tProd na A B) (T.tSort s) -> TT.typing_spine Σ Γ ty args T' -> @@ -1430,27 +1383,10 @@ Proof. eapply IHtyping_spine. now rewrite eq. exact eq. apply Harg. apply X. Defined. - -Lemma destrb (b : bool) : b + ~~ b. -Proof. - destruct b. left; auto. right; auto. -Defined. - -Lemma decompose_app_napp_nonnil t f l : - isApp t -> - decompose_app t = (f, l) -> - ~~ is_empty l. -Proof. - intros isApp. - destruct t; simpl => //. - intros da. - pose proof (decompose_app_notApp _ _ _ da). - apply decompose_app_inv in da. - destruct l using rev_ind. - unfold decompose_app => /=. - destruct f => //. - destruct l => //. -Qed. +(** This is the central lemma for this translation: + any PCUIC typing of an application `t` can be decomposed as + a typing of the head of `t` followed by a typing spine for + its arguments `l`. *) Lemma type_app {cf} {Σ Γ t T} (d : Σ ;;; Γ |- t : T) : wf Σ.1 -> @@ -1470,7 +1406,7 @@ Proof. simpl in da. apply decompose_app_rec_inv' in da as [n [napp [equ eqt]]]. subst t. clear IHd1 IHd3. - rewrite decompose_app_mkApps // in IHd2. + rewrite PCUICAstUtils.decompose_app_mkApps // in IHd2. destruct IHd2 as [fty [d' [sp hd']]]. exists fty, d'. split. lia. @@ -1481,7 +1417,7 @@ Proof. intros app happ. exists app. lia. unfold decompose_app. simpl. - rewrite atom_decompose_app. destruct t => /= //. + rewrite PCUICAstUtils.atom_decompose_app. destruct t => /= //. exists _, d2. split. lia. unshelve eexists. econstructor. exists s; eauto. reflexivity. assumption. constructor. @@ -1490,7 +1426,7 @@ Proof. - destruct (isApp t) eqn:isapp => //. destruct (decompose_app t) eqn:da. assert (l <> []). - { eapply decompose_app_napp_nonnil in da => //. destruct l => //. } + { eapply decompose_app_nonnil in da => //. } destruct IHd1 as [fty [d' [? ?]]]. exists fty, d'. split. lia. destruct s0 as [sp Hsp]. @@ -1498,6 +1434,12 @@ Proof. epose proof (typing_spine_weaken_concl_size wfΣ sp c (s; d2)). simpl in H0. lia. Qed. +(** Finally, for each typing spine built above, assuming we can apply the induction hypothesis + of the translation to any of the typing derivations in the spine, then we can produce a typing + spine in the n-ary application template-coq spec. + + We have two cases to consider at the "end" of the spine: either we have the same translation of the + PCUIC conclusion type, or there is exactly one cumulativity step to get to this type. *) Lemma make_typing_spine {cf} {Σ Γ fty l T} (sp : typing_spine Σ Γ fty l T) n (IH : forall t' T' (Ht' : Σ ;;; Γ |- t' : T'), @@ -1548,7 +1490,9 @@ Theorem pcuic_to_template {cf} (Σ : S.global_env_ext) Γ t T : Proof. intros X X0. revert Σ X Γ t T X0. - apply (typing_ind_env (fun Σ Γ t T => + (** We use an induction principle allowing to apply induction to any subderivation of + functions in applications. *) + apply (typing_ind_env_app_size (fun Σ Γ t T => TT.typing (trans_global Σ) (trans_local Γ) (trans t) (trans T) )%type (fun Σ Γ wfΓ => @@ -1572,7 +1516,7 @@ Proof. intros [fty [d' [hd' [sp hsp]]]]. assert (IHt := X3 _ _ d' hd'). epose proof (make_typing_spine sp (typing_size Ht) X3 hsp) as [T' [IH []]]. - * subst T'. rewrite (decompose_app_inv da). + * subst T'. rewrite (PCUICAstUtils.decompose_app_inv da). rewrite trans_mkApps mkApp_mkApps AstUtils.mkApps_nested. pose proof (AstUtils.mkApps_nested (trans t0) (map trans l) [trans u]). apply decompose_app_notApp in da. @@ -1583,7 +1527,7 @@ Proof. apply IH. apply TT.cumul_refl'. apply X5. * destruct p as [hcum _]. - rewrite (decompose_app_inv da). + rewrite (PCUICAstUtils.decompose_app_inv da). rewrite trans_mkApps mkApp_mkApps AstUtils.mkApps_nested. pose proof (AstUtils.mkApps_nested (trans t0) (map trans l) [trans u]). apply decompose_app_notApp in da. diff --git a/template-coq/theories/AstUtils.v b/template-coq/theories/AstUtils.v index 37bf10920..76a3786b1 100644 --- a/template-coq/theories/AstUtils.v +++ b/template-coq/theories/AstUtils.v @@ -90,6 +90,10 @@ Proof. rewrite <- mkApps_nested. reflexivity. Qed. +Lemma mkAppMkApps s t: + mkApp s t = mkApps s [t]. +Proof. reflexivity. Qed. + Lemma mkApp_tApp f u : isApp f = false -> mkApp f u = tApp f [u]. Proof. intros. destruct f; (discriminate || reflexivity). Qed. diff --git a/template-coq/theories/utils/All_Forall.v b/template-coq/theories/utils/All_Forall.v index aa28009fe..f1ce69c67 100644 --- a/template-coq/theories/utils/All_Forall.v +++ b/template-coq/theories/utils/All_Forall.v @@ -1951,3 +1951,15 @@ Proof. now apply H; simpl. apply IHl. intros x xin; apply H; simpl; auto. Qed. + +Lemma All_forall {X Y} (f:X->Y->Prop) xs: + All (fun a => forall b, f a b) xs -> + (forall b, All (fun a => f a b) xs). +Proof. + intros. + induction X0. + - constructor. + - constructor. + + apply p. + + apply IHX0. +Qed. \ No newline at end of file From 23b0060f264fe179a3a0efc9f19b3572baea1030 Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Sat, 12 Dec 2020 03:35:41 +0100 Subject: [PATCH 61/70] Fix compilation --- template-coq/_PluginProject | 4 + .../gen-src/metacoq_template_plugin.mlpack | 2 + template-coq/gen-src/specFloat.ml.orig | 553 ------------------ 3 files changed, 6 insertions(+), 553 deletions(-) delete mode 100644 template-coq/gen-src/specFloat.ml.orig diff --git a/template-coq/_PluginProject b/template-coq/_PluginProject index 13baec6c9..ae326e125 100644 --- a/template-coq/_PluginProject +++ b/template-coq/_PluginProject @@ -81,6 +81,10 @@ gen-src/list0.ml gen-src/list0.mli gen-src/logic0.ml gen-src/logic0.mli +gen-src/logic1.mli +gen-src/logic1.ml +gen-src/relation.mli +gen-src/relation.ml gen-src/mCPrelude.mli gen-src/mCPrelude.ml gen-src/mCCompare.ml diff --git a/template-coq/gen-src/metacoq_template_plugin.mlpack b/template-coq/gen-src/metacoq_template_plugin.mlpack index 2eb7057d0..56c7d8efa 100644 --- a/template-coq/gen-src/metacoq_template_plugin.mlpack +++ b/template-coq/gen-src/metacoq_template_plugin.mlpack @@ -30,6 +30,8 @@ CRelationClasses Compare_dec Classes0 EqDecInstances +Logic1 +Relation MCPrelude MCList MCRelations diff --git a/template-coq/gen-src/specFloat.ml.orig b/template-coq/gen-src/specFloat.ml.orig deleted file mode 100644 index 48bad30a5..000000000 --- a/template-coq/gen-src/specFloat.ml.orig +++ /dev/null @@ -1,553 +0,0 @@ -open BinInt -open BinPos -open Bool -open Datatypes -open Zbool -open Zpower - -type spec_float = -| S754_zero of bool -| S754_infinity of bool -| S754_nan -| S754_finite of bool * int * int - -(** val emin : int -> int -> int **) - -let emin prec emax = - Z.sub (Z.sub ((fun p->1+2*p) 1) emax) prec - -(** val fexp : int -> int -> int -> int **) - -let fexp prec emax e = - Z.max (Z.sub e prec) (emin prec emax) - -(** val digits2_pos : int -> int **) - -let rec digits2_pos n = - (fun f2p1 f2p f1 p -> - if p<=1 then f1 () else if p mod 2 = 0 then f2p (p/2) else f2p1 (p/2)) - (fun p -> Pos.succ (digits2_pos p)) - (fun p -> Pos.succ (digits2_pos p)) - (fun _ -> 1) - n - -(** val coq_Zdigits2 : int -> int **) - -let coq_Zdigits2 n = - (fun f0 fp fn z -> if z=0 then f0 () else if z>0 then fp z else fn (-z)) - (fun _ -> n) - (fun p -> (digits2_pos p)) - (fun p -> (digits2_pos p)) - n - -(** val canonical_mantissa : int -> int -> int -> int -> bool **) - -let canonical_mantissa prec emax m e = - coq_Zeq_bool (fexp prec emax (Z.add (digits2_pos m) e)) e - -(** val bounded : int -> int -> int -> int -> bool **) - -let bounded prec emax m e = - (&&) (canonical_mantissa prec emax m e) (Z.leb e (Z.sub emax prec)) - -(** val valid_binary : int -> int -> spec_float -> bool **) - -let valid_binary prec emax = function -| S754_finite (_, m, e) -> bounded prec emax m e -| _ -> true - -(** val iter_pos : ('a1 -> 'a1) -> int -> 'a1 -> 'a1 **) - -let rec iter_pos f n x = - (fun f2p1 f2p f1 p -> - if p<=1 then f1 () else if p mod 2 = 0 then f2p (p/2) else f2p1 (p/2)) - (fun n' -> iter_pos f n' (iter_pos f n' (f x))) - (fun n' -> iter_pos f n' (iter_pos f n' x)) - (fun _ -> f x) - n - -type location = -| Coq_loc_Exact -| Coq_loc_Inexact of comparison - -(** val location_rect : 'a1 -> (comparison -> 'a1) -> location -> 'a1 **) - -let location_rect f f0 = function -| Coq_loc_Exact -> f -| Coq_loc_Inexact x -> f0 x - -(** val location_rec : 'a1 -> (comparison -> 'a1) -> location -> 'a1 **) - -let location_rec f f0 = function -| Coq_loc_Exact -> f -| Coq_loc_Inexact x -> f0 x - -type shr_record = { shr_m : int; shr_r : bool; shr_s : bool } - -(** val shr_m : shr_record -> int **) - -let shr_m s = - s.shr_m - -(** val shr_r : shr_record -> bool **) - -let shr_r s = - s.shr_r - -(** val shr_s : shr_record -> bool **) - -let shr_s s = - s.shr_s - -(** val shr_1 : shr_record -> shr_record **) - -let shr_1 mrs = - let { shr_m = m; shr_r = r; shr_s = s } = mrs in - let s0 = (||) r s in - ((fun f0 fp fn z -> if z=0 then f0 () else if z>0 then fp z else fn (-z)) - (fun _ -> { shr_m = 0; shr_r = false; shr_s = s0 }) - (fun p0 -> - (fun f2p1 f2p f1 p -> - if p<=1 then f1 () else if p mod 2 = 0 then f2p (p/2) else f2p1 (p/2)) - (fun p -> { shr_m = p; shr_r = true; shr_s = s0 }) - (fun p -> { shr_m = p; shr_r = false; shr_s = s0 }) - (fun _ -> { shr_m = 0; shr_r = true; shr_s = s0 }) - p0) - (fun p0 -> - (fun f2p1 f2p f1 p -> - if p<=1 then f1 () else if p mod 2 = 0 then f2p (p/2) else f2p1 (p/2)) - (fun p -> { shr_m = ((~-) p); shr_r = true; shr_s = s0 }) - (fun p -> { shr_m = ((~-) p); shr_r = false; shr_s = s0 }) - (fun _ -> { shr_m = 0; shr_r = true; shr_s = s0 }) - p0) - m) - -(** val loc_of_shr_record : shr_record -> location **) - -let loc_of_shr_record mrs = - let { shr_m = _; shr_r = shr_r0; shr_s = shr_s0 } = mrs in - if shr_r0 - then if shr_s0 then Coq_loc_Inexact Gt else Coq_loc_Inexact Eq - else if shr_s0 then Coq_loc_Inexact Lt else Coq_loc_Exact - -(** val shr_record_of_loc : int -> location -> shr_record **) - -let shr_record_of_loc m = function -| Coq_loc_Exact -> { shr_m = m; shr_r = false; shr_s = false } -| Coq_loc_Inexact c -> - (match c with - | Eq -> { shr_m = m; shr_r = true; shr_s = false } - | Lt -> { shr_m = m; shr_r = false; shr_s = true } - | Gt -> { shr_m = m; shr_r = true; shr_s = true }) - -(** val shr : shr_record -> int -> int -> shr_record * int **) - -let shr mrs e n = - (fun f0 fp fn z -> if z=0 then f0 () else if z>0 then fp z else fn (-z)) - (fun _ -> (mrs, e)) - (fun p -> ((iter_pos shr_1 p mrs), (Z.add e n))) - (fun _ -> (mrs, e)) - n - -(** val shr_fexp : - int -> int -> int -> int -> location -> shr_record * int **) - -let shr_fexp prec emax m e l = - shr (shr_record_of_loc m l) e - (Z.sub (fexp prec emax (Z.add (coq_Zdigits2 m) e)) e) - -(** val round_nearest_even : int -> location -> int **) - -let round_nearest_even mx = function -| Coq_loc_Exact -> mx -| Coq_loc_Inexact c -> - (match c with - | Eq -> if Z.even mx then mx else Z.add mx 1 - | Lt -> mx - | Gt -> Z.add mx 1) - -(** val binary_round_aux : - int -> int -> bool -> int -> int -> location -> spec_float **) - -let binary_round_aux prec emax sx mx ex lx = - let (mrs', e') = shr_fexp prec emax mx ex lx in - let (mrs'', e'') = - shr_fexp prec emax - (round_nearest_even mrs'.shr_m (loc_of_shr_record mrs')) e' - Coq_loc_Exact - in - ((fun f0 fp fn z -> if z=0 then f0 () else if z>0 then fp z else fn (-z)) - (fun _ -> S754_zero sx) - (fun m -> - if Z.leb e'' (Z.sub emax prec) - then S754_finite (sx, m, e'') - else S754_infinity sx) - (fun _ -> S754_nan) - mrs''.shr_m) - -(** val shl_align : int -> int -> int -> int * int **) - -let shl_align mx ex ex' = - (fun f0 fp fn z -> if z=0 then f0 () else if z>0 then fp z else fn (-z)) - (fun _ -> (mx, ex)) - (fun _ -> (mx, ex)) - (fun d -> ((shift_pos d mx), ex')) - (Z.sub ex' ex) - -(** val binary_round : int -> int -> bool -> int -> int -> spec_float **) - -let binary_round prec emax sx mx ex = - let (mz, ez) = shl_align mx ex (fexp prec emax (Z.add (digits2_pos mx) ex)) - in - binary_round_aux prec emax sx mz ez Coq_loc_Exact - -(** val binary_normalize : int -> int -> int -> int -> bool -> spec_float **) - -let binary_normalize prec emax m e szero = - (fun f0 fp fn z -> if z=0 then f0 () else if z>0 then fp z else fn (-z)) - (fun _ -> S754_zero szero) - (fun m0 -> binary_round prec emax false m0 e) - (fun m0 -> binary_round prec emax true m0 e) - m - -(** val coq_SFopp : spec_float -> spec_float **) - -let coq_SFopp = function -| S754_zero sx -> S754_zero (negb sx) -| S754_infinity sx -> S754_infinity (negb sx) -| S754_nan -> S754_nan -| S754_finite (sx, mx, ex) -> S754_finite ((negb sx), mx, ex) - -(** val coq_SFabs : spec_float -> spec_float **) - -let coq_SFabs = function -| S754_zero _ -> S754_zero false -| S754_infinity _ -> S754_infinity false -| S754_nan -> S754_nan -| S754_finite (_, mx, ex) -> S754_finite (false, mx, ex) - -(** val coq_SFcompare : spec_float -> spec_float -> comparison option **) - -let coq_SFcompare f1 f2 = - match f1 with - | S754_zero _ -> - (match f2 with - | S754_zero _ -> Some Eq - | S754_infinity s -> Some (if s then Gt else Lt) - | S754_nan -> None - | S754_finite (s, _, _) -> Some (if s then Gt else Lt)) - | S754_infinity s -> - (match f2 with - | S754_infinity s0 -> - Some (if s then if s0 then Eq else Lt else if s0 then Gt else Eq) - | S754_nan -> None - | _ -> Some (if s then Lt else Gt)) - | S754_nan -> None - | S754_finite (s1, m1, e1) -> - (match f2 with - | S754_zero _ -> Some (if s1 then Lt else Gt) - | S754_infinity s -> Some (if s then Gt else Lt) - | S754_nan -> None - | S754_finite (s2, m2, e2) -> - Some - (if s1 - then if s2 - then (match Z.compare e1 e2 with - | Eq -> coq_CompOpp (Pos.compare_cont Eq m1 m2) - | Lt -> Gt - | Gt -> Lt) - else Lt - else if s2 - then Gt - else (match Z.compare e1 e2 with - | Eq -> Pos.compare_cont Eq m1 m2 - | x -> x))) - -(** val coq_SFeqb : spec_float -> spec_float -> bool **) - -let coq_SFeqb f1 f2 = - match coq_SFcompare f1 f2 with - | Some c -> (match c with - | Eq -> true - | _ -> false) - | None -> false - -(** val coq_SFltb : spec_float -> spec_float -> bool **) - -let coq_SFltb f1 f2 = - match coq_SFcompare f1 f2 with - | Some c -> (match c with - | Lt -> true - | _ -> false) - | None -> false - -(** val coq_SFleb : spec_float -> spec_float -> bool **) - -let coq_SFleb f1 f2 = - match coq_SFcompare f1 f2 with - | Some _ -> true - | None -> false - -(** val coq_SFclassify : int -> spec_float -> Float64.float_class **) - -let coq_SFclassify prec = function -| S754_zero s -> if s then PZero else NZero -| S754_infinity s -> if s then NInf else PInf -| S754_nan -> NaN -| S754_finite (s, m, _) -> - if s - then if Pos.eqb (digits2_pos m) (Z.to_pos prec) then NNormal else NSubn - else if Pos.eqb (digits2_pos m) (Z.to_pos prec) then PNormal else PSubn - -(** val coq_SFmul : int -> int -> spec_float -> spec_float -> spec_float **) - -let coq_SFmul prec emax x y = - match x with - | S754_zero sx -> - (match y with - | S754_zero sy -> S754_zero (xorb sx sy) - | S754_finite (sy, _, _) -> S754_zero (xorb sx sy) - | _ -> S754_nan) - | S754_infinity sx -> - (match y with - | S754_infinity sy -> S754_infinity (xorb sx sy) - | S754_finite (sy, _, _) -> S754_infinity (xorb sx sy) - | _ -> S754_nan) - | S754_nan -> S754_nan - | S754_finite (sx, mx, ex) -> - (match y with - | S754_zero sy -> S754_zero (xorb sx sy) - | S754_infinity sy -> S754_infinity (xorb sx sy) - | S754_nan -> S754_nan - | S754_finite (sy, my, ey) -> - binary_round_aux prec emax (xorb sx sy) (Pos.mul mx my) (Z.add ex ey) - Coq_loc_Exact) - -(** val cond_Zopp : bool -> int -> int **) - -let cond_Zopp b m = - if b then Z.opp m else m - -(** val coq_SFadd : int -> int -> spec_float -> spec_float -> spec_float **) - -let coq_SFadd prec emax x y = - match x with - | S754_zero sx -> - (match y with - | S754_zero sy -> if eqb sx sy then x else S754_zero false - | S754_nan -> S754_nan - | _ -> y) - | S754_infinity sx -> - (match y with - | S754_infinity sy -> if eqb sx sy then x else S754_nan - | S754_nan -> S754_nan - | _ -> x) - | S754_nan -> S754_nan - | S754_finite (sx, mx, ex) -> - (match y with - | S754_zero _ -> x - | S754_infinity _ -> y - | S754_nan -> S754_nan - | S754_finite (sy, my, ey) -> - let ez = Z.min ex ey in - binary_normalize prec emax - (Z.add (cond_Zopp sx (fst (shl_align mx ex ez))) - (cond_Zopp sy (fst (shl_align my ey ez)))) ez false) - -(** val coq_SFsub : int -> int -> spec_float -> spec_float -> spec_float **) - -let coq_SFsub prec emax x y = - match x with - | S754_zero sx -> - (match y with - | S754_zero sy -> if eqb sx (negb sy) then x else S754_zero false - | S754_infinity sy -> S754_infinity (negb sy) - | S754_nan -> S754_nan - | S754_finite (sy, my, ey) -> S754_finite ((negb sy), my, ey)) - | S754_infinity sx -> - (match y with - | S754_infinity sy -> if eqb sx (negb sy) then x else S754_nan - | S754_nan -> S754_nan - | _ -> x) - | S754_nan -> S754_nan - | S754_finite (sx, mx, ex) -> - (match y with - | S754_zero _ -> x - | S754_infinity sy -> S754_infinity (negb sy) - | S754_nan -> S754_nan - | S754_finite (sy, my, ey) -> - let ez = Z.min ex ey in - binary_normalize prec emax - (Z.sub (cond_Zopp sx (fst (shl_align mx ex ez))) - (cond_Zopp sy (fst (shl_align my ey ez)))) ez false) - -(** val new_location_even : int -> int -> location **) - -let new_location_even nb_steps k = - if coq_Zeq_bool k 0 - then Coq_loc_Exact - else Coq_loc_Inexact (Z.compare (Z.mul ((fun p->2*p) 1) k) nb_steps) - -(** val new_location_odd : int -> int -> location **) - -let new_location_odd nb_steps k = - if coq_Zeq_bool k 0 - then Coq_loc_Exact - else Coq_loc_Inexact - (match Z.compare (Z.add (Z.mul ((fun p->2*p) 1) k) 1) nb_steps with - | Eq -> Lt - | x -> x) - -(** val new_location : int -> int -> location **) - -let new_location nb_steps = - if Z.even nb_steps - then new_location_even nb_steps - else new_location_odd nb_steps - -(** val coq_SFdiv_core_binary : - int -> int -> int -> int -> int -> int -> (int * int) * location **) - -let coq_SFdiv_core_binary prec emax m1 e1 m2 e2 = - let d1 = coq_Zdigits2 m1 in - let d2 = coq_Zdigits2 m2 in - let e' = - Z.min (fexp prec emax (Z.sub (Z.add d1 e1) (Z.add d2 e2))) (Z.sub e1 e2) - in - let s = Z.sub (Z.sub e1 e2) e' in - let m' = - (fun f0 fp fn z -> if z=0 then f0 () else if z>0 then fp z else fn (-z)) - (fun _ -> m1) - (fun _ -> Z.shiftl m1 s) - (fun _ -> 0) - s - in - let (q, r) = Z.div_eucl m' m2 in ((q, e'), (new_location m2 r)) - -(** val coq_SFdiv : int -> int -> spec_float -> spec_float -> spec_float **) - -let coq_SFdiv prec emax x y = - match x with - | S754_zero sx -> - (match y with - | S754_infinity sy -> S754_zero (xorb sx sy) - | S754_finite (sy, _, _) -> S754_zero (xorb sx sy) - | _ -> S754_nan) - | S754_infinity sx -> - (match y with - | S754_zero sy -> S754_infinity (xorb sx sy) - | S754_finite (sy, _, _) -> S754_infinity (xorb sx sy) - | _ -> S754_nan) - | S754_nan -> S754_nan - | S754_finite (sx, mx, ex) -> - (match y with - | S754_zero sy -> S754_infinity (xorb sx sy) - | S754_infinity sy -> S754_zero (xorb sx sy) - | S754_nan -> S754_nan - | S754_finite (sy, my, ey) -> - let (p, lz) = coq_SFdiv_core_binary prec emax mx ex my ey in - let (mz, ez) = p in binary_round_aux prec emax (xorb sx sy) mz ez lz) - -(** val coq_SFsqrt_core_binary : - int -> int -> int -> int -> (int * int) * location **) - -let coq_SFsqrt_core_binary prec emax m e = - let d = coq_Zdigits2 m in - let e' = Z.min (fexp prec emax (Z.div2 (Z.add (Z.add d e) 1))) (Z.div2 e) in - let s = Z.sub e (Z.mul ((fun p->2*p) 1) e') in - let m' = - (fun f0 fp fn z -> if z=0 then f0 () else if z>0 then fp z else fn (-z)) - (fun _ -> m) - (fun _ -> Z.shiftl m s) - (fun _ -> 0) - s - in - let (q, r) = Z.sqrtrem m' in - let l = - if coq_Zeq_bool r 0 - then Coq_loc_Exact - else Coq_loc_Inexact (if Z.leb r q then Lt else Gt) - in - ((q, e'), l) - -(** val coq_SFsqrt : int -> int -> spec_float -> spec_float **) - -let coq_SFsqrt prec emax x = match x with -| S754_zero _ -> x -| S754_infinity s -> if s then S754_nan else x -| S754_nan -> S754_nan -| S754_finite (sx, mx, ex) -> - if sx - then S754_nan - else let (p, lz) = coq_SFsqrt_core_binary prec emax mx ex in - let (mz, ez) = p in binary_round_aux prec emax false mz ez lz - -(** val coq_SFnormfr_mantissa : int -> spec_float -> int **) - -let coq_SFnormfr_mantissa prec = function -| S754_finite (_, mx, ex) -> if Z.eqb ex (Z.opp prec) then mx else 0 -| _ -> 0 - -(** val coq_SFldexp : int -> int -> spec_float -> int -> spec_float **) - -let coq_SFldexp prec emax f e = - match f with - | S754_finite (sx, mx, ex) -> binary_round prec emax sx mx (Z.add ex e) - | _ -> f - -(** val coq_SFfrexp : int -> int -> spec_float -> spec_float * int **) - -let coq_SFfrexp prec emax f = match f with -| S754_finite (sx, mx, ex) -> - if Pos.leb (Z.to_pos prec) (digits2_pos mx) - then ((S754_finite (sx, mx, (Z.opp prec))), (Z.add ex prec)) - else let d = Z.sub prec (digits2_pos mx) in - ((S754_finite (sx, (shift_pos (Z.to_pos d) mx), (Z.opp prec))), - (Z.sub (Z.add ex prec) d)) -| _ -> (f, (Z.sub (Z.mul ((~-) ((fun p->2*p) 1)) emax) prec)) - -(** val coq_SFone : int -> int -> spec_float **) - -let coq_SFone prec emax = - binary_round prec emax false 1 0 - -(** val coq_SFulp : int -> int -> spec_float -> spec_float **) - -let coq_SFulp prec emax x = - coq_SFldexp prec emax (coq_SFone prec emax) - (fexp prec emax (snd (coq_SFfrexp prec emax x))) - -(** val coq_SFpred_pos : int -> int -> spec_float -> spec_float **) - -let coq_SFpred_pos prec emax x = match x with -| S754_finite (_, mx, _) -> - let d = - if Pos.eqb ((fun p->2*p) mx) (shift_pos (Z.to_pos prec) 1) - then coq_SFldexp prec emax (coq_SFone prec emax) - (fexp prec emax (Z.sub (snd (coq_SFfrexp prec emax x)) 1)) - else coq_SFulp prec emax x - in - coq_SFsub prec emax x d -| _ -> x - -(** val coq_SFmax_float : int -> int -> spec_float **) - -let coq_SFmax_float prec emax = - S754_finite (false, (Pos.sub (shift_pos (Z.to_pos prec) 1) 1), - (Z.sub emax prec)) - -(** val coq_SFsucc : int -> int -> spec_float -> spec_float **) - -let coq_SFsucc prec emax x = match x with -| S754_zero _ -> coq_SFldexp prec emax (coq_SFone prec emax) (emin prec emax) -| S754_infinity s -> if s then coq_SFopp (coq_SFmax_float prec emax) else x -| S754_nan -> x -| S754_finite (s, _, _) -> - if s - then coq_SFopp (coq_SFpred_pos prec emax (coq_SFopp x)) - else coq_SFadd prec emax x (coq_SFulp prec emax x) - -(** val coq_SFpred : int -> int -> spec_float -> spec_float **) - -let coq_SFpred prec emax f = - coq_SFopp (coq_SFsucc prec emax (coq_SFopp f)) From f8ab08d661a22326935db696a1eba3aa789893a9 Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Sat, 12 Dec 2020 04:10:06 +0100 Subject: [PATCH 62/70] Really remove all references to the old checker --- INSTALL.md | 3 +-- README.md | 12 ++-------- configure.sh | 24 +++++++------------ coq-metacoq-checker.opam | 43 ----------------------------------- coq-metacoq-erasure.opam | 1 - coq-metacoq-pcuic.opam | 1 - coq-metacoq-safechecker.opam | 1 - coq-metacoq-translations.opam | 1 - coq-metacoq.opam | 1 - 9 files changed, 11 insertions(+), 76 deletions(-) delete mode 100644 coq-metacoq-checker.opam diff --git a/INSTALL.md b/INSTALL.md index e12f0c11a..6b25d1a10 100644 --- a/INSTALL.md +++ b/INSTALL.md @@ -25,7 +25,6 @@ MetaCoq is split into multiple packages that get all installed using the `coq-metacoq` meta-package: - `coq-metacoq-template` for the Template Monad and quoting plugin - - `coq-metacoq-checker` for the UNverified checker of template-coq terms - `coq-metacoq-pcuic` for the PCUIC development and proof of the Template-Coq -> PCUIC translation - `coq-metacoq-safechecker` for the verified checker on PCUIC terms @@ -103,7 +102,7 @@ the sources directory. Then use: -- `make` to compile the `template-coq` plugin, the `checker`, the `pcuic` +- `make` to compile the `template-coq` plugin, the `pcuic` development and the `safechecker` and `erasure` plugins. You can also selectively build each target. diff --git a/README.md b/README.md index 1e7d14171..34b5bf328 100644 --- a/README.md +++ b/README.md @@ -69,21 +69,13 @@ In addition to this representation of terms, Template Coq includes: checker, and inserting them in the global environment, in the style of MTac. - -### [Checker](https://github.com/MetaCoq/metacoq/tree/coq-8.11/checker) - -A partial type-checker for the Calculus of Inductive Constructions, -whose extraction to ML is runnable as a plugin (using command `MetaCoq -Check foo`). This checker uses _fuel_, so it must be passed a number -of maximal reduction steps to perform when calling conversion, and is -NOT verified. - +- A formalisation of the expected typing rules reflecting the ones of Coq ### [PCUIC](https://github.com/MetaCoq/metacoq/tree/coq-8.11/pcuic) PCUIC, the Polymorphic Cumulative Calculus of Inductive Constructions is a cleaned up version of the term language of Coq and its associated -type system, equivalent to the one of Coq. This version of the +type system, shown equivalent to the one of Coq. This version of the calculus has proofs of standard metatheoretical results: - Weakening for global declarations, weakening and substitution for diff --git a/configure.sh b/configure.sh index efe799abe..6ad783a21 100755 --- a/configure.sh +++ b/configure.sh @@ -6,8 +6,6 @@ make -f Makefile mrproper # Dependencies for local or global builds. # When building the packages separately, dependencies are not set as everything # should already be available in $(COQMF_LIB)/user-contrib/MetaCoq/* -# checker is treated specially: due to code generation, we rebuild the template-coq module locally -# when building the checker package # For local builds, we set specific dependencies of each subproject in */metacoq-config # CWD=`pwd` @@ -18,39 +16,33 @@ then if [ "$1" = "local" ]; then echo "Building MetaCoq locally" - CHECKER_DEPS="-R ../template-coq/theories MetaCoq.Template -I ../template-coq/build" - PCUIC_MLDEPS="-I ../checker/src" - PCUIC_VDEPS="-R ../checker/theories MetaCoq.Checker" - SAFECHECKER_DEPS="${PCUIC_VDEPS} -R ../pcuic/theories MetaCoq.PCUIC" + PCUIC_DEPS="-I ../template-coq/build -R ../template-coq/theories MetaCoq.Template" + SAFECHECKER_DEPS="-R ../pcuic/theories MetaCoq.PCUIC" ERASURE_DEPS="-R ../safechecker/theories MetaCoq.SafeChecker" - TRANSLATIONS_DEPS="${PCUIC_VDEPS}" + TRANSLATIONS_DEPS="" else echo "Building MetaCoq globally (default)" # To find the metacoq template plugin - CHECKER_DEPS="-I ${COQLIB}/user-contrib/MetaCoq/Template" # The pcuic plugin depends on the checker plugin # The safechecker and erasure plugins are self-contained # These dependencies should not be necessary when separate linking of ocaml object # files is supported by coq_makefile - PCUIC_MLDEPS="-I ${COQLIB}/user-contrib/MetaCoq/Checker" + PCUIC_MLDEPS="" PCUIC_VDEPS="" SAFECHECKER_DEPS="" ERASURE_DEPS="" TRANSLATIONS_DEPS="" fi - echo "# DO NOT EDIT THIS FILE: autogenerated from ./configure.sh" > checker/metacoq-config echo "# DO NOT EDIT THIS FILE: autogenerated from ./configure.sh" > pcuic/metacoq-config echo "# DO NOT EDIT THIS FILE: autogenerated from ./configure.sh" > safechecker/metacoq-config echo "# DO NOT EDIT THIS FILE: autogenerated from ./configure.sh" > erasure/metacoq-config echo "# DO NOT EDIT THIS FILE: autogenerated from ./configure.sh" > translations/metacoq-config - echo ${CHECKER_DEPS} >> checker/metacoq-config - # echo "OCAMLPATH = \"${CWD}/template-coq\"" >> checker/metacoq-config - echo ${CHECKER_DEPS} ${PCUIC_MLDEPS} ${PCUIC_VDEPS} >> pcuic/metacoq-config - echo ${CHECKER_DEPS} ${SAFECHECKER_DEPS} >> safechecker/metacoq-config - echo ${CHECKER_DEPS} ${SAFECHECKER_DEPS} ${ERASURE_DEPS} >> erasure/metacoq-config - echo ${CHECKER_DEPS} ${TRANSLATIONS_DEPS} >> translations/metacoq-config + echo ${PCUIC_DEPS} >> pcuic/metacoq-config + echo ${PCUIC_DEPS} ${SAFECHECKER_DEPS} >> safechecker/metacoq-config + echo ${PCUIC_DEPS} ${SAFECHECKER_DEPS} ${ERASURE_DEPS} >> erasure/metacoq-config + echo ${PCUIC_DEPS} ${TRANSLATIONS_DEPS} >> translations/metacoq-config else echo "Error: coqc not found in path" fi diff --git a/coq-metacoq-checker.opam b/coq-metacoq-checker.opam deleted file mode 100644 index d916ec282..000000000 --- a/coq-metacoq-checker.opam +++ /dev/null @@ -1,43 +0,0 @@ -opam-version: "2.0" -maintainer: "matthieu.sozeau@inria.fr" -homepage: "https://metacoq.github.io/metacoq" -dev-repo: "git+https://github.com/MetaCoq/metacoq.git#coq-8.11" -bug-reports: "https://github.com/MetaCoq/metacoq/issues" -authors: ["Abhishek Anand " - "Simon Boulier " - "Cyril Cohen " - "Yannick Forster " - "Fabian Kunze " - "Gregory Malecha " - "Matthieu Sozeau " - "Nicolas Tabareau " - "Théo Winterhalter " -] -license: "MIT" -build: [ - ["sh" "./configure.sh"] - [make "-j%{jobs}%" "checker"] -] -install: [ - [make "-C" "checker" "install"] -] -depends: [ - "ocaml" {>= "4.07.1"} - "coq" {>= "8.11" & < "8.12~"} - "coq-equations" { >= "1.2.3" } - "coq-metacoq-template" {= version} -] -synopsis: "Specification of Coq's type theory and reference checker implementation" -description: """ -MetaCoq is a meta-programming framework for Coq. - -The Checker module provides a complete specification of Coq's typing and conversion -relation along with a reference type-checker that is extracted to a pluging. - -This provides a command: `MetaCoq Check [global_reference]` that can be used -to typecheck a Coq definition using the verified type-checker. -""" -# url { -# src: "https://github.com/MetaCoq/metacoq/archive/v2.1-beta3.tar.gz" -# checksum: "md5=e81b8ecabef788a10337a39b095d54f3" -# } diff --git a/coq-metacoq-erasure.opam b/coq-metacoq-erasure.opam index 69b30542f..9d7a860ae 100644 --- a/coq-metacoq-erasure.opam +++ b/coq-metacoq-erasure.opam @@ -25,7 +25,6 @@ depends: [ "ocaml" {>= "4.07.1"} "coq" {>= "8.11" & < "8.12~"} "coq-metacoq-template" {= version} - "coq-metacoq-checker" {= version} "coq-metacoq-pcuic" {= version} "coq-metacoq-safechecker" {= version} ] diff --git a/coq-metacoq-pcuic.opam b/coq-metacoq-pcuic.opam index 036bb4b8a..9c4a037fb 100644 --- a/coq-metacoq-pcuic.opam +++ b/coq-metacoq-pcuic.opam @@ -26,7 +26,6 @@ depends: [ "coq" {>= "8.11" & < "8.12~"} "coq-equations" {>= "1.2.3"} "coq-metacoq-template" {= version} - "coq-metacoq-checker" {= version} ] synopsis: "A type system equivalent to Coq's and its metatheory" description: """ diff --git a/coq-metacoq-safechecker.opam b/coq-metacoq-safechecker.opam index ae18056f1..e1de6d3fb 100644 --- a/coq-metacoq-safechecker.opam +++ b/coq-metacoq-safechecker.opam @@ -25,7 +25,6 @@ depends: [ "ocaml" {>= "4.07.1"} "coq" {>= "8.11" & < "8.12~"} "coq-metacoq-template" {= version} - "coq-metacoq-checker" {= version} "coq-metacoq-pcuic" {= version} ] synopsis: "Implementation and verification of safe conversion and typechecking algorithms for Coq" diff --git a/coq-metacoq-translations.opam b/coq-metacoq-translations.opam index e9c4c3ef4..fd0922062 100644 --- a/coq-metacoq-translations.opam +++ b/coq-metacoq-translations.opam @@ -21,7 +21,6 @@ depends: [ "ocaml" {>= "4.07.1"} "coq" {>= "8.11" & < "8.12~"} "coq-metacoq-template" {= version} - "coq-metacoq-checker" {= version} ] synopsis: "Translations built on top of MetaCoq" description: """ diff --git a/coq-metacoq.opam b/coq-metacoq.opam index 2dcc212ae..d9d4fb8de 100644 --- a/coq-metacoq.opam +++ b/coq-metacoq.opam @@ -18,7 +18,6 @@ depends: [ "ocaml" {>= "4.07.1"} "coq" {>= "8.11" & < "8.12~"} "coq-metacoq-template" {= version} - "coq-metacoq-checker" {= version} "coq-metacoq-pcuic" {= version} "coq-metacoq-safechecker" {= version} "coq-metacoq-erasure" {= version} From f6e977dae1283864142b2f3c6e4ff98e09ba5360 Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Sat, 12 Dec 2020 04:24:09 +0100 Subject: [PATCH 63/70] Put the Checker in Template Coq as it can be used to play with reified terms --- template-coq/_CoqProject | 1 + template-coq/theories/Checker.v | 912 +++++++++++++++++++++++++++ translations/param_cheap_packed.v | 3 +- translations/param_generous_packed.v | 3 +- translations/param_original.v | 5 +- translations/times_bool_fun.v | 3 +- translations/translation_utils.v | 3 +- 7 files changed, 921 insertions(+), 9 deletions(-) create mode 100644 template-coq/theories/Checker.v diff --git a/template-coq/_CoqProject b/template-coq/_CoqProject index fa2e539e5..16ab96933 100644 --- a/template-coq/_CoqProject +++ b/template-coq/_CoqProject @@ -43,6 +43,7 @@ theories/Reduction.v theories/TypingWf.v theories/Normal.v theories/WcbvEval.v +theories/Checker.v # The Template monad theories/TemplateMonad.v diff --git a/template-coq/theories/Checker.v b/template-coq/theories/Checker.v new file mode 100644 index 000000000..7de4536e3 --- /dev/null +++ b/template-coq/theories/Checker.v @@ -0,0 +1,912 @@ +(* Distributed under the terms of the MIT license. *) +From MetaCoq.Template Require Import config Ast AstUtils utils + LiftSubst UnivSubst uGraph Typing. + +(** * Coq type-checker for kernel terms + + Implemets [typecheck_program] which returns an error and + on success should guarantee that the term has the given type. + Currently uses fuel to implement reduction and is unverified. + + This file implements reduction with a stack machine [reduce_stack], + conversion/cumulativity with the first-order fast-path heuristic [isconv] + that are used to type-check terms in reasonable time. *) + + +Local Notation " () " := Datatypes.unit : type_scope. +Local Notation " () " := tt. + +Module RedFlags. + + Record t := mk + { beta : bool; + iota : bool; + zeta : bool; + delta : bool; + fix_ : bool; + cofix_ : bool }. + + Definition default := mk true true true true true true. +End RedFlags. + +Section Reduce. + Context (flags : RedFlags.t) (Σ : global_env). + + Definition zip (t : term * list term) := mkApps (fst t) (snd t). + + Fixpoint reduce_stack (Γ : context) (n : nat) (t : term) (stack : list term) + : option (term * list term) := + match n with 0 => None | S n => + match t with + + | tRel c => + if RedFlags.zeta flags then + d <- nth_error Γ c ;; + match d.(decl_body) with + | None => ret (t, stack) + | Some b => reduce_stack Γ n (lift0 (S c) b) stack + end + else ret (t, stack) + + | tLetIn _ b _ c => + if RedFlags.zeta flags then + reduce_stack Γ n (subst10 b c) stack + else ret (t, stack) + + | tConst c u => + if RedFlags.delta flags then + match lookup_env Σ c with + | Some (ConstantDecl {| cst_body := Some body |}) => + let body' := subst_instance_constr u body in + reduce_stack Γ n body' stack + | _ => ret (t, stack) + end + else ret (t, stack) + + | tApp f args => reduce_stack Γ n f (args ++ stack) + + | tLambda na ty b => + if RedFlags.beta flags then + match stack with + | a :: args' => + (** CBN reduction: we do not reduce arguments before substitution *) + (* a' <- reduce_stack Γ n a [] ;; *) + reduce_stack Γ n (subst10 a b) args' + | _ => ret (t, stack) + (* b' <- reduce_stack (Γ ,, vass na ty) n b stack ;; *) + (* ret (tLambda na ty (zip b'), stack) *) + end + else ret (t, stack) + + | tFix mfix idx => + if RedFlags.fix_ flags then + nf <- unfold_fix mfix idx ;; + let '(narg, fn) := nf in + match List.nth_error stack narg with + | Some c => + c' <- reduce_stack Γ n c [] ;; + match fst c' with + | tConstruct _ _ _ => reduce_stack Γ n fn stack + | _ => ret (t, stack) + end + | _ => ret (t, stack) + end + else ret (t, stack) + + | tProd _ _ _ => ret (t, stack) + + (* b' <- reduce_stack Γ n b [] ;; *) + (* t' <- reduce_stack (Γ ,, vass na (zip b')) n t [] ;; *) + (* ret (tProd na (zip b') (zip t'), stack) *) + + | tCast c _ _ => reduce_stack Γ n c stack + + | tCase ((ind, par), relevance) p c brs => + if RedFlags.iota flags then + c' <- reduce_stack Γ n c [] ;; + match c' with + | (tConstruct ind c _, args) => reduce_stack Γ n (iota_red par c args brs) stack + | _ => ret (tCase ((ind, par), relevance) p (zip c') brs, stack) + end + else ret (t, stack) + + | _ => ret (t, stack) + + end + end. + + Definition reduce_stack_term Γ n c := + res <- reduce_stack Γ n c [] ;; + ret (zip res). + + Definition fix_decls (l : mfixpoint term) := + let fix aux acc ds := + match ds with + | nil => acc + | d :: ds => aux (vass d.(dname) d.(dtype) :: acc) ds + end + in aux [] l. + + Definition map_constr_with_binders (f : context -> term -> term) Γ (t : term) : term := + match t with + | tRel i => t + | tEvar ev args => tEvar ev (List.map (f Γ) args) + | tLambda na T M => tLambda na (f Γ T) (f Γ M) + | tApp u v => tApp (f Γ u) (List.map (f Γ) v) + | tProd na A B => + let A' := f Γ A in + tProd na A' (f (Γ ,, vass na A') B) + | tCast c kind t => tCast (f Γ c) kind (f Γ t) + | tLetIn na b t c => + let b' := f Γ b in + let t' := f Γ t in + tLetIn na b' t' (f (Γ ,, vdef na b' t') c) + | tCase ind p c brs => + let brs' := List.map (on_snd (f Γ)) brs in + tCase ind (f Γ p) (f Γ c) brs' + | tProj p c => tProj p (f Γ c) + | tFix mfix idx => + let Γ' := fix_decls mfix ++ Γ in + let mfix' := List.map (map_def (f Γ) (f Γ')) mfix in + tFix mfix' idx + | tCoFix mfix k => + let Γ' := fix_decls mfix ++ Γ in + let mfix' := List.map (map_def (f Γ) (f Γ')) mfix in + tCoFix mfix' k + | x => x + end. + + Fixpoint reduce_opt Γ n c := + match n with + | 0 => None + | S n => + match reduce_stack_term Γ n c with + | Some c' => + Some (map_constr_with_binders + (fun Γ t => match reduce_opt Γ n t with + | Some t => t + | None => t end) Γ c') + | None => None + end + end. + +End Reduce. + +Definition isConstruct c := + match c with + | tConstruct _ _ _ => true + | tApp (tConstruct _ _ _) _ => true + | _ => false + end. + +Definition isCoFix c := + match c with + | tCoFix _ _ => true + | _ => false + end. + +Inductive conv_pb := +| Conv +| Cumul. + +Fixpoint eq_term `{checker_flags} (φ : universes_graph) (t u : term) {struct t} := + match t, u with + | tRel n, tRel n' => Nat.eqb n n' + | tEvar ev args, tEvar ev' args' => Nat.eqb ev ev' && forallb2 (eq_term φ) args args' + | tVar id, tVar id' => eq_string id id' + | tSort s, tSort s' => check_eqb_universe φ s s' + | tCast f k T, tCast f' k' T' => eq_term φ f f' && eq_term φ T T' + | tApp f args, tApp f' args' => eq_term φ f f' && forallb2 (eq_term φ) args args' + | tConst c u, tConst c' u' => eq_constant c c' && eqb_univ_instance φ u u' + | tInd i u, tInd i' u' => eq_inductive i i' && eqb_univ_instance φ u u' + | tConstruct i k u, tConstruct i' k' u' => eq_inductive i i' && Nat.eqb k k' + && eqb_univ_instance φ u u' + | tLambda _ b t, tLambda _ b' t' => eq_term φ b b' && eq_term φ t t' + | tProd _ b t, tProd _ b' t' => eq_term φ b b' && eq_term φ t t' + | tLetIn _ b t c, tLetIn _ b' t' c' => eq_term φ b b' && eq_term φ t t' && eq_term φ c c' + | tCase ((ind, par), rel) p c brs, + tCase ((ind',par'), rel') p' c' brs' => + eq_inductive ind ind' && Nat.eqb par par' && + eq_term φ p p' && eq_term φ c c' && forallb2 (fun '(a, b) '(a', b') => eq_term φ b b') brs brs' + | tProj p c, tProj p' c' => eq_projection p p' && eq_term φ c c' + | tFix mfix idx, tFix mfix' idx' => + forallb2 (fun x y => + eq_term φ x.(dtype) y.(dtype) && eq_term φ x.(dbody) y.(dbody)) mfix mfix' && + Nat.eqb idx idx' + | tCoFix mfix idx, tCoFix mfix' idx' => + forallb2 (fun x y => + eq_term φ x.(dtype) y.(dtype) && eq_term φ x.(dbody) y.(dbody)) mfix mfix' && + Nat.eqb idx idx' + | _, _ => false + end. + + +Fixpoint leq_term `{checker_flags} (φ : universes_graph) (t u : term) {struct t} := + match t, u with + | tRel n, tRel n' => Nat.eqb n n' + | tEvar ev args, tEvar ev' args' => Nat.eqb ev ev' && forallb2 (eq_term φ) args args' + | tVar id, tVar id' => eq_string id id' + | tSort s, tSort s' => check_leqb_universe φ s s' + | tApp f args, tApp f' args' => eq_term φ f f' && forallb2 (eq_term φ) args args' + | tCast f k T, tCast f' k' T' => eq_term φ f f' && eq_term φ T T' + | tConst c u, tConst c' u' => eq_constant c c' && eqb_univ_instance φ u u' + | tInd i u, tInd i' u' => eq_inductive i i' && eqb_univ_instance φ u u' + | tConstruct i k u, tConstruct i' k' u' => eq_inductive i i' && Nat.eqb k k' && + eqb_univ_instance φ u u' + | tLambda _ b t, tLambda _ b' t' => eq_term φ b b' && eq_term φ t t' + | tProd _ b t, tProd _ b' t' => eq_term φ b b' && leq_term φ t t' + | tLetIn _ b t c, tLetIn _ b' t' c' => eq_term φ b b' && eq_term φ t t' && leq_term φ c c' + | tCase ((ind, par), rel) p c brs, + tCase ((ind',par'), rel') p' c' brs' => + eq_inductive ind ind' && Nat.eqb par par' && + eq_term φ p p' && eq_term φ c c' && forallb2 (fun '(a, b) '(a', b') => eq_term φ b b') brs brs' + | tProj p c, tProj p' c' => eq_projection p p' && eq_term φ c c' + | tFix mfix idx, tFix mfix' idx' => + forallb2 (fun x y => + eq_term φ x.(dtype) y.(dtype) && eq_term φ x.(dbody) y.(dbody)) mfix mfix' && + Nat.eqb idx idx' + | tCoFix mfix idx, tCoFix mfix' idx' => + forallb2 (fun x y => + eq_term φ x.(dtype) y.(dtype) && eq_term φ x.(dbody) y.(dbody)) mfix mfix' && + Nat.eqb idx idx' + | _, _ => false + end. + +Section Conversion. + + Context `{checker_flags} (flags : RedFlags.t). + Context (Σ : global_env) (G : universes_graph). + + Definition nodelta_flags := RedFlags.mk true true true false true true. + + Definition unfold_one_fix n Γ mfix idx l := + unf <- unfold_fix mfix idx ;; + let '(arg, fn) := unf in + c <- nth_error l arg ;; + cred <- reduce_stack RedFlags.default Σ Γ n c [] ;; + let '(cred, _) := cred in + if negb (isConstruct cred) then None + else Some fn. + + Definition unfold_one_case n Γ c := + cred <- reduce_stack_term RedFlags.default Σ Γ n c ;; + if negb (isConstruct cred || isCoFix cred) then None + else Some cred. + + Definition reducible_head n Γ c l := + match c with + | tFix mfix idx => unfold_one_fix n Γ mfix idx l + | tCase ind' p' c' brs => + match unfold_one_case n Γ c' with + | None => None + | Some c' => Some (tCase ind' p' c' brs) + end + | tProj p c => + match unfold_one_case n Γ c with + | None => None + | Some c' => Some (tProj p c') + end + | tConst c _ => (* TODO Universes *) + match lookup_env Σ c with + | Some (ConstantDecl {| cst_body := Some body |}) => Some body + | _ => None + end + | _ => None + end. + + Definition lookup_env c := lookup_env Σ c. + + Definition opt_bool_to_bool (x : option bool) : bool := + match x with + | Some b => b + | None => false + end. + + + Fixpoint isconv (n : nat) (leq : conv_pb) (Γ : context) + (t1 : term) (l1 : list term) (t2 : term) (l2 : list term) {struct n} : option bool := + match n with 0 => None | S n => + red1 <- reduce_stack nodelta_flags Σ Γ n t1 l1 ;; + red2 <- reduce_stack nodelta_flags Σ Γ n t2 l2 ;; + let '(t1,l1) := red1 in + let '(t2,l2) := red2 in + isconv_prog n leq Γ t1 l1 t2 l2 + end + with isconv_prog (n : nat) (leq : conv_pb) (Γ : context) + (t1 : term) (l1 : list term) (t2 : term) (l2 : list term) + {struct n} : option bool := + match n with 0 => None | S n => + let isconv_stacks l1 l2 := + ret (forallb2 (fun x y => opt_bool_to_bool (isconv n Conv Γ x [] y [])) l1 l2) + in + let on_cond (b : bool) := if b then isconv_stacks l1 l2 else ret false in + (** Test equality at each step ?? *) + (* if eq_term t1 t2 && (match isconv_stacks l1 l2 with Some true => true | _ => false) *) + (* then ret true else *) + let fallback (x : unit) := + match reducible_head n Γ t1 l1 with + | Some t1 => + redt <- reduce_stack nodelta_flags Σ Γ n t1 l1 ;; + let '(t1, l1) := redt in + isconv_prog n leq Γ t1 l1 t2 l2 + | None => + match reducible_head n Γ t2 l2 with + | Some t2 => + redt <- reduce_stack nodelta_flags Σ Γ n t2 l2 ;; + let '(t2, l2) := redt in + isconv_prog n leq Γ t1 l1 t2 l2 + | None => + on_cond (match leq with + | Conv => eq_term G t1 t2 + | Cumul => leq_term G t1 t2 end) + end + end + in + match t1, t2 with + | tApp f args, tApp f' args' => + None (* Impossible *) + + | tCast t _ v, tCast u _ v' => None (* Impossible *) + + | tConst c u, tConst c' u' => (* TODO Universes *) + if eq_constant c c' then + b <- isconv_stacks l1 l2 ;; + if b then ret true (* FO optim *) + else + match lookup_env c with (* Unfold both bodies at once *) + | Some (ConstantDecl {| cst_body := Some body |}) => + isconv n leq Γ body l1 body l2 + | _ => ret false + end + else + match lookup_env c' with + | Some (ConstantDecl {| cst_body := Some body |}) => + isconv n leq Γ t1 l1 body l2 + | _ => + match lookup_env c with + | Some (ConstantDecl {| cst_body := Some body |}) => + isconv n leq Γ body l1 t2 l2 + | _ => ret false + end + end + + | tLambda na b t, tLambda _ b' t' => + cnv <- isconv n Conv Γ b [] b' [] ;; + if (cnv : bool) then + isconv n Conv (Γ ,, vass na b) t [] t' [] + else ret false + + | tProd na b t, tProd _ b' t' => + cnv <- isconv n Conv Γ b [] b' [] ;; + if (cnv : bool) then + isconv n leq (Γ ,, vass na b) t [] t' [] + else ret false + + | tCase (ind, par) p c brs, + tCase (ind',par') p' c' brs' => (* Hnf did not reduce, maybe delta needed in c *) + if eq_term G p p' && eq_term G c c' + && forallb2 (fun '(a, b) '(a', b') => eq_term G b b') brs brs' then + ret true + else + cred <- reduce_stack_term RedFlags.default Σ Γ n c ;; + c'red <- reduce_stack_term RedFlags.default Σ Γ n c' ;; + if eq_term G cred c && eq_term G c'red c' then ret true + else + isconv n leq Γ (tCase (ind, par) p cred brs) l1 (tCase (ind, par) p c'red brs') l2 + + | tProj p c, tProj p' c' => on_cond (eq_projection p p' && eq_term G c c') + + | tFix mfix idx, tFix mfix' idx' => + (* Hnf did not reduce, maybe delta needed *) + if eq_term G t1 t2 && opt_bool_to_bool (isconv_stacks l1 l2) then ret true + else + match unfold_one_fix n Γ mfix idx l1 with + | Some t1 => + redt <- reduce_stack nodelta_flags Σ Γ n t1 l1 ;; + let '(t1, l1) := redt in + isconv_prog n leq Γ t1 l1 t2 l2 + | None => + match unfold_one_fix n Γ mfix' idx' l2 with + | Some t2 => + redt <- reduce_stack nodelta_flags Σ Γ n t2 l2 ;; + let '(t2, l2) := redt in + isconv_prog n leq Γ t1 l1 t2 l2 + | None => ret false + end + end + + | tCoFix mfix idx, tCoFix mfix' idx' => + on_cond (eq_term G t1 t2) + + | _, _ => fallback () + end + end. +End Conversion. + +Definition try_reduce Σ Γ n t := + match reduce_opt RedFlags.default Σ Γ n t with + | Some t' => t' + | None => t + end. + + +Inductive type_error := +| UnboundRel (n : nat) +| UnboundVar (id : string) +| UnboundMeta (m : nat) +| UnboundEvar (ev : nat) +| UndeclaredConstant (c : kername) +| UndeclaredInductive (c : inductive) +| UndeclaredConstructor (c : inductive) (i : nat) +| NotConvertible (Γ : context) (t u t' u' : term) +| NotASort (t : term) +| NotAProduct (t t' : term) +| NotAnInductive (t : term) +| IllFormedFix (m : mfixpoint term) (i : nat) +| UnsatisfiedConstraints (c : ConstraintSet.t) +| UnsatisfiableConstraints (c : ConstraintSet.t) +| NotEnoughFuel (n : nat) +| NotSupported (s : string). + +Definition string_of_type_error (e : type_error) : string := + match e with + | UnboundRel n => "Unboound rel " ^ string_of_nat n + | UnboundVar id => "Unbound var " ^ id + | UnboundMeta m => "Unbound meta " ^ string_of_nat m + | UnboundEvar ev => "Unbound evar " ^ string_of_nat ev + | UndeclaredConstant c => "Undeclared constant " ^ string_of_kername c + | UndeclaredInductive c => "Undeclared inductive " ^ string_of_kername (inductive_mind c) + | UndeclaredConstructor c i => "Undeclared inductive " ^ string_of_kername (inductive_mind c) + | NotConvertible Γ t u t' u' => "Terms are not convertible: " ^ + string_of_term t ^ " " ^ string_of_term u ^ " after reduction: " ^ + string_of_term t' ^ " " ^ string_of_term u' + | NotASort t => "Not a sort" + | NotAProduct t t' => "Not a product" + | NotAnInductive t => "Not an inductive" + | IllFormedFix m i => "Ill-formed recursive definition" + | UnsatisfiedConstraints c => "Unsatisfied constraints" + | UnsatisfiableConstraints c => "Unsatisfiable constraints" + | NotEnoughFuel n => "Not enough fuel" + | NotSupported s => s ^ " are not supported" + end. + +Inductive typing_result (A : Type) := +| Checked (a : A) +| TypeError (t : type_error). +Global Arguments Checked {A} a. +Global Arguments TypeError {A} t. + +Instance typing_monad : Monad typing_result := + {| ret A a := Checked a ; + bind A B m f := + match m with + | Checked a => f a + | TypeError t => TypeError t + end + |}. + +Instance monad_exc : MonadExc type_error typing_result := + { raise A e := TypeError e; + catch A m f := + match m with + | Checked a => m + | TypeError t => f t + end + }. + +Definition check_conv_gen `{checker_flags} {F:Fuel} conv_pb Σ G Γ t u := + match isconv Σ G fuel conv_pb Γ t [] u [] with + | Some b => if b then ret () else raise (NotConvertible Γ t u t u) + | None => raise (NotEnoughFuel fuel) + end. + +Definition check_conv_leq `{checker_flags} {F:Fuel} := check_conv_gen Cumul. +Definition check_conv `{checker_flags} {F:Fuel} := check_conv_gen Conv. + + +Definition is_graph_of_global_env_ext `{checker_flags} Σ G := + is_graph_of_uctx G (global_ext_uctx Σ). + +Lemma conv_spec : forall `{checker_flags} {F:Fuel} Σ G Γ t u, + is_graph_of_global_env_ext Σ G -> + Σ ;;; Γ |- t = u <~> check_conv (fst Σ) G Γ t u = Checked (). +Proof. + intros. todo "Checker.conv_spec". +Defined. + +Lemma cumul_spec : forall `{checker_flags} {F:Fuel} Σ G Γ t u, + is_graph_of_global_env_ext Σ G -> + Σ ;;; Γ |- t <= u <~> check_conv_leq (fst Σ) G Γ t u = Checked (). +Proof. + intros. todo "Checker.cumul_spec". +Defined. + +Lemma reduce_cumul : + forall `{checker_flags} Σ Γ n t, Σ ;;; Γ |- try_reduce (fst Σ) Γ n t <= t. +Proof. intros. todo "Checker.reduce_cumul". Defined. + + +Section Typecheck. + Context {F : Fuel}. + Context (Σ : global_env). + + Definition hnf_stack Γ t := + match reduce_stack RedFlags.default Σ Γ fuel t [] with + | Some t' => ret t' + | None => raise (NotEnoughFuel fuel) + end. + + Definition reduce Γ t := + match reduce_opt RedFlags.default Σ Γ fuel t with + | Some t' => ret t' + | None => raise (NotEnoughFuel fuel) + end. + + Definition reduce_to_sort Γ (t : term) : typing_result Universe.t := + match t with + | tSort s => ret s + | _ => + t' <- hnf_stack Γ t ;; + match t' with + | (tSort s, []) => ret s + | _ => raise (NotASort t) + end + end. + + Definition reduce_to_prod Γ (t : term) : typing_result (term * term) := + match t with + | tProd _ a b => ret (a, b) + | _ => + t' <- hnf_stack Γ t ;; + match t' with + | (tProd _ a b,[]) => ret (a, b) + | _ => raise (NotAProduct t (zip t')) + end + end. + + Definition reduce_to_ind Γ (t : term) : + typing_result (inductive * list Level.t * list term) := + match decompose_app t with + | (tInd i u, l) => ret (i, u, l) + | _ => t' <- hnf_stack Γ t ;; + match t' with + | (tInd i u, l) => ret (i, u, l) + | _ => raise (NotAnInductive t) + end + end. +End Typecheck. + +Section Typecheck. + Context {cf : checker_flags} {F : Fuel}. + Context (Σ : global_env) (G : universes_graph). + + Definition convert_leq Γ (t u : term) : typing_result unit := + if eq_term G t u then ret () + else + match isconv Σ G fuel Cumul Γ t [] u [] with + | Some b => + if b then ret () + else raise (NotConvertible Γ t u t u) + | None => (* fallback *) + t' <- reduce Σ Γ t ;; + u' <- reduce Σ Γ u ;; + if leq_term G t' u' then ret () + else raise (NotConvertible Γ t u t' u') + end. + + Section InferAux. + Variable (infer : context -> term -> typing_result term). + + Fixpoint infer_spine (Γ : context) (ty : term) (l : list term) + {struct l} : typing_result term := + match l with + | nil => ret ty + | cons x xs => + pi <- reduce_to_prod Σ Γ ty ;; + let '(a1, b1) := pi in + tx <- infer Γ x ;; + convert_leq Γ tx a1 ;; + infer_spine Γ (subst10 x b1) xs + end. + + Definition infer_type Γ t := + tx <- infer Γ t ;; + reduce_to_sort Σ Γ tx. + + Definition infer_cumul Γ t t' := + tx <- infer Γ t ;; + convert_leq Γ tx t'. + + End InferAux. + + Definition polymorphic_constraints u := + match u with + | Monomorphic_ctx _ => ConstraintSet.empty + | Polymorphic_ctx ctx => snd (AUContext.repr ctx) + end. + + Definition lookup_constant_type cst u := + match lookup_env Σ cst with + | Some (ConstantDecl {| cst_type := ty; cst_universes := uctx |}) => + ret (subst_instance_constr u ty) + | _ => raise (UndeclaredConstant cst) + end. + + Definition lookup_constant_type_cstrs cst u := + match lookup_env Σ cst with + | Some (ConstantDecl {| cst_type := ty; cst_universes := uctx |}) => + let cstrs := polymorphic_constraints uctx in + ret (subst_instance_constr u ty, subst_instance_cstrs u cstrs) + | _ => raise (UndeclaredConstant cst) + end. + + Definition lookup_ind_decl ind i := + match lookup_env Σ ind with + | Some (InductiveDecl {| ind_bodies := l; ind_universes := uctx |}) => + match nth_error l i with + | Some body => ret (l, uctx, body) + | None => raise (UndeclaredInductive (mkInd ind i)) + end + | _ => raise (UndeclaredInductive (mkInd ind i)) + end. + + Definition lookup_ind_type ind i (u : list Level.t) := + res <- lookup_ind_decl ind i ;; + ret (subst_instance_constr u (snd res).(ind_type)). + + Definition lookup_ind_type_cstrs ind i (u : list Level.t) := + res <- lookup_ind_decl ind i ;; + let '(l, uctx, body) := res in + let cstrs := polymorphic_constraints uctx in + ret (subst_instance_constr u body.(ind_type), subst_instance_cstrs u cstrs). + + Definition lookup_constructor_decl ind i k := + res <- lookup_ind_decl ind i;; + let '(l, uctx, body) := res in + match nth_error body.(ind_ctors) k with + | Some (_, ty, _) => ret (l, uctx, ty) + | None => raise (UndeclaredConstructor (mkInd ind i) k) + end. + + Definition lookup_constructor_type ind i k u := + res <- lookup_constructor_decl ind i k ;; + let '(l, uctx, ty) := res in + ret (subst0 (inds ind u l) (subst_instance_constr u ty)). + + Definition lookup_constructor_type_cstrs ind i k u := + res <- lookup_constructor_decl ind i k ;; + let '(l, uctx, ty) := res in + let cstrs := polymorphic_constraints uctx in + ret (subst0 (inds ind u l) (subst_instance_constr u ty), + subst_instance_cstrs u cstrs). + + Definition check_consistent_constraints cstrs := + if check_constraints G cstrs then ret tt + else raise (UnsatisfiedConstraints cstrs). + + Fixpoint infer (Γ : context) (t : term) : typing_result term := + match t with + | tRel n => + match nth_error Γ n with + | Some d => ret (lift0 (S n) d.(decl_type)) + | None => raise (UnboundRel n) + end + + | tVar n => raise (UnboundVar n) + | tEvar ev args => raise (UnboundEvar ev) + + | tSort s => ret (tSort (Universe.super s)) + + | tCast c k t => + infer_type infer Γ t ;; + infer_cumul infer Γ c t ;; + ret t + + | tProd n t b => + s1 <- infer_type infer Γ t ;; + s2 <- infer_type infer (Γ ,, vass n t) b ;; + ret (tSort (Universe.sort_of_product s1 s2)) + + | tLambda n t b => + infer_type infer Γ t ;; + t2 <- infer (Γ ,, vass n t) b ;; + ret (tProd n t t2) + + | tLetIn n b b_ty b' => + infer_type infer Γ b_ty ;; + infer_cumul infer Γ b b_ty ;; + b'_ty <- infer (Γ ,, vdef n b b_ty) b' ;; + ret (tLetIn n b b_ty b'_ty) + + | tApp t l => + t_ty <- infer Γ t ;; + infer_spine infer Γ t_ty l + + | tConst cst u => + tycstrs <- lookup_constant_type_cstrs cst u ;; + let '(ty, cstrs) := tycstrs in + check_consistent_constraints cstrs;; + ret ty + + | tInd (mkInd ind i) u => + tycstrs <- lookup_ind_type_cstrs ind i u;; + let '(ty, cstrs) := tycstrs in + check_consistent_constraints cstrs;; + ret ty + + | tConstruct (mkInd ind i) k u => + tycstrs <- lookup_constructor_type_cstrs ind i k u ;; + let '(ty, cstrs) := tycstrs in + check_consistent_constraints cstrs;; + ret ty + + | tCase ((ind, par), rel) p c brs => + ty <- infer Γ c ;; + indargs <- reduce_to_ind Σ Γ ty ;; + (** TODO check branches *) + let '(ind', u, args) := indargs in + if eq_inductive ind ind' then + ret (tApp p (List.skipn par args ++ [c])) + else + let ind1 := tInd ind u in + let ind2 := tInd ind' u in + raise (NotConvertible Γ ind1 ind2 ind1 ind2) + + | tProj p c => + ty <- infer Γ c ;; + indargs <- reduce_to_ind Σ Γ ty ;; + (* FIXME *) + ret ty + + | tFix mfix n => + match nth_error mfix n with + | Some f => ret f.(dtype) + | None => raise (IllFormedFix mfix n) + end + + | tCoFix mfix n => + match nth_error mfix n with + | Some f => ret f.(dtype) + | None => raise (IllFormedFix mfix n) + end + + | tInt _ | tFloat _ => raise (NotSupported "primitive types") + end. + + Definition check (Γ : context) (t : term) (ty : term) : typing_result unit := + infer Γ ty ;; + infer_cumul infer Γ t ty ;; + ret (). + + Definition typechecking (Γ : context) (t ty : term) := + match check Γ t ty with + | Checked _ => true + | TypeError _ => false + end. + +End Typecheck. + +Arguments bind _ _ _ _ ! _. +Open Scope monad. + +Definition default_fuel : Fuel := Nat.pow 2 14. + +Fixpoint fresh id (env : global_env) : bool := + match env with + | nil => true + | cons g env => negb (eq_constant g.1 id) && fresh id env + end. + +Section Checker. + + Context {cf : checker_flags} {F : Fuel}. + + Inductive env_error := + | IllFormedDecl (e : string) (e : type_error) + | AlreadyDeclared (id : string). + + Inductive EnvCheck (A : Type) := + | CorrectDecl (a : A) + | EnvError (e : env_error). + Global Arguments EnvError {A} e. + Global Arguments CorrectDecl {A} a. + + Instance envcheck_monad : Monad EnvCheck := + {| ret A a := CorrectDecl a ; + bind A B m f := + match m with + | CorrectDecl a => f a + | EnvError e => EnvError e + end + |}. + + Definition wrap_error {A} (id : string) (check : typing_result A) : EnvCheck A := + match check with + | Checked a => CorrectDecl a + | TypeError e => EnvError (IllFormedDecl id e) + end. + + Definition check_wf_type id Σ G t := + wrap_error id (infer_type Σ (infer Σ G) [] t) ;; ret (). + + Definition check_wf_judgement id Σ G t ty := + wrap_error id (check Σ G [] t ty) ;; ret (). + + Definition infer_term Σ G t := + wrap_error "" (infer Σ G [] t). + + Definition check_wf_decl Σ G kn (g : global_decl) : EnvCheck () := + match g with + | ConstantDecl cst => + match cst.(cst_body) with + | Some term => check_wf_judgement (string_of_kername kn) Σ G term cst.(cst_type) + | None => check_wf_type (string_of_kername kn) Σ G cst.(cst_type) + end + | InductiveDecl inds => + List.fold_left (fun acc body => + acc ;; check_wf_type body.(ind_name) Σ G body.(ind_type)) + inds.(ind_bodies) (ret ()) + end. + + Fixpoint check_fresh id (env : global_env) : EnvCheck () := + match env with + | [] => ret () + | g :: env => + check_fresh id env;; + if eq_constant id g.1 then + EnvError (AlreadyDeclared (string_of_kername id)) + else ret () + end. + + Definition monomorphic_constraints u := + match u with + | Monomorphic_ctx ctx => snd ctx + | Polymorphic_ctx ctx => ConstraintSet.empty + end. + + (* FIXME : universe polym declarations *) + Definition global_decl_univs d := + match d with + | ConstantDecl cb => monomorphic_constraints cb.(cst_universes) + | InductiveDecl mb => monomorphic_constraints mb.(ind_universes) + end. + + Definition add_gc_constraints ctrs (G : universes_graph) : universes_graph + := (G.1.1, GoodConstraintSet.fold + (fun ctr => wGraph.EdgeSet.add (edge_of_constraint ctr)) ctrs G.1.2, + G.2). + + Fixpoint check_wf_env (g : global_env) + : EnvCheck universes_graph := + match g with + | [] => ret init_graph + | g :: env => + G <- check_wf_env env ;; + match gc_of_constraints (global_decl_univs g.2) with + | None => + EnvError (IllFormedDecl (string_of_kername g.1) + (UnsatisfiableConstraints (global_decl_univs g.2))) + | Some ctrs => + wrap_error "" (check_consistent_constraints G (global_decl_univs g.2)) ;; + let G' := add_gc_constraints ctrs G in + check_wf_decl env G' g.1 g.2 ;; + check_fresh g.1 env ;; + ret G' + end + end. + + Definition typecheck_program (p : program) : EnvCheck term := + let Σ := fst p in + G <- check_wf_env Σ ;; + infer_term Σ G (snd p). + +End Checker. + +(* for compatibility, will go away *) +Definition infer' `{checker_flags} `{Fuel} (Σ : global_env_ext) Γ t + := let uctx := (global_ext_uctx Σ) in + match gc_of_uctx uctx with + | None => raise (UnsatisfiableConstraints uctx.2) + | Some uctx => infer (fst Σ) (make_graph uctx) Γ t + end. + diff --git a/translations/param_cheap_packed.v b/translations/param_cheap_packed.v index 57055a733..e7e746b07 100644 --- a/translations/param_cheap_packed.v +++ b/translations/param_cheap_packed.v @@ -1,6 +1,5 @@ (* Distributed under the terms of the MIT license. *) -From MetaCoq.Template Require Import utils All. -From MetaCoq.Checker Require Import All. +From MetaCoq.Template Require Import utils All Checker. From MetaCoq.Translations Require Import translation_utils sigma. Local Existing Instance config.default_checker_flags. diff --git a/translations/param_generous_packed.v b/translations/param_generous_packed.v index f4e44a5f6..f1052ded5 100644 --- a/translations/param_generous_packed.v +++ b/translations/param_generous_packed.v @@ -1,6 +1,5 @@ (* Distributed under the terms of the MIT license. *) -From MetaCoq.Template Require Import utils All. -From MetaCoq.Checker Require Import All. +From MetaCoq.Template Require Import utils Checker All. From MetaCoq.Translations Require Import translation_utils MiniHoTT_paths. diff --git a/translations/param_original.v b/translations/param_original.v index 8a07f3bc1..b4d6f7b61 100644 --- a/translations/param_original.v +++ b/translations/param_original.v @@ -404,6 +404,9 @@ Module Axioms. intros H A B []; exact (H A A 1). Defined. + (* The import of CRelationClasses breaks rewrite *) + Set Typeclasses Depth 4. + Theorem Univalence'_provably_parametric : forall h : Univalence', Univalence'ᵗ h. Proof. unfold Univalence', Univalence'ᵗ. @@ -418,7 +421,7 @@ Module Axioms. intros x xᵗ; cbn. eapply pathsᵗ_ok2. set (coh x). set (q1 x) in *. set (q2 x) in *. clearbody p p1 p0; clear; cbn in *. - set (g x) in *. clearbody a. + set (g x) in *. clearbody a. simpl. rewrite transport_pp. destruct p1. cbn in *. match goal with diff --git a/translations/times_bool_fun.v b/translations/times_bool_fun.v index 7c828f648..92ad91548 100644 --- a/translations/times_bool_fun.v +++ b/translations/times_bool_fun.v @@ -1,6 +1,5 @@ (* Distributed under the terms of the MIT license. *) -From MetaCoq.Template Require Import utils All. -From MetaCoq Require Import Checker.All. +From MetaCoq.Template Require Import utils All Checker. From MetaCoq.Translations Require Import translation_utils MiniHoTT. diff --git a/translations/translation_utils.v b/translations/translation_utils.v index 61865e073..b9acffcf9 100644 --- a/translations/translation_utils.v +++ b/translations/translation_utils.v @@ -1,6 +1,5 @@ (* Distributed under the terms of the MIT license. *) -From MetaCoq.Template Require Import utils All. -Require Import MetaCoq.Checker.All. +From MetaCoq.Template Require Import utils Checker All. (* Should be in AstUtils probably *) Fixpoint subst_app (t : term) (us : list term) : term := From 0352ad3cc301189e4e6725e5c0f72557af424ea2 Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Sat, 12 Dec 2020 12:23:16 +0100 Subject: [PATCH 64/70] Fix configure.sh --- configure.sh | 7 ++----- 1 file changed, 2 insertions(+), 5 deletions(-) diff --git a/configure.sh b/configure.sh index 6ad783a21..31779b413 100755 --- a/configure.sh +++ b/configure.sh @@ -22,13 +22,10 @@ then TRANSLATIONS_DEPS="" else echo "Building MetaCoq globally (default)" - # To find the metacoq template plugin - # The pcuic plugin depends on the checker plugin - # The safechecker and erasure plugins are self-contained + # The safechecker and erasure plugins depend on the extractable template-coq plugin # These dependencies should not be necessary when separate linking of ocaml object # files is supported by coq_makefile - PCUIC_MLDEPS="" - PCUIC_VDEPS="" + PCUIC_DEPS="-I ${COQLIB}/user-contrib/MetaCoq/Template" SAFECHECKER_DEPS="" ERASURE_DEPS="" TRANSLATIONS_DEPS="" From ee6cc501570e3e8558c198b8a1b9411002c3880a Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Sat, 12 Dec 2020 12:52:59 +0100 Subject: [PATCH 65/70] TemplateToPCUIC proof --- pcuic/theories/PCUICToTemplateCorrectness.v | 11 +- pcuic/theories/TemplateToPCUICCorrectness.v | 321 +++++++++++--------- 2 files changed, 195 insertions(+), 137 deletions(-) diff --git a/pcuic/theories/PCUICToTemplateCorrectness.v b/pcuic/theories/PCUICToTemplateCorrectness.v index 5bdd399ab..cba3e00fe 100644 --- a/pcuic/theories/PCUICToTemplateCorrectness.v +++ b/pcuic/theories/PCUICToTemplateCorrectness.v @@ -3,7 +3,7 @@ From Coq Require Import ssreflect ssrbool CRelationClasses. From Equations.Type Require Import Relation Relation_Properties. From MetaCoq.PCUIC Require Import PCUICAst PCUICAstUtils PCUICInduction PCUICLiftSubst PCUICEquality PCUICReduction PCUICUnivSubst PCUICTyping PCUICGeneration - TemplateToPCUICCorrectness. (* We use the back and forth to show transitivity of cumulativity *) + PCUICConversion. (* Needs transitivity of cumulativity *) Set Warnings "-notation-overridden". From MetaCoq.Template Require Import config utils Ast TypingWf WfInv UnivSubst @@ -1270,6 +1270,15 @@ Axiom cofix_guard_trans : ------------------------ derivations for example. |- tApp f u : B [0 := u] + The typing_spine_nil constructor allows to stack cumulativity steps using transitivity of cumulativity, + following from confluence. + + In the end a typing derivation for an application that can mix application and cumulativity steps at any + point: + + tApp (tApp f u) v : T' can be translated to + + typing_spine fty [u; v] T' *) Import PCUICAst PCUICLiftSubst PCUICTyping. diff --git a/pcuic/theories/TemplateToPCUICCorrectness.v b/pcuic/theories/TemplateToPCUICCorrectness.v index 1e19bf359..5ee0afce2 100644 --- a/pcuic/theories/TemplateToPCUICCorrectness.v +++ b/pcuic/theories/TemplateToPCUICCorrectness.v @@ -13,7 +13,7 @@ Implicit Types cf : checker_flags. (* Source = Template, Target (unqualified) = Coq *) Module S := Template.Ast. Module SEq := Template.TermEquality. -Module STy := Template.Typing. +Module ST := Template.Typing. Module SL := Template.LiftSubst. Lemma mkApps_morphism (f : term -> term) u v : @@ -108,10 +108,10 @@ Qed. Require Import ssreflect. Lemma forall_decls_declared_constant Σ cst decl : - STy.declared_constant Σ cst decl -> + ST.declared_constant Σ cst decl -> declared_constant (trans_global_decls Σ) cst (trans_constant_body decl). Proof. - unfold declared_constant, STy.declared_constant. + unfold declared_constant, ST.declared_constant. induction Σ => //; try discriminate. case: a => // /= k b. unfold eq_kername; destruct kername_eq_dec; subst; auto. @@ -119,10 +119,10 @@ Proof. Qed. Lemma forall_decls_declared_minductive Σ cst decl : - STy.declared_minductive Σ cst decl -> + ST.declared_minductive Σ cst decl -> declared_minductive (trans_global_decls Σ) cst (trans_minductive_body decl). Proof. - unfold declared_minductive, STy.declared_minductive. + unfold declared_minductive, ST.declared_minductive. induction Σ => //; try discriminate. case: a => // /= k b. unfold eq_kername; destruct kername_eq_dec; subst; auto. @@ -130,10 +130,10 @@ Proof. Qed. Lemma forall_decls_declared_inductive Σ mdecl ind decl : - STy.declared_inductive Σ mdecl ind decl -> + ST.declared_inductive Σ mdecl ind decl -> declared_inductive (trans_global_decls Σ) (trans_minductive_body mdecl) ind (trans_one_ind_body decl). Proof. - unfold declared_inductive, STy.declared_inductive. + unfold declared_inductive, ST.declared_inductive. move=> [decl' Hnth]. pose proof (forall_decls_declared_minductive _ _ _ decl'). eexists. eauto. destruct decl'; simpl in *. @@ -142,11 +142,11 @@ Proof. Qed. Lemma forall_decls_declared_constructor Σ cst mdecl idecl decl : - STy.declared_constructor Σ mdecl idecl cst decl -> + ST.declared_constructor Σ mdecl idecl cst decl -> declared_constructor (trans_global_decls Σ) (trans_minductive_body mdecl) (trans_one_ind_body idecl) cst ((fun '(x, y, z) => (x, trans y, z)) decl). Proof. - unfold declared_constructor, STy.declared_constructor. + unfold declared_constructor, ST.declared_constructor. move=> [decl' Hnth]. pose proof (forall_decls_declared_inductive _ _ _ _ decl'). split; auto. destruct idecl; simpl. @@ -154,11 +154,11 @@ Proof. Qed. Lemma forall_decls_declared_projection Σ cst mdecl idecl decl : - STy.declared_projection Σ mdecl idecl cst decl -> + ST.declared_projection Σ mdecl idecl cst decl -> declared_projection (trans_global_decls Σ) (trans_minductive_body mdecl) (trans_one_ind_body idecl) cst ((fun '(x, y) => (x, trans y)) decl). Proof. - unfold declared_constructor, STy.declared_constructor. + unfold declared_constructor, ST.declared_constructor. move=> [decl' [Hnth Hnpar]]. pose proof (forall_decls_declared_inductive _ _ _ _ decl'). split; auto. destruct idecl; simpl. @@ -237,9 +237,9 @@ Qed. Definition on_pair {A B C D} (f : A -> B) (g : C -> D) (x : A * C) := (f (fst x), g (snd x)). -Lemma trans_inds kn u bodies : map trans (STy.inds kn u bodies) = inds kn u (map trans_one_ind_body bodies). +Lemma trans_inds kn u bodies : map trans (ST.inds kn u bodies) = inds kn u (map trans_one_ind_body bodies). Proof. - unfold inds, STy.inds. rewrite map_length. + unfold inds, ST.inds. rewrite map_length. induction bodies. simpl. reflexivity. simpl; f_equal. auto. Qed. @@ -247,7 +247,7 @@ Lemma trans_instantiate_params_subst params args s t : All TypingWf.wf_decl params -> All Ast.wf s -> All Ast.wf args -> forall s' t', - STy.instantiate_params_subst params args s t = Some (s', t') -> + ST.instantiate_params_subst params args s t = Some (s', t') -> instantiate_params_subst (map trans_decl params) (map trans args) (map trans s) (trans t) = Some (map trans s', trans t'). @@ -278,14 +278,14 @@ Lemma trans_instantiate_params params args t : All TypingWf.wf_decl params -> All Ast.wf args -> forall t', - STy.instantiate_params params args t = Some t' -> + ST.instantiate_params params args t = Some t' -> instantiate_params (map trans_decl params) (map trans args) (trans t) = Some (trans t'). Proof. intros wft wfpars wfargs t' eq. revert eq. - unfold STy.instantiate_params. - case_eq (STy.instantiate_params_subst (List.rev params) args [] t). + unfold ST.instantiate_params. + case_eq (ST.instantiate_params_subst (List.rev params) args [] t). all: try discriminate. intros [ctx u] e eq. inversion eq. subst. clear eq. assert (wfargs' : Forall Ast.wf args) by (apply All_Forall ; assumption). @@ -389,42 +389,91 @@ Proof. rewrite decompose_prod_assum_mkApps_nonnil //. Qed. -Lemma trans_build_branches_type : - forall ind mdecl idecl args u p brtys, - map_option_out (STy.build_branches_type ind mdecl idecl args u p) - = Some brtys -> - map_option_out - (build_branches_type ind (trans_minductive_body mdecl) - (trans_one_ind_body idecl) (map trans args) u - (trans p)) - = Some (map (on_snd trans) brtys). +(* Lemma trans_isApp t : Ast.isApp t = false -> PCUICAst.isApp (trans t) = false. +Proof. + destruct t => //. simpl. + now destruct prim as [? []]. +Qed. *) + +Lemma trans_decompose_app_args t f l : + Ast.wf t -> + AstUtils.decompose_app t = (f, l) -> + (decompose_app (trans t)).2 = map trans l. +Proof. + induction 1 using Template.Induction.term_wf_forall_list_ind; simpl; + intros [= <- <-]; auto. admit. + rewrite decompose_app_mkApps. + destruct (AstUtils.decompose_app t). +Admitted. + +Lemma trans_build_branches_type {cf} Σ ind mdecl idecl args u p brtys : + (ST.on_ind_body (ST.lift_typing ST.typing) Σ (inductive_mind ind) mdecl (inductive_ind ind) idecl) -> + map_option_out (ST.build_branches_type ind mdecl idecl args u p) + = Some brtys -> + map_option_out + (build_branches_type ind (trans_minductive_body mdecl) + (trans_one_ind_body idecl) (map trans args) u + (trans p)) + = Some (map (on_snd trans) brtys). +Proof. + intros onind. + pose proof (ST.onConstructors onind) as onc. + unfold ST.build_branches_type. + unfold build_branches_type. + rewrite mapi_map. + eapply All2_map_option_out_mapi_Some_spec. eapply onc. + intros i [[id ty] argn] [nargs br] s oncs. + simpl. + destruct ST.instantiate_params eqn:ipars => //. + apply trans_instantiate_params in ipars. + rewrite trans_subst in ipars. + rewrite -trans_inds. + rewrite -trans_subst_instance_constr. + rewrite [map _ _]trans_local_subst_instance_context in ipars. + rewrite ipars. + assert (wft : S.wf t). admit. + move: (trans_decompose_prod_assum [] t wft). + destruct AstUtils.decompose_prod_assum eqn:dp => -> /=. + destruct (AstUtils.decompose_app t0) eqn:da'. simpl. + destruct chop as [params argsl] eqn:ceq. + destruct oncs. simpl in cstr_eq. + rewrite [ty]cstr_eq in ipars. + intros [= -> <-]. + + rewrite (chop_map _ _ _ _ _ ceq). + intros [= ->]. f_equal. unfold on_snd. simpl. f_equal. subst br. + rewrite trans_it_mkProd_or_LetIn trans_mkApps map_app /= trans_mkApps /= map_app. + now rewrite trans_to_extended_list trans_lift map_length. +Qed. +intros. + Admitted. Lemma trans_build_case_predicate_type ind mdecl idecl params u ps : build_case_predicate_type ind (trans_minductive_body mdecl) (trans_one_ind_body idecl) (map trans params) u ps - = option_map trans (STy.build_case_predicate_type ind mdecl idecl params u ps). + = option_map trans (ST.build_case_predicate_type ind mdecl idecl params u ps). Admitted. (* Lemma trans_types_of_case (Σ : S.global_env) ind mdecl idecl args p u pty indctx pctx ps btys : *) (* S.wf p -> S.wf pty -> S.wf (S.ind_type idecl) -> *) (* All S.wf args -> *) -(* STy.wf Σ -> *) -(* STy.declared_inductive Σ mdecl ind idecl -> *) -(* STy.types_of_case ind mdecl idecl args u p pty = Some (indctx, pctx, ps, btys) -> *) +(* ST.wf Σ -> *) +(* ST.declared_inductive Σ mdecl ind idecl -> *) +(* ST.types_of_case ind mdecl idecl args u p pty = Some (indctx, pctx, ps, btys) -> *) (* types_of_case ind (trans_minductive_body mdecl) (trans_one_ind_body idecl) *) (* (map trans args) u (trans p) (trans pty) = *) (* Some (trans_local indctx, trans_local pctx, ps, map (on_snd trans) btys). *) (* Proof. *) (* intros wfp wfpty wfdecl wfargs wfΣ Hidecl. *) (* pose proof (on_declared_inductive wfΣ Hidecl) as [onmind onind]. *) -(* apply STy.onParams in onmind as Hparams. *) +(* apply ST.onParams in onmind as Hparams. *) (* (* Maybe have a lemma for this we do it all the time *) *) (* assert (wc : Forall wf_decl (UnivSubst.subst_instance_context u (S.ind_params mdecl))). *) (* { assert (h : Forall wf_decl (S.ind_params mdecl)). *) (* { eapply typing_all_wf_decl ; revgoals. *) -(* - apply STy.onParams in onmind. *) -(* unfold STy.on_context in onmind. *) +(* - apply ST.onParams in onmind. *) +(* unfold ST.on_context in onmind. *) (* eassumption. *) (* - simpl. assumption. *) (* } *) @@ -438,11 +487,11 @@ Admitted. (* { eapply closed_wf_local ; eauto. eauto. } *) (* assert (wfparams : All wf_decl (Ast.ind_params mdecl)). *) (* { apply Forall_All. eapply typing_all_wf_decl ; eauto. simpl. eauto. } *) -(* unfold STy.types_of_case, types_of_case. simpl. *) +(* unfold ST.types_of_case, types_of_case. simpl. *) (* match goal with *) -(* | |- context [ STy.instantiate_params ?p ?a ?t ] => *) +(* | |- context [ ST.instantiate_params ?p ?a ?t ] => *) (* pose proof (trans_instantiate_params p a t) as ht ; *) -(* case_eq (STy.instantiate_params p a t) *) +(* case_eq (ST.instantiate_params p a t) *) (* end. *) (* 2: discriminate. *) (* intros ity e. *) @@ -455,16 +504,16 @@ Admitted. (* apply wf_instantiate_params in e as wfity. *) (* all: auto with wf. *) (* pose proof (trans_destArity [] ity wfity) as e'. *) -(* destruct STy.destArity as [[ctx s] | ]. 2: discriminate. *) +(* destruct ST.destArity as [[ctx s] | ]. 2: discriminate. *) (* rewrite e'. *) (* pose proof (trans_destArity [] pty wfpty) as e''. *) -(* destruct STy.destArity as [[ctx' s'] | ]. 2: discriminate. *) +(* destruct ST.destArity as [[ctx' s'] | ]. 2: discriminate. *) (* simpl in e''. rewrite e''. *) -(* pose proof (STy.onConstructors onind) as onc. *) +(* pose proof (ST.onConstructors onind) as onc. *) (* assert ( *) (* hb : *) (* forall brtys, *) -(* map_option_out (STy.build_branches_type ind mdecl idecl args u p) *) +(* map_option_out (ST.build_branches_type ind mdecl idecl args u p) *) (* = Some brtys -> *) (* map_option_out *) (* (build_branches_type ind (trans_minductive_body mdecl) *) @@ -473,18 +522,18 @@ Admitted. (* = Some (map (on_snd trans) brtys) *) (* ). *) (* { intro brtys. *) -(* unfold STy.build_branches_type, build_branches_type. *) +(* unfold ST.build_branches_type, build_branches_type. *) (* unfold trans_one_ind_body. simpl. rewrite -> mapi_map. *) -(* unfold STy.on_constructors in onc. *) +(* unfold ST.on_constructors in onc. *) (* eapply All2_map_option_out_mapi_Some_spec. *) (* - eapply onc. *) (* - intros i [[id t] n] [t0 ar] z. *) (* unfold on_snd. simpl. *) (* intros [ont [cs ?]]. simpl in *. *) -(* unfold STy.on_type in ont. simpl in ont. *) +(* unfold ST.on_type in ont. simpl in ont. *) (* destruct ont. *) -(* unfold STy.instantiate_params, instantiate_params. *) -(* destruct STy.instantiate_params_subst eqn:he. 2: discriminate. *) +(* unfold ST.instantiate_params, instantiate_params. *) +(* destruct ST.instantiate_params_subst eqn:he. 2: discriminate. *) (* destruct p0 as [s0 ty]. *) (* apply instantiate_params_subst_make_context_subst in he as he'. *) (* destruct he' as [ctx'' hctx'']. *) @@ -627,14 +676,14 @@ Qed. Lemma typing_wf_wf {cf}: forall (Σ : Template.Ast.global_env), - STy.wf Σ -> - STy.Forall_decls_typing + ST.wf Σ -> + ST.Forall_decls_typing (fun (_ : Template.Ast.global_env_ext) (_ : Tcontext) (t T : Tterm) => Ast.wf t /\ Ast.wf T) Σ. Proof. intros Σ. eapply on_global_env_impl. clear. intros Σ Γ t S. - red. unfold STy.lift_typing. + red. unfold ST.lift_typing. intros ong. destruct S. * intros ty. now eapply typing_wf. * intros [s ty]. exists s. @@ -642,7 +691,7 @@ Proof. Qed. Lemma trans_R_global_instance {cf} Σ Re Rle gref napp u u' : - STy.wf Σ -> + ST.wf Σ -> SEq.R_global_instance Σ Re Rle gref napp u u' -> R_global_instance (trans_global_decls Σ) Re Rle gref napp u u'. Proof. @@ -678,7 +727,7 @@ Ltac tc := typeclasses eauto. Lemma trans_eq_term_upto_univ {cf} : forall Σ Re Rle t u napp, RelationClasses.subrelation Re Rle -> - STy.wf Σ -> + ST.wf Σ -> S.wf t -> S.wf u -> SEq.eq_term_upto_univ_napp Σ Re Rle napp t u -> @@ -795,7 +844,7 @@ Proof. Qed. Lemma trans_leq_term {cf} Σ ϕ T U : - STy.wf Σ -> + ST.wf Σ -> S.wf T -> S.wf U -> SEq.leq_term Σ ϕ T U -> leq_term (trans_global_decls Σ) ϕ (trans T) (trans U). Proof. @@ -804,7 +853,7 @@ Proof. Qed. Lemma trans_eq_term {cf} Σ φ t u : - STy.wf Σ -> + ST.wf Σ -> S.wf t -> S.wf u -> SEq.eq_term Σ φ t u -> eq_term (trans_global_decls Σ) φ (trans t) (trans u). Proof. @@ -814,7 +863,7 @@ Qed. Lemma trans_eq_term_list {cf}: forall Σ φ l l', - STy.wf Σ -> + ST.wf Σ -> List.Forall S.wf l -> List.Forall S.wf l' -> All2 (SEq.eq_term Σ φ) l l' -> @@ -851,10 +900,10 @@ Proof. Qed. Lemma trans_iota_red pars c args brs : - trans (STy.iota_red pars c args brs) = + trans (ST.iota_red pars c args brs) = iota_red pars c (List.map trans args) (List.map (on_snd trans) brs). Proof. - unfold STy.iota_red, iota_red. + unfold ST.iota_red, iota_red. rewrite trans_mkApps. f_equal. induction brs in c |- *; simpl; destruct c; trivial. now rewrite map_skipn. @@ -871,17 +920,17 @@ Qed. Lemma trans_unfold_fix mfix idx narg fn : List.Forall (fun def : def Tterm => S.wf (dtype def) /\ S.wf (dbody def)) mfix -> - STy.unfold_fix mfix idx = Some (narg, fn) -> + ST.unfold_fix mfix idx = Some (narg, fn) -> unfold_fix (map (map_def trans trans) mfix) idx = Some (narg, trans fn). Proof. - unfold STy.unfold_fix, unfold_fix. intros wffix. + unfold ST.unfold_fix, unfold_fix. intros wffix. rewrite nth_error_map. destruct (nth_error mfix idx) eqn:Hdef => //. cbn. intros [= <- <-]. simpl. repeat f_equal. rewrite trans_subst. f_equal. clear Hdef. - unfold fix_subst, STy.fix_subst. rewrite map_length. + unfold fix_subst, ST.fix_subst. rewrite map_length. generalize mfix at 1 3. induction wffix; trivial. simpl; intros mfix. f_equal. @@ -890,15 +939,15 @@ Qed. Lemma trans_unfold_cofix mfix idx narg fn : List.Forall (fun def : def Tterm => S.wf (dtype def) /\ S.wf (dbody def)) mfix -> - STy.unfold_cofix mfix idx = Some (narg, fn) -> + ST.unfold_cofix mfix idx = Some (narg, fn) -> unfold_cofix (map (map_def trans trans) mfix) idx = Some (narg, trans fn). Proof. - unfold STy.unfold_cofix, unfold_cofix. intros wffix. + unfold ST.unfold_cofix, unfold_cofix. intros wffix. rewrite nth_error_map. destruct (nth_error mfix idx) eqn:Hdef. intros [= <- <-]. simpl. repeat f_equal. rewrite trans_subst. f_equal. clear Hdef. - unfold cofix_subst, STy.cofix_subst. rewrite map_length. + unfold cofix_subst, ST.cofix_subst. rewrite map_length. generalize mfix at 1 3. induction wffix; trivial. simpl; intros mfix. f_equal. @@ -909,10 +958,10 @@ Definition isApp t := match t with tApp _ _ => true | _ => false end. Lemma trans_is_constructor: forall (args : list Tterm) (narg : nat), - STy.is_constructor narg args = true -> is_constructor narg (map trans args) = true. + ST.is_constructor narg args = true -> is_constructor narg (map trans args) = true. Proof. intros args narg. - unfold STy.is_constructor, is_constructor. + unfold ST.is_constructor, is_constructor. rewrite nth_error_map. destruct nth_error. simpl. intros. destruct t; try discriminate || reflexivity. simpl in H. destruct t; try discriminate || reflexivity. @@ -932,7 +981,7 @@ Proof. Qed. Ltac wf_inv H := try apply wf_inv in H; simpl in H; rdest. -Lemma wf_wf_decl_pred {cf} Σ : STy.wf Σ -> Typing.on_global_env (fun _ => wf_decl_pred) Σ. +Lemma wf_wf_decl_pred {cf} Σ : ST.wf Σ -> Typing.on_global_env (fun _ => wf_decl_pred) Σ. Proof. move/typing_wf_wf. apply on_global_env_impl. @@ -944,14 +993,14 @@ Qed. Hint Resolve wf_wf_decl_pred : wf. Lemma trans_red1 {cf} Σ Γ T U : - STy.wf Σ -> + ST.wf Σ -> List.Forall wf_decl Γ -> S.wf T -> - STy.red1 Σ Γ T U -> + ST.red1 Σ Γ T U -> red1 (map (on_snd trans_global_decl) Σ) (trans_local Γ) (trans T) (trans U). Proof. intros wfΣ wfΓ Hwf. - induction 1 using STy.red1_ind_all; wf_inv Hwf; simpl in *; + induction 1 using ST.red1_ind_all; wf_inv Hwf; simpl in *; try solve [econstructor; eauto]. - simpl. wf_inv H1. apply Forall_All in H2. inv H2. @@ -1038,7 +1087,7 @@ Proof. red. rewrite <- !map_dtype. rewrite <- !map_dbody. intuition eauto. + unfold Template.Ast.app_context, trans_local in b. simpl in a. rewrite -> map_app in b. - unfold app_context. unfold STy.fix_context in b. + unfold app_context. unfold ST.fix_context in b. rewrite map_rev map_mapi in b. simpl in b. unfold fix_context. rewrite mapi_map. simpl. forward b. @@ -1073,7 +1122,7 @@ Proof. red. rewrite <- !map_dtype. rewrite <- !map_dbody. intuition eauto. + unfold Template.Ast.app_context, trans_local in b. simpl in a. rewrite -> map_app in b. - unfold app_context. unfold STy.fix_context in b. + unfold app_context. unfold ST.fix_context in b. rewrite map_rev map_mapi in b. simpl in b. unfold fix_context. rewrite mapi_map. simpl. forward b. @@ -1093,7 +1142,7 @@ Proof. Qed. Lemma global_levels_trans Σ - : global_levels (trans_global_decls Σ) = STy.global_levels Σ. + : global_levels (trans_global_decls Σ) = ST.global_levels Σ. Proof. induction Σ; simpl; auto. rewrite IHΣ. f_equal. clear. @@ -1101,19 +1150,19 @@ Proof. Qed. Lemma global_ext_levels_trans Σ - : global_ext_levels (trans_global Σ) = STy.global_ext_levels Σ. + : global_ext_levels (trans_global Σ) = ST.global_ext_levels Σ. Proof. destruct Σ. - unfold trans_global, STy.global_ext_levels, global_ext_levels; simpl. + unfold trans_global, ST.global_ext_levels, global_ext_levels; simpl. f_equal. clear u. now rewrite global_levels_trans. Qed. Lemma global_ext_constraints_trans Σ - : global_ext_constraints (trans_global Σ) = STy.global_ext_constraints Σ. + : global_ext_constraints (trans_global Σ) = ST.global_ext_constraints Σ. Proof. destruct Σ. - unfold trans_global, STy.global_ext_constraints, global_ext_constraints; simpl. + unfold trans_global, ST.global_ext_constraints, global_ext_constraints; simpl. f_equal. clear u. induction g. - reflexivity. @@ -1122,9 +1171,9 @@ Proof. Qed. Lemma trans_cumul {cf} (Σ : Ast.global_env_ext) Γ T U : - STy.wf Σ -> + ST.wf Σ -> List.Forall wf_decl Γ -> - S.wf T -> S.wf U -> STy.cumul Σ Γ T U -> + S.wf T -> S.wf U -> ST.cumul Σ Γ T U -> trans_global Σ ;;; trans_local Γ |- trans T <= trans U. Proof. intros wfΣ. @@ -1146,7 +1195,7 @@ Definition Tlift_typing (P : Template.Ast.global_env_ext -> Tcontext -> Tterm -> | None => { s : Universe.t & P Σ Γ t (S.tSort s) } end. -Definition TTy_wf_local {cf : checker_flags} Σ Γ := STy.All_local_env (STy.lift_typing STy.typing Σ) Γ. +Definition TTy_wf_local {cf : checker_flags} Σ Γ := ST.All_local_env (ST.lift_typing ST.typing Σ) Γ. Lemma trans_wf_local {cf}: forall (Σ : Template.Ast.global_env_ext) (Γ : Tcontext) (wfΓ : TTy_wf_local Σ Γ), @@ -1156,7 +1205,7 @@ Lemma trans_wf_local {cf}: trans_global Σ0;;; trans_local Γ0 |- trans t : trans T) in wf (trans_global Σ).1 -> - STy.All_local_env_over STy.typing P Σ Γ wfΓ -> + ST.All_local_env_over ST.typing P Σ Γ wfΓ -> wf_local (trans_global Σ) (trans_local Γ). Proof. intros. @@ -1170,10 +1219,10 @@ Proof. Qed. Lemma trans_wf_local_env {cf} Σ Γ : - STy.All_local_env - (STy.lift_typing + ST.All_local_env + (ST.lift_typing (fun (Σ : Ast.global_env_ext) (Γ : Tcontext) (b ty : Tterm) => - STy.typing Σ Γ b ty × trans_global Σ;;; trans_local Γ |- trans b : trans ty) Σ) + ST.typing Σ Γ b ty × trans_global Σ;;; trans_local Γ |- trans b : trans ty) Σ) Γ -> wf_local (trans_global Σ) (trans_local Γ). Proof. @@ -1187,7 +1236,7 @@ Proof. red. red in t1. destruct t1. eapply t2. Qed. -(* eapply STy.on_global_decls_impl. 2:eapply wf. eauto. intros * ongl ont. destruct t. *) +(* eapply ST.on_global_decls_impl. 2:eapply wf. eauto. intros * ongl ont. destruct t. *) (* red in ont. *) (* eapply typing_wf; eauto. destruct ont. exists x; eapply typing_wf; intuition eauto. *) (* Qed. *) @@ -1196,12 +1245,12 @@ Hint Resolve trans_wf_local : trans. Axiom fix_guard_trans : forall Σ Γ mfix, - STy.fix_guard Σ Γ mfix -> + ST.fix_guard Σ Γ mfix -> fix_guard (trans_global Σ) (trans_local Γ) (map (map_def trans trans) mfix). Axiom cofix_guard_trans : forall Σ Γ mfix, - STy.cofix_guard Σ Γ mfix -> + ST.cofix_guard Σ Γ mfix -> cofix_guard (trans_global Σ) (trans_local Γ) (map (map_def trans trans) mfix). Notation Swf_fix def := (S.wf (dtype def) /\ S.wf (dbody def)). @@ -1218,7 +1267,7 @@ Proof. now rewrite !trans_subst map_length. Qed. -Lemma trans_smash_context Γ Δ : trans_local (STy.smash_context Γ Δ) = smash_context (trans_local Γ) (trans_local Δ). +Lemma trans_smash_context Γ Δ : trans_local (ST.smash_context Γ Δ) = smash_context (trans_local Γ) (trans_local Δ). Proof. induction Δ in Γ |- *; simpl; auto. destruct a as [na [b|] ty] => /=. @@ -1267,10 +1316,10 @@ Qed. Lemma trans_check_one_fix mfix ind : Swf_fix mfix -> - STy.check_one_fix mfix = Some ind -> + ST.check_one_fix mfix = Some ind -> check_one_fix (map_def trans trans mfix) = Some ind. Proof. - unfold STy.check_one_fix, check_one_fix. + unfold ST.check_one_fix, check_one_fix. case: mfix => [na ty arg rarg] /= [wfty wfarg]. move: (trans_decompose_prod_assum [] ty wfty) => /=. destruct AstUtils.decompose_prod_assum as [ctx p] eqn:dp => /= // ->. @@ -1310,7 +1359,7 @@ Qed. Lemma map_option_out_check_one_fix {mfix} : Forall (fun def => (S.wf (dtype def) /\ S.wf (dbody def))) mfix -> forall l, - map_option_out (map (fun x => STy.check_one_fix x) mfix) = Some l -> + map_option_out (map (fun x => ST.check_one_fix x) mfix) = Some l -> map_option_out (map (fun x => check_one_fix (map_def trans trans x)) mfix) = Some l. Proof. eapply Forall_map_option_out_map_Some_spec => x kn. @@ -1319,10 +1368,10 @@ Qed. Lemma trans_check_one_cofix mfix ind : Swf_fix mfix -> - STy.check_one_cofix mfix = Some ind -> + ST.check_one_cofix mfix = Some ind -> check_one_cofix (map_def trans trans mfix) = Some ind. Proof. - unfold STy.check_one_cofix, check_one_cofix. + unfold ST.check_one_cofix, check_one_cofix. case: mfix => [na ty arg rarg] /= [wfty wfarg]. move: (trans_decompose_prod_assum [] ty wfty) => /=. destruct AstUtils.decompose_prod_assum as [ctx p] eqn:dp => /= // ->. @@ -1337,7 +1386,7 @@ Qed. Lemma map_option_out_check_one_cofix {mfix} : Forall (fun def => (S.wf (dtype def) /\ S.wf (dbody def))) mfix -> forall l, - map_option_out (map (fun x => STy.check_one_cofix x) mfix) = Some l -> + map_option_out (map (fun x => ST.check_one_cofix x) mfix) = Some l -> map_option_out (map (fun x => check_one_cofix (map_def trans trans x)) mfix) = Some l. Proof. apply Forall_map_option_out_map_Some_spec => x kn. @@ -1345,19 +1394,19 @@ Proof. Qed. Lemma trans_check_rec_kind {Σ k f} : - STy.check_recursivity_kind Σ k f = check_recursivity_kind (trans_global_decls Σ) k f. + ST.check_recursivity_kind Σ k f = check_recursivity_kind (trans_global_decls Σ) k f. Proof. - unfold STy.check_recursivity_kind, check_recursivity_kind. + unfold ST.check_recursivity_kind, check_recursivity_kind. rewrite trans_lookup. destruct S.lookup_env as [[]|] => //. Qed. Lemma trans_wf_fixpoint Σ mfix : Forall (fun def => (S.wf (dtype def) /\ S.wf (dbody def))) mfix -> - STy.wf_fixpoint Σ mfix -> + ST.wf_fixpoint Σ mfix -> wf_fixpoint (trans_global_decls Σ) (map (map_def trans trans) mfix). Proof. - unfold STy.wf_fixpoint, wf_fixpoint. + unfold ST.wf_fixpoint, wf_fixpoint. rewrite map_map_compose. intros wf. destruct map_option_out eqn:ma => //. @@ -1367,10 +1416,10 @@ Qed. Lemma trans_wf_cofixpoint Σ mfix : Forall (fun def => (S.wf (dtype def) /\ S.wf (dbody def))) mfix -> - STy.wf_cofixpoint Σ mfix -> + ST.wf_cofixpoint Σ mfix -> wf_cofixpoint (trans_global_decls Σ) (map (map_def trans trans) mfix). Proof. - unfold STy.wf_cofixpoint, wf_cofixpoint. + unfold ST.wf_cofixpoint, wf_cofixpoint. rewrite map_map_compose. intros wf. destruct map_option_out eqn:ma => //. @@ -1379,27 +1428,27 @@ Proof. Qed. Lemma trans_global_decl_universes d : - STy.universes_decl_of_decl d = + ST.universes_decl_of_decl d = universes_decl_of_decl (trans_global_decl d). Proof. destruct d; reflexivity. Qed. Lemma trans_consistent_instance_ext {cf:checker_flags} Σ d u : - STy.consistent_instance_ext Σ (STy.universes_decl_of_decl d) u -> + ST.consistent_instance_ext Σ (ST.universes_decl_of_decl d) u -> consistent_instance_ext (trans_global Σ) (universes_decl_of_decl (trans_global_decl d)) u. Proof. - unfold STy.consistent_instance_ext, consistent_instance_ext. + unfold ST.consistent_instance_ext, consistent_instance_ext. rewrite global_ext_levels_trans global_ext_constraints_trans trans_global_decl_universes. trivial. Qed. Theorem template_to_pcuic {cf} : - STy.env_prop (fun Σ Γ t T => + ST.env_prop (fun Σ Γ t T => wf (trans_global Σ).1 -> typing (trans_global Σ) (trans_local Γ) (trans t) (trans T)). Proof. - apply (STy.typing_ind_env (fun Σ Γ t T => + apply (ST.typing_ind_env (fun Σ Γ t T => wf (trans_global Σ).1 -> typing (trans_global Σ) (trans_local Γ) (trans t) (trans T) )%type). @@ -1477,7 +1526,7 @@ Proof. now apply (trans_consistent_instance_ext _ (S.InductiveDecl mdecl)). - pose proof (forall_decls_declared_constructor _ _ _ _ _ isdecl). - unfold STy.type_of_constructor in *. + unfold ST.type_of_constructor in *. rewrite trans_subst. rewrite trans_subst_instance_constr. rewrite trans_inds. simpl. @@ -1516,8 +1565,8 @@ Proof. - eapply refine_type. assert (fix_context (map (map_def trans trans) mfix) = - trans_local (STy.fix_context mfix)). - { unfold trans_local, STy.fix_context. + trans_local (ST.fix_context mfix)). + { unfold trans_local, ST.fix_context. rewrite map_rev map_mapi /fix_context mapi_map. f_equal. apply mapi_ext; intros i x. simpl. rewrite trans_lift. reflexivity. } @@ -1541,8 +1590,8 @@ Proof. - eapply refine_type. assert (fix_context (map (map_def trans trans) mfix) = - trans_local (STy.fix_context mfix)). - { unfold trans_local, STy.fix_context. + trans_local (ST.fix_context mfix)). + { unfold trans_local, ST.fix_context. rewrite map_rev map_mapi /fix_context mapi_map. f_equal. apply mapi_ext => i x. simpl. rewrite trans_lift. reflexivity. } @@ -1579,10 +1628,10 @@ Proof. induction 1; constructor; auto. Qed. -Definition trans_constructor_shape (t : STy.constructor_shape) : constructor_shape := - {| cshape_args := trans_local t.(STy.cshape_args); - cshape_indices := map trans t.(STy.cshape_indices); - cshape_sorts := t.(STy.cshape_sorts) |}. +Definition trans_constructor_shape (t : ST.constructor_shape) : constructor_shape := + {| cshape_args := trans_local t.(ST.cshape_args); + cshape_indices := map trans t.(ST.cshape_indices); + cshape_sorts := t.(ST.cshape_sorts) |}. Lemma trans_reln l p Γ : map trans (TemplateEnvironment.reln l p Γ) = PCUICEnvironment.reln (map trans l) p (trans_local Γ). @@ -1619,10 +1668,10 @@ Proof. Qed. Lemma trans_on_global_env `{checker_flags} Σ P Q : - (forall Σ Γ t T, STy.on_global_env P Σ.1 -> P Σ Γ t T -> + (forall Σ Γ t T, ST.on_global_env P Σ.1 -> P Σ Γ t T -> on_global_env Q (trans_global_decls Σ.1) -> Q (trans_global Σ) (trans_local Γ) (trans t) (option_map trans T)) -> - STy.on_global_env P Σ -> on_global_env Q (trans_global_decls Σ). + ST.on_global_env P Σ -> on_global_env Q (trans_global_decls Σ). Proof. intros X X0. simpl in *. induction X0; simpl; constructor; auto. @@ -1651,20 +1700,20 @@ Proof. * destruct o0 as [onI onP onNP]. constructor; auto. -- eapply Alli_map. eapply Alli_impl. exact onI. eauto. intros. - unshelve refine {| ind_indices := trans_local X1.(STy.ind_indices); - ind_sort := X1.(STy.ind_sort); - ind_cshapes := map trans_constructor_shape X1.(STy.ind_cshapes) |}. - --- simpl; rewrite X1.(STy.ind_arity_eq). + unshelve refine {| ind_indices := trans_local X1.(ST.ind_indices); + ind_sort := X1.(ST.ind_sort); + ind_cshapes := map trans_constructor_shape X1.(ST.ind_cshapes) |}. + --- simpl; rewrite X1.(ST.ind_arity_eq). now rewrite !trans_it_mkProd_or_LetIn. - --- apply STy.onArity in X1. unfold on_type in *; simpl in *. + --- apply ST.onArity in X1. unfold on_type in *; simpl in *. now apply (X (Σ, Ast.ind_universes m) [] (Ast.ind_type x) None). - --- pose proof X1.(STy.onConstructors) as X11. red in X11. + --- pose proof X1.(ST.onConstructors) as X11. red in X11. red. eapply All2_map. eapply All2_impl; eauto. simpl. intros [[? ?] ?] cs onc. destruct onc; unshelve econstructor; eauto. + simpl. unfold trans_local. rewrite context_assumptions_map. now rewrite cstr_args_length. - + simpl; unfold cdecl_type, STy.cdecl_type in cstr_eq |- *; simpl in *. + + simpl; unfold cdecl_type, ST.cdecl_type in cstr_eq |- *; simpl in *. rewrite cstr_eq. rewrite !trans_it_mkProd_or_LetIn. autorewrite with len. f_equal. f_equal. rewrite !trans_mkApps //. @@ -1674,12 +1723,12 @@ Proof. rewrite /trans_local !map_length. unfold TemplateEnvironment.to_extended_list_k. now rewrite trans_reln. - + unfold cdecl_type, STy.cdecl_type in on_ctype |- *; simpl in *. + + unfold cdecl_type, ST.cdecl_type in on_ctype |- *; simpl in *. red. move: (X (Σ, Ast.ind_universes m) (Ast.arities_context (Ast.ind_bodies m)) t None). now rewrite trans_arities_context. + clear -X0 IHX0 X on_cargs. revert on_cargs. simpl. - generalize (STy.cshape_args cs), (STy.cshape_sorts cs). + generalize (ST.cshape_args cs), (ST.cshape_sorts cs). have foo := (X (Σ, udecl) _ _ _ X0). rewrite -trans_arities_context. induction c; destruct l; simpl; auto; @@ -1697,19 +1746,19 @@ Proof. revert on_cindices. rewrite trans_lift_context /trans_local -map_rev. simpl. rewrite {2}/trans_local map_length. - generalize (List.rev (LiftSubst.lift_context #|STy.cshape_args cs| 0 (STy.ind_indices X1))). - generalize (STy.cshape_indices cs). + generalize (List.rev (LiftSubst.lift_context #|ST.cshape_args cs| 0 (ST.ind_indices X1))). + generalize (ST.cshape_indices cs). rewrite -trans_arities_context. induction 1; simpl; constructor; auto; have foo := (X (Σ, Ast.ind_universes m) _ _ _ X0); specialize (foo (Ast.app_context (Ast.app_context (Ast.arities_context (Ast.ind_bodies m)) - (Ast.ind_params m)) (STy.cshape_args cs))). + (Ast.ind_params m)) (ST.cshape_args cs))). rewrite /trans_local !map_app in foo. now apply (foo i (Some t)). now rewrite (trans_subst_telescope [i] 0) in IHon_cindices. now rewrite (trans_subst_telescope [b] 0) in IHon_cindices. + clear -IHX0 on_ctype_positive. - unfold STy.cdecl_type in *. unfold cdecl_type. simpl in *. + unfold ST.cdecl_type in *. unfold cdecl_type. simpl in *. change [] with (map trans_decl []). revert on_ctype_positive. generalize (@nil Ast.context_decl). induction 1; simpl. rewrite trans_mkApps. simpl. @@ -1726,11 +1775,11 @@ Proof. apply IHon_ctype_positive. + clear -on_ctype_variance. intros v indv. admit. - --- simpl; intros. have onp := X1.(STy.onProjections). + --- simpl; intros. have onp := X1.(ST.onProjections). admit. - --- have inds := X1.(STy.ind_sorts). + --- have inds := X1.(ST.ind_sorts). admit. - --- have inds := X1.(STy.onIndices). + --- have inds := X1.(ST.onIndices). admit. -- red in onP. red. admit. @@ -1741,11 +1790,11 @@ Lemma template_to_pcuic_env {cf} Σ : Template.Typing.wf Σ -> wf (trans_global_ Proof. intros Hu. eapply trans_on_global_env; eauto. simpl; intros. - epose proof (STy.env_prop_typing _ template_to_pcuic _ X Γ). + epose proof (ST.env_prop_typing _ template_to_pcuic _ X Γ). forward X2. red in X0. destruct T. - now eapply STy.typing_wf_local. - destruct X0 as [s Hs]. eapply STy.typing_wf_local; eauto. + now eapply ST.typing_wf_local. + destruct X0 as [s Hs]. eapply ST.typing_wf_local; eauto. destruct T; simpl in *. - eapply X2; eauto. - destruct X0 as [s Hs]. exists s. @@ -1765,12 +1814,12 @@ Proof. Qed. Theorem template_to_pcuic_typing {cf} Σ Γ t T : - STy.wf Σ.1 -> - STy.typing Σ Γ t T -> + ST.wf Σ.1 -> + ST.typing Σ Γ t T -> typing (trans_global Σ) (trans_local Γ) (trans t) (trans T). Proof. intros wf ty. - apply (STy.env_prop_typing _ template_to_pcuic _ wf); auto. - now eapply STy.typing_wf_local. + apply (ST.env_prop_typing _ template_to_pcuic _ wf); auto. + now eapply ST.typing_wf_local. now apply template_to_pcuic_env. Qed. From 5b34d94eb44b0c4a16397eb9d5a3bcbe5e62ec17 Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Sat, 12 Dec 2020 17:02:23 +0100 Subject: [PATCH 66/70] Remove remaining references to checker/ --- dependency-graph/dependency-graph.md | 2 +- examples/_CoqProject | 1 - pcuic/theories/TemplateToPCUICCorrectness.v | 248 +++++++++++++++++--- test-suite/_CoqProject | 4 +- 4 files changed, 220 insertions(+), 35 deletions(-) diff --git a/dependency-graph/dependency-graph.md b/dependency-graph/dependency-graph.md index 4dfabf0d7..a5332c4f8 100644 --- a/dependency-graph/dependency-graph.md +++ b/dependency-graph/dependency-graph.md @@ -11,7 +11,7 @@ cd dependency-graph # Generate the dependency graph between files by hand (obsolete) -1. In each folder (template-coq + checker + pcuic + safechecker + erasure), generate the dot file with: +1. In each folder (template-coq + pcuic + safechecker + erasure), generate the dot file with: ``` coqdep -f _CoqProject -dumpgraph plop.dot > /dev/null ``` diff --git a/examples/_CoqProject b/examples/_CoqProject index a84ae72c0..c68a2627f 100644 --- a/examples/_CoqProject +++ b/examples/_CoqProject @@ -2,7 +2,6 @@ -I ../safechecker/src -I ../erasure/src -Q ../template-coq/theories MetaCoq.Template --Q ../checker/theories MetaCoq.Checker -Q ../pcuic/theories MetaCoq.PCUIC -Q ../safechecker/theories MetaCoq.SafeChecker -Q ../erasure/theories MetaCoq.Erasure diff --git a/pcuic/theories/TemplateToPCUICCorrectness.v b/pcuic/theories/TemplateToPCUICCorrectness.v index 5ee0afce2..18b010637 100644 --- a/pcuic/theories/TemplateToPCUICCorrectness.v +++ b/pcuic/theories/TemplateToPCUICCorrectness.v @@ -394,7 +394,7 @@ Proof. destruct t => //. simpl. now destruct prim as [? []]. Qed. *) - +(* Lemma trans_decompose_app_args t f l : Ast.wf t -> AstUtils.decompose_app t = (f, l) -> @@ -404,10 +404,92 @@ Proof. intros [= <- <-]; auto. admit. rewrite decompose_app_mkApps. destruct (AstUtils.decompose_app t). -Admitted. +Admitted. *) + +Lemma trans_ind_params mdecl : trans_local (Ast.ind_params mdecl) = ind_params (trans_minductive_body mdecl). +Proof. reflexivity. Qed. + +Lemma trans_ind_bodies mdecl : map trans_one_ind_body (Ast.ind_bodies mdecl) = ind_bodies (trans_minductive_body mdecl). +Proof. reflexivity. Qed. +From MetaCoq.PCUIC Require Import PCUICClosed PCUICInductiveInversion. + +Lemma instantiate_params_spec params paramsi concl ty : + instantiate_params params paramsi (it_mkProd_or_LetIn params concl) = Some ty -> + ty = (subst (List.rev paramsi) 0 (expand_lets params concl)). +Proof. + intros h. eapply instantiate_params_make_context_subst in h as [ctx'' [ms [s' [da [dp ->]]]]]. + eapply make_context_subst_spec in dp. + rewrite List.rev_involutive in dp. + pose proof (PCUICContexts.context_subst_length2 dp). + rewrite decompose_prod_n_assum_it_mkProd app_nil_r in da. noconf da. + apply context_subst_subst_extended_subst in dp as ->. + rewrite map_subst_expand_lets ?List.rev_length //. +Qed. + +Lemma trans_ind_bodies_length mdecl : #|TemplateEnvironment.ind_bodies mdecl| = #|ind_bodies (trans_minductive_body mdecl)|. +Proof. simpl. now rewrite map_length. Qed. + +Lemma trans_ind_params_length mdecl : #|TemplateEnvironment.ind_params mdecl| = #|ind_params (trans_minductive_body mdecl)|. +Proof. simpl. now rewrite map_length. Qed. + +Lemma trans_ind_npars mdecl : Ast.ind_npars mdecl = ind_npars (trans_minductive_body mdecl). +Proof. simpl. reflexivity. Qed. + +Lemma trans_reln l p Γ : map trans (Ast.reln l p Γ) = + reln (map trans l) p (trans_local Γ). +Proof. + induction Γ as [|[na [b|] ty] Γ] in l, p |- *; simpl; auto. + now rewrite IHΓ. +Qed. + +Lemma trans_to_extended_list Γ n : map trans (Ast.to_extended_list_k Γ n) = to_extended_list_k (trans_local Γ) n. +Proof. + now rewrite /to_extended_list_k trans_reln. +Qed. + +Definition trans_constructor_shape (t : ST.constructor_shape) : constructor_shape := + {| cshape_args := trans_local t.(ST.cshape_args); + cshape_indices := map trans t.(ST.cshape_indices); + cshape_sorts := t.(ST.cshape_sorts) |}. + +Lemma trans_cshape_args cs : trans_local (ST.cshape_args cs) = cshape_args (trans_constructor_shape cs). +Proof. reflexivity. Qed. -Lemma trans_build_branches_type {cf} Σ ind mdecl idecl args u p brtys : +Lemma trans_cshape_args_length cs : #|ST.cshape_args cs| = #|cshape_args (trans_constructor_shape cs)|. +Proof. now rewrite -trans_cshape_args map_length. Qed. + +Lemma context_assumptions_map ctx : context_assumptions (map trans_decl ctx) = Ast.context_assumptions ctx. +Proof. + induction ctx as [|[na [b|] ty] ctx]; simpl; auto. +Qed. + +(* Lemma decompose_prod_assum_mkApps ctx t f l : + decompose_prod_assum ctx t = (ctx', l) -> + it_mkProd_or_LetIn ctx t = it_mkProd_or_LetIn ctx' (mkApps t' -> + () *) +(* +Lemma decompose_app_trans_inv t ind u l : + Ast.wf t -> + decompose_app (trans t) = (tInd ind u, l) -> + ∑ l', l = map trans l' /\ AstUtils.decompose_app t = (Ast.tInd ind u, l'). +Proof. + destruct t => //. simpl. + intros wf. + destruct decompose_app eqn:da. + pose proof (decompose_app_notApp _ _ _ da). + rewrite decompose_app_mkApps in da. depelim wf. destruct t => //. + destruct t0 => //. + intros [= -> -> ->]. + exists args. noconf da. split; auto. f_equal. rewrite -H0 in H. + depelim wf. + destruct t => //. simpl in H2. noconf H2. reflexivity. + intros. simpl in H0. noconf H0. + exists []. split; auto. +Qed. *) +Lemma trans_build_branches_type ind mdecl idecl args u p brtys : + (* (ST.on_inductive (ST.lift_typing ST.typing) Σ (inductive_mind ind) mdecl) -> (ST.on_ind_body (ST.lift_typing ST.typing) Σ (inductive_mind ind) mdecl (inductive_ind ind) idecl) -> + inductive_ind ind < #|ind_bodies (trans_minductive_body mdecl)| -> *) map_option_out (ST.build_branches_type ind mdecl idecl args u p) = Some brtys -> map_option_out @@ -416,7 +498,10 @@ Lemma trans_build_branches_type {cf} Σ ind mdecl idecl args u p brtys : (trans p)) = Some (map (on_snd trans) brtys). Proof. - intros onind. +Admitted. +(* Will likely change with the change of representation of cases *) +(* + intros onmind onind indlt. pose proof (ST.onConstructors onind) as onc. unfold ST.build_branches_type. unfold build_branches_type. @@ -425,29 +510,103 @@ Proof. intros i [[id ty] argn] [nargs br] s oncs. simpl. destruct ST.instantiate_params eqn:ipars => //. + pose proof ipars as ipars'. apply trans_instantiate_params in ipars. - rewrite trans_subst in ipars. - rewrite -trans_inds. - rewrite -trans_subst_instance_constr. - rewrite [map _ _]trans_local_subst_instance_context in ipars. + rewrite trans_subst trans_inds trans_subst_instance_constr in ipars. + rewrite [map _ _]trans_local_subst_instance_context trans_ind_params + trans_ind_bodies in ipars. + + rewrite trans_ind_params trans_ind_bodies. rewrite ipars. - assert (wft : S.wf t). admit. + assert (wft : S.wf t). eapply wf_instantiate_params. 4:eapply ipars'. 1-3:admit. + pose proof (trans_decompose_prod_assum [] t wft). + destruct (AstUtils.decompose_prod_assum [] t) eqn:da'. + rewrite H. + destruct chop eqn:eqchop. + intros [= -> <-]. + destruct (chop _ (decompose_app (trans t0)).2) eqn:c'. + f_equal. f_equal. + rewrite [ty]oncs.(ST.cstr_eq) in ipars. + rewrite trans_it_mkProd_or_LetIn subst_instance_constr_it_mkProd_or_LetIn + subst_it_mkProd_or_LetIn in ipars. len in ipars. + rewrite closed_ctx_subst in ipars. + rewrite [map _ _]trans_ind_params. admit. + apply instantiate_params_spec in ipars. + rewrite trans_it_mkProd_or_LetIn. f_equal. + rewrite trans_mkApps map_length trans_lift. f_equal. + rewrite map_app /= trans_mkApps /= map_app trans_to_extended_list. + assert (l1 = map trans l /\ l2 = map trans l0) as [-> ->]. + { simpl in H. + move: ipars. + rewrite trans_it_mkProd_or_LetIn subst_instance_constr_it_mkProd_or_LetIn subst_it_mkProd_or_LetIn. + rewrite /expand_lets expand_lets_it_mkProd_or_LetIn. len. + rewrite subst_it_mkProd_or_LetIn. + rewrite trans_mkApps. + rewrite /ST.cstr_concl_head. cbn -[subst]. + rewrite trans_ind_bodies. len. + rewrite trans_ind_bodies_length trans_ind_params_length. + rewrite map_app trans_to_extended_list trans_ind_params trans_cshape_args_length. + rewrite (subst_cstr_concl_head ind u (trans_minductive_body mdecl)) //. + rewrite expand_lets_k_mkApps subst_mkApps /=. + intros eqit. + rewrite eqit in H. + rewrite decompose_prod_assum_it_mkProd // in H. + apply is_ind_app_head_mkApps. + injection H. clear H. rewrite app_nil_r. + intros eqind _. + apply (f_equal decompose_app) in eqind. + destruct (decompose_app (trans t0)) eqn:dt0. + simpl in *. + rewrite decompose_app_mkApps // in eqind. noconf eqind. + + noconf H. + move: H. + + rewrite !map_app map_map_compose chop_n_app. len. + rewrite context_assumptions_map. now rewrite onmind.(ST.onNpars). + destruct AstUtils.decompose_prod_assum eqn:da'. + rewrite trans_it_mkProd_or_LetIn trans_mkApps. len. + simpl in H. rewrite H. + + + + reflexivity. + + + + + + f_equal. f_equal. rewrite map_app. + rewrite trans_to_extended_list. f_equal. + + + + len. + + + apply instantiate_params_make_context_subst in ipars as [ctx' [ty'' [s' [dass [makes eq]]]]]. + rewrite eq. + eapply make_context_subst_spec in makes. + rewrite List.rev_involutive in makes. + + + move: (trans_decompose_prod_assum [] t wft). + destruct oncs. simpl in cstr_eq. + rewrite trans_inds in ipars. + rewrite trans_subst_instance_constr in ipars. + intros [= -> <-]. + destruct AstUtils.decompose_prod_assum eqn:dp => -> /=. destruct (AstUtils.decompose_app t0) eqn:da'. simpl. destruct chop as [params argsl] eqn:ceq. - destruct oncs. simpl in cstr_eq. - rewrite [ty]cstr_eq in ipars. - intros [= -> <-]. rewrite (chop_map _ _ _ _ _ ceq). intros [= ->]. f_equal. unfold on_snd. simpl. f_equal. subst br. rewrite trans_it_mkProd_or_LetIn trans_mkApps map_app /= trans_mkApps /= map_app. now rewrite trans_to_extended_list trans_lift map_length. Qed. -intros. - -Admitted. +*) Lemma trans_build_case_predicate_type ind mdecl idecl params u ps : build_case_predicate_type ind (trans_minductive_body mdecl) @@ -669,9 +828,50 @@ Proof. + now rewrite IHΣ. Qed. -Lemma context_assumptions_map ctx : context_assumptions (map trans_decl ctx) = Ast.context_assumptions ctx. +Lemma on_global_env_impl `{checker_flags} Σ P Q : + (forall Σ Γ t T, ST.on_global_env P Σ.1 -> P Σ Γ t T -> Q Σ Γ t T) -> + ST.on_global_env P Σ -> ST.on_global_env Q Σ. Proof. - induction ctx as [|[na [b|] ty] ctx]; simpl; auto. + intros X X0. + simpl in *. induction X0; constructor; auto. + clear IHX0. destruct d; simpl. + - destruct c; simpl. destruct cst_body; simpl in *. + red in o |- *. simpl in *. now eapply X. + red in o |- *. simpl in *. now eapply X. + - red in o. simpl in *. + destruct o0 as [onI onP onNP]. + constructor; auto. + -- eapply Alli_impl. exact onI. eauto. intros. + refine {| ST.ind_indices := X1.(ST.ind_indices); + ST.ind_arity_eq := X1.(ST.ind_arity_eq); + ST.ind_cshapes := X1.(ST.ind_cshapes) |}. + --- apply ST.onArity in X1. unfold on_type in *; simpl in *. + now eapply X. + --- pose proof X1.(ST.onConstructors) as X11. red in X11. + eapply All2_impl; eauto. + simpl. intros. destruct X2 as [? ? ? ?]; unshelve econstructor; eauto. + * apply X; eauto. + * clear -X0 X on_cargs. revert on_cargs. + generalize (ST.cshape_args y), (ST.cshape_sorts y). + induction c; destruct l; simpl; auto; + destruct a as [na [b|] ty]; simpl in *; auto; + split; intuition eauto. + * clear -X0 X on_cindices. + revert on_cindices. + generalize (List.rev (SL.lift_context #|ST.cshape_args y| 0 (ST.ind_indices X1))). + generalize (ST.cshape_indices y). + induction 1; simpl; constructor; auto. + --- simpl; intros. pose (ST.onProjections X1 H0). simpl in *; auto. + --- destruct X1. simpl. unfold ST.check_ind_sorts in *. + destruct Universe.is_prop, Universe.is_sprop; auto. + split. + * apply ind_sorts. + * destruct indices_matter; auto. + eapply ST.type_local_ctx_impl. eapply ind_sorts. auto. + --- eapply X1.(ST.onIndices). + -- red in onP. red. + eapply ST.All_local_env_impl. eauto. + intros. now apply X. Qed. Lemma typing_wf_wf {cf}: @@ -1546,7 +1746,7 @@ Proof. -- rewrite global_ext_constraints_trans; exact H1. -- rewrite trans_mkApps in X2; auto with wf. -- apply H2. - -- apply trans_build_branches_type in H3. + -- eapply trans_build_branches_type in H3; eauto. rewrite firstn_map. exact H3. -- eapply All2_map. solve_all. destruct b0 as [s [Hs IHs]]; eauto. @@ -1628,18 +1828,6 @@ Proof. induction 1; constructor; auto. Qed. -Definition trans_constructor_shape (t : ST.constructor_shape) : constructor_shape := - {| cshape_args := trans_local t.(ST.cshape_args); - cshape_indices := map trans t.(ST.cshape_indices); - cshape_sorts := t.(ST.cshape_sorts) |}. - -Lemma trans_reln l p Γ : map trans (TemplateEnvironment.reln l p Γ) = - PCUICEnvironment.reln (map trans l) p (trans_local Γ). -Proof. - induction Γ as [|[na [b|] ty] Γ] in l, p |- *; simpl; auto. - now rewrite IHΓ. -Qed. - Lemma trans_arities_context m : trans_local (Ast.arities_context (Ast.ind_bodies m)) = arities_context (map trans_one_ind_body (Ast.ind_bodies m)). Proof. diff --git a/test-suite/_CoqProject b/test-suite/_CoqProject index 4163b0a62..9d9922631 100644 --- a/test-suite/_CoqProject +++ b/test-suite/_CoqProject @@ -1,9 +1,7 @@ -I ../template-coq/build --I ../checker/src -I ../safechecker/src -I ../erasure/src -Q ../template-coq/theories MetaCoq.Template --Q ../checker/theories MetaCoq.Checker -Q ../pcuic/theories MetaCoq.PCUIC -Q ../safechecker/theories MetaCoq.SafeChecker -Q ../erasure/theories MetaCoq.Erasure @@ -22,6 +20,7 @@ case.v castprop.v # CheckerTest.v disabled cofix.v +vs.v erasure_live_test.v erasure_test.v evars.v @@ -43,7 +42,6 @@ tmInferInstance.v TypingTests.v unfold.v univ.v -vs.v tmVariable.v order_rec.v primitive.v \ No newline at end of file From 643424ba6f18f9b48a8d488f7ed83b1cad4bc3c9 Mon Sep 17 00:00:00 2001 From: Matthieu Sozeau Date: Sat, 12 Dec 2020 22:34:09 +0100 Subject: [PATCH 67/70] Remove test-suite relying on unproven checker --- test-suite/TypingTests.v | 164 --------------------------------------- test-suite/_CoqProject | 2 - test-suite/test_term.v | 13 ---- 3 files changed, 179 deletions(-) delete mode 100644 test-suite/TypingTests.v delete mode 100644 test-suite/test_term.v diff --git a/test-suite/TypingTests.v b/test-suite/TypingTests.v deleted file mode 100644 index c32b957f9..000000000 --- a/test-suite/TypingTests.v +++ /dev/null @@ -1,164 +0,0 @@ -Require Import Recdef Morphisms. -From MetaCoq.Template Require Import utils All. -Require Import MetaCoq.Checker.All. - -Unset Template Cast Propositions. - -MetaCoq Quote Recursively Definition idq := @Coq.Classes.Morphisms.Proper. - -Existing Instance config.default_checker_flags. -Existing Instance Checker.default_fuel. - -Definition test0 := Eval vm_compute in typecheck_program idq. -Definition nAnon := {| binder_name := nAnon; binder_relevance := Relevant |}. - -Definition timpl x y := tProd nAnon x (LiftSubst.lift0 1 y). - -MetaCoq Quote Recursively Definition four := (2 + 2). -Unset Printing Matching. - -Ltac typecheck := try red; cbn; intros; - match goal with - |- ?Σ ;;; ?Γ |- ?t : ?T => - refine (infer_correct Σ _ _ Γ t T _ _); [reflexivity|constructor|vm_compute; reflexivity] - end. -Ltac infer := try red; - match goal with - |- ?Σ ;;; ?Γ |- ?t : ?T => - refine (infer_correct Σ _ _ Γ t T _ _); [reflexivity|constructor| - let t' := eval vm_compute in (infer' Σ Γ t) in - change (t' = Checked T); reflexivity] - end. - -MetaCoq Quote Definition natr := nat. - -Definition type_program (p : program) (ty : term) := - let Σ := empty_ext (fst p) in - Σ ;;; [] |- snd p : ty. - -Example typecheck_four : type_program four natr:= ltac:(typecheck). - -Goal { ty & type_program four ty }. -Proof. - eexists. infer. -Qed. - -(* Uase template-coq to make a [program] from function defined above *) - -(* Eval native_compute in typecheck_program p_Plus1. *) - -Definition test_reduction (p : program) := - let Σ := empty_ext (fst p) in - reduce (fst Σ) [] (snd p). - -Definition string_of_env_error e := - match e with - | IllFormedDecl s e => ("IllFormedDecl " ^ s ^ "\nType error: " ^ string_of_type_error e)%string - | AlreadyDeclared s => ("Alreadydeclared " ^ s)%string - end. - -Definition out_typing c := - match c with - | Checked t => t - | TypeError e => tVar ("Typing error")%string - end. - -Definition out_check c := - match c with - | CorrectDecl t => t - | EnvError e => tVar ("Check error: " ++ string_of_env_error e)%string - end. - -Ltac interp_red c := - let t:= eval vm_compute in (out_typing (test_reduction c)) in exact t. - -Ltac interp_infer c := - let t:= eval vm_compute in (out_check (typecheck_program c)) in exact t. - -Ltac term_type c := - let X := type of c in exact X. - -Ltac quote_type c := - let X := type of c in - quote_term X ltac:(fun Xast => exact Xast). - -Notation convertible x y := (@eq_refl _ x : x = y). - -Module Test1. - Definition term := (Nat.mul 2 62). - Load "test_term.v". -End Test1. - -Module Test2. - Definition term := (fun (f : nat -> nat) (x : nat) => f (f x)). - Load "test_term.v". -End Test2. - -Module Test3. - (* Definition term := (id 0). *) - (* Load "test_term.v". *) -End Test3. - -Module Test4. - Definition term := @id. - Set Printing Universes. - Load "test_term.v". -End Test4. - -Module Test5. - - (** A function defined using measure or well-founded relation **) - (* Function Plus1 (n: nat) {measure id n} : nat := - match n with - | 0 => 1 - | S p => S (Plus1 p) - end. - - intros. unfold id. abstract omega. - Defined. *) - - (* Time Template Check Plus1. *) - (* Time Template Check Coq.ZArith.BinInt.Z.succ_pred. (* -> 16 s *) *) - (* MetaCoq Quote Recursively Definition plop := Coq.ZArith.BinInt.Z.succ_pred. *) - (* Eval native_compute in (typecheck_program plop). (* -> 31 min!! *) *) - - - (* (* Too long with universes on *) *) - (* MetaCoq Quote Recursively Definition p_Plus1 := Plus1. *) - - (* Definition term := Plus1. *) - (* Definition ast := p_Plus1. *) - (* Set Printing Universes. *) - (* (** Check typing *) *) - - (* (* Yay! Typechecking an actually non-trivial term. (173s) *) *) - - (* MetaCoq Unquote Definition inferred_type := ltac:(interp_infer ast). *) - (* Definition inferred_type' := Eval cbv delta in inferred_type. *) - (* Print inferred_type'. *) - (* Check convertible ltac:(term_type term) inferred_type. *) -End Test5. - -Universe i j. - -Definition f1 := (forall (A:Type@{i}) (B: Prop), A -> B -> A). -(* : Type@{Set+1, i+1} *) - -Definition f2 := (forall (A:Type@{i}) (B: Prop), A -> B -> B). -(* : Prop *) - -MetaCoq Quote Definition f1' := (forall (A:Type@{i}) (B: Prop), A -> B -> A). - -Definition test1 := Eval lazy in infer' (empty_ext []) nil f1'. - -MetaCoq Quote Definition f2' := (forall (A:Type@{i}) (B: Prop), A -> B -> B). - -Definition test2 := Eval lazy in infer' (empty_ext []) nil f2'. - -Definition f := (forall (A:Type@{i}) (B: Type@{j}), A -> B -> A). -(* : Type@{i+1, j+1} *) - -MetaCoq Quote Definition f' := (forall (A:Type@{i}) (B:Type@{j}), A -> B -> A). - -MetaCoq Quote Definition f'' := (forall (B: Type@{j}), B -> B). - -Definition test3 := Eval lazy in infer' (empty_ext []) nil f'. diff --git a/test-suite/_CoqProject b/test-suite/_CoqProject index 9d9922631..8f0e6f89a 100644 --- a/test-suite/_CoqProject +++ b/test-suite/_CoqProject @@ -35,11 +35,9 @@ opaque.v proj.v run_in_tactic.v safechecker_test.v -# test_term.v -> loaded in TypingTests.v tmExistingInstance.v tmFreshName.v tmInferInstance.v -TypingTests.v unfold.v univ.v tmVariable.v diff --git a/test-suite/test_term.v b/test-suite/test_term.v deleted file mode 100644 index 88f561c2b..000000000 --- a/test-suite/test_term.v +++ /dev/null @@ -1,13 +0,0 @@ -(** Check reduction *) -MetaCoq Quote Recursively Definition ast := term. -MetaCoq Unquote Definition normal_form := ltac:(interp_red ast). - -Definition normal_form' := Eval vm_compute in normal_form. -(* Print normal_form'. *) -Check convertible term normal_form. - -(** Check typing *) -MetaCoq Unquote Definition inferred_type := ltac:(interp_infer ast). -Definition inferred_type' := Eval cbv delta in inferred_type. -(* Print inferred_type'. *) -Check convertible ltac:(term_type term) inferred_type. From f0f58ccabdf52ed665c73217ebe862e6b38bd78e Mon Sep 17 00:00:00 2001 From: Jakob Botsch Nielsen Date: Thu, 17 Dec 2020 11:48:14 +0100 Subject: [PATCH 68/70] Remove wcbv evaluation of axioms in PCUIC In PCUIC we treated axioms as values, but we did not consistently treat eg. fixpoints and cases stuck on axioms as values. This removes the evaluation of axioms in PCUIC and gets rid of the axiom_free assumption that was needed for erasure because of it. --- erasure/theories/EArities.v | 4 +- erasure/theories/EOptimizePropDiscr.v | 14 +-- erasure/theories/ErasureCorrectness.v | 38 +++--- erasure/theories/ErasureFunction.v | 4 +- erasure/theories/Prelim.v | 6 +- pcuic/theories/PCUICCanonicity.v | 165 +++++++++++++++++--------- pcuic/theories/PCUICWcbvEval.v | 65 +--------- template-coq/theories/WcbvEval.v | 62 +--------- 8 files changed, 141 insertions(+), 217 deletions(-) diff --git a/erasure/theories/EArities.v b/erasure/theories/EArities.v index 9637f483f..7918dda63 100644 --- a/erasure/theories/EArities.v +++ b/erasure/theories/EArities.v @@ -548,7 +548,6 @@ Qed. Lemma Is_type_eval (Σ : global_env_ext) t v: wf Σ -> - axiom_free Σ -> eval Σ t v -> isErasable Σ [] t -> isErasable Σ [] v. @@ -563,13 +562,12 @@ Qed. Lemma Is_type_eval_inv (Σ : global_env_ext) t v: wf_ext Σ -> - axiom_free Σ -> PCUICSafeLemmata.welltyped Σ [] t -> PCUICWcbvEval.eval Σ t v -> isErasable Σ [] v -> ∥ isErasable Σ [] t ∥. Proof. - intros wfΣ axfree [T HT] ev [vt [Ht Hp]]. + intros wfΣ [T HT] ev [vt [Ht Hp]]. eapply wcbeval_red in ev; eauto. pose proof (subject_reduction _ _ _ _ _ wfΣ.1 HT ev). pose proof (common_typing _ wfΣ Ht X) as [P [Pvt [Pt vP]]]. diff --git a/erasure/theories/EOptimizePropDiscr.v b/erasure/theories/EOptimizePropDiscr.v index d995ae094..0307689b9 100644 --- a/erasure/theories/EOptimizePropDiscr.v +++ b/erasure/theories/EOptimizePropDiscr.v @@ -232,17 +232,15 @@ Proof. Qed. Lemma erasable_tBox_value (wfl := Ee.default_wcbv_flags) (Σ : global_env_ext) (wfΣ : wf_ext Σ) t T v : - axiom_free Σ.1 -> forall wt : Σ ;;; [] |- t : T, Σ |-p t ▷ v -> erases Σ [] v tBox -> ∥ isErasable Σ [] t ∥. Proof. intros. - depind H0. + depind H. eapply Is_type_eval_inv; eauto. eexists; eauto. Qed. Lemma erase_eval_to_box (wfl := Ee.default_wcbv_flags) {Σ : global_env_ext} {wfΣ : wf_ext Σ} {t v Σ' t' deps} : - axiom_free Σ.1 -> forall wt : welltyped Σ [] t, erase Σ (sq wfΣ) [] t wt = t' -> KernameSet.subset (term_global_deps t') deps -> @@ -250,9 +248,9 @@ Lemma erase_eval_to_box (wfl := Ee.default_wcbv_flags) {Σ : global_env_ext} {w PCUICWcbvEval.eval Σ t v -> @Ee.eval Ee.default_wcbv_flags Σ' t' tBox -> ∥ isErasable Σ [] t ∥. Proof. - intros axiomfree [T wt]. + intros [T wt]. intros. - destruct (erase_correct Σ wfΣ _ _ _ _ _ axiomfree _ H H0 H1 X) as [ev [eg [eg']]]. + destruct (erase_correct Σ wfΣ _ _ _ _ _ _ H H0 H1 X) as [ev [eg [eg']]]. pose proof (Ee.eval_deterministic H2 eg'). subst. eapply erasable_tBox_value; eauto. Qed. @@ -457,7 +455,6 @@ Proof. Qed. Lemma erase_opt_correct (wfl := Ee.default_wcbv_flags) (Σ : global_env_ext) (wfΣ : wf_ext Σ) t v Σ' t' : - axiom_free Σ.1 -> forall wt : welltyped Σ [] t, erase Σ (sq wfΣ) [] t wt = t' -> erase_global (term_global_deps t') Σ (sq wfΣ.1) = Σ' -> @@ -465,10 +462,9 @@ Lemma erase_opt_correct (wfl := Ee.default_wcbv_flags) (Σ : global_env_ext) (wf ∃ v' : term, Σ;;; [] |- v ⇝ℇ v' ∧ ∥ @Ee.eval Ee.opt_wcbv_flags (optimize_env Σ') (optimize Σ' t') (optimize Σ' v') ∥. Proof. - intros axiomfree wt. + intros wt. generalize (sq wfΣ.1) as swfΣ. intros swfΣ HΣ' Ht' ev. - assert (extraction_pre Σ) by now constructor. pose proof (erases_erase (wfΣ := sq wfΣ) wt); eauto. rewrite HΣ' in H. destruct wt as [T wt]. @@ -485,5 +481,3 @@ Proof. eapply KernameSet.subset_spec. intros x hin; auto. Qed. - -Print Assumptions erase_opt_correct. \ No newline at end of file diff --git a/erasure/theories/ErasureCorrectness.v b/erasure/theories/ErasureCorrectness.v index ab746583e..2112a51a2 100644 --- a/erasure/theories/ErasureCorrectness.v +++ b/erasure/theories/ErasureCorrectness.v @@ -429,14 +429,7 @@ Qed. (** ** The correctness proof *) -Record extraction_pre (Σ : global_env_ext) : Type - := Build_extraction_pre - { extr_env_axiom_free' : axiom_free (fst Σ); - extr_env_wf' : wf_ext Σ }. - Hint Constructors PCUICWcbvEval.eval erases : core. -Arguments extr_env_wf' {Σ}. -Arguments extr_env_axiom_free' {Σ}. Definition EisConstruct_app := fun t => match (EAstUtils.decompose_app t).1 with @@ -682,16 +675,16 @@ Proof. Qed. Lemma erases_correct (wfl := default_wcbv_flags) Σ t T t' v Σ' : - extraction_pre Σ -> + wf_ext Σ -> Σ;;; [] |- t : T -> Σ;;; [] |- t ⇝ℇ t' -> erases_deps Σ Σ' t' -> Σ |-p t ▷ v -> exists v', Σ;;; [] |- v ⇝ℇ v' /\ ∥ Σ' ⊢ t' ▷ v' ∥. Proof. - intros pre Hty He Hed H. + intros wfΣ Hty He Hed H. revert T Hty t' He Hed. - induction H; intros T Hty t' He Hed; destruct pre as [axfree wfΣ]. + induction H; intros T Hty t' He Hed. - assert (Hty' := Hty). assert (eval Σ (PCUICAst.tApp f a) res) by eauto. eapply inversion_App in Hty as (? & ? & ? & ? & ? & ?). @@ -805,10 +798,6 @@ Proof. + exists EAst.tBox. split. econstructor. eapply Is_type_eval. 3: eassumption. eauto. eauto. eauto. constructor. econstructor. eauto. - - destruct Σ as (Σ, univs). - cbn in *. - eapply axfree in isdecl. congruence. - - assert (Hty' := Hty). assert (Σ |-p tCase (ind, pars) p discr brs ▷ res) by eauto. eapply inversion_Case in Hty' as [u' [args' [mdecl [idecl [ps [pty [btys @@ -906,7 +895,7 @@ Proof. eapply subject_reduction. eauto. exact Hty. etransitivity. eapply PCUICReduction.red_case_c. eapply wcbeval_red. eauto. - now eapply PCUICClosed.subject_closed in t0. eauto. eauto. + eauto. eauto. etransitivity. constructor. constructor. unfold iota_red. rewrite <- nth_default_eq. unfold nth_default. @@ -949,7 +938,7 @@ Proof. eapply subject_reduction. eauto. exact Hty. etransitivity. eapply PCUICReduction.red_case_c. eapply wcbeval_red. eauto. - now eapply PCUICClosed.subject_closed in t0; eauto. eauto. eauto. + eauto. eauto. etransitivity. constructor. constructor. unfold iota_red. rewrite <- nth_default_eq. reflexivity. @@ -1062,7 +1051,7 @@ Proof. eapply erases_deps_mkApps_inv in Hty_vc' as (? & ?). now eapply nth_error_forall in H1; eauto. + exists EAst.tBox. split. econstructor. - eapply Is_type_eval. 4: eassumption. all:eauto. constructor. econstructor. eauto. + eapply Is_type_eval. 3: eassumption. all:eauto. constructor. econstructor. eauto. - assert (Hty' := Hty). assert (Hunf := H). @@ -1080,7 +1069,7 @@ Proof. + exists EAst.tBox. split; [|now constructor; constructor]. econstructor. - eapply Is_type_eval. 4:eapply X. eauto. eauto. + eapply Is_type_eval. 3:eapply X. eauto. eapply eval_fix; eauto. rewrite /cunfold_fix e0 //. congruence. + depelim Hed. @@ -1151,10 +1140,11 @@ Proof. assert(Σ ;;; [] |- mkApps (tFix mfix idx) (argsv ++ [av]) : PCUICLiftSubst.subst [av] 0 x1). { rewrite -mkApps_nested. eapply PCUICValidity.type_App'; eauto. eapply subject_reduction_eval; eauto. } - epose proof (fix_app_is_constructor Σ (args:=argsv ++ [av]) axfree X). + epose proof (fix_app_is_constructor Σ (args:=argsv ++ [av]) X). rewrite /unfold_fix e0 in X0. specialize (X0 eq_refl). simpl in X0. rewrite nth_error_snoc in X0. auto. apply X0. + eapply value_axiom_free, eval_to_value; eauto. eapply value_whnf; eauto. eapply eval_closed; eauto. now eapply PCUICClosed.subject_closed in t0. eapply eval_to_value; eauto. } @@ -1214,7 +1204,7 @@ Proof. -- exists EAst.tBox. split. ++ econstructor. - eapply Is_type_eval. 4:eauto. all:eauto. + eapply Is_type_eval. 3:eauto. all:eauto. rewrite -mkApps_nested. eapply eval_fix; eauto. 1-2:eapply value_final, eval_to_value; eauto. @@ -1232,7 +1222,7 @@ Proof. destruct Hty' as (? & ? & ? & ? & ? & ?). eapply subject_reduction in t as typ_stuck_fix; [|eauto|]; first last. - { eapply wcbeval_red. 4:eauto. all:eauto. } + { eapply wcbeval_red. 3:eauto. all:eauto. } eapply erases_App in He as He'; [|eauto]. destruct He' as [(-> & [])|(? & ? & -> & ? & ?)]. @@ -1242,12 +1232,12 @@ Proof. eapply Is_type_red. * eauto. * eapply PCUICReduction.red_app. - -- eapply wcbeval_red; [eauto|eauto| |eauto]. eauto. - -- eapply wcbeval_red; [eauto|eauto| |eauto]. eauto. + -- eapply wcbeval_red; [eauto| |eauto]. eauto. + -- eapply wcbeval_red; [eauto| |eauto]. eauto. * eauto. + depelim Hed. eapply subject_reduction in t0 as typ_arg; [|eauto|]; first last. - { eapply wcbeval_red; [eauto|eauto| |eauto]. eauto. } + { eapply wcbeval_red; [eauto| |eauto]. eauto. } eapply IHeval1 in H1 as (? & ? & [?]); [|now eauto|now eauto]. eapply IHeval2 in H2 as (? & ? & [?]); [|now eauto|now eauto]. diff --git a/erasure/theories/ErasureFunction.v b/erasure/theories/ErasureFunction.v index 31429f511..247fd006d 100644 --- a/erasure/theories/ErasureFunction.v +++ b/erasure/theories/ErasureFunction.v @@ -1187,7 +1187,6 @@ Proof. Qed. Lemma erase_correct (wfl := Ee.default_wcbv_flags) (Σ : global_env_ext) (wfΣ : wf_ext Σ) t v Σ' t' deps : - axiom_free Σ.1 -> forall wt : welltyped Σ [] t, erase Σ (sq wfΣ) [] t wt = t' -> KernameSet.subset (term_global_deps t') deps -> @@ -1195,10 +1194,9 @@ Lemma erase_correct (wfl := Ee.default_wcbv_flags) (Σ : global_env_ext) (wfΣ : Σ |-p t ▷ v -> exists v', Σ;;; [] |- v ⇝ℇ v' /\ ∥ Σ' ⊢ t' ▷ v' ∥. Proof. - intros axiomfree wt. + intros wt. generalize (sq wfΣ.1) as swfΣ. intros swfΣ HΣ' Hsub Ht' ev. - assert (extraction_pre Σ) by now constructor. pose proof (erases_erase (wfΣ := sq wfΣ) wt); eauto. rewrite HΣ' in H. destruct wt as [T wt]. diff --git a/erasure/theories/Prelim.v b/erasure/theories/Prelim.v index 3746e7034..042748fdb 100644 --- a/erasure/theories/Prelim.v +++ b/erasure/theories/Prelim.v @@ -16,8 +16,6 @@ Module P := PCUICWcbvEval. Ltac inv H := inversion H; subst; clear H. -Existing Class axiom_free. - Lemma nth_error_app_inv X (x : X) n l1 l2 : nth_error (l1 ++ l2) n = Some x -> (n < #|l1| /\ nth_error l1 n = Some x) \/ (n >= #|l1| /\ nth_error l2 (n - List.length l1) = Some x). Proof. @@ -121,7 +119,7 @@ Proof. now exists A. Qed. -Theorem subject_reduction_eval {Σ :global_env_ext} {t u T} {wfΣ : wf Σ} {axfree : axiom_free Σ} : +Theorem subject_reduction_eval {Σ :global_env_ext} {t u T} {wfΣ : wf Σ} : Σ ;;; [] |- t : T -> PCUICWcbvEval.eval Σ t u -> Σ ;;; [] |- u : T. Proof. intros Hty Hred. @@ -133,7 +131,7 @@ Lemma typing_spine_eval: (X : All2 (PCUICWcbvEval.eval Σ) args args') (bla : wf Σ) (T x x0 : PCUICAst.term) (t0 : typing_spine Σ [] x args x0) (c : Σ;;; [] |- x0 <= T) (x1 : PCUICAst.term) - (c0 : Σ;;; [] |- x1 <= x), axiom_free Σ -> isType Σ [] T -> typing_spine Σ [] x1 args' T. + (c0 : Σ;;; [] |- x1 <= x), isType Σ [] T -> typing_spine Σ [] x1 args' T. Proof. intros. eapply typing_spine_red; eauto. eapply typing_spine_wt in t0; auto. diff --git a/pcuic/theories/PCUICCanonicity.v b/pcuic/theories/PCUICCanonicity.v index abc7b956d..52f3d911d 100644 --- a/pcuic/theories/PCUICCanonicity.v +++ b/pcuic/theories/PCUICCanonicity.v @@ -802,7 +802,7 @@ Section WeakNormalization. Transparent construct_cofix_discr. - Lemma value_whnf t : closed t -> value Σ t -> wh_normal Σ [] t. + Lemma value_whnf t : closed t -> value t -> wh_normal Σ [] t. Proof. intros cl ev. induction ev in cl |- * using value_values_ind. @@ -814,10 +814,6 @@ Section WeakNormalization. now rewrite nth_error_nil. - eapply (whnf_cofixapp _ _ [] _ _ []). - unfold value_head in H. destruct t => //. - constructor; eapply whne_mkApps. - cbn in H; destruct lookup_env eqn:eq => //. - destruct g => //. destruct c => //. destruct cst_body => //. - eapply whne_const; eauto. - destruct f => //. cbn in H. destruct cunfold_fix as [[rarg body]|] eqn:unf => //. pose proof cl as cl'. @@ -1014,41 +1010,92 @@ Section WeakNormalization. eapply PCUICConfluence.red_mkApps_tInd in r as [? [eq _]]; auto. solve_discr. Qed. - - Lemma wh_neutral_empty_gen t Γ : axiom_free Σ -> wh_neutral Σ Γ t -> forall ty, Σ ;;; Γ |- t : ty -> Γ = [] -> False - with wh_normal_empty_gen t Γ i u args : axiom_free Σ -> wh_normal Σ Γ t -> Σ ;;; Γ |- t : mkApps (tInd i u) args -> - Γ = [] -> construct_cofix_discr (head t). + + Fixpoint axiom_free_value Σ args t := + match t with + | tApp hd arg => axiom_free_value Σ (axiom_free_value Σ [] arg :: args) hd + | tConst kn _ => match lookup_env Σ kn with + | Some (ConstantDecl {| cst_body := Some _ |}) => true + | _ => false + end + | tCase _ _ discr _ => axiom_free_value Σ [] discr + | tProj _ t => axiom_free_value Σ [] t + | tFix defs i => + match nth_error defs i with + | Some def => nth (rarg def) args true + | None => true + end + | _ => true + end. + + Lemma axiom_free_value_mkApps Σ' args hd args' : + axiom_free_value Σ' args (mkApps hd args') = + axiom_free_value Σ' (map (axiom_free_value Σ' []) args' ++ args) hd. Proof. - intros axfree ne ty typed. - 2:intros axfree ne typed. - all:pose proof (subject_closed wfΣ typed) as cl; - destruct ne; intros eqΓ; simpl in *; try discriminate. - - rewrite eqΓ in cl => //. + revert hd args. + induction args' using MCList.rev_ind; intros hd args; cbn; auto. + rewrite -mkApps_nested /=. + rewrite IHargs'. + now rewrite map_app /= -app_assoc. + Qed. + + Lemma wh_neutral_empty_gen Γ free t ty : + axiom_free_value Σ free t -> + wh_neutral Σ [] t -> + Σ ;;; Γ |- t : ty -> + Γ = [] -> + False. + Proof. + intros axfree ne typed. + induction ne in free, t, ty, axfree, ne, typed |- *; intros ->; simpl in *; try discriminate. + - apply inversion_Rel in typed as (?&?&?&?); auto. + rewrite nth_error_nil in e0; discriminate. - now eapply typing_var in typed. - now eapply typing_evar in typed. - - clear wh_neutral_empty_gen wh_normal_empty_gen. subst. - apply inversion_Const in typed as [decl' [wfd [declc [cu cum]]]]; eauto. - specialize (axfree _ _ declc). - red in declc. rewrite declc in e. noconf e. congruence. - - simpl in cl; move/andP: cl => [clf cla]. - eapply inversion_App in typed as [na [A [B [Hf _]]]]; eauto. - - specialize (wh_neutral_empty_gen _ _ axfree ne). subst. - simpl in cl. - eapply inversion_mkApps in typed as (? & ? & ?); eauto. + - apply inversion_Const in typed as [decl' [wfd [declc [cu cum]]]]; eauto. + red in declc. + rewrite declc in e, axfree. + noconf e. + destruct decl; cbn in *. + rewrite e0 in axfree; congruence. + - eapply inversion_App in typed as [na [A [B [Hf _]]]]; eauto. + - eapply inversion_mkApps in typed as (? & ? & ?); eauto. eapply inversion_Fix in t as (? & ? & ? & ? & ? & ? & ?); auto. eapply typing_spine_strengthen in t0; eauto. eapply nth_error_all in a; eauto. simpl in a. rewrite /unfold_fix in e. rewrite e1 in e. noconf e. eapply (wf_fixpoint_spine wfΣ) in t0; eauto. rewrite e0 in t0. destruct t0 as [ind [u [indargs [tyarg ckind]]]]. - clear wh_normal_empty_gen. - now specialize (wh_neutral_empty_gen _ tyarg eq_refl). - - move/andP: cl => [/andP[_ clc] _]. - eapply inversion_Case in typed as (? & ? & ? & ? & ? & ? & ? & ? & ? & ? & ? & ? & ? & ? & ? & ? & ?); auto. - eapply wh_neutral_empty_gen; eauto. - - eapply inversion_Proj in typed as (? & ? & ? & ? & ? & ? & ? & ? & ?); auto. - eapply wh_neutral_empty_gen; eauto. - - eapply wh_neutral_empty_gen in w; eauto. + rewrite axiom_free_value_mkApps in axfree. + cbn in axfree. + rewrite e1 nth_nth_error nth_error_app1 in axfree. + 1: { rewrite map_length. + apply nth_error_Some_length in e0; auto. } + rewrite nth_error_map e0 in axfree. + cbn in axfree. + eauto. + - eapply inversion_Case in typed as + (? & ? & ? & ? & ? & ? & ? & ? & ? & ? & ? & ? & ? & ? & ? & ? & ?); eauto. + - eapply inversion_Proj in typed as (? & ? & ? & ? & ? & ? & ? & ? & ?); eauto. + Qed. + + Lemma wh_neutral_empty t ty : + axiom_free_value Σ [] t -> + wh_neutral Σ [] t -> + Σ ;;; [] |- t : ty -> + False. + Proof. eauto using wh_neutral_empty_gen. Qed. + + Lemma wh_normal_ind_discr t i u args : + axiom_free_value Σ [] t -> + wh_normal Σ [] t -> + Σ ;;; [] |- t : mkApps (tInd i u) args -> + construct_cofix_discr (head t). + Proof. + intros axfree ne typed. + pose proof (subject_closed wfΣ typed) as cl. + depelim ne; simpl in *. + - eauto using wh_neutral_empty. - eapply inversion_Sort in typed as (? & ? & ?); auto. eapply invert_cumul_sort_l in c as (? & ? & ?); auto. eapply red_mkApps_tInd in r as (? & eq & ?); eauto; eauto. @@ -1068,20 +1115,8 @@ Section WeakNormalization. - now eapply inversion_Prim in typed. Qed. - Lemma wh_neutral_empty t ty : axiom_free Σ -> - Σ ;;; [] |- t : ty -> - wh_neutral Σ [] t -> - False. - Proof. intros; eapply wh_neutral_empty_gen; eauto. Qed. - - Lemma wh_normal_ind_discr t i u args : axiom_free Σ -> - Σ ;;; [] |- t : mkApps (tInd i u) args -> - wh_normal Σ [] t -> - construct_cofix_discr (head t). - Proof. intros. eapply wh_normal_empty_gen; eauto. Qed. - Lemma whnf_ind_finite t ind u indargs : - axiom_free Σ -> + axiom_free_value Σ [] t -> Σ ;;; [] |- t : mkApps (tInd ind u) indargs -> wh_normal Σ [] t -> check_recursivity_kind Σ (inductive_mind ind) Finite -> @@ -1099,15 +1134,14 @@ Section WeakNormalization. Qed. Lemma fix_app_is_constructor {mfix idx args ty narg fn} : - axiom_free Σ -> Σ;;; [] |- mkApps (tFix mfix idx) args : ty -> unfold_fix mfix idx = Some (narg, fn) -> match nth_error args narg return Type with - | Some a => wh_normal Σ [] a -> isConstruct_app a + | Some a => axiom_free_value Σ [] a -> wh_normal Σ [] a -> isConstruct_app a | None => ∑ na dom codom, Σ ;;; [] |- tProd na dom codom <= ty end. Proof. - intros axfree typed unf. + intros typed unf. eapply inversion_mkApps in typed as (? & ? & ?); eauto. eapply inversion_Fix in t as (? & ? & ? & ? & ? & ? & ?); auto. eapply typing_spine_strengthen in t0; eauto. @@ -1117,10 +1151,32 @@ Section WeakNormalization. eapply (wf_fixpoint_spine wfΣ) in t0; eauto. rewrite /is_constructor. destruct (nth_error args (rarg x0)) eqn:hnth. destruct_sigma t0. destruct t0. - intros norm. + intros axfree norm. eapply whnf_ind_finite in t0; eauto. assumption. Qed. + + Lemma value_axiom_free Σ' t : + value t -> + axiom_free_value Σ' [] t. + Proof. + intros val. + induction val using value_values_ind. + - destruct t; try discriminate; auto. + cbn. + destruct ?; auto. + destruct ?; auto. + - rewrite axiom_free_value_mkApps. + destruct t; auto. + - rewrite axiom_free_value_mkApps. + destruct f; try discriminate. + cbn. + unfold isStuckFix, cunfold_fix in H. + destruct nth_error; auto. + rewrite nth_overflow; auto. + rewrite app_nil_r map_length; auto. + toProp; auto. + Qed. (** Evaluation on well-typed terms corresponds to reduction. It differs in two ways from standard reduction: @@ -1129,11 +1185,10 @@ Section WeakNormalization. have a constructor at their recursive argument as it is ensured by typing. *) Lemma wcbeval_red t ty u : - axiom_free Σ -> Σ ;;; [] |- t : ty -> eval Σ t u -> red Σ [] t u. Proof. - intros axfree Hc He. + intros Hc He. revert ty Hc. induction He; simpl; move=> ty Ht; try solve[econstructor; eauto]. @@ -1220,7 +1275,7 @@ Section WeakNormalization. eapply red_fix; eauto. assert (Σ ;;; [] |- mkApps (tFix mfix idx) (argsv ++ [av]) : B {0 := av}). { rewrite -mkApps_nested /=. eapply type_App'; eauto. } - epose proof (fix_app_is_constructor axfree X0 e); eauto. + epose proof (fix_app_is_constructor X0 e); eauto. rewrite /is_constructor. destruct nth_error eqn:hnth => //. assert (All (closedn 0) (argsv ++ [av])). @@ -1228,7 +1283,7 @@ Section WeakNormalization. rewrite closedn_mkApps in X0. move/andP: X0 => [clfix clargs]. now eapply forallb_All in clargs. } - assert (All (value Σ) (argsv ++ [av])). + assert (All value (argsv ++ [av])). { eapply All_app_inv; [|constructor; [|constructor]]. eapply eval_to_value in He1. eapply value_mkApps_inv in He1 as [[[-> Hat]|[vh vargs]]|[hstuck vargs]] => //. @@ -1236,6 +1291,7 @@ Section WeakNormalization. solve_all. eapply nth_error_all in X3; eauto. simpl in X3. destruct X3 as [cl val]. eapply X1, value_whnf; auto. + eapply value_axiom_free; auto. eapply nth_error_None in hnth; len in hnth; simpl in *. lia. } redt _; eauto. @@ -1273,14 +1329,15 @@ Section WeakNormalization. Qed. Lemma eval_ind_canonical t i u args : - axiom_free Σ -> Σ ;;; [] |- t : mkApps (tInd i u) args -> forall t', eval Σ t t' -> construct_cofix_discr (head t'). Proof. - intros axfree Ht t' eval. + intros Ht t' eval. pose proof (subject_closed wfΣ Ht). eapply subject_reduction in Ht. 3:eapply wcbeval_red; eauto. 2:auto. + eapply eval_to_value in eval as axfree. + eapply value_axiom_free in axfree. eapply eval_whne in eval; auto. eapply wh_normal_ind_discr; eauto. Qed. diff --git a/pcuic/theories/PCUICWcbvEval.v b/pcuic/theories/PCUICWcbvEval.v index d5b17f105..772cbd61a 100644 --- a/pcuic/theories/PCUICWcbvEval.v +++ b/pcuic/theories/PCUICWcbvEval.v @@ -93,26 +93,6 @@ Definition isConstruct t := | _ => false end. -Definition isAssRel Γ x := - match x with - | tRel i => - match option_map decl_body (nth_error Γ i) with - | Some None => true - | _ => false - end - | _ => false - end. - -Definition isAxiom Σ x := - match x with - | tConst c u => - match lookup_env Σ c with - | Some (ConstantDecl {| cst_body := None |}) => true - | _ => false - end - | _ => false - end. - Definition substl defs body : term := fold_left (fun bod term => csubst term 0 bod) defs body. @@ -165,29 +145,12 @@ Section Wcbv. eval (csubst b0' 0 b1) res -> eval (tLetIn na b0 t b1) res - (** - (** Local variables: defined or undefined *) - | eval_rel_def i body res : - option_map decl_body (nth_error Γ i) = Some (Some body) -> - eval (lift0 (S i) body) res -> - eval (tRel i) res - - | eval_rel_undef i : - option_map decl_body (nth_error Γ i) = Some None -> - eval (tRel i) (tRel i) - *) - (** Constant unfolding *) | eval_delta c decl body (isdecl : declared_constant Σ c decl) u res : decl.(cst_body) = Some body -> eval (subst_instance_constr u body) res -> eval (tConst c u) res - (** Axiom *) - | eval_axiom c decl (isdecl : declared_constant Σ c decl) u : - decl.(cst_body) = None -> - eval (tConst c u) (tConst c u) - (** Case *) | eval_iota ind pars discr c u args p brs res : eval discr (mkApps (tConstruct ind c u) args) -> @@ -257,14 +220,13 @@ Section Wcbv. *) Definition value_head x := - isInd x || isConstruct x || isCoFix x || isAxiom Σ x. + isInd x || isConstruct x || isCoFix x. (* Lemma value_head_atom x : value_head x -> atom x. *) (* Proof. destruct x; auto. Qed. *) Inductive value : term -> Type := | value_atom t : atom t -> value t - (* | value_evar n l l' : Forall value l -> Forall value l' -> value (mkApps (tEvar n l) l') *) | value_app t l : value_head t -> All value l -> value (mkApps t l) | value_stuck_fix f args : All value args -> @@ -274,8 +236,6 @@ Section Wcbv. Lemma value_values_ind : forall P : term -> Type, (forall t, atom t -> P t) -> - (* (forall n l l', Forall value l -> Forall P l -> Forall value l' -> Forall P l' -> *) - (* P (mkApps (tEvar n l) l')) -> *) (forall t l, value_head t -> All value l -> All P l -> P (mkApps t l)) -> (forall f args, All value args -> @@ -335,11 +295,6 @@ Section Wcbv. Lemma eval_to_value e e' : eval e e' -> value e'. Proof. induction 1; simpl; auto using value. - - eapply (value_app (tConst c u) []). - red in isdecl. - rewrite /value_head /= isdecl. - destruct decl as [? [b|] ?]; try discriminate. - constructor. constructor. - change (tApp ?h ?a) with (mkApps h [a]). rewrite mkApps_nested. apply value_mkApps_inv in IHX1; [|easy]. @@ -443,15 +398,6 @@ Section Wcbv. move/(_ H) => Ht. induction l using rev_ind. simpl. destruct t; try discriminate. - (* * constructor. - unfold value_head in H. simpl in H. destruct option_map as [[o|]|] => //. *) - * unfold value_head in H. simpl in H. - destruct lookup_env eqn:Heq => //. - destruct g eqn:Heq' => //. - destruct c as [? [b|] ?] eqn:Heq'' => //. subst. - eapply eval_axiom. red. - rewrite Heq. reflexivity. - easy. * now eapply eval_atom. * now eapply eval_atom. * now eapply eval_atom. @@ -723,10 +669,6 @@ Section Wcbv. assert (e0 = e) as -> by now apply uip. assert (isdecl0 = isdecl) as -> by now apply uip. now specialize (IHev _ ev'); noconf IHev. - - depelim ev'; try go. - pose proof (PCUICWeakeningEnv.declared_constant_inj _ _ isdecl isdecl0) as <-. - assert (isdecl0 = isdecl) as -> by now apply uip. - now assert (e0 = e) as -> by now apply uip. - depelim ev'; try go. + specialize (IHev1 _ ev'1); noconf IHev1. apply (f_equal pr1) in IHev1 as apps_eq; cbn in *. @@ -861,13 +803,10 @@ Section Wcbv. ∑ decl, declared_constant Σ c decl * match cst_body decl with | Some body => eval (subst_instance_constr u body) v - | None => v = tConst c u + | None => False end. Proof. intros H; depelim H. - - exists decl. - split; [easy|]. - now rewrite e. - exists decl. split; [easy|]. now rewrite e. diff --git a/template-coq/theories/WcbvEval.v b/template-coq/theories/WcbvEval.v index 6aa05b0b9..ad96f1edf 100644 --- a/template-coq/theories/WcbvEval.v +++ b/template-coq/theories/WcbvEval.v @@ -71,26 +71,6 @@ Definition isConstruct t := | _ => false end. -Definition isAssRel Γ x := - match x with - | tRel i => - match option_map decl_body (nth_error Γ i) with - | Some None => true - | _ => false - end - | _ => false - end. - -Definition isAxiom Σ x := - match x with - | tConst c u => - match lookup_env Σ c with - | Some (ConstantDecl {| cst_body := None |}) => true - | _ => false - end - | _ => false - end. - Definition isStuckFix t args := match t with | tFix mfix idx => @@ -128,27 +108,18 @@ Section Wcbv. eval (subst10 b0' b1) res -> eval (tLetIn na b0 t b1) res - (** Local variables: defined or undefined *) + (** Local variable with bodies *) | eval_rel_def i body res : option_map decl_body (nth_error Γ i) = Some (Some body) -> eval (lift0 (S i) body) res -> eval (tRel i) res - | eval_rel_undef i : - option_map decl_body (nth_error Γ i) = Some None -> - eval (tRel i) (tRel i) - (** Constant unfolding *) | eval_delta c decl body (isdecl : declared_constant Σ c decl) u res : decl.(cst_body) = Some body -> eval (subst_instance_constr u body) res -> eval (tConst c u) res - (** Axiom *) - | eval_axiom c decl (isdecl : declared_constant Σ c decl) u : - decl.(cst_body) = None -> - eval (tConst c u) (tConst c u) - (** Case *) | eval_iota ind pars r discr c u args p brs res : eval discr (mkApps (tConstruct ind c u) args) -> @@ -223,14 +194,11 @@ Section Wcbv. (forall (i : nat) (body res : term), option_map decl_body (nth_error Γ i) = Some (Some body) -> eval ((lift0 (S i)) body) res -> P ((lift0 (S i)) body) res -> P (tRel i) res) -> - (forall i : nat, option_map decl_body (nth_error Γ i) = Some None -> P (tRel i) (tRel i)) -> (forall c (decl : constant_body) (body : term), declared_constant Σ c decl -> forall (u : Instance.t) (res : term), cst_body decl = Some body -> eval (subst_instance_constr u body) res -> P (subst_instance_constr u body) res -> P (tConst c u) res) -> - (forall c (decl : constant_body), - declared_constant Σ c decl -> forall u : Instance.t, cst_body decl = None -> P (tConst c u) (tConst c u)) -> (forall (ind : inductive) (pars : nat) r (discr : term) (c : nat) (u : Instance.t) (args : list term) (p : term) (brs : list (nat × term)) (res : term), eval discr (mkApps (tConstruct ind c u) args) -> @@ -277,15 +245,13 @@ Section Wcbv. All2 eval a a' -> All2 P a a' -> P (tApp f a) (mkApps f' a')) -> (forall t : term, atom t -> P t t) -> forall t t0 : term, eval t t0 -> P t t0. Proof. - intros P Hbeta Hlet Hreldef Hrelvar Hcst Hax Hcase Hproj Hfix Hstuckfix Hcofixcase Hcofixproj Happcong Hatom. + intros P Hbeta Hlet Hreldef Hcst Hcase Hproj Hfix Hstuckfix Hcofixcase Hcofixproj Happcong Hatom. fix eval_evals_ind 3. destruct 1; try solve [match goal with [ H : _ |- _ ] => match type of H with forall t t0, eval t t0 -> _ => fail 1 | _ => eapply H end end; eauto]. - - eapply Hrelvar, e. - - eapply Hax; [eapply isdecl|eapply e]. - eapply Hfix; eauto. clear -a eval_evals_ind. revert args argsv a. @@ -308,7 +274,7 @@ Section Wcbv. *) Definition value_head x := - isConstruct x || isCoFix x || isAssRel Γ x || isAxiom Σ x. + isConstruct x || isCoFix x. (* Lemma value_head_atom x : value_head x -> atom x. *) (* Proof. destruct x; auto. Qed. *) @@ -390,12 +356,6 @@ Section Wcbv. Proof. intros eve. induction eve using eval_evals_ind; simpl; intros; auto using value. - - eapply (value_app (tRel i) []). now rewrite /value_head /= H. constructor. - - eapply (value_app (tConst c u) []). - red in H. - rewrite /value_head /= H. - destruct decl as [? [b|] ?]; try discriminate. - constructor. constructor. - eapply value_stuck_fix. + apply All_app_inv. * now eapply value_mkApps_values. @@ -433,17 +393,8 @@ Section Wcbv. eval t t. Proof. destruct t; intros vt nt; try discriminate. - * constructor. - unfold value_head in vt. simpl in vt. destruct option_map as [[o|]|] => //. - * unfold value_head in vt. simpl in vt. - destruct lookup_env eqn:Heq => //. - destruct g eqn:Heq' => //. - destruct c0 as [? [b|] ?] eqn:Heq'' => //. subst. - intros. eapply eval_axiom. red. - now rewrite Heq. - easy. - * now eapply eval_atom. - * now eapply eval_atom. + - now eapply eval_atom. + - now eapply eval_atom. Qed. Lemma value_final e : value e -> eval e e. @@ -584,12 +535,11 @@ Section Wcbv. ∑ decl, declared_constant Σ c decl * match cst_body decl with | Some body => eval (subst_instance_constr u body) v - | None => v = tConst c u + | None => False end. Proof. intros H; depind H; try solve_discr'; try now easy. - exists decl. intuition auto. now rewrite e. - - exists decl. intuition auto. now rewrite e. - symmetry in H1. eapply mkApps_nisApp in H1 => //; intuition subst; auto. depelim a. eapply eval_to_stuck_fix_inv in H; [|easy]. From f1655e7d22e4d385bec489754167b9943fbe0877 Mon Sep 17 00:00:00 2001 From: Jakob Botsch Nielsen Date: Thu, 17 Dec 2020 12:56:30 +0100 Subject: [PATCH 69/70] Add a proof of consistency using safe reduction and canonicity --- pcuic/theories/PCUICCanonicity.v | 253 +----------------------- safechecker/_CoqProject.in | 1 + safechecker/theories/PCUICConsistency.v | 220 +++++++++++++++++++++ 3 files changed, 229 insertions(+), 245 deletions(-) create mode 100644 safechecker/theories/PCUICConsistency.v diff --git a/pcuic/theories/PCUICCanonicity.v b/pcuic/theories/PCUICCanonicity.v index 52f3d911d..86594c38b 100644 --- a/pcuic/theories/PCUICCanonicity.v +++ b/pcuic/theories/PCUICCanonicity.v @@ -606,188 +606,6 @@ Section Spines. End Spines. -(* -Section Normalization. - Context {cf:checker_flags} (Σ : global_env_ext). - Context {wfΣ : wf Σ}. - - Section reducible. - Lemma reducible Γ t : sum (∑ t', red1 Σ Γ t t') (forall t', red1 Σ Γ t t' -> False). - Proof. - Local Ltac lefte := left; eexists; econstructor; eauto. - Local Ltac leftes := left; eexists; econstructor; solve [eauto]. - Local Ltac righte := right; intros t' red; depelim red; solve_discr; eauto 2. - induction t in Γ |- * using term_forall_list_ind. - (*all:try solve [righte]. - - destruct (nth_error Γ n) eqn:hnth. - destruct c as [na [b|] ty]; [lefte|righte]. - * rewrite hnth; reflexivity. - * rewrite hnth /= // in e. - * righte. rewrite hnth /= // in e. - - admit. - - destruct (IHt1 Γ) as [[? ?]|]; [lefte|]. - destruct (IHt2 (Γ ,, vass n t1)) as [[? ?]|]; [|righte]. - leftes. - - destruct (IHt1 Γ) as [[? ?]|]; [lefte|]. - destruct (IHt2 (Γ ,, vass n t1)) as [[? ?]|]; [|righte]. - leftes. - - destruct (IHt1 Γ) as [[? ?]|]; [lefte|]. - destruct (IHt2 Γ) as [[? ?]|]; [lefte|]. - destruct (IHt3 (Γ ,, vdef n t1 t2)) as [[? ?]|]; [|]. - leftes. lefte. - - destruct (IHt1 Γ) as [[? ?]|]; [lefte|]. - destruct (IHt2 Γ) as [[? ?]|]; [leftes|]. - destruct (PCUICParallelReductionConfluence.view_lambda_fix_app t1 t2). - * rewrite [tApp _ _](mkApps_nested _ _ [a]). - destruct (unfold_fix mfix i) as [[rarg body]|] eqn:unf. - destruct (is_constructor rarg (l ++ [a])) eqn:isc; [leftes|]; eauto. - right => t' red; depelim red; solve_discr; eauto. - rewrite -mkApps_nested in H. noconf H. eauto. - rewrite -mkApps_nested in H. noconf H. eauto. - eapply (f_equal (@length _)) in H1. rewrite /= app_length /= // in H1; lia. - eapply (f_equal (@length _)) in H1. rewrite /= app_length /= // in H1; lia. - righte; try (rewrite -mkApps_nested in H; noconf H); eauto. - eapply (f_equal (@length _)) in H1. rewrite /= app_length /= // in H1; lia. - eapply (f_equal (@length _)) in H1. rewrite /= app_length /= // in H1; lia. - * admit. - * righte. destruct args using rev_case; solve_discr; noconf H. - rewrite H in i. eapply negb_False; eauto. - rewrite -mkApps_nested; eapply isFixLambda_app_mkApps' => //. - - admit. - - admit. - - admit. - - admit. - - admit.*) - - Admitted. - End reducible. - - Lemma reducible' Γ t : sum (∑ t', red1 Σ Γ t t') (normal Σ Γ t). - Proof. - Ltac lefte := left; eexists; econstructor; eauto. - Ltac leftes := left; eexists; econstructor; solve [eauto]. - Ltac righte := right; (solve [repeat (constructor; eauto)])||(repeat constructor). - induction t in Γ |- * using term_forall_list_ind. - all:try solve [righte]. - - destruct (nth_error Γ n) eqn:hnth. - destruct c as [na [b|] ty]; [lefte|]. - * rewrite hnth; reflexivity. - * right. do 2 constructor; rewrite hnth /= //. - * righte. rewrite hnth /= //. - - admit. - - destruct (IHt1 Γ) as [[? ?]|]; [lefte|]. - destruct (IHt2 (Γ ,, vass n t1)) as [[? ?]|]; [|]. - leftes. right; solve[constructor; eauto]. - - destruct (IHt1 Γ) as [[? ?]|]; [lefte|]. - destruct (IHt2 (Γ ,, vass n t1)) as [[? ?]|]; [leftes|leftes]. - - destruct (IHt1 Γ) as [[? ?]|]; [lefte|]. - destruct (IHt2 Γ) as [[? ?]|]; [leftes|]. - destruct (PCUICParallelReductionConfluence.view_lambda_fix_app t1 t2). - * rewrite [tApp _ _](mkApps_nested _ _ [a]). - destruct (unfold_fix mfix i) as [[rarg body]|] eqn:unf. - destruct (is_constructor rarg (l ++ [a])) eqn:isc; [leftes|]; eauto. - right; constructor. rewrite -mkApps_nested. constructor. admit. admit. admit. - * admit. - * admit. - - admit. - - admit. - - admit. - - admit. - - admit. - Admitted. - - Lemma normalizer {Γ t ty} : - Σ ;;; Γ |- t : ty -> - ∑ nf, (red Σ.1 Γ t nf) * normal Σ Γ nf. - Proof. - intros Hty. - unshelve epose proof (PCUICSN.normalisation Σ Γ t (iswelltyped _ _ _ ty Hty)). - clear ty Hty. - move: t H. eapply Fix_F. - intros x IH. - destruct (reducible' Γ x) as [[t' red]|nred]. - specialize (IH t'). forward IH by (constructor; auto). - destruct IH as [nf [rednf norm]]. - exists nf; split; auto. now transitivity t'. - exists x. split; [constructor|assumption]. - Qed. - - Derive Signature for neutral normal. - - Lemma typing_var {Γ n ty} : Σ ;;; Γ |- (tVar n) : ty -> False. - Proof. intros Hty; depind Hty; eauto. Qed. - - Lemma typing_evar {Γ n l ty} : Σ ;;; Γ |- (tEvar n l) : ty -> False. - Proof. intros Hty; depind Hty; eauto. Qed. - - Definition axiom_free Σ := - forall c decl, declared_constant Σ c decl -> cst_body decl <> None. - - Lemma neutral_empty t ty : axiom_free Σ -> Σ ;;; [] |- t : ty -> neutral Σ [] t -> False. - Proof. - intros axfree typed ne. - pose proof (PCUICClosed.subject_closed wfΣ typed) as cl. - depind ne. - - now simpl in cl. - - now eapply typing_var in typed. - - now eapply typing_evar in typed. - - eapply inversion_Const in typed as [decl [wfd [declc [cu cum]]]]; eauto. - specialize (axfree _ _ declc). specialize (H decl). - destruct (cst_body decl); try congruence. - now specialize (H t declc eq_refl). - - simpl in cl; move/andP: cl => [clf cla]. - eapply inversion_App in typed as [na [A [B [Hf _]]]]; eauto. - - simpl in cl; move/andP: cl => [/andP[_ clc] _]. - eapply inversion_Case in typed; pcuicfo eauto. - - eapply inversion_Proj in typed; pcuicfo auto. - Qed. - - Lemma ind_normal_constructor t i u args : - axiom_free Σ -> - Σ ;;; [] |- t : mkApps (tInd i u) args -> normal Σ [] t -> construct_cofix_discr (head t). - Proof. - intros axfree Ht capp. destruct capp. - - eapply neutral_empty in H; eauto. - - eapply inversion_Sort in Ht as (? & ? & ? & ? & ?); auto. - eapply invert_cumul_sort_l in c as (? & ? & ?). - eapply red_mkApps_tInd in r as (? & eq & ?); eauto; eauto. - solve_discr. - - eapply inversion_Prod in Ht as (? & ? & ? & ? & ?); auto. - eapply invert_cumul_sort_l in c as (? & ? & ?). - eapply red_mkApps_tInd in r as (? & eq & ?); eauto; eauto. - solve_discr. - - eapply inversion_Lambda in Ht as (? & ? & ? & ? & ?); auto. - eapply invert_cumul_prod_l in c as (? & ? & ? & (? & ?) & ?); auto. - eapply red_mkApps_tInd in r as (? & eq & ?); eauto; eauto. - solve_discr. - - now rewrite head_mkApps /= /head /=. - - eapply PCUICValidity.inversion_mkApps in Ht as (? & ? & ?); auto. - eapply inversion_Ind in t as (? & ? & ? & decli & ? & ?); auto. - eapply PCUICSpine.typing_spine_strengthen in t0; eauto. - pose proof (on_declared_inductive wfΣ decli) as [onind oib]. - rewrite oib.(ind_arity_eq) in t0. - rewrite !subst_instance_constr_it_mkProd_or_LetIn in t0. - eapply typing_spine_arity_mkApps_Ind in t0; eauto. - eexists; split; [sq|]; eauto. - now do 2 eapply isArity_it_mkProd_or_LetIn. - - admit. (* wf of fixpoints *) - - now rewrite /head /=. - Admitted. - - Lemma red_normal_constructor t i u args : - axiom_free Σ -> - Σ ;;; [] |- t : mkApps (tInd i u) args -> - ∑ hnf, (red Σ.1 [] t hnf) * construct_cofix_discr (head hnf). - Proof. - intros axfree Ht. destruct (normalizer Ht) as [nf [rednf capp]]. - exists nf; split; auto. - eapply subject_reduction in Ht; eauto. - now eapply ind_normal_constructor. - Qed. - -End Normalization. -*) - (** Evaluation is a subrelation of reduction: *) Tactic Notation "redt" uconstr(y) := eapply (CRelationClasses.transitivity (R:=red _ _) (y:=y)). @@ -833,69 +651,12 @@ Section WeakNormalization. now eapply value_whnf. Qed. - (* - Lemma reducible Γ t : sum (∑ t', red1 Σ Γ t t') (wh_normal Σ Γ t). - Proof. - Ltac lefte := left; eexists; econstructor; eauto. - Ltac leftes := left; eexists; econstructor; solve [eauto]. - Ltac righte := right; (solve [repeat (constructor; eauto)])||(repeat constructor). - induction t in Γ |- * using term_forall_list_ind. - all:try solve [righte]. - - destruct (nth_error Γ n) eqn:hnth. - destruct c as [na [b|] ty]; [lefte|]. - * rewrite hnth; reflexivity. - * right. do 2 constructor; rewrite hnth /= //. - * righte. rewrite hnth /= //. admit. - - destruct (IHt1 Γ) as [[? ?]|]; [lefte|]. - destruct (IHt2 Γ) as [[? ?]|]; [leftes|]. - destruct (IHt2 (Γ ,, vass n t1)) as [[? ?]|]; [|]. - leftes. leftes. - - destruct (IHt1 Γ) as [[? ?]|]; [lefte|]. - destruct (IHt2 Γ) as [[? ?]|]; [leftes|]. - destruct (PCUICParallelReductionConfluence.view_lambda_fix_app t1 t2). - * rewrite [tApp _ _](mkApps_nested _ _ [a]). - destruct (unfold_fix mfix i) as [[rarg body]|] eqn:unf. - + destruct (is_constructor rarg (l ++ [a])) eqn:isc; [leftes|]; eauto. - right. rewrite /is_constructor in isc. - destruct nth_error eqn:eq. - ++ constructor; eapply whne_fixapp; eauto. admit. - ++ eapply whnf_fixapp. rewrite unf //. - + right. eapply whnf_fixapp. rewrite unf //. - * left. induction l; simpl. eexists. constructor. - eexists. eapply app_red_l. eapply red1_mkApps_l. constructor. - * admit. - - admit. - - admit. - - admit. - - admit. - - admit. - Admitted. - - Lemma normalizer {Γ t ty} : - Σ ;;; Γ |- t : ty -> - ∑ nf, (red Σ.1 Γ t nf) * wh_normal Σ Γ nf. - Proof. - intros Hty. - unshelve epose proof (PCUICSN.normalisation Σ Γ t (iswelltyped _ _ _ ty Hty)). - clear ty Hty. - move: t H. eapply Fix_F. - intros x IH. - destruct (reducible Γ x) as [[t' red]|nred]. - specialize (IH t'). forward IH by (constructor; auto). - destruct IH as [nf [rednf norm]]. - exists nf; split; auto. now transitivity t'. - exists x. split; [constructor|assumption]. - Qed. *) - Lemma typing_var {Γ n ty} : Σ ;;; Γ |- (tVar n) : ty -> False. Proof. intros Hty; depind Hty; eauto. Qed. Lemma typing_evar {Γ n l ty} : Σ ;;; Γ |- (tEvar n l) : ty -> False. Proof. intros Hty; depind Hty; eauto. Qed. - Definition axiom_free Σ := - forall c decl, declared_constant Σ c decl -> cst_body decl <> None. - Lemma invert_cumul_prod_ind {Γ na dom codom ind u args} : Σ ;;; Γ |- tProd na dom codom <= mkApps (tInd ind u) args -> False. Proof. @@ -1015,8 +776,8 @@ Section WeakNormalization. match t with | tApp hd arg => axiom_free_value Σ (axiom_free_value Σ [] arg :: args) hd | tConst kn _ => match lookup_env Σ kn with - | Some (ConstantDecl {| cst_body := Some _ |}) => true - | _ => false + | Some (ConstantDecl {| cst_body := None |}) => false + | _ => true end | tCase _ _ discr _ => axiom_free_value Σ [] discr | tProj _ t => axiom_free_value Σ [] t @@ -1119,7 +880,7 @@ Section WeakNormalization. axiom_free_value Σ [] t -> Σ ;;; [] |- t : mkApps (tInd ind u) indargs -> wh_normal Σ [] t -> - check_recursivity_kind Σ (inductive_mind ind) Finite -> + ~check_recursivity_kind Σ (inductive_mind ind) CoFinite -> isConstruct_app t. Proof. intros axfree typed whnf ck. @@ -1130,7 +891,7 @@ Section WeakNormalization. destruct hd eqn:eqh => //. subst hd. eapply decompose_app_inv in da. subst. eapply typing_cofix_coind in typed. - now move: (check_recursivity_kind_inj typed ck). + auto. Qed. Lemma fix_app_is_constructor {mfix idx args ty narg fn} : @@ -1149,11 +910,13 @@ Section WeakNormalization. rewrite /unfold_fix in unf. rewrite e in unf. noconf unf. eapply (wf_fixpoint_spine wfΣ) in t0; eauto. - rewrite /is_constructor. destruct (nth_error args (rarg x0)) eqn:hnth. + rewrite /is_constructor. destruct (nth_error args (rarg x0)) eqn:hnth; [|assumption]. destruct_sigma t0. destruct t0. intros axfree norm. eapply whnf_ind_finite in t0; eauto. - assumption. + intros chk. + pose proof (check_recursivity_kind_inj chk i1). + discriminate. Qed. Lemma value_axiom_free Σ' t : diff --git a/safechecker/_CoqProject.in b/safechecker/_CoqProject.in index 29115f2f4..1b751f2da 100644 --- a/safechecker/_CoqProject.in +++ b/safechecker/_CoqProject.in @@ -10,5 +10,6 @@ theories/PCUICTypeChecker.v theories/PCUICSafeChecker.v theories/SafeTemplateChecker.v theories/PCUICSafeRetyping.v +theories/PCUICConsistency.v theories/Extraction.v diff --git a/safechecker/theories/PCUICConsistency.v b/safechecker/theories/PCUICConsistency.v new file mode 100644 index 000000000..297ca7f33 --- /dev/null +++ b/safechecker/theories/PCUICConsistency.v @@ -0,0 +1,220 @@ +(* The safe checker gives us a sound and complete wh-normalizer for + PCUIC, assuming strong normalization. Combined with canonicity, + this allows us to prove that PCUIC is consistent, i.e. there + is no axiom-free proof of [forall (P : Prop), P] in the empty + context. To do so we use weakening to add an empty inductive, the + provided term to build an inhabitant and then canonicity to show + that this is a contradiction. *) + +From Coq Require Import Ascii String. +From Equations Require Import Equations. +From MetaCoq.PCUIC Require Import PCUICAst. +From MetaCoq.PCUIC Require Import PCUICAstUtils. +From MetaCoq.PCUIC Require Import PCUICCanonicity. +From MetaCoq.PCUIC Require Import PCUICInductiveInversion. +From MetaCoq.PCUIC Require Import PCUICInversion. +From MetaCoq.PCUIC Require Import PCUICLiftSubst. +From MetaCoq.PCUIC Require Import PCUICSR. +From MetaCoq.PCUIC Require Import PCUICSafeLemmata. +From MetaCoq.PCUIC Require Import PCUICTyping. +From MetaCoq.PCUIC Require Import PCUICUnivSubst. +From MetaCoq.PCUIC Require Import PCUICValidity. +From MetaCoq.PCUIC Require Import PCUICWeakeningEnv. +From MetaCoq.Template Require Import config utils. +From MetaCoq.SafeChecker Require Import PCUICSafeReduce. + +Local Opaque hnf. + +Fixpoint string_repeat c (n : nat) : string := + match n with + | 0 => "" + | S n => String c (string_repeat c n) + end. + +Lemma string_repeat_length c n : + String.length (string_repeat c n) = n. +Proof. + induction n; cbn; auto. +Qed. + +Definition max_name_length (Σ : global_env) : nat := + fold_right max 0 (map (fun '(kn, _) => String.length (string_of_kername kn)) Σ). + +Lemma max_name_length_ge Σ : + Forall (fun '(kn, _) => String.length (string_of_kername kn) <= max_name_length Σ) Σ. +Proof. + induction Σ as [|(kn&decl) Σ IH]; cbn; constructor. + - lia. + - eapply Forall_impl; eauto. + intros (?&?); cbn; intros. + fold (max_name_length Σ). + lia. +Qed. + +Definition make_fresh_name (Σ : global_env) : kername := + (MPfile [], string_repeat "a"%char (S (max_name_length Σ))). + +Lemma make_fresh_name_fresh Σ : + fresh_global (make_fresh_name Σ) Σ. +Proof. + pose proof (max_name_length_ge Σ) as all. + eapply Forall_impl; eauto. + cbn. + intros (kn&decl) le. + cbn. + intros ->. + unfold make_fresh_name in le. + cbn in le. + rewrite string_repeat_length in le. + lia. +Qed. + +Definition Prop_univ := Universe.of_levels (inl PropLevel.lProp). + +Definition False_oib : one_inductive_body := + {| ind_name := ""; + ind_type := tSort Prop_univ; + ind_kelim := IntoAny; + ind_ctors := []; + ind_projs := []; + ind_relevance := Relevant |}. + +Definition False_mib : mutual_inductive_body := + {| ind_finite := BiFinite; + ind_npars := 0; + ind_params := []; + ind_bodies := [False_oib]; + ind_universes := Monomorphic_ctx ContextSet.empty; + ind_variance := None |}. + +Definition axiom_free Σ := + forall c decl, declared_constant Σ c decl -> cst_body decl <> None. + +Lemma axiom_free_axiom_free_value Σ t : + axiom_free Σ -> + axiom_free_value Σ [] t. +Proof. + intros axfree. + cut (Forall is_true []); [|constructor]. + generalize ([] : list bool). + induction t; intros axfree_args all_true; cbn; auto. + - destruct lookup_env eqn:find; auto. + destruct g; auto. + destruct c; auto. + apply axfree in find; cbn in *. + now destruct cst_body. + - destruct nth_error; auto. + rewrite nth_nth_error. + destruct nth_error eqn:nth; auto. + eapply nth_error_forall in nth; eauto. +Qed. + +Definition binder := {| binder_name := nNamed "P"; binder_relevance := Relevant |}. + +Theorem pcuic_consistent {cf:checker_flags} Σ t : + wf_ext Σ -> + axiom_free Σ -> + (* t : forall (P : Prop), P *) + Σ ;;; [] |- t : tProd binder (tSort Prop_univ) (tRel 0) -> + False. +Proof. + intros wfΣ axfree cons. + set (Σext := ((make_fresh_name Σ, InductiveDecl False_mib) :: Σ.1, Σ.2)). + assert (wf': wf_ext Σext). + { constructor; [constructor|]. + - destruct wfΣ; auto. + - apply make_fresh_name_fresh. + - red. + cbn. + split. + { now intros ? ?%LevelSet.empty_spec. } + split. + { now intros ? ?%ConstraintSet.empty_spec. } + split; auto. + destruct wfΣ as (?&(?&?&?&[val sat])). + exists val. + intros l isin. + apply sat; auto. + apply ConstraintSet.union_spec. + apply ConstraintSet.union_spec in isin as [?%ConstraintSet.empty_spec|]; auto. + - hnf. + constructor. + + constructor. + * econstructor; cbn. + -- instantiate (2 := []); reflexivity. + -- exists (Universe.super Prop_univ). + constructor; auto. + constructor. + -- instantiate (1 := []). + constructor. + -- intros. + congruence. + -- constructor. + -- intros ? [=]. + * constructor. + + constructor. + + reflexivity. + + reflexivity. + - destruct wfΣ; auto. } + eapply (env_prop_typing _ _ PCUICWeakeningEnv.weakening_env) in cons; auto. + 3: exists [(make_fresh_name Σ, InductiveDecl False_mib)]; reflexivity. + 2: now destruct wf'. + + set (Σ' := _ ++ _) in cons. + set (False_ty := tInd (mkInd (make_fresh_name Σ) 0) []). + assert (typ_false: (Σ', Σ.2);;; [] |- tApp t False_ty : False_ty). + { apply validity_term in cons as typ_prod; auto. + destruct typ_prod. + eapply type_App with (B := tRel 0) (u := False_ty); eauto. + eapply type_Ind with (u := []) (mdecl := False_mib) (idecl := False_oib); eauto. + - hnf. + cbn. + unfold declared_minductive. + cbn. + rewrite eq_kername_refl. + auto. + - cbn. + auto. } + assert (sqwf: ∥ wf (Σ', Σ.2).1 ∥) by now destruct wf'. + pose proof (iswelltyped _ _ _ _ typ_false) as wt. + pose proof (@hnf_sound _ _ sqwf _ _ wt) as [r]. + pose proof (@hnf_complete _ _ sqwf _ _ wt) as [w]. + eapply subject_reduction in typ_false; eauto. + eapply whnf_ind_finite with (indargs := []) in typ_false as ctor; auto. + - unfold isConstruct_app in ctor. + destruct decompose_app eqn:decomp. + apply decompose_app_inv in decomp. + rewrite decomp in typ_false. + destruct t0; try discriminate ctor. + apply inversion_mkApps in typ_false as H; auto. + destruct H as (?&typ_ctor&_). + apply inversion_Construct in typ_ctor as (?&?&?&?&?&?&?); auto. + unshelve eapply Construct_Ind_ind_eq with (args' := []) in typ_false. + 5: eassumption. + 1: eauto. + destruct on_declared_constructor. + destruct p. + destruct s. + destruct p. + destruct typ_false as ((((->&_)&_)&_)&_). + clear -d. + destruct d as ((?&?)&?). + cbn in *. + red in H. + cbn in *. + rewrite eq_kername_refl in H. + noconf H. + noconf H0. + cbn in H1. + rewrite nth_error_nil in H1. + discriminate. + - eapply axiom_free_axiom_free_value. + intros kn decl isdecl. + hnf in isdecl. + cbn in isdecl. + destruct eq_kername; [noconf isdecl|]. + eapply axfree; eauto. + - unfold check_recursivity_kind. + cbn. + rewrite eq_kername_refl; auto. +Qed. From ae198c3c349ebaf36b91e257336d741f9bdd40cb Mon Sep 17 00:00:00 2001 From: Yannick Forster Date: Mon, 18 Jan 2021 12:31:20 +0100 Subject: [PATCH 70/70] fix compilation --- pcuic/theories/PCUICToTemplateCorrectness.v | 4 ++-- template-coq/gen-src/specFloat.ml.rej | 26 ++++++++------------- template-coq/src/ast_denoter.ml | 2 +- template-coq/src/constr_denoter.ml | 2 +- template-coq/src/run_template_monad.ml | 1 - 5 files changed, 14 insertions(+), 21 deletions(-) diff --git a/pcuic/theories/PCUICToTemplateCorrectness.v b/pcuic/theories/PCUICToTemplateCorrectness.v index cba3e00fe..c537f943b 100644 --- a/pcuic/theories/PCUICToTemplateCorrectness.v +++ b/pcuic/theories/PCUICToTemplateCorrectness.v @@ -1427,7 +1427,7 @@ Proof. unfold decompose_app. simpl. rewrite PCUICAstUtils.atom_decompose_app. destruct t => /= //. - exists _, d2. split. lia. + eexists _, d2. split. lia. unshelve eexists. econstructor. exists s; eauto. reflexivity. assumption. constructor. simpl. lia. @@ -1640,4 +1640,4 @@ Proof. + now eapply trans_cumul. Qed. -Print Assumptions pcuic_to_template. \ No newline at end of file +Print Assumptions pcuic_to_template. diff --git a/template-coq/gen-src/specFloat.ml.rej b/template-coq/gen-src/specFloat.ml.rej index 04dcccf83..294627074 100644 --- a/template-coq/gen-src/specFloat.ml.rej +++ b/template-coq/gen-src/specFloat.ml.rej @@ -1,16 +1,10 @@ -*************** -*** 4,9 **** - open Datatypes - open Zbool - open Zpower - - type spec_float = - | S754_zero of bool ---- 4,10 ---- - open Datatypes - open Zbool - open Zpower -+ open Float64 - - type spec_float = - | S754_zero of bool +--- gen-src/specFloat.ml.orig 2020-12-04 21:48:20.000000000 +0100 ++++ gen-src/specFloat.ml 2020-12-04 21:48:33.000000000 +0100 +@@ -4,6 +4,7 @@ + open Datatypes + open Zbool + open Zpower ++open Float64 + + type spec_float = + | S754_zero of bool diff --git a/template-coq/src/ast_denoter.ml b/template-coq/src/ast_denoter.ml index 144321ec1..bfb59c939 100644 --- a/template-coq/src/ast_denoter.ml +++ b/template-coq/src/ast_denoter.ml @@ -129,7 +129,7 @@ struct let unquote_evar env evm n l = let id = Evar.unsafe_of_int (unquote_int n) in - evm, mkEvar (id, Array.of_list l) + evm, mkEvar (id, l) let unquote_bool (q : quoted_bool) : bool = q diff --git a/template-coq/src/constr_denoter.ml b/template-coq/src/constr_denoter.ml index 2bc45bfbb..e8388c1cd 100644 --- a/template-coq/src/constr_denoter.ml +++ b/template-coq/src/constr_denoter.ml @@ -147,7 +147,7 @@ struct else let id = unquote_nat id in let ev = Evar.unsafe_of_int id in - evm, Constr.mkEvar (ev, Array.of_list args) + evm, Constr.mkEvar (ev, args) let unquote_relevance trm = if Constr.equal trm (Lazy.force tRelevant) then diff --git a/template-coq/src/run_template_monad.ml b/template-coq/src/run_template_monad.ml index 5d379ec38..e5874195a 100644 --- a/template-coq/src/run_template_monad.ml +++ b/template-coq/src/run_template_monad.ml @@ -227,7 +227,6 @@ let unquote_one_inductive_entry env evm trm (* of type one_inductive_entry *) : | id::ar::cnames::ctms::[] -> let id = unquote_ident id in let evm, ar = denote_term env evm ar in - let template = unquote_bool template in let cnames = List.map unquote_ident (unquote_list cnames) in let evm, ctms = map_evm (denote_term env) evm (unquote_list ctms) in evm, { mind_entry_typename = id ;

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