From 24a6297164bc422f09edfa65131ea04d0f2176e9 Mon Sep 17 00:00:00 2001
From: schnellerhase <56360279+schnellerhase@users.noreply.github.com>
Date: Sun, 2 Mar 2025 13:13:51 +0100
Subject: [PATCH 01/19] Add ignore all mypy config to pyproject.toml

---
 pyproject.toml | 19 +++++++++++++++++++
 1 file changed, 19 insertions(+)

diff --git a/pyproject.toml b/pyproject.toml
index 555a334d2..4def28f48 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -82,3 +82,22 @@ allowed-confusables = ["𝐚", "𝐀", "∕", "γ", "⨯", "∨"]
 
 [tool.ruff.lint.pydocstyle]
 convention = "google"
+
+[tool.mypy]
+disable_error_code = [
+    "arg-type",
+    "assignment",
+    "attr-defined",
+    "has-type",
+    "import-not-found",
+    "import-untyped",
+    "index",
+    "method-assign",
+    "misc",
+    "name-defined",
+    "operator",
+    "override",
+    "return-value",
+    "type-var",
+    "var-annotated",
+]

From 6d58936aab0afcee297b6ea5cb78cc9d03584abd Mon Sep 17 00:00:00 2001
From: schnellerhase <56360279+schnellerhase@users.noreply.github.com>
Date: Sun, 2 Mar 2025 13:14:05 +0100
Subject: [PATCH 02/19] Add py.typed

---
 ufl/py.typed | 0
 1 file changed, 0 insertions(+), 0 deletions(-)
 create mode 100644 ufl/py.typed

diff --git a/ufl/py.typed b/ufl/py.typed
new file mode 100644
index 000000000..e69de29bb

From 367897c0c194ef6ba2645aa17400a4c3febbdfc0 Mon Sep 17 00:00:00 2001
From: schnellerhase <56360279+schnellerhase@users.noreply.github.com>
Date: Sun, 2 Mar 2025 13:14:22 +0100
Subject: [PATCH 03/19] Add mypy check to CI

---
 .github/workflows/pythonapp.yml | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/.github/workflows/pythonapp.yml b/.github/workflows/pythonapp.yml
index 8a636e91b..c038a1261 100644
--- a/.github/workflows/pythonapp.yml
+++ b/.github/workflows/pythonapp.yml
@@ -46,6 +46,8 @@ jobs:
           ruff format --check .
       - name: Install UFL
         run: python -m pip install .[ci]
+      - name: Lint with mypy
+        run: mypy -p ufl
       - name: Run unit tests
         run: |
           python -m pytest -n auto --cov=ufl/ --junitxml=junit/test-results-${{ matrix.os }}-${{ matrix.python-version }}.xml test/

From aba7a3d97b6e857dfefc9d7f66e88f73d596167b Mon Sep 17 00:00:00 2001
From: schnellerhase <56360279+schnellerhase@users.noreply.github.com>
Date: Sun, 2 Mar 2025 13:16:05 +0100
Subject: [PATCH 04/19] Add mypy to CI dependency

---
 pyproject.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/pyproject.toml b/pyproject.toml
index 4def28f48..2b23743b6 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -24,7 +24,7 @@ issues = "https://github.com/FEniCS/ufl/issues"
 funding = "https://numfocus.org/donate"
 
 [project.optional-dependencies]
-lint = ["ruff"]
+lint = ["mypy", "ruff"]
 docs = ["sphinx", "sphinx_rtd_theme"]
 test = ["pytest"]
 ci = [

From 6ac4a31b2745b46ff1e454f36c6453718ce67a5e Mon Sep 17 00:00:00 2001
From: schnellerhase <56360279+schnellerhase@users.noreply.github.com>
Date: Sun, 2 Mar 2025 13:29:31 +0100
Subject: [PATCH 05/19] Fix mypy error code 'index'

---
 pyproject.toml | 1 -
 ufl/cell.py    | 2 +-
 2 files changed, 1 insertion(+), 2 deletions(-)

diff --git a/pyproject.toml b/pyproject.toml
index 2b23743b6..c72edb91a 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -91,7 +91,6 @@ disable_error_code = [
     "has-type",
     "import-not-found",
     "import-untyped",
-    "index",
     "method-assign",
     "misc",
     "name-defined",
diff --git a/ufl/cell.py b/ufl/cell.py
index 6d565d7fd..01fa16613 100644
--- a/ufl/cell.py
+++ b/ufl/cell.py
@@ -184,7 +184,7 @@ def peak_types(self) -> typing.Tuple[AbstractCell, ...]:
         return self.sub_entity_types(tdim - 3)
 
 
-_sub_entity_celltypes = {
+_sub_entity_celltypes: typing.Dict[str, list[tuple[str, ...]]] = {
     "vertex": [("vertex",)],
     "interval": [tuple("vertex" for i in range(2)), ("interval",)],
     "triangle": [

From 6993281d219c523ea8e7feea9974a810ad4e7826 Mon Sep 17 00:00:00 2001
From: schnellerhase <56360279+schnellerhase@users.noreply.github.com>
Date: Sun, 2 Mar 2025 13:39:44 +0100
Subject: [PATCH 06/19] Fix mypy error code 'name-defined'

---
 pyproject.toml  | 1 -
 ufl/objects.py  | 4 ++--
 ufl/pullback.py | 2 +-
 3 files changed, 3 insertions(+), 4 deletions(-)

diff --git a/pyproject.toml b/pyproject.toml
index c72edb91a..2b774075d 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -93,7 +93,6 @@ disable_error_code = [
     "import-untyped",
     "method-assign",
     "misc",
-    "name-defined",
     "operator",
     "override",
     "return-value",
diff --git a/ufl/objects.py b/ufl/objects.py
index 64704d275..bd71556c5 100644
--- a/ufl/objects.py
+++ b/ufl/objects.py
@@ -20,10 +20,10 @@
     globals()[measure_name] = Measure(integral_type)
 
 # TODO: Firedrake hack, remove later
-ds_tb = ds_b + ds_t  # noqa: F821
+ds_tb = ds_b + ds_t # type: ignore # noqa: F821
 
 # Default measure dX including both uncut and cut cells
-dX = dx + dC  # noqa: F821
+dX = dx + dC  # type: ignore # noqa: F821
 
 # Create objects for builtin known cell types
 vertex = Cell("vertex")
diff --git a/ufl/pullback.py b/ufl/pullback.py
index 696ae9653..057d5e618 100644
--- a/ufl/pullback.py
+++ b/ufl/pullback.py
@@ -462,7 +462,7 @@ class SymmetricPullback(AbstractPullback):
     """Pull back for an element with symmetry."""
 
     def __init__(
-        self, element: _AbstractFiniteElement, symmetry: typing.Dict[typing.tuple[int, ...], int]
+        self, element: _AbstractFiniteElement, symmetry: typing.Dict[typing.Tuple[int, ...], int]
     ):
         """Initalise.
 

From f887c4205b8b5f6d104b8f027978473cf01ae85c Mon Sep 17 00:00:00 2001
From: schnellerhase <56360279+schnellerhase@users.noreply.github.com>
Date: Sun, 2 Mar 2025 13:50:55 +0100
Subject: [PATCH 07/19] Fix mypy error code 'return-value'

---
 pyproject.toml       |  1 -
 ufl/cell.py          | 16 ++++++++--------
 ufl/functionspace.py |  2 +-
 ufl/objects.py       |  2 +-
 4 files changed, 10 insertions(+), 11 deletions(-)

diff --git a/pyproject.toml b/pyproject.toml
index 2b774075d..4b95bb151 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -95,7 +95,6 @@ disable_error_code = [
     "misc",
     "operator",
     "override",
-    "return-value",
     "type-var",
     "var-annotated",
 ]
diff --git a/ufl/cell.py b/ufl/cell.py
index 01fa16613..c58ccef55 100644
--- a/ufl/cell.py
+++ b/ufl/cell.py
@@ -358,7 +358,7 @@ def __init__(self, *cells: Cell):
         if not isinstance(self._tdim, numbers.Integral):
             raise ValueError("Expecting integer topological_dimension.")
 
-    def sub_cells(self) -> typing.List[AbstractCell]:
+    def sub_cells(self) -> typing.Tuple[AbstractCell, ...]:
         """Return list of cell factors."""
         return self._cells
 
@@ -398,21 +398,21 @@ def num_sub_entities(self, dim: int) -> int:
     def sub_entities(self, dim: int) -> typing.Tuple[AbstractCell, ...]:
         """Get the sub-entities of the given dimension."""
         if dim < 0 or dim > self._tdim:
-            return []
+            return ()
         if dim == 0:
-            return [Cell("vertex") for i in range(self.num_sub_entities(0))]
+            return tuple(Cell("vertex") for i in range(self.num_sub_entities(0)))
         if dim == self._tdim:
-            return [self]
+            return (self,)
         raise NotImplementedError(f"TensorProductCell.sub_entities({dim}) is not implemented.")
 
     def sub_entity_types(self, dim: int) -> typing.Tuple[AbstractCell, ...]:
         """Get the unique sub-entity types of the given dimension."""
         if dim < 0 or dim > self._tdim:
-            return []
+            return ()
         if dim == 0:
-            return [Cell("vertex")]
+            return (Cell("vertex"),)
         if dim == self._tdim:
-            return [self]
+            return (self,)
         raise NotImplementedError(f"TensorProductCell.sub_entities({dim}) is not implemented.")
 
     def _lt(self, other) -> bool:
@@ -434,7 +434,7 @@ def _ufl_hash_data_(self) -> typing.Hashable:
         """UFL hash data."""
         return tuple(c._ufl_hash_data_() for c in self._cells)
 
-    def reconstruct(self, **kwargs: typing.Any) -> Cell:
+    def reconstruct(self, **kwargs: typing.Any) -> Cell | TensorProductCell:
         """Reconstruct this cell, overwriting properties by those in kwargs."""
         for key, value in kwargs.items():
             raise TypeError(f"reconstruct() got unexpected keyword argument '{key}'")
diff --git a/ufl/functionspace.py b/ufl/functionspace.py
index 558b6bd73..fc78dd6c2 100644
--- a/ufl/functionspace.py
+++ b/ufl/functionspace.py
@@ -80,7 +80,7 @@ def components(self) -> typing.Dict[typing.Tuple[int, ...], int]:
         if len(self._ufl_element.sub_elements) == 0:
             return {(): 0}
 
-        components = {}
+        components: dict[tuple[int, ...], int] = {}
         offset = 0
         c_offset = 0
         for s in self.ufl_sub_spaces():
diff --git a/ufl/objects.py b/ufl/objects.py
index bd71556c5..c88af62b9 100644
--- a/ufl/objects.py
+++ b/ufl/objects.py
@@ -20,7 +20,7 @@
     globals()[measure_name] = Measure(integral_type)
 
 # TODO: Firedrake hack, remove later
-ds_tb = ds_b + ds_t # type: ignore # noqa: F821
+ds_tb = ds_b + ds_t  # type: ignore # noqa: F821
 
 # Default measure dX including both uncut and cut cells
 dX = dx + dC  # type: ignore # noqa: F821

From 95c76d5ae6fec1677d17f9b305240c529d881cbd Mon Sep 17 00:00:00 2001
From: schnellerhase <56360279+schnellerhase@users.noreply.github.com>
Date: Sun, 2 Mar 2025 13:52:43 +0100
Subject: [PATCH 08/19] Fix mypy error code 'has-type'

---
 pyproject.toml | 1 -
 1 file changed, 1 deletion(-)

diff --git a/pyproject.toml b/pyproject.toml
index 4b95bb151..f8c49ef96 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -88,7 +88,6 @@ disable_error_code = [
     "arg-type",
     "assignment",
     "attr-defined",
-    "has-type",
     "import-not-found",
     "import-untyped",
     "method-assign",

From 35c2d5f82d41739dfd96bbbb1161dbcd81d50b95 Mon Sep 17 00:00:00 2001
From: schnellerhase <56360279+schnellerhase@users.noreply.github.com>
Date: Sun, 2 Mar 2025 14:00:07 +0100
Subject: [PATCH 09/19] Add types-colorama to typing dependecies

---
 pyproject.toml | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/pyproject.toml b/pyproject.toml
index f8c49ef96..bce4aff6d 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -25,6 +25,7 @@ funding = "https://numfocus.org/donate"
 
 [project.optional-dependencies]
 lint = ["mypy", "ruff"]
+typing = ["types-colorama"]
 docs = ["sphinx", "sphinx_rtd_theme"]
 test = ["pytest"]
 ci = [
@@ -35,6 +36,7 @@ ci = [
     "fenics-ufl[docs]",
     "fenics-ufl[lint]",
     "fenics-ufl[test]",
+    "fenics-ufl[typing]",
 ]
 
 [tool.setuptools]

From 8d69bd1600f8256352bdcf222054aa41e8196895 Mon Sep 17 00:00:00 2001
From: schnellerhase <56360279+schnellerhase@users.noreply.github.com>
Date: Sun, 2 Mar 2025 14:03:55 +0100
Subject: [PATCH 10/19] Fix mypy error code 'import-untyped'

---
 pyproject.toml       | 1 -
 ufl/mathfunctions.py | 2 +-
 2 files changed, 1 insertion(+), 2 deletions(-)

diff --git a/pyproject.toml b/pyproject.toml
index bce4aff6d..bdf453a4d 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -91,7 +91,6 @@ disable_error_code = [
     "assignment",
     "attr-defined",
     "import-not-found",
-    "import-untyped",
     "method-assign",
     "misc",
     "operator",
diff --git a/ufl/mathfunctions.py b/ufl/mathfunctions.py
index 4c2d87996..bdf57b19e 100644
--- a/ufl/mathfunctions.py
+++ b/ufl/mathfunctions.py
@@ -421,7 +421,7 @@ def evaluate(self, x, mapping, component, index_values):
         """Evaluate."""
         a = self.ufl_operands[1].evaluate(x, mapping, component, index_values)
         try:
-            import scipy.special
+            import scipy.special  # type: ignore
         except ImportError:
             raise ValueError(
                 "You must have scipy installed to evaluate bessel functions in python."

From ddccf07f4469f7a5adf898eb8293f22e31a30266 Mon Sep 17 00:00:00 2001
From: schnellerhase <56360279+schnellerhase@users.noreply.github.com>
Date: Sun, 2 Mar 2025 14:12:46 +0100
Subject: [PATCH 11/19] Change base class of TensorProductCell to Cell

---
 ufl/cell.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/ufl/cell.py b/ufl/cell.py
index c58ccef55..7af0b3548 100644
--- a/ufl/cell.py
+++ b/ufl/cell.py
@@ -340,7 +340,7 @@ def reconstruct(self, **kwargs: typing.Any) -> Cell:
         return Cell(self._cellname)
 
 
-class TensorProductCell(AbstractCell):
+class TensorProductCell(Cell):
     """Tensor product cell."""
 
     __slots__ = ("_cells", "_tdim")
@@ -434,7 +434,7 @@ def _ufl_hash_data_(self) -> typing.Hashable:
         """UFL hash data."""
         return tuple(c._ufl_hash_data_() for c in self._cells)
 
-    def reconstruct(self, **kwargs: typing.Any) -> Cell | TensorProductCell:
+    def reconstruct(self, **kwargs: typing.Any) -> Cell:
         """Reconstruct this cell, overwriting properties by those in kwargs."""
         for key, value in kwargs.items():
             raise TypeError(f"reconstruct() got unexpected keyword argument '{key}'")

From 28e3e6b887c4b7fff042c7e65bd9c9e4cfef84a5 Mon Sep 17 00:00:00 2001
From: schnellerhase <56360279+schnellerhase@users.noreply.github.com>
Date: Sun, 2 Mar 2025 14:16:15 +0100
Subject: [PATCH 12/19] Fix mypy error code 'override'

---
 pyproject.toml       | 1 -
 ufl/finiteelement.py | 4 ++--
 2 files changed, 2 insertions(+), 3 deletions(-)

diff --git a/pyproject.toml b/pyproject.toml
index bdf453a4d..7b5d254d6 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -94,7 +94,6 @@ disable_error_code = [
     "method-assign",
     "misc",
     "operator",
-    "override",
     "type-var",
     "var-annotated",
 ]
diff --git a/ufl/finiteelement.py b/ufl/finiteelement.py
index 3aceef689..9c4fb4b1d 100644
--- a/ufl/finiteelement.py
+++ b/ufl/finiteelement.py
@@ -53,7 +53,7 @@ def __hash__(self) -> int:
         """Return a hash."""
 
     @_abc.abstractmethod
-    def __eq__(self, other: AbstractFiniteElement) -> bool:
+    def __eq__(self, other: object) -> bool:
         """Check if this element is equal to another element."""
 
     @_abc.abstractproperty
@@ -112,7 +112,7 @@ def sub_elements(self) -> _typing.List:
         of sub-elements.
         """
 
-    def __ne__(self, other: AbstractFiniteElement) -> bool:
+    def __ne__(self, other: object) -> bool:
         """Check if this element is different to another element."""
         return not self.__eq__(other)
 

From 7f777aa9f323105be72bdcf7d6b63dc85fa4df25 Mon Sep 17 00:00:00 2001
From: schnellerhase <56360279+schnellerhase@users.noreply.github.com>
Date: Sun, 2 Mar 2025 14:29:35 +0100
Subject: [PATCH 13/19] Switch to tpying.Tuple

---
 ufl/functionspace.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/ufl/functionspace.py b/ufl/functionspace.py
index fc78dd6c2..42477fc10 100644
--- a/ufl/functionspace.py
+++ b/ufl/functionspace.py
@@ -80,7 +80,7 @@ def components(self) -> typing.Dict[typing.Tuple[int, ...], int]:
         if len(self._ufl_element.sub_elements) == 0:
             return {(): 0}
 
-        components: dict[tuple[int, ...], int] = {}
+        components: dict[typing.Tuple[int, ...], int] = {}
         offset = 0
         c_offset = 0
         for s in self.ufl_sub_spaces():

From a036787272bd399c647daf4cc997d0343a5d2410 Mon Sep 17 00:00:00 2001
From: schnellerhase <56360279+schnellerhase@users.noreply.github.com>
Date: Sun, 2 Mar 2025 18:20:58 +0100
Subject: [PATCH 14/19] Removed unused code

---
 ufl/exprequals.py | 7 -------
 1 file changed, 7 deletions(-)

diff --git a/ufl/exprequals.py b/ufl/exprequals.py
index cf0359d31..6df5ff53b 100644
--- a/ufl/exprequals.py
+++ b/ufl/exprequals.py
@@ -1,12 +1,5 @@
 """Expr equals."""
 
-from collections import defaultdict
-
-hash_total = defaultdict(int)
-hash_collisions = defaultdict(int)
-hash_equals = defaultdict(int)
-hash_notequals = defaultdict(int)
-
 
 def expr_equals(self, other):
     """Checks whether the two expressions are represented the exact same way.

From 9ff27d7dcbc9dcf8a4b8372c3a70b8b09e570a6a Mon Sep 17 00:00:00 2001
From: schnellerhase <56360279+schnellerhase@users.noreply.github.com>
Date: Sun, 2 Mar 2025 18:46:49 +0100
Subject: [PATCH 15/19] Fix mypy error code 'var-annotated'

---
 pyproject.toml                 | 1 -
 ufl/algorithms/formsplitter.py | 3 ++-
 ufl/algorithms/signature.py    | 4 +++-
 ufl/algorithms/transformer.py  | 3 ++-
 ufl/constantvalue.py           | 5 +++--
 ufl/core/expr.py               | 7 ++++---
 ufl/core/multiindex.py         | 6 ++++--
 ufl/core/ufl_type.py           | 8 ++++----
 ufl/corealg/multifunction.py   | 3 ++-
 9 files changed, 24 insertions(+), 16 deletions(-)

diff --git a/pyproject.toml b/pyproject.toml
index 7b5d254d6..5c5a684af 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -95,5 +95,4 @@ disable_error_code = [
     "misc",
     "operator",
     "type-var",
-    "var-annotated",
 ]
diff --git a/ufl/algorithms/formsplitter.py b/ufl/algorithms/formsplitter.py
index a81176b5c..aeb955310 100644
--- a/ufl/algorithms/formsplitter.py
+++ b/ufl/algorithms/formsplitter.py
@@ -8,6 +8,7 @@
 #
 # Modified by Cecile Daversin-Catty, 2018
 
+import typing
 from typing import Optional
 
 import numpy as np
@@ -127,7 +128,7 @@ def extract_blocks(form, i: Optional[int] = None, j: Optional[None] = None):
             num_sub_elements = arguments[0].ufl_element().num_sub_elements
             forms = []
             for pi in range(num_sub_elements):
-                form_i = []
+                form_i: typing.List[typing.Optional[object]] = []
                 for pj in range(num_sub_elements):
                     f = fs.split(form, pi, pj)
                     if f.empty():
diff --git a/ufl/algorithms/signature.py b/ufl/algorithms/signature.py
index 807fa5c00..9395ecd12 100644
--- a/ufl/algorithms/signature.py
+++ b/ufl/algorithms/signature.py
@@ -6,6 +6,7 @@
 # SPDX-License-Identifier:    LGPL-3.0-or-later
 
 import hashlib
+import typing
 
 from ufl.algorithms.domain_analysis import canonicalize_metadata
 from ufl.classes import (
@@ -20,6 +21,7 @@
     Label,
     MultiIndex,
 )
+from ufl.core.ufl_type import UFLObject
 from ufl.corealg.traversal import traverse_unique_terminals, unique_post_traversal
 
 
@@ -94,7 +96,7 @@ def compute_terminal_hashdata(expressions, renumbering):
 
 def compute_expression_hashdata(expression, terminal_hashdata) -> bytes:
     """Compute expression hashdata."""
-    cache = {}
+    cache: typing.Dict[UFLObject, bytes] = {}
 
     for expr in unique_post_traversal(expression):
         # Uniquely traverse tree and hash each node
diff --git a/ufl/algorithms/transformer.py b/ufl/algorithms/transformer.py
index 23f49acc2..c20948a28 100644
--- a/ufl/algorithms/transformer.py
+++ b/ufl/algorithms/transformer.py
@@ -14,6 +14,7 @@
 # Modified by Anders Logg, 2009-2010
 
 import inspect
+import typing
 
 from ufl.algorithms.map_integrands import map_integrands
 from ufl.classes import Variable, all_ufl_classes
@@ -35,7 +36,7 @@ class Transformer(object):
     transform expression trees from one representation to another.
     """
 
-    _handlers_cache = {}
+    _handlers_cache: typing.Dict[type, typing.Tuple[str, bool]] = {}
 
     def __init__(self, variable_cache=None):
         """Initialise."""
diff --git a/ufl/constantvalue.py b/ufl/constantvalue.py
index 007350680..3ac0385cb 100644
--- a/ufl/constantvalue.py
+++ b/ufl/constantvalue.py
@@ -10,6 +10,7 @@
 # Modified by Massimiliano Leoni, 2016.
 
 import numbers
+import typing
 from math import atan2
 
 import ufl
@@ -65,7 +66,7 @@ class Zero(ConstantValue):
 
     __slots__ = ("ufl_free_indices", "ufl_index_dimensions", "ufl_shape")
 
-    _cache = {}
+    _cache: typing.Dict[typing.Tuple[int], typing.Self] = {}
 
     def __getnewargs__(self):
         """Get new args."""
@@ -362,7 +363,7 @@ class IntValue(RealValue):
 
     __slots__ = ()
 
-    _cache = {}
+    _cache: typing.Dict[int, typing.Self] = {}
 
     def __getnewargs__(self):
         """Get new args."""
diff --git a/ufl/core/expr.py b/ufl/core/expr.py
index 93149e2f6..0ef5d4c75 100644
--- a/ufl/core/expr.py
+++ b/ufl/core/expr.py
@@ -16,9 +16,10 @@
 # Modified by Anders Logg, 2008
 # Modified by Massimiliano Leoni, 2016
 
+import typing
 import warnings
 
-from ufl.core.ufl_type import UFLType, update_ufl_type_attributes
+from ufl.core.ufl_type import UFLObject, UFLType, update_ufl_type_attributes
 
 
 class Expr(object, metaclass=UFLType):
@@ -204,10 +205,10 @@ def __init__(self):
 
     # A global dict mapping language_operator_name to the type it
     # produces
-    _ufl_language_operators_ = {}
+    _ufl_language_operators_: typing.Dict[str, object] = {}
 
     # List of all terminal modifier types
-    _ufl_terminal_modifiers_ = []
+    _ufl_terminal_modifiers_: typing.List[UFLObject] = []
 
     # --- Mechanism for profiling object creation and deletion ---
 
diff --git a/ufl/core/multiindex.py b/ufl/core/multiindex.py
index 416fb8c82..6a6bef73b 100644
--- a/ufl/core/multiindex.py
+++ b/ufl/core/multiindex.py
@@ -8,6 +8,8 @@
 #
 # Modified by Massimiliano Leoni, 2016.
 
+import typing
+
 from ufl.core.terminal import Terminal
 from ufl.core.ufl_type import ufl_type
 from ufl.utils.counted import Counted
@@ -30,7 +32,7 @@ class FixedIndex(IndexBase):
 
     __slots__ = ("_hash", "_value")
 
-    _cache = {}
+    _cache: typing.Dict[int, typing.Self] = {}
 
     def __getnewargs__(self):
         """Get new args."""
@@ -116,7 +118,7 @@ class MultiIndex(Terminal):
 
     __slots__ = ("_indices",)
 
-    _cache = {}
+    _cache: typing.Dict[typing.Tuple[int], typing.Self] = {}
 
     def __getnewargs__(self):
         """Get new args."""
diff --git a/ufl/core/ufl_type.py b/ufl/core/ufl_type.py
index c409d05fb..e0b6d8ce4 100644
--- a/ufl/core/ufl_type.py
+++ b/ufl/core/ufl_type.py
@@ -416,18 +416,18 @@ class UFLType(type):
     _ufl_handler_name_ = "ufl_type"
 
     # A global array of all Expr and BaseForm subclasses, indexed by typecode
-    _ufl_all_classes_ = []
+    _ufl_all_classes_: typing.List[UFLObject] = []
 
     # A global set of all handler names added
-    _ufl_all_handler_names_ = set()
+    _ufl_all_handler_names_: typing.Set[str] = set()
 
     # A global array of the number of initialized objects for each
     # typecode
-    _ufl_obj_init_counts_ = []
+    _ufl_obj_init_counts_: typing.List[int] = []
 
     # A global array of the number of deleted objects for each
     # typecode
-    _ufl_obj_del_counts_ = []
+    _ufl_obj_del_counts_: typing.List[int] = []
 
     # Type trait: If the type is abstract.  An abstract class cannot
     # be instantiated and does not need all properties specified.
diff --git a/ufl/corealg/multifunction.py b/ufl/corealg/multifunction.py
index 559ec98f2..ba17fb3f5 100644
--- a/ufl/corealg/multifunction.py
+++ b/ufl/corealg/multifunction.py
@@ -7,6 +7,7 @@
 #
 # Modified by Massimiliano Leoni, 2016
 
+import typing
 from inspect import signature
 
 from ufl.core.expr import Expr
@@ -46,7 +47,7 @@ class MultiFunction(object):
     algorithm object. Of course Python's function call overhead still applies.
     """
 
-    _handlers_cache = {}
+    _handlers_cache: typing.Dict[type, typing.Tuple[typing.List[str], bool]] = {}
 
     def __init__(self):
         """Initialise."""

From e5c95aff091f5bb62e412190d0ca33ffefa18a3d Mon Sep 17 00:00:00 2001
From: schnellerhase <56360279+schnellerhase@users.noreply.github.com>
Date: Sun, 2 Mar 2025 18:56:42 +0100
Subject: [PATCH 16/19] Replace typing.Self with older python variant

---
 ufl/constantvalue.py   | 4 ++--
 ufl/core/multiindex.py | 4 ++--
 2 files changed, 4 insertions(+), 4 deletions(-)

diff --git a/ufl/constantvalue.py b/ufl/constantvalue.py
index 3ac0385cb..c97e7cff7 100644
--- a/ufl/constantvalue.py
+++ b/ufl/constantvalue.py
@@ -66,7 +66,7 @@ class Zero(ConstantValue):
 
     __slots__ = ("ufl_free_indices", "ufl_index_dimensions", "ufl_shape")
 
-    _cache: typing.Dict[typing.Tuple[int], typing.Self] = {}
+    _cache: typing.Dict[typing.Tuple[int], 'Zero'] = {}
 
     def __getnewargs__(self):
         """Get new args."""
@@ -363,7 +363,7 @@ class IntValue(RealValue):
 
     __slots__ = ()
 
-    _cache: typing.Dict[int, typing.Self] = {}
+    _cache: typing.Dict[int, 'IntValue'] = {}
 
     def __getnewargs__(self):
         """Get new args."""
diff --git a/ufl/core/multiindex.py b/ufl/core/multiindex.py
index 6a6bef73b..d9c930839 100644
--- a/ufl/core/multiindex.py
+++ b/ufl/core/multiindex.py
@@ -32,7 +32,7 @@ class FixedIndex(IndexBase):
 
     __slots__ = ("_hash", "_value")
 
-    _cache: typing.Dict[int, typing.Self] = {}
+    _cache: typing.Dict[int, 'FixedIndex'] = {}
 
     def __getnewargs__(self):
         """Get new args."""
@@ -118,7 +118,7 @@ class MultiIndex(Terminal):
 
     __slots__ = ("_indices",)
 
-    _cache: typing.Dict[typing.Tuple[int], typing.Self] = {}
+    _cache: typing.Dict[typing.Tuple[int], 'MultiIndex'] = {}
 
     def __getnewargs__(self):
         """Get new args."""

From 9f25a0f638d91ff07ba987837b6b8bacde0d4389 Mon Sep 17 00:00:00 2001
From: schnellerhase <56360279+schnellerhase@users.noreply.github.com>
Date: Sun, 2 Mar 2025 18:59:36 +0100
Subject: [PATCH 17/19] Fix mypy error code 'method-assign'

---
 pyproject.toml | 1 -
 1 file changed, 1 deletion(-)

diff --git a/pyproject.toml b/pyproject.toml
index 5c5a684af..f54517cf6 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -91,7 +91,6 @@ disable_error_code = [
     "assignment",
     "attr-defined",
     "import-not-found",
-    "method-assign",
     "misc",
     "operator",
     "type-var",

From c64d04731f3993f355f13487758cf9dcefccc55a Mon Sep 17 00:00:00 2001
From: schnellerhase <56360279+schnellerhase@users.noreply.github.com>
Date: Sun, 2 Mar 2025 19:04:34 +0100
Subject: [PATCH 18/19] Fix mypy error code 'import-not-found'

---
 pyproject.toml | 1 -
 1 file changed, 1 deletion(-)

diff --git a/pyproject.toml b/pyproject.toml
index f54517cf6..552c6b6a7 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -90,7 +90,6 @@ disable_error_code = [
     "arg-type",
     "assignment",
     "attr-defined",
-    "import-not-found",
     "misc",
     "operator",
     "type-var",

From cdbb08afecb96fccceb5d94d740e51a9fd391c6e Mon Sep 17 00:00:00 2001
From: schnellerhase <56360279+schnellerhase@users.noreply.github.com>
Date: Sun, 2 Mar 2025 19:07:10 +0100
Subject: [PATCH 19/19] Ruff

---
 ufl/constantvalue.py   | 4 ++--
 ufl/core/multiindex.py | 4 ++--
 2 files changed, 4 insertions(+), 4 deletions(-)

diff --git a/ufl/constantvalue.py b/ufl/constantvalue.py
index c97e7cff7..aa72c59c7 100644
--- a/ufl/constantvalue.py
+++ b/ufl/constantvalue.py
@@ -66,7 +66,7 @@ class Zero(ConstantValue):
 
     __slots__ = ("ufl_free_indices", "ufl_index_dimensions", "ufl_shape")
 
-    _cache: typing.Dict[typing.Tuple[int], 'Zero'] = {}
+    _cache: typing.Dict[typing.Tuple[int], "Zero"] = {}
 
     def __getnewargs__(self):
         """Get new args."""
@@ -363,7 +363,7 @@ class IntValue(RealValue):
 
     __slots__ = ()
 
-    _cache: typing.Dict[int, 'IntValue'] = {}
+    _cache: typing.Dict[int, "IntValue"] = {}
 
     def __getnewargs__(self):
         """Get new args."""
diff --git a/ufl/core/multiindex.py b/ufl/core/multiindex.py
index d9c930839..a5074b388 100644
--- a/ufl/core/multiindex.py
+++ b/ufl/core/multiindex.py
@@ -32,7 +32,7 @@ class FixedIndex(IndexBase):
 
     __slots__ = ("_hash", "_value")
 
-    _cache: typing.Dict[int, 'FixedIndex'] = {}
+    _cache: typing.Dict[int, "FixedIndex"] = {}
 
     def __getnewargs__(self):
         """Get new args."""
@@ -118,7 +118,7 @@ class MultiIndex(Terminal):
 
     __slots__ = ("_indices",)
 
-    _cache: typing.Dict[typing.Tuple[int], 'MultiIndex'] = {}
+    _cache: typing.Dict[typing.Tuple[int], "MultiIndex"] = {}
 
     def __getnewargs__(self):
         """Get new args."""