From 2f32a92a8e2c611bb5327fad107f0aaf613df3c3 Mon Sep 17 00:00:00 2001 From: "Dennis E. Hamilton" Date: Sat, 21 Dec 2024 14:27:57 -0800 Subject: [PATCH] 0.3.6 lambda/index.md trapped in a twisty maze of symbolic forms all alike --- docs/lambda/index.md | 29 ++++++++++++++++------------- 1 file changed, 16 insertions(+), 13 deletions(-) diff --git a/docs/lambda/index.md b/docs/lambda/index.md index 646d4bd..007f363 100644 --- a/docs/lambda/index.md +++ b/docs/lambda/index.md @@ -1,4 +1,4 @@ - + 0.3.6 2024-12-21T22:25Z @@ -68,7 +68,7 @@ structure and not on any applicative interpretation of `M`. Although `σ.s M` determines an ob, that ob has no occurrences of `s`. In this sense, `σ.s M` has `s` abstracted away; `(σ.s M) s` determines `M` as-is. -There are handy companion functions, `δ(s, N` and `subst(N, s)`, for use in +There are handy companion functions, `δ(s, N)` and `subst(N, s)`, for use in particular circumstances, often when one or more particular operands are known in advance. @@ -89,15 +89,16 @@ self-evident, however suggestive the form might be. Purpose for a symbolic form is revealed only in the context of its usage. The harmony of symbolic form and applicative-expression, when that -interpretation is the case, is anchored on the fact that the computational -interpretation of `f :: g :: x` is tantamount to the Frugalese applicative -expression `f g x`, both being right-associative and equivalent to `f(g x)`. +interpretation is the case, is encouraged by the computational interpretation +of `f :: g :: x` being tantamount to the Frugalese applicative expression +`f g x`, both being right-associative and equivalent to `f(g x)` were the +lindies `f`, `g`, and `x` taken to be variables for appropriate obs. The oFrugal definitions of applicative-procedure abstraction rely on that -structural nicety, facilitating abstraction of applicative-function scripts -and confirmation of their operation. +structural nicety, transforming symbolic forms into applicative-function +scripts in a manner that supports confirmation of correct operation. -#### 2.2.1 Examples of symbolic-form preservation +#### 2.2.1 Symbolic-form preservation When a symbolic form is evaluated or applied directly, the symbolic form is preserved. @@ -129,7 +130,7 @@ with result `x :: y` in accordance with the distinguishing of symbolic forms. The oMiser computational model's application function treats lindies as individuals having no definable/separate applicative interpretations. -Lindies are individual symbolic forms. +Lindies are taken as individual symbolic forms. When application operator `p` and operand `x` are both symbolic forms, the result of application is the composed symbolic form `(p) :: x`. @@ -138,8 +139,8 @@ When `p` is a symbolic form, `(p)::.NIL` is a symbolic form. Otherwise when only `p` is a symbolic form, the result of application is `(p) :: ‵ x`, itself a symbolic form even though `x` may be an ob of any form. -As is done in the examples (2.2.1), symbolic forms are usually written in -canonical form, omitting unnecessary parentheses. +As is done in the examples (2.2.1, above), symbolic forms are usually written +in canonical form, omitting unnecessary parentheses. ## 3. Functional Abstraction Heuristics @@ -185,7 +186,9 @@ from time to time.