From aab63ee9b9f9336fce4a3530ffa1e0cc5e5f584c Mon Sep 17 00:00:00 2001
From: Alexandru Fikl <alexfikl@gmail.com>
Date: Tue, 28 Oct 2025 12:57:15 +0200
Subject: [PATCH 01/18] feat(typing): update type annotations in symbolic

---
 loopy/symbolic.py | 999 ++++++++++++++++++++++++++++------------------
 1 file changed, 615 insertions(+), 384 deletions(-)

diff --git a/loopy/symbolic.py b/loopy/symbolic.py
index c666dd935..cac49ea05 100644
--- a/loopy/symbolic.py
+++ b/loopy/symbolic.py
@@ -24,6 +24,7 @@
 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
 THE SOFTWARE.
 """
+
 import contextlib
 import re
 from collections import defaultdict
@@ -36,8 +37,8 @@
     Any,
     ClassVar,
     Concatenate,
-    Generic,
-    Literal as LiteralT,
+    Literal as TypingLiteral,
+    TypeAlias,
     TypeVar,
     cast,
 )
@@ -50,7 +51,6 @@
 import islpy as isl
 import pymbolic.primitives as p
 import pytools.lex
-from islpy import dim_type
 from pymbolic.mapper import (
     CachedCombineMapper as CombineMapperBase,
     CachedIdentityMapper as IdentityMapperBase,
@@ -62,7 +62,10 @@
     ResultT,
     WalkMapper as UncachedWalkMapperBase,
 )
-from pymbolic.mapper.coefficient import CoefficientCollector as CoefficientCollectorBase
+from pymbolic.mapper.coefficient import (
+    CoefficientCollector as CoefficientCollectorBase,
+    CoeffsT,
+)
 from pymbolic.mapper.constant_folder import (
     ConstantFoldingMapper as ConstantFoldingMapperBase,
 )
@@ -75,7 +78,10 @@
 from pymbolic.mapper.substitutor import (
     CachedSubstitutionMapper as SubstitutionMapperBase,
 )
-from pymbolic.mapper.unifier import UnidirectionalUnifier as UnidirectionalUnifierBase
+from pymbolic.mapper.unifier import (
+    UnidirectionalUnifier as UnidirectionalUnifierBase,
+    UnificationRecord,
+)
 from pymbolic.parser import Parser as ParserBase
 from pymbolic.typing import (
     ArithmeticExpression,
@@ -150,32 +156,33 @@
 # {{{ mappers with support for loopy-specific primitives
 
 class IdentityMapperMixin(Mapper[Expression, P]):
-    def map_literal(self,
-                    expr: Literal, *args: P.args, **kwargs: P.kwargs) -> Expression:
+    def map_literal(self, expr: Literal,
+                    *args: P.args, **kwargs: P.kwargs) -> Expression:
         return expr
 
-    def map_array_literal(
-                self,
-                expr: ArrayLiteral, *args: P.args, **kwargs: P.kwargs
-            ) -> Expression:
+    def map_array_literal(self, expr: ArrayLiteral,
+                          *args: P.args, **kwargs: P.kwargs) -> Expression:
         return type(expr)(tuple(self.rec(ch, *args, **kwargs)
                                 for ch in expr.children))
 
-    def map_group_hw_index(self, expr, *args: P.args, **kwargs: P.kwargs) -> Expression:
+    def map_group_hw_index(self, expr: GroupHardwareAxisIndex | RuleArgument,
+                           *args: P.args, **kwargs: P.kwargs) -> Expression:
         return expr
 
-    def map_local_hw_index(self, expr, *args: P.args, **kwargs: P.kwargs) -> Expression:
+    def map_local_hw_index(self, expr: LocalHardwareAxisIndex,
+                           *args: P.args, **kwargs: P.kwargs) -> Expression:
         return expr
 
-    def map_loopy_function_identifier(self, expr, *args: P.args, **kwargs: P.kwargs):
+    def map_loopy_function_identifier(self, expr: FunctionIdentifier,
+                                      *args: P.args, **kwargs: P.kwargs) -> Expression:
         return expr
 
-    def map_reduction(self,
-                      expr: Reduction, *args: P.args, **kwargs: P.kwargs) -> Expression:
+    def map_reduction(self, expr: Reduction,
+                      *args: P.args, **kwargs: P.kwargs) -> Expression:
         mapped_inames = [self.rec(p.Variable(iname), *args, **kwargs)
                          for iname in expr.inames]
 
-        new_inames = []
+        new_inames: list[str] = []
         for iname, new_sym_iname in zip(expr.inames, mapped_inames, strict=True):
             if not isinstance(new_sym_iname, p.Variable):
                 from loopy.diagnostic import LoopyError
@@ -198,10 +205,8 @@ def map_tagged_variable(self, expr: TaggedVariable,
         # leaf, doesn't change
         return expr
 
-    def map_type_annotation(
-                self, expr: TypeAnnotation,
-                *args: P.args, **kwargs: P.kwargs
-            ) -> Expression:
+    def map_type_annotation(self, expr: TypeAnnotation,
+                            *args: P.args, **kwargs: P.kwargs) -> Expression:
         new_child = self.rec(expr.child, *args, **kwargs)
 
         if new_child is expr.child:
@@ -224,14 +229,13 @@ def map_sub_array_ref(self, expr: SubArrayRef,
 
         return SubArrayRef(cast("tuple[p.Variable, ...]", new_inames), new_subscript)
 
-    def map_resolved_function(self, expr, *args: P.args, **kwargs: P.kwargs):
+    def map_resolved_function(self, expr: ResolvedFunction,
+                              *args: P.args, **kwargs: P.kwargs) -> Expression:
         # leaf, doesn't change
         return expr
 
-    def map_type_cast(
-                self, expr: TypeCast,
-                *args: P.args, **kwargs: P.kwargs
-            ) -> Expression:
+    def map_type_cast(self, expr: TypeCast,
+                      *args: P.args, **kwargs: P.kwargs) -> Expression:
         new_child = self.rec(expr.child, *args, **kwargs)
 
         if new_child is expr.child:
@@ -239,15 +243,17 @@ def map_type_cast(
 
         return type(expr)(expr.type, new_child)
 
-    map_linear_subscript = IdentityMapperBase.map_subscript
+    map_linear_subscript: Callable[Concatenate[Self, LinearSubscript, P],
+                                   Expression] = IdentityMapperBase.map_subscript
+    map_rule_argument: Callable[Concatenate[Self, RuleArgument, P],
+                                Expression] = map_group_hw_index
+    map_fortran_division: Callable[Concatenate[Self, FortranDivision, P],
+                                   Expression] = IdentityMapperBase.map_quotient
 
-    map_rule_argument = map_group_hw_index
 
-    map_fortran_division = IdentityMapperBase.map_quotient
-
-
-class FlattenMapper(FlattenMapperBase, IdentityMapperMixin):
-    # FIXME: Lies! This needs to be made precise.
+class FlattenMapper(FlattenMapperBase, IdentityMapperMixin[[]]):
+    # FIXME(pyright): Lies! This needs to be made precise.
+    @override
     def is_expr_integer_valued(self, expr: Expression) -> bool:
         return True
 
@@ -256,7 +262,7 @@ def flatten(expr: ArithmeticOrExpressionT) -> ArithmeticOrExpressionT:
     return cast("ArithmeticOrExpressionT", FlattenMapper()(expr))
 
 
-class IdentityMapper(IdentityMapperBase, IdentityMapperMixin, Generic[P]):
+class IdentityMapper(IdentityMapperBase[P], IdentityMapperMixin[P]):
     pass
 
 
@@ -266,60 +272,60 @@ class UncachedIdentityMapper(UncachedIdentityMapperBase[P],
 
 
 class PartialEvaluationMapper(
-        EvaluationMapperBase, IdentityMapperMixin[[]]):
-    def map_variable(self, expr):
+        EvaluationMapperBase[Expression], IdentityMapperMixin[[]]):
+    @override
+    def map_variable(self, expr: p.Variable) -> Expression:
         return expr
 
-    def map_common_subexpression_uncached(self, expr):
+    @override
+    def map_common_subexpression_uncached(
+                self, expr: p.CommonSubexpression) -> Expression:
         return type(expr)(self.rec(expr.child), expr.prefix, expr.scope)
 
 
 class WalkMapperMixin(WalkMapperBase[P]):
-    def map_literal(self, expr, *args: P.args, **kwargs: P.kwargs) -> None:
+    def map_literal(self, expr: Literal,
+                    *args: P.args, **kwargs: P.kwargs) -> None:
         self.visit(expr, *args, **kwargs)
 
-    def map_array_literal(self, expr, *args: P.args, **kwargs: P.kwargs) -> None:
+    def map_array_literal(self, expr: ArrayLiteral,
+                          *args: P.args, **kwargs: P.kwargs) -> None:
         if not self.visit(expr, *args, **kwargs):
             return
 
         for ch in expr.children:
             self.rec(ch, *args, **kwargs)
 
-    def map_group_hw_index(self,
-                expr: GroupHardwareAxisIndex,
-                *args: P.args,
-                **kwargs: P.kwargs
-            ) -> None:
+    def map_group_hw_index(self, expr: GroupHardwareAxisIndex | RuleArgument,
+                           *args: P.args, **kwargs: P.kwargs) -> None:
         self.visit(expr, *args, **kwargs)
 
-    def map_local_hw_index(self,
-                expr: LocalHardwareAxisIndex,
-                *args: P.args,
-                **kwargs: P.kwargs
-            ) -> None:
+    def map_local_hw_index(self, expr: LocalHardwareAxisIndex,
+                           *args: P.args, **kwargs: P.kwargs) -> None:
         self.visit(expr, *args, **kwargs)
 
-    def map_reduction(self, expr: Reduction, *args: P.args, **kwargs: P.kwargs) -> None:
+    def map_reduction(self, expr: Reduction,
+                      *args: P.args, **kwargs: P.kwargs) -> None:
         if not self.visit(expr, *args, **kwargs):
             return
 
         self.rec(expr.expr, *args, **kwargs)
 
-    def map_type_cast(self, expr: TypeCast, *args: P.args, **kwargs: P.kwargs) -> None:
+    def map_type_cast(self, expr: TypeCast,
+                      *args: P.args, **kwargs: P.kwargs) -> None:
         if not self.visit(expr, *args, **kwargs):
             return
         self.rec(expr.child, *args, **kwargs)
 
-    map_tagged_variable = WalkMapperBase.map_variable
+    map_tagged_variable: Callable[Concatenate[Self, TaggedVariable, P],
+                                  None] = WalkMapperBase.map_variable
 
-    def map_loopy_function_identifier(
-                self, expr, *args: P.args, **kwargs: P.kwargs
-            ) -> None:
+    def map_loopy_function_identifier(self, expr: FunctionIdentifier,
+                                      *args: P.args, **kwargs: P.kwargs) -> None:
         self.visit(expr, *args, **kwargs)
 
-    def map_linear_subscript(self,
-                expr: LinearSubscript,
-                *args: P.args, **kwargs: P.kwargs) -> None:
+    def map_linear_subscript(self, expr: LinearSubscript,
+                             *args: P.args, **kwargs: P.kwargs) -> None:
         if not self.visit(expr, *args, **kwargs):
             return
 
@@ -328,26 +334,26 @@ def map_linear_subscript(self,
 
         self.post_visit(expr, *args, **kwargs)
 
-    map_rule_argument = map_group_hw_index
+    map_rule_argument: Callable[Concatenate[Self, RuleArgument, P],
+                                None] = map_group_hw_index
 
-    def map_sub_array_ref(self, expr: SubArrayRef, *args: P.args, **kwargs: P.kwargs):
+    def map_sub_array_ref(self, expr: SubArrayRef,
+                          *args: P.args, **kwargs: P.kwargs):
         if not self.visit(expr, *args, **kwargs):
             return
 
         self.rec(expr.swept_inames, *args, **kwargs)
         self.rec(expr.subscript, *args, **kwargs)
 
-    def map_resolved_function(self,
-                expr: ResolvedFunction,
-                *args: P.args,
-                **kwargs: P.kwargs
-            ):
+    def map_resolved_function(self, expr: ResolvedFunction,
+                              *args: P.args, **kwargs: P.kwargs):
         if not self.visit(expr, *args, **kwargs):
             return
 
         self.rec(expr.function, *args, **kwargs)
 
-    map_fortran_division = WalkMapperBase.map_quotient
+    map_fortran_division: Callable[Concatenate[Self, FortranDivision, P],
+                                   None] = WalkMapperBase.map_quotient
 
 
 class WalkMapper(WalkMapperMixin[P], WalkMapperBase[P]):
@@ -358,34 +364,39 @@ class UncachedWalkMapper(WalkMapperMixin[P], UncachedWalkMapperBase[P]):
     pass
 
 
-class CallbackMapper(IdentityMapperMixin, CallbackMapperBase):
-    map_reduction = CallbackMapperBase.map_constant
-    map_resolved_function = CallbackMapperBase.map_constant
+class CallbackMapper(IdentityMapperMixin[P],
+                     CallbackMapperBase[Expression, P]):
+    map_reduction: Callable[Concatenate[Self, Reduction, P],
+                            Expression] = CallbackMapperBase.map_constant
+    map_resolved_function: Callable[Concatenate[Self, ResolvedFunction, P],
+                                    Expression] = CallbackMapperBase.map_constant
 
 
 class CombineMapper(CombineMapperBase[ResultT, P]):
-    def map_reduction(self, expr, *args: P.args, **kwargs: P.kwargs):
+    def map_reduction(self, expr: Reduction,
+                      *args: P.args, **kwargs: P.kwargs) -> ResultT:
         return self.rec(expr.expr, *args, **kwargs)
 
-    def map_type_cast(self, expr, *args: P.args, **kwargs: P.kwargs):
+    def map_type_cast(self, expr: TypeCast, /,
+                      *args: P.args, **kwargs: P.kwargs) -> ResultT:
         return self.rec(expr.child, *args, **kwargs)
 
-    def map_sub_array_ref(self, expr, *args: P.args, **kwargs: P.kwargs):
+    def map_sub_array_ref(self, expr: SubArrayRef,
+                          *args: P.args, **kwargs: P.kwargs) -> ResultT:
         return self.combine((
             self.rec(expr.subscript, *args, **kwargs),
             self.combine(tuple(
                          self.rec(idx, *args, **kwargs)
                          for idx in expr.swept_inames))))
 
-    def map_linear_subscript(self,
-                expr: LinearSubscript, *args: P.args, **kwargs: P.kwargs
-            ) -> ResultT:
+    def map_linear_subscript(self, expr: LinearSubscript,
+                             *args: P.args, **kwargs: P.kwargs) -> ResultT:
         return self.combine(
                 [self.rec(expr.aggregate, *args, **kwargs),
                     self.rec(expr.index, *args, **kwargs)])
 
-    def map_fortran_division(self,
-            expr: FortranDivision, *args: P.args, **kwargs: P.kwargs) -> ResultT:
+    def map_fortran_division(self, expr: FortranDivision,
+                             *args: P.args, **kwargs: P.kwargs) -> ResultT:
         return self.combine((
             self.rec(expr.numerator, *args, **kwargs),
             self.rec(expr.denominator, *args, **kwargs)))
@@ -393,12 +404,12 @@ def map_fortran_division(self,
 
 class SubstitutionMapper(
         SubstitutionMapperBase, IdentityMapperMixin[[]]):
-    def map_common_subexpression_uncached(self, expr):
+    def map_common_subexpression_uncached(
+                self, expr: p.CommonSubexpression) -> Expression:
         return type(expr)(self.rec(expr.child), expr.prefix, expr.scope)
 
 
-class ConstantFoldingMapper(ConstantFoldingMapperBase,
-        IdentityMapperMixin):
+class ConstantFoldingMapper(ConstantFoldingMapperBase, IdentityMapperMixin[[]]):
     pass
 
 
@@ -406,18 +417,19 @@ class StringifyMapper(StringifyMapperBase[[]]):
     def map_literal(self, expr: Literal, enclosing_prec: int) -> str:
         return expr.s
 
-    def map_array_literal(self, expr, enclosing_prec):
+    def map_array_literal(self, expr: ArrayLiteral, enclosing_prec: int) -> str:
         from pymbolic.mapper.stringifier import PREC_NONE
-
         return "{%s}" % ", ".join(self.rec(ch, PREC_NONE) for ch in expr.children)
 
-    def map_group_hw_index(self, expr, enclosing_prec):
-        return "grp.%d" % expr.index
+    def map_group_hw_index(self, expr: GroupHardwareAxisIndex,
+                           enclosing_prec: int) -> str:
+        return "grp.%d" % expr.axis
 
-    def map_local_hw_index(self, expr, enclosing_prec):
-        return "loc.%d" % expr.index
+    def map_local_hw_index(self, expr: LocalHardwareAxisIndex,
+                           enclosing_prec: int) -> str:
+        return "loc.%d" % expr.axis
 
-    def map_reduction(self, expr, prec):
+    def map_reduction(self, expr: Reduction, enclosing_prec: int) -> str:
         from pymbolic.mapper.stringifier import PREC_NONE
 
         return "{}reduce({}, [{}], {})".format(
@@ -425,10 +437,10 @@ def map_reduction(self, expr, prec):
                 expr.operation, ", ".join(expr.inames),
                 self.rec(expr.expr, PREC_NONE))
 
-    def map_tagged_variable(self, expr, prec):
+    def map_tagged_variable(self, expr: TaggedVariable, enclosing_prec: int) -> str:
         return f"{expr.name}${{{', '.join(str(t) for t in expr.tags)}}}"
 
-    def map_linear_subscript(self, expr, enclosing_prec):
+    def map_linear_subscript(self, expr: LinearSubscript, enclosing_prec: int) -> str:
         from pymbolic.mapper.stringifier import PREC_CALL, PREC_NONE
         return self.parenthesize_if_needed(
                 self.format("%s[[%s]]",
@@ -436,54 +448,66 @@ def map_linear_subscript(self, expr, enclosing_prec):
                     self.rec(expr.index, PREC_NONE)),
                 enclosing_prec, PREC_CALL)
 
-    def map_loopy_function_identifier(self, expr, enclosing_prec):
-        return "{}<{}>".format(
-                type(expr).__name__,
-                ", ".join(str(a) for a in expr.__getinitargs__()))
+    def map_loopy_function_identifier(
+            self, expr: FunctionIdentifier, enclosing_prec: int) -> str:
+        from dataclasses import fields
+        initargs = tuple(getattr(self, fld.name) for fld in fields(expr))
+
+        return "{}<{}>".format(type(expr).__name__, ", ".join(str(a) for a in initargs))
 
-    def map_rule_argument(self, expr, enclosing_prec):
+    def map_rule_argument(self, expr: RuleArgument, enclosing_prec: int) -> str:
         return "<arg%d>" % expr.index
 
-    def map_type_cast(self, expr, enclosing_prec):
+    def map_type_cast(self, expr: TypeCast, enclosing_prec: int) -> str:
         from pymbolic.mapper.stringifier import PREC_NONE
         child = self.rec(expr.child, PREC_NONE)
         return f"cast({expr.type!r}, {child})"
 
-    def map_resolved_function(self, expr, prec):
+    def map_resolved_function(self, expr: ResolvedFunction, enclosing_prec: int) -> str:
         # underlining a resolved call
         return "\u0332".join(str(expr.function))
 
-    def map_sub_array_ref(self, expr, prec):
+    def map_sub_array_ref(self, expr: SubArrayRef, enclosing_prec: int) -> str:
         return "[{inames}]: {subscr}".format(
-                inames=",".join(self.rec(iname, prec) for iname in
+                inames=",".join(self.rec(iname, enclosing_prec) for iname in
                     expr.swept_inames),
-                subscr=self.rec(expr.subscript, prec))
+                subscr=self.rec(expr.subscript, enclosing_prec))
 
-    def map_fortran_division(self, expr, enclosing_prec):
+    def map_fortran_division(self, expr: FortranDivision, enclosing_prec: int) -> str:
         from pymbolic.mapper.stringifier import PREC_NONE
-        result = self.map_quotient(expr, PREC_NONE)
+        result = self.map_quotient(expr, PREC_NONE)  # pyright: ignore[reportArgumentType]
         return f"[FORTRANDIV]({result})"
 
 
 class UnidirectionalUnifier(UnidirectionalUnifierBase):
-    def map_reduction(self, expr, other, unis):
+    def map_reduction(
+                self,
+                expr: Reduction,
+                other: Expression,
+                urecs: Sequence[UnificationRecord]) -> Sequence[UnificationRecord]:
         if not isinstance(other, type(expr)):
-            return self.treat_mismatch(expr, other, unis)
+            return self.treat_mismatch(expr, other, urecs)
+
         if (expr.inames != other.inames
-                or type(expr.function) is not type(other.function)):
+                or type(expr.operation) is not type(other.operation)):
             return []
 
-        return self.rec(expr.expr, other.expr, unis)
+        return self.rec(expr.expr, other.expr, urecs)
 
-    def map_tagged_variable(self, expr, other, urecs):
-        new_uni_record = self.unification_record_from_equation(
-                expr, other)
+    def map_tagged_variable(
+                self,
+                expr: TaggedVariable,
+                other: Expression,
+                urecs: Sequence[UnificationRecord]) -> Sequence[UnificationRecord]:
+        new_uni_record = self.unification_record_from_equation(expr, other)
         if new_uni_record is None:
             # Check if the variables match literally--that's ok, too.
             if (isinstance(other, TaggedVariable)
                     and expr.name == other.name
                     and expr.tags == other.tags
-                    and expr.name not in self.lhs_mapping_candidates):
+                    and (
+                        self.lhs_mapping_candidates is None
+                        or expr.name not in self.lhs_mapping_candidates)):
                 return urecs
             else:
                 return []
@@ -493,80 +517,86 @@ def map_tagged_variable(self, expr, other, urecs):
 
 
 class DependencyMapper(DependencyMapperBase[P]):
-    def map_group_hw_index(
-                self,
-                expr: GroupHardwareAxisIndex, *args: P.args, **kwargs: P.kwargs
-            ) -> Dependencies:
+    def map_group_hw_index(self, expr: GroupHardwareAxisIndex,
+                           *args: P.args, **kwargs: P.kwargs) -> Dependencies:
         return set()
 
-    def map_local_hw_index(
-                self,
-                expr: LocalHardwareAxisIndex, *args: P.args, **kwargs: P.kwargs
-            ) -> Dependencies:
+    def map_local_hw_index(self, expr: LocalHardwareAxisIndex,
+                           *args: P.args, **kwargs: P.kwargs) -> Dependencies:
         return set()
 
-    def map_call(
-                self,
-                expr: p.Call, *args: P.args, **kwargs: P.kwargs
-            ) -> Dependencies:
+    @override
+    def map_call(self, expr: p.Call,
+                 *args: P.args, **kwargs: P.kwargs) -> Dependencies:
         # Loopy does not have first-class functions. Do not descend
         # into 'function' attribute of Call.
         return self.rec(expr.parameters, *args, **kwargs)
 
-    def map_reduction(
-                self,
-                expr: Reduction, *args: P.args, **kwargs: P.kwargs
-            ) -> Dependencies:
+    def map_reduction(self, expr: Reduction,
+                      *args: P.args, **kwargs: P.kwargs) -> Dependencies:
         deps = self.rec(expr.expr, *args, **kwargs)
         return deps - {p.Variable(iname) for iname in expr.inames}
 
-    def map_tagged_variable(
-                self,
-                expr: TaggedVariable, *args: P.args, **kwargs: P.kwargs
-            ) -> Dependencies:
+    def map_tagged_variable(self, expr: TaggedVariable,
+                            *args: P.args, **kwargs: P.kwargs) -> Dependencies:
         return {expr}
 
-    def map_loopy_function_identifier(self, expr, *args: P.args, **kwargs: P.kwargs):
+    def map_loopy_function_identifier(
+                self, expr: FunctionIdentifier,
+                *args: P.args, **kwargs: P.kwargs) -> Dependencies:
         return set()
 
-    def map_sub_array_ref(self, expr, *args: P.args, **kwargs: P.kwargs):
+    def map_sub_array_ref(self, expr: SubArrayRef,
+                          *args: P.args, **kwargs: P.kwargs) -> Dependencies:
         deps = self.rec(expr.subscript, *args, **kwargs)
         return deps - set(expr.swept_inames)
 
-    map_linear_subscript = DependencyMapperBase.map_subscript
+    map_linear_subscript: Callable[Concatenate[Self, LinearSubscript, P],
+                                   Dependencies] = DependencyMapperBase.map_subscript
 
-    def map_type_cast(self, expr, *args: P.args, **kwargs: P.kwargs):
+    def map_type_cast(self, expr: TypeCast,
+                      *args: P.args, **kwargs: P.kwargs) -> Dependencies:
         return self.rec(expr.child, *args, **kwargs)
 
-    def map_resolved_function(self, expr, *args: P.args, **kwargs: P.kwargs):
+    def map_resolved_function(self, expr: ResolvedFunction,
+                              *args: P.args, **kwargs: P.kwargs) -> Dependencies:
         return self.rec(expr.function, *args, **kwargs)
 
-    def map_literal(self, expr, *args: P.args, **kwargs: P.kwargs):
+    def map_literal(self, expr: Literal,
+                    *args: P.args, **kwargs: P.kwargs) -> Dependencies:
         return set()
 
-    def map_call_with_kwargs(self, expr, *args: P.args, **kwargs: P.kwargs):
+    @override
+    def map_call_with_kwargs(self, expr: p.CallWithKwargs,
+                             *args: P.args, **kwargs: P.kwargs) -> Dependencies:
         # See https://github.com/inducer/loopy/pull/323
         raise NotImplementedError
 
-    map_fortran_division = DependencyMapperBase.map_quotient
+    map_fortran_division: Callable[Concatenate[Self, FortranDivision, P],
+                                   Dependencies] = DependencyMapperBase.map_quotient
 
 
 class SubstitutionRuleExpander(IdentityMapper[[]]):
+    rules: Mapping[str, SubstitutionRule]
+
     def __init__(self, rules: Mapping[str, SubstitutionRule]) -> None:
-        self.rules = rules
         super().__init__()
+        self.rules = rules
 
+    @override
     def __call__(self, expr: Expression) -> Expression:
         if not self.rules:
             return expr
         return super().__call__(expr)
 
+    @override
     def map_variable(self, expr: p.Variable) -> Expression:
         if expr.name in self.rules:
             return self.map_subst_rule(expr.name, self.rules[expr.name], ())
         else:
             return super().map_variable(expr)
 
+    @override
     def map_call(self, expr: p.Call) -> Expression:
         assert isinstance(expr.function, p.Variable | ResolvedFunction)
         if expr.function.name in self.rules:
@@ -620,6 +650,8 @@ class Literal(LoopyExpressionBase):
         Only used in the output of
         :mod:`loopy.target.c.codegen.expression.ExpressionToCExpressionMapper` (and
         similar mappers). Not for use in Loopy source representation.
+
+    .. autoattribute:: s
     """
 
     s: str
@@ -634,6 +666,8 @@ class ArrayLiteral(LoopyExpressionBase):
         Only used in the output of
         :mod:`loopy.target.c.codegen.expression.ExpressionToCExpressionMapper` (and
         similar mappers). Not for use in Loopy source representation.
+
+    .. autoattribute:: children
     """
 
     children: tuple[Expression, ...]
@@ -652,8 +686,11 @@ class GroupHardwareAxisIndex(HardwareAxisIndex):
         Only used in the output of
         :mod:`loopy.target.c.expression.ExpressionToCExpressionMapper` (and
         similar mappers). Not for use in Loopy source representation.
+
+    .. autoattribute:: axis
     """
-    mapper_method = "map_group_hw_index"
+
+    mapper_method: ClassVar[str] = "map_group_hw_index"
 
 
 @p.expr_dataclass()
@@ -664,15 +701,18 @@ class LocalHardwareAxisIndex(HardwareAxisIndex):
         Only used in the output of
         :mod:`loopy.target.c.expression.ExpressionToCExpressionMapper` (and
         similar mappers). Not for use in Loopy source representation.
+
+    .. autoattribute:: axis
     """
-    mapper_method = "map_local_hw_index"
+
+    mapper_method: ClassVar[str] = "map_local_hw_index"
 
 
 @p.expr_dataclass()
 class FunctionIdentifier(LoopyExpressionBase):
     """A base class for symbols representing functions."""
 
-    mapper_method = "map_loopy_function_identifier"
+    mapper_method: ClassVar[str] = "map_loopy_function_identifier"
 
 
 @p.expr_dataclass()
@@ -685,7 +725,8 @@ class TypedCSE(LoopyExpressionBase, p.CommonSubexpression):
 
     dtype: LoopyType | None = None
 
-    def get_extra_properties(self):
+    @override
+    def get_extra_properties(self) -> dict[str, Any]:
         return {"dtype": self.dtype}
 
 
@@ -698,6 +739,7 @@ class TypeAnnotation(LoopyExpressionBase):
     .. autoattribute:: child
     """
 
+    # FIXME(pyright): this is set to lp.Optional in `LoopyParser.parse_prefix`
     type: LoopyType
     child: Expression
 
@@ -711,26 +753,26 @@ class TypeCast(LoopyExpressionBase):
     .. autoattribute:: type
     """
 
+    child: Expression
+    """The expression to be cast."""
+
     # We're storing the type as a name for now to avoid
     # numpy pickling bug madness. (see loopy.types)
     _type_name: str
 
-    child: Expression
-    """The expression to be cast."""
-
-    def __init__(self, type: ToLoopyTypeConvertible, child: Expression):
+    def __init__(self, type: ToLoopyTypeConvertible, child: Expression) -> None:
         super().__init__()
 
         from loopy.types import NumpyType, to_loopy_type
-        type = to_loopy_type(type)
+        ltype = to_loopy_type(type)
 
-        if (not isinstance(type, NumpyType)
-                or not issubclass(type.dtype.type, np.number)):
+        if (not isinstance(ltype, NumpyType)
+                or not issubclass(ltype.dtype.type, np.number)):
             from loopy.diagnostic import LoopyError
-            raise LoopyError("TypeCast only supports numerical numpy types, "
-                    "not '%s'" % type)
+            raise LoopyError(
+                f"TypeCast only supports numerical numpy types: got '{ltype}'")
 
-        object.__setattr__(self, "_type_name", type.dtype.name)
+        object.__setattr__(self, "_type_name", ltype.dtype.name)
         object.__setattr__(self, "child", child)
 
     @property
@@ -771,7 +813,9 @@ def __init__(self, name: str, tags: ToTagSetConvertible) -> None:
 
         object.__setattr__(self, "tags", tags)
 
-    def copy(self, *, name=None, tags=None):
+    def copy(self, *,
+             name: str | None = None,
+             tags: ToTagSetConvertible = None) -> TaggedVariable:
         name = self.name if name is None else name
         tags = self.tags if tags is None else tags
         return TaggedVariable(name, tags)
@@ -791,9 +835,7 @@ class Reduction(LoopyExpressionBase):
     operation: ReductionOperation
 
     inames: Sequence[str]
-    """The inames across which reduction on :attr:`expr` is being
-    carried out.
-    """
+    """The inames across which reduction on :attr:`expr` is being carried out."""
 
     expr: Expression
     """An expression which may have tuple type. If the expression has tuple
@@ -805,8 +847,8 @@ class Reduction(LoopyExpressionBase):
     """
 
     allow_simultaneous: bool
-    """If not *True*, an iname is allowed to be used
-    in precisely one reduction, to avoid misnesting errors.
+    """If not *True*, an iname is allowed to be used in precisely one reduction,
+    to avoid misnesting errors.
     """
 
     def __init__(self,
@@ -823,7 +865,7 @@ def __init__(self,
 
         assert isinstance(inames, tuple)
 
-        def strip_var(iname: Any) -> str:
+        def strip_var(iname: str | p.Variable) -> str:
             if isinstance(iname, p.Variable):
                 iname = iname.name
 
@@ -864,11 +906,11 @@ def strip_var(iname: Any) -> str:
         object.__setattr__(self, "allow_simultaneous", allow_simultaneous)
 
     @property
-    def is_tuple_typed(self):
+    def is_tuple_typed(self) -> bool:
         return self.operation.arg_count > 1
 
     @cached_property
-    def inames_set(self):
+    def inames_set(self) -> set[str]:
         return set(self.inames)
 
 
@@ -938,7 +980,9 @@ class EvaluatorWithDeficientContext(PartialEvaluationMapper):
 
     Returns the expression with the values mapped from :attr:`context`.
     """
-    def map_variable(self, expr):
+
+    @override
+    def map_variable(self, expr: p.Variable) -> Expression:
         if expr.name in self.context:
             return self.context[expr.name]
         else:
@@ -946,18 +990,24 @@ def map_variable(self, expr):
 
 
 class VariableInAnExpression(CombineMapper[bool, []]):
+    variables_to_search: Collection[p.Variable]
+
     def __init__(self, variables_to_search: Collection[p.Variable]) -> None:
-        assert all(isinstance(variable, p.Variable) for variable in
-            variables_to_search)
+        assert all(isinstance(variable, p.Variable) for variable in variables_to_search)
+
+        super().__init__()
         self.variables_to_search = variables_to_search
 
-    def combine(self, values) -> bool:
+    @override
+    def combine(self, values: Iterable[bool]) -> bool:
         return any(values)
 
-    def map_variable(self, expr) -> bool:
+    @override
+    def map_variable(self, expr: p.Variable) -> bool:
         return expr in self.variables_to_search
 
-    def map_constant(self, expr) -> bool:
+    @override
+    def map_constant(self, expr: object) -> bool:
         return False
 
 
@@ -965,17 +1015,22 @@ class SweptInameStrideCollector(CoefficientCollectorBase):
     """
     Mapper to compute the coefficient swept inames for :class:`SubArrayRef`.
     """
-    def map_algebraic_leaf(self, expr):
+
+    @override
+    def map_algebraic_leaf(self, expr: p.AlgebraicLeaf) -> CoeffsT:
         # subscripts that are not involved in :attr:`target_names` are treated
         # as constants.
-        if isinstance(expr, p.Subscript) and (self.target_names is None
-                or expr.aggregate.name not in self.target_names):
+        if isinstance(expr, p.Subscript) and (
+                self.target_names is None
+                or getattr(expr.aggregate, "name", None) not in self.target_names):
             return {1: expr}
 
         return super().map_algebraic_leaf(expr)
 
 
-def get_start_subscript_from_sar(sar, kernel):
+def get_start_subscript_from_sar(
+            sar: SubArrayRef, kernel: LoopKernel,
+        ) -> p.Variable | p.Subscript:
     """
     Returns an instance of :class:`pymbolic.primitives.Subscript`, the
     beginning subscript of the array swept by the *SubArrayRef*.
@@ -984,16 +1039,18 @@ def get_start_subscript_from_sar(sar, kernel):
     subscript would be ``a[0, j, 0, l]``
     """
 
-    def _get_lower_bound(iname):
+    def _get_lower_bound(iname: str) -> int:
         pwaff = kernel.get_iname_bounds(iname).lower_bound_pw_aff
         return int(pw_aff_to_expr(pwaff))
 
     swept_inames_to_zeros = {
-            swept_iname.name: _get_lower_bound(swept_iname.name) for
-            swept_iname in sar.swept_inames}
+            swept_iname.name: _get_lower_bound(swept_iname.name)
+            for swept_iname in sar.swept_inames}
+
+    result = EvaluatorWithDeficientContext(swept_inames_to_zeros)(sar.subscript)
+    assert isinstance(result, (p.Variable, p.Subscript))
 
-    return EvaluatorWithDeficientContext(swept_inames_to_zeros)(
-            sar.subscript)
+    return result
 
 
 @p.expr_dataclass()
@@ -1015,10 +1072,11 @@ class SubArrayRef(LoopyExpressionBase):
 
     .. automethod:: is_equal
     """
+
     swept_inames: tuple[p.Variable, ...]
     subscript: p.Subscript
 
-    def __post_init__(self):
+    def __post_init__(self) -> None:
         # {{{ sanity checks
 
         if not isinstance(self.swept_inames, tuple):
@@ -1051,10 +1109,26 @@ class FortranDivision(p.QuotientBase, LoopyExpressionBase):
 
 
 class DependencyMapperWithReductionInames(DependencyMapper[P]):
-    def __init__(self, *args, **kwargs) -> None:
-        super().__init__(*args, **kwargs)
-        self.reduction_inames: set[str] = set()
+    reduction_inames: set[str]
+
+    def __init__(
+        self,
+        include_subscripts: bool = True,
+        include_lookups: bool = True,
+        include_calls: bool | TypingLiteral["descend_args"] = True,
+        include_cses: bool = False,
+        composite_leaves: bool | None = None,
+    ) -> None:
+        super().__init__(
+            include_subscripts=include_subscripts,
+            include_lookups=include_lookups,
+            include_calls=include_calls,
+            include_cses=include_cses,
+            composite_leaves=composite_leaves,
+        )
+        self.reduction_inames = set()
 
+    @override
     def map_reduction(
                 self,
                 expr: Reduction, *args: P.args, **kwargs: P.kwargs
@@ -1067,8 +1141,9 @@ def map_reduction(
 def _get_dependencies_and_reduction_inames(
             expr: Expression
         ) -> tuple[frozenset[str], frozenset[str]]:
-    dep_mapper: DependencyMapperWithReductionInames[[]] = \
-        DependencyMapperWithReductionInames(composite_leaves=False)
+    dep_mapper: DependencyMapperWithReductionInames[[]] = (
+        DependencyMapperWithReductionInames(composite_leaves=False))
+
     deps = frozenset(cast("p.Variable", dep).name for dep in dep_mapper(expr))
     reduction_inames = dep_mapper.reduction_inames
     return frozenset(deps), frozenset(reduction_inames)
@@ -1083,32 +1158,43 @@ def get_reduction_inames(expr: Expression) -> frozenset[str]:
 
 
 class SubArrayRefSweptInamesCollector(CombineMapper[Set[str], []]):
+    @override
     def combine(self, values: Iterable[Set[str]]) -> Set[str]:
-        import operator
-        return reduce(operator.or_, values, frozenset())
+        result: Set[str] = set()
+        for value in values:
+            result |= value
 
-    def map_sub_array_ref(self, expr) -> Set[str]:
+        return frozenset(result)
+
+    @override
+    def map_sub_array_ref(self, expr: SubArrayRef) -> Set[str]:
         return frozenset({iname.name for iname in expr.swept_inames})
 
-    def map_constant(self, expr) -> Set[str]:
+    @override
+    def map_constant(
+                self, expr: (
+                    object
+                    | p.Variable | p.FunctionSymbol | p.NaN
+                    | TaggedVariable | TypeCast | ResolvedFunction)) -> Set[str]:
         return frozenset()
 
-    map_variable = map_constant
-    map_function_symbol = map_constant
-    map_tagged_variable = map_constant
-    map_type_cast = map_constant
-    map_resolved_function = map_constant
-    map_nan = map_constant
+    map_variable: Callable[[Self, p.Variable], Set[str]] = map_constant
+    map_function_symbol: Callable[[Self, p.FunctionSymbol], Set[str]] = map_constant
+    map_nan: Callable[[Self, p.NaN], Set[str]] = map_constant
+    map_tagged_variable: Callable[[Self, TaggedVariable], Set[str]] = map_constant
+    map_type_cast: Callable[[Self, TypeCast], Set[str]] = map_constant
+    map_resolved_function: Callable[[Self, ResolvedFunction], Set[str]] = map_constant
 
 
-def get_sub_array_ref_swept_inames(expr):
+def get_sub_array_ref_swept_inames(expr: SubArrayRef) -> Set[str]:
     return SubArrayRefSweptInamesCollector()(expr)
 
 
 # {{{ rule-aware mappers
 
-def parse_tagged_name(expr):
+def parse_tagged_name(expr: Expression) -> tuple[str, Set[Tag] | None]:
     from loopy.library.reduction import ArgExtOp, SegmentedOp
+
     if isinstance(expr, TaggedVariable):
         return expr.name, expr.tags
     elif isinstance(expr, ResolvedFunction):
@@ -1122,22 +1208,20 @@ def parse_tagged_name(expr):
 @dataclass(frozen=True)
 class ExpansionState:
     """
-    .. attribute:: kernel
-    .. attribute:: instruction
-
-    .. attribute:: stack
-
-        a tuple representing the current expansion stack, as a tuple
-        of (name, tag) pairs.
-
-    .. attribute:: arg_context
-
-        a dict representing current argument values
+    .. autoattribute:: kernel
+    .. autoattribute:: instruction
+    .. autoattribute:: stack
+    .. autoattribute:: arg_context
     """
+
     kernel: LoopKernel
     instruction: InstructionBase
     stack: tuple[ConcreteMatchable, ...]
+    """A tuple representing the current expansion stack, as a tuple of
+    ``(name, tag)`` pairs.
+    """
     arg_context: Mapping[str, Expression]
+    """A mapping representing current argument values."""
 
     def __post_init__(self) -> None:
         hash(self.arg_context)
@@ -1145,6 +1229,7 @@ def __post_init__(self) -> None:
     def copy(self, **kwargs: Any) -> Self:
         return replace(self, **kwargs)
 
+    @override
     def __hash__(self) -> int:
         # do not try to be precise about hash of loopy kernel
         # or the instruction as computing the hash of pymbolic
@@ -1163,10 +1248,13 @@ def apply_arg_context(self, expr: Expression) -> Expression:
 
 
 class SubstitutionRuleRenamer(IdentityMapper[[]]):
-    def __init__(self, renames):
+    renames: dict[str, str]
+
+    def __init__(self, renames: dict[str, str]) -> None:
         self.renames = renames
         super().__init__()
 
+    @override
     def map_call(self, expr: p.Call) -> Expression:
         if not isinstance(expr.function, p.Variable):
             return super().map_call(expr)
@@ -1184,6 +1272,7 @@ def map_call(self, expr: p.Call) -> Expression:
 
         return type(expr)(sym, tuple(self.rec(child) for child in expr.parameters))
 
+    @override
     def map_variable(self, expr: p.Variable) -> Expression:
         name, tags = parse_tagged_name(expr)
 
@@ -1197,7 +1286,9 @@ def map_variable(self, expr: p.Variable) -> Expression:
             return p.Variable(new_name)
 
 
-def rename_subst_rules_in_instructions(insns, renames):
+def rename_subst_rules_in_instructions(
+            insns: Sequence[InstructionBase], renames: dict[str, str]
+        ) -> Sequence[InstructionBase]:
     subst_renamer = SubstitutionRuleRenamer(renames)
 
     return [
@@ -1206,26 +1297,22 @@ def rename_subst_rules_in_instructions(insns, renames):
 
 
 class SubstitutionRuleMappingContext:
+    old_subst_rules: dict[str, SubstitutionRule]
     make_unique_var_name: Callable[[str], str]
 
-    def _get_subst_rule_key(self, args, body):
-        subst_dict = {
-                arg: RuleArgument(i)
-                for i, arg in enumerate(args)}
-
-        from pymbolic.mapper.substitutor import make_subst_func
-        arg_subst_map = SubstitutionMapper(make_subst_func(subst_dict))
+    subst_rule_registry: dict[Expression, tuple[str, Sequence[str], Expression]]
+    subst_rule_old_names: dict[Expression, list[str]]
 
-        return arg_subst_map(body)
-
-    def __init__(self, old_subst_rules, make_unique_var_name):
+    def __init__(self,
+                 old_subst_rules: dict[str, SubstitutionRule],
+                 make_unique_var_name: Callable[[str], str]) -> None:
         self.old_subst_rules = old_subst_rules
         self.make_unique_var_name = make_unique_var_name
 
         # maps subst rule (args, bodies) to (names, original_name)
         self.subst_rule_registry = {
                 self._get_subst_rule_key(rule.arguments, rule.expression):
-                (name, rule.arguments, rule.expression)
+                    (name, rule.arguments, rule.expression)
                 for name, rule in old_subst_rules.items()}
 
         # maps subst rule (args, bodies) to a list of old names,
@@ -1234,7 +1321,20 @@ def __init__(self, old_subst_rules, make_unique_var_name):
         # name
         self.subst_rule_old_names = {}
 
-    def register_subst_rule(self, original_name, args, body):
+    def _get_subst_rule_key(self,
+                            args: Sequence[str],
+                            body: Expression) -> Expression:
+        subst_dict = {
+                arg: RuleArgument(i)
+                for i, arg in enumerate(args)}
+
+        from pymbolic.mapper.substitutor import make_subst_func
+        arg_subst_map = SubstitutionMapper(make_subst_func(subst_dict))
+
+        return arg_subst_map(body)
+
+    def register_subst_rule(self, original_name: str,
+                            args: Sequence[str], body: Expression) -> str:
         """Returns a name (as a string) for a newly created substitution
         rule.
         """
@@ -1251,7 +1351,9 @@ def register_subst_rule(self, original_name, args, body):
         self.subst_rule_old_names.setdefault(key, []).append(original_name)
         return new_name
 
-    def _get_new_substitutions_and_renames(self):
+    def _get_new_substitutions_and_renames(
+                self
+            ) -> tuple[dict[str, SubstitutionRule], dict[str, str]]:
         """This makes a new dictionary of substitutions from the ones
         encountered in mapping all the encountered expressions.
         It tries hard to keep substitution names the same--i.e.
@@ -1270,10 +1372,9 @@ def _get_new_substitutions_and_renames(self):
 
         from loopy.kernel.data import SubstitutionRule
 
-        result = {}
-        renames = {}
-
-        used_names = set()
+        result: dict[str, SubstitutionRule] = {}
+        renames: dict[str, str] = {}
+        used_names: set[str] = set()
 
         for key, (name, args, body) in self.subst_rule_registry.items():
             orig_names = self.subst_rule_old_names.get(key, [])
@@ -1310,7 +1411,7 @@ def _get_new_substitutions_and_renames(self):
 
         return renamed_result, renames
 
-    def finish_kernel(self, kernel: LoopKernel):
+    def finish_kernel(self, kernel: LoopKernel) -> LoopKernel:
         new_substs, renames = self._get_new_substitutions_and_renames()
         if not renames:
             return kernel.copy(substitutions=new_substs)
@@ -1330,10 +1431,13 @@ class RuleAwareIdentityMapper(IdentityMapper[Concatenate[ExpansionState, P]]):
     are in :attr:`ExpansionState.arg_context`.
     """
 
+    rule_mapping_context: SubstitutionRuleMappingContext
+
     def __init__(self, rule_mapping_context: SubstitutionRuleMappingContext) -> None:
         self.rule_mapping_context = rule_mapping_context
         super().__init__()
 
+    @override
     def map_variable(
                 self, expr: p.Variable, expn_state: ExpansionState,
                 *args: P.args, **kwargs: P.kwargs
@@ -1344,6 +1448,7 @@ def map_variable(
         else:
             return self.map_subst_rule(name, tags, (), expn_state, *args, **kwargs)
 
+    @override
     def map_call(
                 self, expr: p.Call, expn_state: ExpansionState,
                 *args: P.args, **kwargs: P.kwargs
@@ -1356,13 +1461,9 @@ def map_call(
         if name not in self.rule_mapping_context.old_subst_rules:
             return super().map_call(expr, expn_state, *args, **kwargs)
         else:
-            return self.map_subst_rule(name, tags,
-                                         self.rec(expr.parameters,
-                                                  expn_state,
-                                                  *args,
-                                                  **kwargs),
-                                         expn_state,
-                                         *args, **kwargs)
+            params = tuple(self.rec(param, expn_state, *args, **kwargs)
+                           for param in expr.parameters)
+            return self.map_subst_rule(name, tags, params, expn_state, *args, **kwargs)
 
     @staticmethod
     def make_new_arg_context(
@@ -1383,12 +1484,20 @@ def make_new_arg_context(
         })
 
     def map_subst_rule(
-                self, name: str, tags, arguments, expn_state: ExpansionState,
+                self,
+                name: str,
+                tags: Set[Tag] | None,
+                arguments: Sequence[Expression],
+                expn_state: ExpansionState,
                 *args: P.args, **kwargs: P.kwargs
             ) -> Expression:
+        if tags is None:
+            tags = frozenset()
+        tags = frozenset(tags)
+
         rule = self.rule_mapping_context.old_subst_rules[name]
 
-        rec_arguments = self.rec(arguments, expn_state, *args, **kwargs)
+        rec_arguments = self.rec(tuple(arguments), expn_state, *args, **kwargs)
         assert isinstance(rec_arguments, tuple)
 
         from loopy.match import ConcreteMatchable
@@ -1412,22 +1521,30 @@ def map_subst_rule(
         else:
             return sym
 
-    def __call__(self, expr, kernel, insn):
+    @override
+    def __call__(self,  # pyright: ignore[reportIncompatibleMethodOverride]
+                 expr: Expression,
+                 kernel: LoopKernel,
+                 insn: InstructionBase,
+                 *args: P.args, **kwargs: P.kwargs) -> Expression:
         """
         :arg insn: A :class:`~loopy.kernel.InstructionBase` of which *expr* is
             a part of, or *None* if *expr*'s source is not an instruction.
         """
-        from loopy.kernel.data import InstructionBase
+        from loopy.kernel.instruction import InstructionBase
         assert insn is None or isinstance(insn, InstructionBase)
 
-        return super().__call__(expr,
-                ExpansionState(
-                    kernel=kernel,
-                    instruction=insn,
-                    stack=(),
-                    arg_context=constantdict()))
+        expn_state = ExpansionState(
+                kernel=kernel,
+                instruction=insn,
+                stack=(),
+                arg_context=constantdict())
 
-    def map_instruction(self, kernel, insn):
+        return super().__call__(expr, expn_state, *args, **kwargs)
+
+    def map_instruction(self,
+                        kernel: LoopKernel,
+                        insn: InstructionBase) -> InstructionBase:
         return insn
 
     def map_kernel(self,
@@ -1443,7 +1560,7 @@ def map_kernel(self,
             insn if not kernel.substitutions and not within(kernel, insn, ()) else
             self.map_instruction(kernel,
                 insn.with_transformed_expressions(
-                    lambda expr: self(expr, kernel, insn)))  # noqa: B023
+                    lambda expr: self(expr, kernel, insn)))  # noqa: B023 # pyright: ignore[reportCallIssue]
             for insn in kernel.instructions]
 
         from functools import partial
@@ -1504,19 +1621,23 @@ class RuleAwareSubstitutionMapper(RuleAwareIdentityMapper[[]]):
         :meth:`SubstitutionRuleMappingContext.finish_kernel` to perform any
         renaming mandated by the rule expression divergences.
     """
+
+    subst_func: Callable[[Expression], Expression | None]
+    _within: StackMatch
+
     def __init__(self,
-                rule_mapping_context: SubstitutionRuleMappingContext,
-                subst_func,
-                within: StackMatch):
+                 rule_mapping_context: SubstitutionRuleMappingContext,
+                 subst_func: Callable[[Expression], Expression | None],
+                 within: StackMatch) -> None:
         super().__init__(rule_mapping_context)
 
         self.subst_func = subst_func
-        self._within: StackMatch = within
+        self._within = within
 
     def within(self,
                 kernel: LoopKernel,
                 instruction: InstructionBase | None,
-                stack: RuleStack):
+                stack: RuleStack) -> bool:
         if instruction is None:
             # always perform substitutions on expressions not coming from
             # instructions.
@@ -1537,15 +1658,17 @@ def map_variable(self, expr: p.Variable, expn_state: ExpansionState) -> Expressi
         if result is not None:
             return result
         else:
-            return super().map_variable(
-                    expr, expn_state)
+            return super().map_variable(expr, expn_state)
 
 
 class RuleAwareSubstitutionRuleExpander(RuleAwareIdentityMapper[[]]):
+    rules: dict[str, SubstitutionRule]
+    within: StackMatch
+
     def __init__(self,
-                rule_mapping_context: SubstitutionRuleMappingContext,
-                rules,
-                within: StackMatch):
+                 rule_mapping_context: SubstitutionRuleMappingContext,
+                 rules: dict[str, SubstitutionRule],
+                 within: StackMatch) -> None:
         super().__init__(rule_mapping_context)
 
         self.rules = rules
@@ -1553,8 +1676,15 @@ def __init__(self,
 
     @override
     def map_subst_rule(
-                self, name: str, tags, arguments, expn_state: ExpansionState
+                self, name: str,
+                tags: Set[Tag] | None,
+                arguments: Sequence[Expression],
+                expn_state: ExpansionState
             ) -> Expression:
+        if tags is None:
+            tags = frozenset()
+        tags = frozenset(tags)
+
         from loopy.match import ConcreteMatchable
         new_stack = (*expn_state.stack, ConcreteMatchable(name, tags))
 
@@ -1586,7 +1716,8 @@ def map_subst_rule(
 # {{{ functions to primitives, parsing
 
 class VarToTaggedVarMapper(IdentityMapper[[]]):
-    def map_variable(self, expr: p.Variable) -> p.Variable:
+    @override
+    def map_variable(self, expr: p.Variable) -> Expression:
         dollar_idx = expr.name.find("$")
         if dollar_idx == -1:
             return expr
@@ -1602,7 +1733,7 @@ def map_variable(self, expr: p.Variable) -> p.Variable:
 
 class FunctionToPrimitiveMapper(UncachedIdentityMapper[[]]):
     """Looks for invocations of a function called 'cse' or 'reduce' and
-    turns those into the actual pymbolic primitives used for that.
+    turns those into the actual :mod:`pymbolic` primitives used for that.
     """
 
     def _parse_reduction(self,
@@ -1633,6 +1764,7 @@ def _parse_reduction(self,
         return Reduction(operation, tuple(processed_inames), expr_or_exprs,
                 allow_simultaneous=allow_simultaneous)
 
+    @override
     def map_call(self, expr: p.Call) -> Expression:
         from loopy.library.reduction import parse_reduction_op
 
@@ -1719,8 +1851,11 @@ class LoopyParser(ParserBase):
             *ParserBase.lex_table
             ]
 
-    def parse_float(self, s):
+    @override
+    def parse_float(self, s: str) -> np.inexact[Any] | float:
         match = TRAILING_FLOAT_TAG_RE.match(s)
+        if match is None:
+            raise RuntimeError(f"cannot parse string as float: '{s}'")
 
         val = match.group(1)
         tag = frozenset(match.group(2))
@@ -1735,7 +1870,8 @@ def parse_float(self, s):
         else:
             return float(val)  # generic float
 
-    def parse_prefix(self, pstate):
+    @override
+    def parse_prefix(self, pstate: pytools.lex.LexIterator) -> Expression:
         from pymbolic.parser import (
             _PREC_UNARY,
             _closebracket,
@@ -1792,7 +1928,11 @@ def parse_prefix(self, pstate):
         else:
             return super().parse_prefix(pstate)
 
-    def parse_postfix(self, pstate, min_precedence, left_exp):
+    @override
+    def parse_postfix(self,
+                pstate: pytools.lex.LexIterator,
+                min_precedence: int,
+                left_exp: Expression) -> tuple[Expression, bool]:
         from pymbolic.parser import _PREC_CALL, _closebracket
         if pstate.next_tag() is _open_dbl_bracket and min_precedence < _PREC_CALL:
             pstate.advance()
@@ -1811,9 +1951,8 @@ def parse_postfix(self, pstate, min_precedence, left_exp):
 # }}}
 
 
-def parse(expr_str):
-    return VarToTaggedVarMapper()(
-            FunctionToPrimitiveMapper()(LoopyParser()(expr_str)))
+def parse(expr_str: str) -> Expression:
+    return VarToTaggedVarMapper()(FunctionToPrimitiveMapper()(LoopyParser()(expr_str)))
 
 # }}}
 
@@ -1821,12 +1960,14 @@ def parse(expr_str):
 # {{{ coefficient collector
 
 class CoefficientCollector(CoefficientCollectorBase):
-    map_tagged_variable = CoefficientCollectorBase.map_variable
+    map_tagged_variable: Callable[[Self, TaggedVariable],
+                                  CoeffsT] = CoefficientCollectorBase.map_variable
 
-    def map_subscript(self, expr):
+    @override
+    def map_subscript(self, expr: p.Subscript) -> CoeffsT:
         from loopy.diagnostic import ExpressionNotAffineError
-        raise ExpressionNotAffineError("cannot gather coefficients--"
-                "indirect addressing in use")
+        raise ExpressionNotAffineError(
+                "cannot gather coefficients -- indirect addressing in use")
 
 # }}}
 
@@ -1834,25 +1975,32 @@ def map_subscript(self, expr):
 # {{{ variable index expression collector
 
 class ArrayAccessFinder(CombineMapper[Set[p.Subscript], []]):
+    tgt_vector_name: str | None
+
     def __init__(self, tgt_vector_name: str | None = None) -> None:
         self.tgt_vector_name = tgt_vector_name
         super().__init__()
 
-    def combine(self, values):
+    @override
+    def combine(self, values: Iterable[Set[p.Subscript]]) -> Set[p.Subscript]:
         from pytools import flatten
         return set(flatten(values))
 
+    @override
     def map_constant(self, expr: object) -> Set[p.Subscript]:
         return set()
 
-    def map_algebraic_leaf(self, expr) -> Set[p.Subscript]:
+    @override
+    def map_algebraic_leaf(self, expr: p.AlgebraicLeaf) -> Set[p.Subscript]:
         return set()
 
-    def map_subscript(self, expr) -> Set[p.Subscript]:
+    @override
+    def map_subscript(self, expr: p.Subscript) -> Set[p.Subscript]:
         assert isinstance(expr.aggregate, p.Variable)
 
-        if self.tgt_vector_name is None \
-                or expr.aggregate.name == self.tgt_vector_name:
+        if (
+                self.tgt_vector_name is None
+                or expr.aggregate.name == self.tgt_vector_name):
             return {expr} | self.rec(expr.index)
         else:
             return super().map_subscript(expr)
@@ -1868,15 +2016,15 @@ def aff_to_expr(aff: isl.Aff) -> ArithmeticExpression:
     denom = aff.get_denominator_val().to_python()
 
     result = (aff.get_constant_val()*denom).to_python()
-    for dt in [dim_type.in_, dim_type.param]:
+    for dt in [isl.dim_type.in_, isl.dim_type.param]:
         for i in range(aff.dim(dt)):
             coeff = (aff.get_coefficient_val(dt, i)*denom).to_python()
             if coeff:
                 dim_name = not_none(aff.get_dim_name(dt, i))
                 result += coeff*var(dim_name)
 
-    for i in range(aff.dim(dim_type.div)):
-        coeff = (aff.get_coefficient_val(dim_type.div, i)*denom).to_python()
+    for i in range(aff.dim(isl.dim_type.div)):
+        coeff = (aff.get_coefficient_val(isl.dim_type.div, i)*denom).to_python()
         if coeff:
             result += coeff*aff_to_expr(aff.get_div(i))
 
@@ -1885,12 +2033,12 @@ def aff_to_expr(aff: isl.Aff) -> ArithmeticExpression:
 
 
 def pw_aff_to_expr(
-            pw_aff: isl.PwAff | isl.Aff,
+            pw_aff: int | isl.PwAff | isl.Aff,
             int_ok: bool = False
         ) -> ArithmeticExpression:
     if isinstance(pw_aff, int):
         if not int_ok:
-            warn("expected PwAff, got int", stacklevel=2)
+            warn(f"expected PwAff, got int: {pw_aff}", stacklevel=2)
 
         return pw_aff
 
@@ -1901,6 +2049,7 @@ def pw_aff_to_expr(
              for constr_set, aff in pieces[:-1]]
 
     from pymbolic.primitives import If
+
     expr = last_expr
     for condition, then_expr in reversed(pairs):
         expr = If(condition, then_expr, expr)
@@ -1930,57 +2079,64 @@ def pw_aff_to_pw_aff_implemented_by_expr(pw_aff: isl.PwAff) -> isl.PwAff:
 # {{{ (pw)aff_from_expr
 
 class PwAffEvaluationMapper(EvaluationMapperBase[isl.PwAff]):
-    def __init__(self, space, vars_to_zero):
+    zero: isl.Aff
+    pw_zero: isl.PwAff
+
+    def __init__(self,
+                 space: isl.Space,
+                 vars_to_zero: Collection[str] | None) -> None:
+        if vars_to_zero is None:
+            vars_to_zero = ()
+
         self.zero = isl.Aff.zero_on_domain(isl.LocalSpace.from_space(space))
+        self.pw_zero = isl.PwAff.from_aff(self.zero)
 
-        context = {}
+        context: dict[str, isl.PwAff] = {}
         for name, (dt, pos) in space.get_var_dict().items():
-            if dt == dim_type.set:
-                dt = dim_type.in_
+            if dt == isl.dim_type.set:
+                dt = isl.dim_type.in_
 
             context[name] = isl.PwAff.from_aff(
                     self.zero.set_coefficient_val(dt, pos, 1))
 
         for v in vars_to_zero:
-            context[v] = self.zero
-
-        self.pw_zero = isl.PwAff.from_aff(self.zero)
+            context[v] = self.pw_zero
 
         super().__init__(context)
 
     @override
-    def map_constant(self, expr: object):
+    def map_constant(self, expr: object) -> isl.PwAff:
         iexpr = int(cast("int", expr))
 
         return self.pw_zero + iexpr
 
     @override
-    def map_min(self, expr: p.Min):
+    def map_min(self, expr: p.Min) -> isl.PwAff:
         from functools import reduce
         return reduce(
                 lambda a, b: a.min(b),
                 (self.rec(ch) for ch in expr.children))
 
     @override
-    def map_max(self, expr: p.Max):
+    def map_max(self, expr: p.Max) -> isl.PwAff:
         from functools import reduce
         return reduce(
                 lambda a, b: a.max(b),
                 (self.rec(ch) for ch in expr.children))
 
     @override
-    def map_quotient(self, expr: p.Quotient):
+    def map_quotient(self, expr: p.Quotient) -> isl.PwAff:
         raise TypeError("true division in '%s' not supported "
                 "for as-pwaff evaluation" % expr)
 
     @override
-    def map_floor_div(self, expr: p.FloorDiv):
+    def map_floor_div(self, expr: p.FloorDiv) -> isl.PwAff:
         num = self.rec(expr.numerator)
         denom = self.rec(expr.denominator)
         return num.div(denom).floor()
 
     @override
-    def map_remainder(self, expr: p.Remainder):
+    def map_remainder(self, expr: p.Remainder) -> isl.PwAff:
         num = self.rec(expr.numerator)
         denom = self.rec(expr.denominator)
         if not denom.is_cst():
@@ -1992,16 +2148,16 @@ def map_remainder(self, expr: p.Remainder):
 
         return num.mod_val(denom)
 
-    def map_literal(self, expr):
+    def map_literal(self, expr: Literal) -> isl.PwAff:
         raise TypeError("literal '%s' not supported "
                         "for as-pwaff evaluation" % expr)
 
-    def map_reduction(self, expr: Reduction):
+    def map_reduction(self, expr: Reduction) -> isl.PwAff:
         raise TypeError("reduction in '%s' not supported "
                 "for as-pwaff evaluation" % expr)
 
     @override
-    def map_call(self, expr: p.Call):
+    def map_call(self, expr: p.Call) -> isl.PwAff:
         # FIXME: There are some things here that we could handle, e.g. "abs".
         raise TypeError(f"call in '{expr}' not supported "
                 "for as-pwaff evaluation")
@@ -2094,32 +2250,38 @@ def guarded_pwaff_from_expr(
 # {{{ (pw_)?qpoly_from_expr
 
 class PwQPolyEvaluationMapper(EvaluationMapperBase[isl.PwQPolynomial]):
-    def __init__(self, space, vars_to_zero):
-        zero_qpoly = isl.QPolynomial.zero_on_domain(space)
+    pw_zero: isl.PwQPolynomial
+
+    def __init__(self,
+                 space: isl.Space,
+                 vars_to_zero: Collection[str] | None = None) -> None:
+        if vars_to_zero is None:
+            vars_to_zero = ()
 
-        context = {}
+        context: dict[str, isl.PwQPolynomial] = {}
         for name, (dt, pos) in space.get_var_dict().items():
-            if dt == dim_type.set:
-                dt = dim_type.in_
+            if dt == isl.dim_type.set:
+                dt = isl.dim_type.in_
 
             context[name] = isl.PwQPolynomial.from_qpolynomial(
                     isl.QPolynomial.var_on_domain(space, dt, pos))
 
+        pw_zero = isl.PwQPolynomial.from_qpolynomial(
+                    isl.QPolynomial.zero_on_domain(space))
         for v in vars_to_zero:
-            context[v] = zero_qpoly
-
-        self.pw_zero = isl.PwQPolynomial.from_qpolynomial(zero_qpoly)
+            context[v] = pw_zero
 
+        self.pw_zero = pw_zero
         super().__init__(context)
 
     @override
-    def map_constant(self, expr: object):
+    def map_constant(self, expr: object) -> isl.PwQPolynomial:
         iexpr = int(cast("int", expr))
 
         return self.pw_zero + iexpr
 
     @override
-    def map_quotient(self, expr: p.Quotient):
+    def map_quotient(self, expr: p.Quotient) -> isl.PwQPolynomial:
         raise TypeError("true division in '%s' not supported "
                 "for as-pwqpoly evaluation" % expr)
 
@@ -2136,11 +2298,14 @@ def map_power(self, expr: p.Power) -> isl.PwQPolynomial:
         return self.rec(expr.base) ** iexponent
 
 
-def pw_qpolynomial_from_expr(space, expr, vars_to_zero=frozenset()):
+def pw_qpolynomial_from_expr(
+            space: isl.Space,
+            expr: Expression,
+            vars_to_zero: Collection[str] | None = None) -> isl.PwQPolynomial:
     return PwQPolyEvaluationMapper(space, vars_to_zero)(expr)
 
 
-def qpolynomial_from_expr(space, expr):
+def qpolynomial_from_expr(space: isl.Space, expr: Expression) -> isl.QPolynomial:
     pw_qpoly = pw_qpolynomial_from_expr(space, expr).coalesce()
 
     pieces = pw_qpoly.get_pieces()
@@ -2156,9 +2321,8 @@ def qpolynomial_from_expr(space, expr):
 
 # {{{ simplify using aff
 
-def simplify_via_aff(expr):
+def simplify_via_aff(expr: Expression) -> Expression:
     from loopy.diagnostic import ExpressionToAffineConversionError
-    from loopy.symbolic import aff_to_expr, get_dependencies, guarded_aff_from_expr
 
     deps = sorted(get_dependencies(expr))
     try:
@@ -2189,7 +2353,7 @@ def simplify_using_aff(
     domain = (
             kernel
             .get_inames_domain(inames)
-            .project_out_except(inames, [dim_type.set]))
+            .project_out_except(inames, [isl.dim_type.set]))
 
     non_inames = deps - set(domain.get_var_dict().keys())
     non_inames = {name for name in set(non_inames) if name.isidentifier()}
@@ -2216,23 +2380,30 @@ def simplify_using_aff(
 
 # {{{ qpolynomial_to_expr
 
-def _get_monomial_coeff_from_term(space, term):
+def _get_monomial_coeff_from_term(
+            space: isl.Space, term: isl.Term
+        ) -> tuple[ArithmeticExpression, isl.Val]:
     result = 1
 
     for dt in isl._CHECK_DIM_TYPES:
         for i in range(term.dim(dt)):
             exp = term.get_exp(dt, i)
             if exp:
-                result = result*p.Variable(space.get_dim_name(dt, i))**exp
+                name = space.get_dim_name(dt, i)
+                assert name is not None
+
+                result = result*p.Variable(name)**exp
 
-    for i in range(term.dim(dim_type.div)):
-        exp = term.get_exp(dim_type.div, i)
+    for i in range(term.dim(isl.dim_type.div)):
+        exp = term.get_exp(isl.dim_type.div, i)
         result *= (aff_to_expr(term.get_div(i))**exp)
 
     return result, term.get_coefficient_val()
 
 
-def _take_common_denominator(coeffs):
+def _take_common_denominator(
+            coeffs: Sequence[isl.Val],
+        ) -> tuple[tuple[int, ...], int]:
     denominators = [coeff.get_den_val() for coeff in coeffs]
     numerators = [coeff * den for coeff, den in zip(coeffs, denominators, strict=True)]
 
@@ -2250,7 +2421,7 @@ def _take_common_denominator(coeffs):
             common_denominator.to_python())
 
 
-def qpolynomial_to_expr(qpoly):
+def qpolynomial_to_expr(qpoly: isl.QPolynomial) -> Expression:
     from pymbolic.primitives import FloorDiv
 
     space = qpoly.space
@@ -2280,7 +2451,7 @@ def qpolynomial_to_expr(qpoly):
 
 # {{{ expression/set <-> constraint conversion
 
-def constraint_to_cond_expr(cns):
+def constraint_to_cond_expr(cns: isl.Constraint) -> ArithmeticExpression:
     # Looks like this is ok after all--get_aff() performs some magic.
     # Not entirely sure though... FIXME
     #
@@ -2311,22 +2482,45 @@ class ConditionExpressionToBooleanOpsExpression(IdentityMapper[[]]):
         - ``i>10 and j`` becomes ``i>10 and j!=0``
     """
 
-    def map_comparison(self, expr):
+    @override
+    def map_comparison(self, expr: p.Comparison) -> Expression:
         return expr
 
-    def _get_expr_neq_0(self, expr):
+    def _get_expr_neq_0(self, expr: (
+                p.Variable | p.Subscript | p.Power
+                | p.Sum | p.Product | p.Call)) -> Expression:
         return p.Comparison(expr, "!=", 0)
 
-    map_variable = _get_expr_neq_0
-    map_subscript = _get_expr_neq_0
-    map_sum = _get_expr_neq_0
-    map_product = _get_expr_neq_0
-    map_constant = _get_expr_neq_0
-    map_call = _get_expr_neq_0
-    map_power = _get_expr_neq_0
-    map_power = _get_expr_neq_0
+    @override
+    def map_constant(self, expr: object) -> Expression:
+        return p.Comparison(expr, "!=", 0)
+
+    @override
+    def map_variable(self, expr: p.Variable) -> Expression:
+        return self._get_expr_neq_0(expr)
+
+    @override
+    def map_subscript(self, expr: p.Subscript) -> Expression:
+        return self._get_expr_neq_0(expr)
+
+    @override
+    def map_sum(self, expr: p.Sum) -> Expression:
+        return self._get_expr_neq_0(expr)
+
+    @override
+    def map_product(self, expr: p.Product) -> Expression:
+        return self._get_expr_neq_0(expr)
 
-    def map_reduction(self, expr):
+    @override
+    def map_call(self, expr: p.Call) -> Expression:
+        return self._get_expr_neq_0(expr)
+
+    @override
+    def map_power(self, expr: p.Power) -> Expression:
+        return self._get_expr_neq_0(expr)
+
+    @override
+    def map_reduction(self, expr: Reduction) -> Expression:
         raise ExpressionToAffineConversionError("cannot (yet) convert reduction "
                 "to affine")
 
@@ -2341,7 +2535,7 @@ class AffineConditionToISLSetMapper(Mapper[isl.Set, []]):
     space: isl.Space
 
     @override
-    def map_comparison(self, expr: p.Comparison):
+    def map_comparison(self, expr: p.Comparison) -> isl.Set:
         if expr.operator == "!=":
             return self.rec(p.LogicalNot(p.Comparison(expr.left, "==", expr.right)))
 
@@ -2363,22 +2557,27 @@ def map_comparison(self, expr: p.Comparison):
 
         return isl.Set.universe(self.space).add_constraint(cnst)
 
-    def _map_logical_reduce(self, expr, f):
+    def _map_logical_reduce(self,
+                            expr: p.LogicalOr | p.LogicalAnd,
+                            f: Callable[[isl.Set, isl.Set], isl.Set]) -> isl.Set:
         """
         :arg f: Reduction callable.
         """
         sets = [self.rec(child) for child in expr.children]
         return reduce(f, sets)
 
-    def map_logical_or(self, expr: p.LogicalOr):
+    @override
+    def map_logical_or(self, expr: p.LogicalOr) -> isl.Set:
         import operator
         return self._map_logical_reduce(expr, operator.or_)
 
-    def map_logical_and(self, expr: p.LogicalAnd):
+    @override
+    def map_logical_and(self, expr: p.LogicalAnd) -> isl.Set:
         import operator
         return self._map_logical_reduce(expr, operator.and_)
 
-    def map_logical_not(self, expr: p.LogicalNot):
+    @override
+    def map_logical_not(self, expr: p.LogicalNot) -> isl.Set:
         set_ = self.rec(expr.child)
         return set_.complement()
 
@@ -2396,10 +2595,10 @@ def isl_set_from_expr(space: isl.Space, expr: Expression) -> isl.Set:
     return set_
 
 
-def condition_to_set(space, expr):
+def condition_to_set(space: isl.Space, expr: Expression) -> isl.Set | None:
     """
     Returns an instance of :class:`islpy.Set` if *expr* can be expressed as an
-    ISL-set on *space*, if not then returns *None*.
+    :class:`isl.Set` on *space*, if not then returns *None*.
     """
     from loopy.symbolic import get_dependencies
     if get_dependencies(expr) <= frozenset(
@@ -2452,18 +2651,23 @@ def set_to_cond_expr(isl_set: isl.Set) -> Expression:
 
 # {{{ Reduction callback mapper
 
+CallbackType: TypeAlias = """Callable[
+    Concatenate[Expression,
+                Callable[Concatenate[Expression, P], Expression],
+                P], Expression | None]"""
+
+
 class ReductionCallbackMapper(UncachedIdentityMapper[P]):
-    def __init__(
-                self,
-                callback: Callable[[
-                    Reduction,
-                    Callable[Concatenate[Expression, P], Expression]
-                ], Expression]) -> None:
+    callback: CallbackType[P]
+
+    def __init__(self, callback: CallbackType[P]) -> None:
         self.callback = callback
         super().__init__()
 
-    def map_reduction(self, expr, *args: P.args, **kwargs: P.kwargs) -> Expression:
-        result = self.callback(expr, self.rec, **kwargs)
+    @override
+    def map_reduction(self, expr: Reduction,
+                      *args: P.args, **kwargs: P.kwargs) -> Expression:
+        result = self.callback(expr, self.rec, *args, **kwargs)
         if result is None:
             return super().map_reduction(expr, *args, **kwargs)
         return result
@@ -2473,37 +2677,50 @@ def map_reduction(self, expr, *args: P.args, **kwargs: P.kwargs) -> Expression:
 
 # {{{ index dependency finding
 
-class IndexVariableFinder(CombineMapper[Set[Expression], []]):
+class IndexVariableFinder(CombineMapper[Set[str], []]):
+    include_reduction_inames: bool
+
     def __init__(self, include_reduction_inames: bool) -> None:
+        super().__init__()
         self.include_reduction_inames = include_reduction_inames
 
-    def combine(self, values):
-        import operator
-        return reduce(operator.or_, values, set())
+    @override
+    def combine(self, values: Iterable[Set[str]]) -> Set[str]:
+        result = set()
+        for value in values:
+            result |= value
+
+        return result
 
-    def map_constant(self, expr):
+    @override
+    def map_constant(self, expr: object) -> Set[str]:
         return set()
 
-    def map_algebraic_leaf(self, expr):
+    @override
+    def map_algebraic_leaf(self, expr: p.AlgebraicLeaf) -> Set[str]:
         return set()
 
-    def map_subscript(self, expr):
+    @override
+    def map_subscript(self, expr: p.Subscript) -> Set[str]:
         idx_vars = DependencyMapper()(expr.index)
 
-        result = set()
+        result: set[str] = set()
         for idx_var in idx_vars:
             if isinstance(idx_var, p.Variable):
                 result.add(idx_var.name)
             else:
                 raise RuntimeError("index variable not understood: %s" % idx_var)
+
         return result
 
-    def map_reduction(self, expr):
+    @override
+    def map_reduction(self, expr: Reduction) -> Set[str]:
         result = self.rec(expr.expr)
 
         if not (expr.inames_set & result):
             raise RuntimeError("reduction '%s' does not depend on "
                     "reduction inames (%s)" % (expr, ",".join(expr.inames)))
+
         if self.include_reduction_inames:
             return result
         else:
@@ -2514,12 +2731,15 @@ def map_reduction(self, expr):
 
 # {{{ wildcard -> unique variable mapper
 
-class WildcardToUniqueVariableMapper(IdentityMapper):
+class WildcardToUniqueVariableMapper(IdentityMapper[[]]):
+    unique_var_name_factory: Callable[[], str]
+
     def __init__(self, unique_var_name_factory: Callable[[], str]) -> None:
         self.unique_var_name_factory = unique_var_name_factory
         super().__init__()
 
-    def map_wildcard(self, expr: p.Wildcard) -> p.Variable:
+    @override
+    def map_wildcard(self, expr: p.Wildcard) -> Expression:
         from pymbolic import var
         return var(self.unique_var_name_factory())
 
@@ -2529,19 +2749,24 @@ def map_wildcard(self, expr: p.Wildcard) -> p.Variable:
 # {{{ prime ("'") adder
 
 class PrimeAdder(IdentityMapper[[]]):
-    def __init__(self, which_vars):
+    which_vars: Collection[str]
+
+    def __init__(self, which_vars: Collection[str]) -> None:
         self.which_vars = which_vars
+        super().__init__()
 
-    def map_variable(self, expr):
+    @override
+    def map_variable(self, expr: p.Variable) -> Expression:
         from pymbolic import var
         if expr.name in self.which_vars:
-            return var(expr.name+"'")
+            return var(f"{expr.name}'")
         else:
             return expr
 
-    def map_tagged_variable(self, expr):
+    @override
+    def map_tagged_variable(self, expr: TaggedVariable) -> Expression:
         if expr.name in self.which_vars:
-            return TaggedVariable(expr.name+"'", expr.tags)
+            return TaggedVariable(f"{expr.name}'", expr.tags)
         else:
             return expr
 
@@ -2598,18 +2823,18 @@ def get_access_map(
 
     if allowed_constant_names is not None:
         allowed_constant_names = set(allowed_constant_names) - {
-                access_map.get_dim_name(dim_type.param, i)
-                for i in range(access_map.dim(dim_type.param))}
+                access_map.get_dim_name(isl.dim_type.param, i)
+                for i in range(access_map.dim(isl.dim_type.param))}
 
-        par_base = access_map.dim(dim_type.param)
-        access_map = access_map.insert_dims(dim_type.param, par_base,
+        par_base = access_map.dim(isl.dim_type.param)
+        access_map = access_map.insert_dims(isl.dim_type.param, par_base,
                 len(allowed_constant_names))
         for i, const_name in enumerate(allowed_constant_names):
             access_map = access_map.set_dim_name(
-                    dim_type.param, par_base+i, const_name)
+                    isl.dim_type.param, par_base+i, const_name)
 
-    dn = access_map.dim(dim_type.set)
-    access_map = access_map.insert_dims(dim_type.set, dn, dims)
+    dn = access_map.dim(isl.dim_type.set)
+    access_map = access_map.insert_dims(isl.dim_type.set, dn, dims)
 
     from loopy.diagnostic import ExpressionToAffineConversionError
 
@@ -2638,10 +2863,10 @@ def get_access_map(
 
             upper_bound_cns = isl.Constraint.inequality_from_aff(
                     shape_aff.set_coefficient_val(
-                        dim_type.in_, dn+idim, -1) - 1)
+                        isl.dim_type.in_, dn+idim, -1) - 1)
             lower_bound_cns = isl.Constraint.inequality_from_aff(
                     isl.Aff.zero_on_domain(access_map.space).set_coefficient_val(
-                        dim_type.in_, dn+idim, 1))
+                        isl.dim_type.in_, dn+idim, 1))
 
             access_map = access_map.add_constraint(upper_bound_cns)
             access_map = access_map.add_constraint(lower_bound_cns)
@@ -2650,7 +2875,7 @@ def get_access_map(
             # successfully converted subscript[idim] -> idx_aff
 
             idx_aff = idx_aff.set_coefficient_val(
-                    dim_type.in_, dn+idim, -1)
+                    isl.dim_type.in_, dn+idim, -1)
 
             access_map = access_map.add_constraint(
                     isl.Constraint.equality_from_aff(idx_aff))
@@ -2658,8 +2883,8 @@ def get_access_map(
     access_map_as_map = isl.Map.universe(access_map.get_space())
     access_map_as_map = access_map_as_map.intersect_range(access_map)
     access_map = access_map_as_map.move_dims(
-            dim_type.in_, 0,
-            dim_type.out, 0, dn)
+            isl.dim_type.in_, 0,
+            isl.dim_type.out, 0, dn)
 
     return access_map
 
@@ -2731,8 +2956,8 @@ def map_subscript(self, expr: p.Subscript, inames: Set[str]) -> None:
             other_access_map = next(iter(self.access_maps[arg_name].values()))
             assert other_access_map is not None
 
-            if (other_access_map.dim(dim_type.set)
-                    != access_map.dim(dim_type.set)):
+            if (other_access_map.dim(isl.dim_type.set)
+                    != access_map.dim(isl.dim_type.set)):
                 raise RuntimeError(
                         "error while determining shape of argument '%s': "
                         "varying number of indices encountered"
@@ -2758,7 +2983,7 @@ def map_linear_subscript(
             self.bad_subscripts[expr.aggregate.name].append(expr)
 
     @override
-    def map_reduction(self, expr: Reduction, inames: Set[str]):
+    def map_reduction(self, expr: Reduction, inames: Set[str]) -> None:
         return WalkMapper.map_reduction(self, expr, inames | set(expr.inames))
 
     @override
@@ -2780,6 +3005,7 @@ def map_sub_array_ref(self, expr: SubArrayRef, inames: Set[str]) -> None:
 
         amap = self.access_maps[arg_name].pop(total_inames)
         for iname in expr.swept_inames:
+            assert amap is not None
             dt, pos = amap.get_var_dict()[iname.name]
             amap = amap.project_out(dt, pos, 1)
 
@@ -2805,20 +3031,25 @@ class AccessRangeMapper:
     BatchedAccessMapMapper does the same traversal in *O(m + n)* time.
     """
 
-    def __init__(self, kernel, var_name, overestimate=None):
+    var_name: str
+    inner_mapper: BatchedAccessMapMapper
+
+    def __init__(self,
+                 kernel: LoopKernel,
+                 var_name: str,
+                 overestimate: bool = False) -> None:
         self.var_name = var_name
-        self.inner_mapper = BatchedAccessMapMapper(
-                kernel, [var_name], overestimate)
+        self.inner_mapper = BatchedAccessMapMapper(kernel, [var_name], overestimate)
 
-    def __call__(self, expr, inames):
+    def __call__(self, expr: Expression, inames: Set[str]) -> None:
         return self.inner_mapper(expr, inames)
 
     @property
-    def access_range(self):
+    def access_range(self) -> isl.Set | None:
         return self.inner_mapper.get_access_range(self.var_name)
 
     @property
-    def bad_subscripts(self):
+    def bad_subscripts(self) -> Sequence[p.Subscript | LinearSubscript]:
         return self.inner_mapper.bad_subscripts[self.var_name]
 
 # }}}
@@ -2833,14 +3064,14 @@ class AccessRangeOverlapChecker:
     kernel: LoopKernel
 
     @cached_property
-    def vars(self):
+    def vars(self) -> Set[str]:
         return (self.kernel.get_written_variables()
                 | self.kernel.get_read_variables())
 
     @memoize_method
     def _get_access_ranges(self,
                 insn_id: InsnId,
-                access_dir: LiteralT["w"] | LiteralT["any"]
+                access_dir: TypingLiteral["w"] | TypingLiteral["any"]
             ):
         insn = self.kernel.id_to_insn[insn_id]
 
@@ -2867,7 +3098,7 @@ def _get_access_ranges(self,
 
     def _get_access_range_for_var(self,
                 insn_id: str,
-                access_dir: LiteralT["w"] | LiteralT["any"],
+                access_dir: TypingLiteral["w"] | TypingLiteral["any"],
                 var_name: str
             ):
         assert access_dir in ["w", "any"]
@@ -2886,9 +3117,9 @@ def _get_access_range_for_var(self,
 
     def do_access_ranges_overlap_conservative(self,
                 insn1: InsnId,
-                insn1_dir: LiteralT["w"] | LiteralT["any"],
+                insn1_dir: TypingLiteral["w"] | TypingLiteral["any"],
                 insn2: InsnId,
-                insn2_dir: LiteralT["w"] | LiteralT["any"],
+                insn2_dir: TypingLiteral["w"] | TypingLiteral["any"],
                 var_name: str,
             ):
         """Determine whether the access ranges to *var_name* in the two
@@ -2920,7 +3151,7 @@ def do_access_ranges_overlap_conservative(self,
 
 # {{{ is_expression_equal
 
-def is_expression_equal(a: Expression, b: Expression) -> bool:
+def is_expression_equal(a: Expression | None, b: Expression | None) -> bool:
     if a == b:
         return True
 

From e84912908c8ee443d7183ebb300096caf5d7e2f0 Mon Sep 17 00:00:00 2001
From: Alexandru Fikl <alexfikl@gmail.com>
Date: Wed, 29 Oct 2025 21:31:57 +0200
Subject: [PATCH 02/18] feat: use more f-strings in symbolic

---
 loopy/symbolic.py | 120 ++++++++++++++++++++++++----------------------
 1 file changed, 63 insertions(+), 57 deletions(-)

diff --git a/loopy/symbolic.py b/loopy/symbolic.py
index cac49ea05..9adfa37f8 100644
--- a/loopy/symbolic.py
+++ b/loopy/symbolic.py
@@ -186,8 +186,8 @@ def map_reduction(self, expr: Reduction,
         for iname, new_sym_iname in zip(expr.inames, mapped_inames, strict=True):
             if not isinstance(new_sym_iname, p.Variable):
                 from loopy.diagnostic import LoopyError
-                raise LoopyError("%s did not map iname '%s' to a variable"
-                        % (type(self).__name__, iname))
+                raise LoopyError(
+                    f"{type(self).__name__} did not map iname '{iname}' to a variable")
 
             new_inames.append(new_sym_iname.name)
 
@@ -419,29 +419,32 @@ def map_literal(self, expr: Literal, enclosing_prec: int) -> str:
 
     def map_array_literal(self, expr: ArrayLiteral, enclosing_prec: int) -> str:
         from pymbolic.mapper.stringifier import PREC_NONE
-        return "{%s}" % ", ".join(self.rec(ch, PREC_NONE) for ch in expr.children)
+
+        children = ", ".join(self.rec(ch, PREC_NONE) for ch in expr.children)
+        return f"{{{children}}}"
 
     def map_group_hw_index(self, expr: GroupHardwareAxisIndex,
                            enclosing_prec: int) -> str:
-        return "grp.%d" % expr.axis
+        return f"grp.{expr.axis}"
 
     def map_local_hw_index(self, expr: LocalHardwareAxisIndex,
                            enclosing_prec: int) -> str:
-        return "loc.%d" % expr.axis
+        return f"loc.{expr.axis}"
 
     def map_reduction(self, expr: Reduction, enclosing_prec: int) -> str:
         from pymbolic.mapper.stringifier import PREC_NONE
 
-        return "{}reduce({}, [{}], {})".format(
-                "simul_" if expr.allow_simultaneous else "",
-                expr.operation, ", ".join(expr.inames),
-                self.rec(expr.expr, PREC_NONE))
+        simul = "simul_" if expr.allow_simultaneous else ""
+        inames = ", ".join(expr.inames)
+        child = self.rec(expr.expr, PREC_NONE)
+        return f"{simul}reduce({expr.operation}, [{inames}], {child})"
 
     def map_tagged_variable(self, expr: TaggedVariable, enclosing_prec: int) -> str:
         return f"{expr.name}${{{', '.join(str(t) for t in expr.tags)}}}"
 
     def map_linear_subscript(self, expr: LinearSubscript, enclosing_prec: int) -> str:
         from pymbolic.mapper.stringifier import PREC_CALL, PREC_NONE
+
         return self.parenthesize_if_needed(
                 self.format("%s[[%s]]",
                     self.rec(expr.aggregate, PREC_CALL),
@@ -451,12 +454,12 @@ def map_linear_subscript(self, expr: LinearSubscript, enclosing_prec: int) -> st
     def map_loopy_function_identifier(
             self, expr: FunctionIdentifier, enclosing_prec: int) -> str:
         from dataclasses import fields
-        initargs = tuple(getattr(self, fld.name) for fld in fields(expr))
+        initargs = ", ".join(f"{getattr(expr, fld.name)}" for fld in fields(expr))
 
-        return "{}<{}>".format(type(expr).__name__, ", ".join(str(a) for a in initargs))
+        return f"{type(expr).__name__}<{initargs}>"
 
     def map_rule_argument(self, expr: RuleArgument, enclosing_prec: int) -> str:
-        return "<arg%d>" % expr.index
+        return f"<arg{expr.index}>"
 
     def map_type_cast(self, expr: TypeCast, enclosing_prec: int) -> str:
         from pymbolic.mapper.stringifier import PREC_NONE
@@ -468,10 +471,11 @@ def map_resolved_function(self, expr: ResolvedFunction, enclosing_prec: int) ->
         return "\u0332".join(str(expr.function))
 
     def map_sub_array_ref(self, expr: SubArrayRef, enclosing_prec: int) -> str:
-        return "[{inames}]: {subscr}".format(
-                inames=",".join(self.rec(iname, enclosing_prec) for iname in
-                    expr.swept_inames),
-                subscr=self.rec(expr.subscript, enclosing_prec))
+        inames = ",".join(self.rec(iname, enclosing_prec)
+                          for iname in expr.swept_inames)
+        subscr = self.rec(expr.subscript, enclosing_prec)
+
+        return f"[{inames}]: {subscr}"
 
     def map_fortran_division(self, expr: FortranDivision, enclosing_prec: int) -> str:
         from pymbolic.mapper.stringifier import PREC_NONE
@@ -615,8 +619,8 @@ def map_subst_rule(self,
                     ) -> Expression:
         if len(rule.arguments) != len(arguments):
             from loopy.diagnostic import LoopyError
-            raise LoopyError("number of arguments to '%s' does not match "
-                    "definition" % name)
+            raise LoopyError(
+                    f"number of arguments to '{name}' does not match definition")
 
         from pymbolic.mapper.substitutor import make_subst_func
         submap = SubstitutionMapper(
@@ -892,7 +896,7 @@ def strip_var(iname: str | p.Variable) -> str:
             if not isinstance(expr, (tuple, Reduction, Call)):
                 raise LoopyError("reduction argument must be one of "
                                  "a tuple, reduction, or call; "
-                                 "got '%s'" % type(expr).__name__)
+                                 f"got '{type(expr).__name__}'")
         else:
             # Sanity checks
             if isinstance(expr, tuple):
@@ -966,8 +970,8 @@ def name(self) -> str | ReductionOpFunction:
         elif isinstance(self.function, ReductionOpFunction):
             return self.function
         else:
-            raise LoopyError("Unexpected function type %s in ResolvedFunction." %
-                    type(self.function))
+            raise LoopyError(
+                f"Unexpected function type {type(self.function)} in ResolvedFunction.")
 
 # }}}
 
@@ -1202,7 +1206,7 @@ def parse_tagged_name(expr: Expression) -> tuple[str, Set[Tag] | None]:
     elif isinstance(expr, (p.Variable, ArgExtOp, SegmentedOp)):
         return expr.name, None
     else:
-        raise RuntimeError("subst rule name not understood: %s" % expr)
+        raise RuntimeError(f"subst rule name not understood: {expr!r}")
 
 
 @dataclass(frozen=True)
@@ -1343,7 +1347,7 @@ def register_subst_rule(self, original_name: str,
 
         if reg_value is None:
             # These names are temporary and won't stick around.
-            new_name = self.make_unique_var_name("_lpy_tmp_"+original_name)
+            new_name = self.make_unique_var_name(f"_lpy_tmp_{original_name}")
             self.subst_rule_registry[key] = (new_name, args, body)
         else:
             new_name, _, _ = reg_value
@@ -1473,8 +1477,9 @@ def make_new_arg_context(
             arg_context: Mapping[str, Expression]
             ) -> Mapping[str, Expression]:
         if len(arg_names) != len(arguments):
-            raise RuntimeError("Rule '%s' invoked with %d arguments (needs %d)"
-                    % (rule_name, len(arguments), len(arg_names), ))
+            raise RuntimeError(
+                    f"Rule '{rule_name}' invoked with {len(arguments)} arguments "
+                    f" (needs {len(arg_names)})")
 
         from pymbolic.mapper.substitutor import make_subst_func
         arg_subst_map = SubstitutionMapper(make_subst_func(arg_context))
@@ -1824,11 +1829,10 @@ def map_call(self, expr: p.Call) -> Expression:
             if operation:
                 # arg_count counts arguments but not inames
                 if len(expr.parameters) != 1 + operation.arg_count:
-                    raise RuntimeError("invalid invocation of "
-                            "reduction operation '%s': expected %d arguments, "
-                            "got %d instead" % (expr.function.name,
-                                                1 + operation.arg_count,
-                                                len(expr.parameters)))
+                    raise RuntimeError(
+                        "invalid invocation of reduction operation "
+                        f"'{expr.function.name}': expected {operation.arg_count + 1} "
+                        f"arguments: got {len(expr.parameters)} instead")
 
                 inames = expr.parameters[0]
                 red_exprs = tuple(self.rec(param) for param in expr.parameters[1:])
@@ -2126,8 +2130,8 @@ def map_max(self, expr: p.Max) -> isl.PwAff:
 
     @override
     def map_quotient(self, expr: p.Quotient) -> isl.PwAff:
-        raise TypeError("true division in '%s' not supported "
-                "for as-pwaff evaluation" % expr)
+        raise TypeError(
+            f"true division in '{expr}' not supported for as-pwaff evaluation")
 
     @override
     def map_floor_div(self, expr: p.FloorDiv) -> isl.PwAff:
@@ -2140,8 +2144,9 @@ def map_remainder(self, expr: p.Remainder) -> isl.PwAff:
         num = self.rec(expr.numerator)
         denom = self.rec(expr.denominator)
         if not denom.is_cst():
-            raise TypeError("modulo non-constant in '%s' not supported "
-                    "for as-pwaff evaluation" % expr)
+            raise TypeError(
+                    f"modulo non-constant in '{expr}' not supported "
+                    "for as-pwaff evaluation")
 
         (_s, denom_aff), = denom.get_pieces()
         denom = denom_aff.get_constant_val()
@@ -2149,12 +2154,11 @@ def map_remainder(self, expr: p.Remainder) -> isl.PwAff:
         return num.mod_val(denom)
 
     def map_literal(self, expr: Literal) -> isl.PwAff:
-        raise TypeError("literal '%s' not supported "
-                        "for as-pwaff evaluation" % expr)
+        raise TypeError(f"literal '{expr}' not supported for as-pwaff evaluation")
 
     def map_reduction(self, expr: Reduction) -> isl.PwAff:
-        raise TypeError("reduction in '%s' not supported "
-                "for as-pwaff evaluation" % expr)
+        raise TypeError(
+                f"reduction in '{expr}' not supported for as-pwaff evaluation")
 
     @override
     def map_call(self, expr: p.Call) -> isl.PwAff:
@@ -2179,8 +2183,9 @@ def aff_from_expr(
         return aff
     else:
         from loopy.diagnostic import ExpressionNotAffineError
-        raise ExpressionNotAffineError("expression '%s' could not be converted to a "
-                "non-piecewise quasi-affine expression" % expr)
+        raise ExpressionNotAffineError(
+                f"expression '{expr}' could not be converted to a "
+                "non-piecewise quasi-affine expression")
 
 
 def pwaff_from_expr(
@@ -2219,8 +2224,8 @@ def with_aff_conversion_guard(
     assert err is not None
     from loopy.diagnostic import ExpressionToAffineConversionError
     raise ExpressionToAffineConversionError(
-            "could not convert expression '%s' to affine representation: "
-            "%s: %s" % (expr, type(err).__name__, str(err)))
+            f"could not convert expression '{expr}' to affine representation: "
+            f"{type(err).__name__}: {err}")
 
 
 def guarded_aff_from_expr(
@@ -2282,8 +2287,9 @@ def map_constant(self, expr: object) -> isl.PwQPolynomial:
 
     @override
     def map_quotient(self, expr: p.Quotient) -> isl.PwQPolynomial:
-        raise TypeError("true division in '%s' not supported "
-                "for as-pwqpoly evaluation" % expr)
+        raise TypeError(
+                f"true division in '{expr}' not supported "
+                "for as-pwqpoly evaluation")
 
     @override
     def map_power(self, expr: p.Power) -> isl.PwQPolynomial:
@@ -2313,8 +2319,9 @@ def qpolynomial_from_expr(space: isl.Space, expr: Expression) -> isl.QPolynomial
         (_s, qpoly), = pieces
         return qpoly
     else:
-        raise RuntimeError("expression '%s' could not be converted to a "
-                "non-piecewise quasi-polynomial expression" % expr)
+        raise RuntimeError(
+                f"expression '{expr}' could not be converted to a "
+                "non-piecewise quasi-polynomial expression")
 
 # }}}
 
@@ -2709,7 +2716,7 @@ def map_subscript(self, expr: p.Subscript) -> Set[str]:
             if isinstance(idx_var, p.Variable):
                 result.add(idx_var.name)
             else:
-                raise RuntimeError("index variable not understood: %s" % idx_var)
+                raise RuntimeError(f"index variable not understood: {idx_var}")
 
         return result
 
@@ -2718,8 +2725,9 @@ def map_reduction(self, expr: Reduction) -> Set[str]:
         result = self.rec(expr.expr)
 
         if not (expr.inames_set & result):
-            raise RuntimeError("reduction '%s' does not depend on "
-                    "reduction inames (%s)" % (expr, ",".join(expr.inames)))
+            inames = ", ".join(expr.inames)
+            raise RuntimeError(
+                f"reduction '{expr}' does not depend on reduction inames ({inames})")
 
         if self.include_reduction_inames:
             return result
@@ -2852,12 +2860,11 @@ def get_access_map(
 
             if shape_aff is None:
                 # failed to convert shape[idim] to aff
+                subs = ", ".join(str(si) for si in subscript)
                 raise UnableToDetermineAccessRangeError(
-                        "unable to determine access range of subscript: [%s] "
-                        "(encountered %s: %s)"
-                        % (", ".join(str(si) for si in subscript),
-                            # intentionally using 'outer' err
-                            type(err).__name__, str(err))) from err
+                        # intentionally using 'outer' err
+                        f"unable to determine access range of subscript: [{subs}] "
+                        f"(encountered {type(err).__name__}: {err})") from err
 
             # successfully converted shape[idim] to aff, but not subscript[idim]
 
@@ -2959,9 +2966,8 @@ def map_subscript(self, expr: p.Subscript, inames: Set[str]) -> None:
             if (other_access_map.dim(isl.dim_type.set)
                     != access_map.dim(isl.dim_type.set)):
                 raise RuntimeError(
-                        "error while determining shape of argument '%s': "
-                        "varying number of indices encountered"
-                        % arg_name)
+                        f"error while determining shape of argument '{arg_name}': "
+                        "varying number of indices encountered")
 
         # }}}
 

From 90c2c10c034920b4e983535b9b9fd5c205a284ec Mon Sep 17 00:00:00 2001
From: Alexandru Fikl <alexfikl@gmail.com>
Date: Wed, 29 Oct 2025 21:55:03 +0200
Subject: [PATCH 03/18] docs: updates for symbolic

---
 loopy/symbolic.py | 82 +++++++++++++++++++++++++++++------------------
 1 file changed, 51 insertions(+), 31 deletions(-)

diff --git a/loopy/symbolic.py b/loopy/symbolic.py
index 9adfa37f8..490f7cc68 100644
--- a/loopy/symbolic.py
+++ b/loopy/symbolic.py
@@ -116,24 +116,36 @@
 Loopy-specific expression types
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
 
+.. autoclass:: LoopyExpressionBase
+    :show-inheritance:
 .. autoclass:: Literal
+    :show-inheritance:
 .. autoclass:: ArrayLiteral
+    :show-inheritance:
+.. autoclass:: GroupHardwareAxisIndex
+.. autoclass:: LocalHardwareAxisIndex
 .. autoclass:: FunctionIdentifier
+    :show-inheritance:
 .. autoclass:: TypedCSE
+    :show-inheritance:
 
 .. currentmodule:: loopy
 
 .. autoclass:: TypeCast
+    :show-inheritance:
 .. autoclass:: TaggedVariable
+    :show-inheritance:
 .. autoclass:: Reduction
-.. autoclass:: LinearSubscript
+    :show-inheritance:
 
 .. currentmodule:: loopy.symbolic
-.. autoclass:: SubArrayRef
-
 
+.. autoclass:: SubArrayRef
+    :show-inheritance:
 .. autoclass:: RuleArgument
+    :show-inheritance:
 .. autoclass:: ResolvedFunction
+    :show-inheritance:
 
 Rule-aware Mappers
 ^^^^^^^^^^^^^^^^^^
@@ -142,7 +154,6 @@
 .. autoclass:: ExpansionState
 .. autoclass:: RuleAwareIdentityMapper
 
-
 Expression Manipulation Helpers
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
 
@@ -684,7 +695,8 @@ class HardwareAxisIndex(LoopyExpressionBase):
 
 @p.expr_dataclass()
 class GroupHardwareAxisIndex(HardwareAxisIndex):
-    """
+    """Inherits: :class:`LoopyExpressionBase`.
+
     .. note::
 
         Only used in the output of
@@ -699,7 +711,8 @@ class GroupHardwareAxisIndex(HardwareAxisIndex):
 
 @p.expr_dataclass()
 class LocalHardwareAxisIndex(HardwareAxisIndex):
-    """
+    """Inherits: :class:`LoopyExpressionBase`.
+
     .. note::
 
         Only used in the output of
@@ -721,8 +734,7 @@ class FunctionIdentifier(LoopyExpressionBase):
 
 @p.expr_dataclass()
 class TypedCSE(LoopyExpressionBase, p.CommonSubexpression):
-    """A :class:`pymbolic.primitives.CommonSubexpression` annotated with
-    a type.
+    """A :class:`pymbolic.primitives.CommonSubexpression` annotated with a type.
 
     .. autoattribute:: dtype
     """
@@ -754,7 +766,7 @@ class TypeCast(LoopyExpressionBase):
     :meth:`numpy.ndarray.astype`.
 
     .. autoattribute:: child
-    .. autoattribute:: type
+    .. autoproperty:: type
     """
 
     child: Expression
@@ -793,9 +805,6 @@ class TaggedVariable(LoopyExpressionBase, p.Variable, Taggable):
     accesses tagged a certain way.
 
     .. autoattribute:: tags
-
-    Inherits from :class:`pymbolic.primitives.Variable`
-    and :class:`pytools.tag.Taggable`.
     """
 
     tags: frozenset[Tag]
@@ -922,6 +931,9 @@ def inames_set(self) -> set[str]:
 class LinearSubscript(LoopyExpressionBase):
     """Represents a linear index into a multi-dimensional array, completely
     ignoring any multi-dimensional layout.
+
+    .. autoattribute:: aggregate
+    .. autoattribute:: index
     """
     aggregate: Expression
     index: Expression
@@ -935,8 +947,11 @@ def __post_init__(self) -> None:
 @p.expr_dataclass()
 class RuleArgument(LoopyExpressionBase):
     """Represents a (numbered) argument of a :class:`loopy.SubstitutionRule`.
-    Only used internally in the rule-aware mappers to match subst rules
+
+    Only used internally in the rule-aware mappers to match substitution rules
     independently of argument names.
+
+    .. autoattribute:: index
     """
 
     index: int
@@ -944,15 +959,16 @@ class RuleArgument(LoopyExpressionBase):
 
 @p.expr_dataclass(init=False)
 class ResolvedFunction(LoopyExpressionBase):
-    """
-    A function identifier whose definition is known in a :mod:`loopy` program.
+    """A function identifier whose definition is known in a :mod:`loopy` program.
+
     A function is said to be *known* in a :class:`~loopy.TranslationUnit` if its
     name maps to  an :class:`~loopy.kernel.function_interface.InKernelCallable`
     in :attr:`loopy.TranslationUnit.callables_table`. Refer to :ref:`func-interface`.
 
     .. autoattribute:: function
-    .. autoattribute:: name
+    .. autoproperty:: name
     """
+
     function: p.Variable | ReductionOpFunction
 
     def __init__(self, function: p.Variable | ReductionOpFunction) -> None:
@@ -1100,8 +1116,10 @@ def __post_init__(self) -> None:
 class FortranDivision(p.QuotientBase, LoopyExpressionBase):
     """This exists for the benefit of the Fortran frontend, which specializes
     to floating point division for floating point inputs and round-to-zero
-    division for integer inputs. Despite the name, this would also be usable
-    for C semantics. (:mod:`loopy` division semantics match Python's.)
+    division for integer inputs.
+
+    Despite the name, this would also be usable for C semantics. (:mod:`loopy`
+    division semantics match Python's.)
 
     .. note::
 
@@ -1433,9 +1451,14 @@ class RuleAwareIdentityMapper(IdentityMapper[Concatenate[ExpansionState, P]]):
 
     Subclasses of this must be careful to not touch identifiers that
     are in :attr:`ExpansionState.arg_context`.
+
+    .. autoattribute:: rule_mapping_context
     """
 
     rule_mapping_context: SubstitutionRuleMappingContext
+    """An instance of :class:`SubstitutionRuleMappingContext` to record
+    divergence of substitution rules.
+    """
 
     def __init__(self, rule_mapping_context: SubstitutionRuleMappingContext) -> None:
         self.rule_mapping_context = rule_mapping_context
@@ -1608,17 +1631,9 @@ class RuleAwareSubstitutionMapper(RuleAwareIdentityMapper[[]]):
     Mapper to substitute expressions and record any divergence of substitution
     rule expressions of :class:`loopy.LoopKernel`.
 
-    .. attribute:: rule_mapping_context
-
-        An instance of :class:`SubstitutionRuleMappingContext` to record
-        divergence of substitution rules.
-
-    .. attribute:: within
-
-        An instance of :class:`loopy.match.StackMatchComponent`.
-        :class:`RuleAwareSubstitutionMapper` would perform
-        substitutions in the expression if the stack match is ``True`` or
-        if the expression does not arise from an :class:`~loopy.InstructionBase`.
+    .. autoattribute:: rule_mapping_context
+    .. autoattribute:: subst_func
+    .. automethod:: within
 
     .. note::
 
@@ -1643,6 +1658,11 @@ def within(self,
                 kernel: LoopKernel,
                 instruction: InstructionBase | None,
                 stack: RuleStack) -> bool:
+        """:class:`RuleAwareSubstitutionMapper` will perform
+        substitutions in the expression if the stack match is *True* or
+        if the expression does not arise from an :class:`~loopy.InstructionBase`.
+        """
+
         if instruction is None:
             # always perform substitutions on expressions not coming from
             # instructions.
@@ -3029,12 +3049,12 @@ class AccessRangeMapper:
     Using this class *will likely* lead to performance bottlenecks.
 
     To avoid performance issues, rewrite your code to use
-    BatchedAccessMapMapper if at all possible.
+    :class:`BatchedAccessMapMapper` if at all possible.
 
     For *n* variables and *m* expressions, calling this class to compute the
     access ranges will take *O(mn)* time for traversing the expressions.
 
-    BatchedAccessMapMapper does the same traversal in *O(m + n)* time.
+    :class:`BatchedAccessMapMapper` does the same traversal in *O(m + n)* time.
     """
 
     var_name: str

From 6fc75d30f9869ac8c82191a79d6608c489d73e0f Mon Sep 17 00:00:00 2001
From: Alexandru Fikl <alexfikl@gmail.com>
Date: Mon, 20 Oct 2025 13:34:37 +0300
Subject: [PATCH 04/18] feat(typing): improve typing in
 kernel.function_interface

---
 loopy/kernel/function_interface.py | 324 ++++++++++++++++++-----------
 loopy/transform/callable.py        |   8 +-
 loopy/typing.py                    |   3 +-
 3 files changed, 207 insertions(+), 128 deletions(-)

diff --git a/loopy/kernel/function_interface.py b/loopy/kernel/function_interface.py
index d5582882e..a0c0f0d04 100644
--- a/loopy/kernel/function_interface.py
+++ b/loopy/kernel/function_interface.py
@@ -30,19 +30,18 @@
 from constantdict import constantdict
 from typing_extensions import Self, override
 
+import pymbolic.primitives as p
+
 from loopy.diagnostic import LoopyError
 from loopy.kernel.array import ArrayBase, ArrayDimImplementationTag
-from loopy.kernel.data import AddressSpace, ArrayArg, ValueArg
-from loopy.symbolic import DependencyMapper, WalkMapper
+from loopy.kernel.data import AddressSpace, ArrayArg, KernelArgument, ValueArg
+from loopy.symbolic import DependencyMapper, SubArrayRef, WalkMapper
 
 
 if TYPE_CHECKING:
-    from collections.abc import Callable, Mapping, Sequence
-
-    from typing_extensions import Self
+    from collections.abc import Iterator, Mapping, Sequence, Set
 
     import islpy as isl
-    import pymbolic.primitives as p
     from pymbolic.typing import Expression
 
     from loopy.kernel import LoopKernel
@@ -76,12 +75,15 @@
 ArgDescriptorT = TypeVar("ArgDescriptorT", bound="ArgDescriptor")
 
 
+# FIXME(pyright): ArrayArgDescriptor also maps its
+#       shape: tuple[ArithmeticExpression, ...]`
+class SubstitutionCallable(Protocol):
+    def __call__(self, arg: ArgDescriptorT) -> ArgDescriptorT: ...
+
+
 class ArgDescriptor(ABC):
     @abstractmethod
-    def map_expr(
-                self,
-                subst_mapper: Callable[[ArgDescriptorT], ArgDescriptorT]
-            ) -> Self:
+    def map_expr(self, subst_mapper: SubstitutionCallable) -> Self:
         ...
 
     @abstractmethod
@@ -95,13 +97,15 @@ def copy(self, **kwargs: Any) -> Self:
 
 @dataclass(frozen=True)
 class ValueArgDescriptor(ArgDescriptor):
-
-    def map_expr(self, subst_mapper):
+    @override
+    def map_expr(self, subst_mapper: SubstitutionCallable) -> Self:
         return self
 
-    def depends_on(self):
+    @override
+    def depends_on(self) -> frozenset[str]:
         return frozenset()
 
+    @override
     def copy(self, **kwargs: Any) -> Self:
         return replace(self, **kwargs)
 
@@ -109,10 +113,10 @@ def copy(self, **kwargs: Any) -> Self:
 @dataclass(frozen=True)
 class ArrayArgDescriptor(ArgDescriptor):
     """
-    Records information about an array argument to an in-kernel callable. To be
-    passed to and returned from
-    :meth:`~loopy.InKernelCallable.with_descrs`, used for
-    matching shape and address space of caller and callee kernels.
+    Records information about an array argument to an in-kernel callable.
+
+    To be passed to and returned from :meth:`~loopy.InKernelCallable.with_descrs`,
+    and used for matching shape and address space of caller and callee kernels.
 
     .. autoattribute:: shape
     .. autoattribute:: address_space
@@ -125,54 +129,58 @@ class ArrayArgDescriptor(ArgDescriptor):
     shape: ShapeType | None
     address_space: AddressSpace
     dim_tags: Sequence[ArrayDimImplementationTag] | None
-    """See :ref:`data-dim-tags`.
-    """
+    """See :ref:`data-dim-tags`."""
 
     if __debug__:
-        def __post_init__(self):
+        def __post_init__(self) -> None:
             # {{{ sanity checks
 
             from loopy.kernel.array import ArrayDimImplementationTag
-            from loopy.kernel.data import auto
+            from loopy.typing import auto
 
             assert isinstance(self.shape, tuple) or self.shape in [None, auto]
             assert isinstance(self.dim_tags, tuple) or self.dim_tags is None
 
             if self.dim_tags:
-                # FIXME at least vector dim tags should be supported
-                assert all(isinstance(dim_tag, ArrayDimImplementationTag) for dim_tag in
-                        self.dim_tags)
+                # FIXME: at least vector dim tags should be supported
+                assert all(isinstance(dim_tag, ArrayDimImplementationTag)
+                           for dim_tag in self.dim_tags)
 
             # }}}
 
+    @override
     def copy(self, **kwargs: Any) -> Self:
         return replace(self, **kwargs)
 
-    def map_expr(self, f):
+    @override
+    def map_expr(self, subst_mapper: SubstitutionCallable) -> Self:
         """
-        Returns an instance of :class:`ArrayArgDescriptor` with its shapes, strides,
-        mapped by *f*.
+        :returns: an instance of :class:`ArrayArgDescriptor` with its shapes
+            and strides mapped by *subst_mapper*.
         """
         if self.shape is not None:
-            new_shape = tuple(f(axis_len) for axis_len in self.shape)
+            new_shape = tuple(subst_mapper(axis_len) for axis_len in self.shape)
         else:
             new_shape = None
 
         if self.dim_tags is not None:
-            new_dim_tags = tuple(dim_tag.map_expr(f) for dim_tag in self.dim_tags)
+            new_dim_tags = tuple(
+                dim_tag.map_expr(subst_mapper) for dim_tag in self.dim_tags
+            )
         else:
             new_dim_tags = None
 
         return self.copy(shape=new_shape, dim_tags=new_dim_tags)
 
-    def depends_on(self):
+    @override
+    def depends_on(self) -> frozenset[str]:
         """
         Returns :class:`frozenset` of all the variable names the
         :class:`ArrayArgDescriptor` depends on.
         """
-        from loopy.kernel.data import auto
-        result = set()
+        from loopy.typing import auto
 
+        result: set[p.Variable] = set()
         if self.shape:
             dep_mapper = DependencyMapper(composite_leaves=False)
             for axis_len in self.shape:
@@ -190,22 +198,28 @@ def depends_on(self):
 class ExpressionIsScalarChecker(WalkMapper[[]]):
     kernel: LoopKernel
 
-    def __post_init__(self):
+    def __post_init__(self) -> None:
         super().__init__()
 
-    def map_sub_array_ref(self, expr):
+    @override
+    def map_sub_array_ref(self, expr: SubArrayRef) -> None:
         raise LoopyError("Sub-array refs can only be used as call's parameters"
                 f" or assignees. '{expr}' violates this.")
 
-    def map_call(self, expr):
+    @override
+    def map_call(self, expr: p.Call) -> None:
         self.rec(expr.parameters)
 
-    def map_subscript(self, expr):
+    @override
+    def map_subscript(self, expr: p.Subscript) -> None:
         for child in expr.index_tuple:
             self.rec(child)
 
-    def map_variable(self, expr):
-        from loopy.kernel.data import ArrayArg, TemporaryVariable, auto
+    @override
+    def map_variable(self, expr: p.Variable) -> None:
+        from loopy.kernel.data import ArrayArg, TemporaryVariable
+        from loopy.typing import auto
+
         if expr.name in self.kernel.all_inames():
             # inames are scalar
             return
@@ -218,31 +232,37 @@ def map_variable(self, expr):
                     var.shape != () and var.shape is not auto):
                 raise LoopyError("Array regions can only passed as sub-array refs.")
 
-    def map_slice(self, expr):
+    @override
+    def map_slice(self, expr: p.Slice) -> None:
         raise LoopyError("Array regions can only passed as sub-array refs.")
 
-    def map_call_with_kwargs(self, expr):
+    @override
+    def map_call_with_kwargs(self, expr: p.CallWithKwargs) -> None:
         # See https://github.com/inducer/loopy/pull/323
         raise NotImplementedError
 
 
-def get_arg_descriptor_for_expression(kernel: LoopKernel, expr: Expression):
+def get_arg_descriptor_for_expression(
+            kernel: LoopKernel, expr: Expression) -> ArgDescriptor:
     """
     :returns: a :class:`ArrayArgDescriptor` or a :class:`ValueArgDescriptor`
         describing the argument expression *expr* which occurs
         in a call in the code of *kernel*.
     """
     from loopy.kernel.data import ArrayArg, TemporaryVariable
-    from loopy.symbolic import SubArrayRef, SweptInameStrideCollector, pw_aff_to_expr
+    from loopy.symbolic import SweptInameStrideCollector, pw_aff_to_expr
 
     if isinstance(expr, SubArrayRef):
-        name = expr.subscript.aggregate.name
+        aggregate = expr.subscript.aggregate
+        assert isinstance(aggregate, p.Variable)
+
+        name = aggregate.name
         arg = kernel.get_var_descriptor(name)
 
         if not isinstance(arg, (TemporaryVariable, ArrayArg)):
-            raise LoopyError("unsupported argument type "
-                    "'%s' of '%s' in call statement"
-                    % (type(arg).__name__, expr.name))
+            raise LoopyError(
+                f"unsupported argument type '{type(arg).__name__}' of '{arg.name}' "
+                "in call statement")
 
         aspace = arg.address_space
 
@@ -303,21 +323,23 @@ class AbstractExpressionToCodeMapper(Protocol):
     .. automethod:: __call__
     """
 
-    def infer_type(self, expr: Expression) -> LoopyType:
-        ...
+    def infer_type(self, expr: Expression) -> LoopyType: ...
 
     def __call__(self,
                  expr: Expression,
                  prec: int | None = None,
                  type_context: str | None = None,
-                 needed_dtype: LoopyType | None = None
-             ) -> GeneratedExpression:
-        ...
+                 needed_dtype: LoopyType | None = None) -> GeneratedExpression: ...
+
+    def rec(self,
+            expr: Expression,
+            type_context: str | None = None,
+            needed_dtype: LoopyType | None = None) -> GeneratedExpression: ...
 
 
 # {{{ helper function for in-kernel callables
 
-def get_kw_pos_association(kernel: LoopKernel):
+def get_kw_pos_association(kernel: LoopKernel) -> tuple[dict[str, int], dict[int, str]]:
     """
     Returns a tuple of ``(kw_to_pos, pos_to_kw)`` for the arguments in
     *kernel*.
@@ -380,6 +402,7 @@ class InKernelCallable(ABC):
           return value with (0-based) index *i*.
 
     """
+
     arg_id_to_dtype: Mapping[int | str, LoopyType] | None
     arg_id_to_descr: Mapping[int | str, ArgDescriptor] | None
 
@@ -504,7 +527,8 @@ def get_hw_axes_sizes(self,
         ...
 
     @abstractmethod
-    def get_used_hw_axes(self, callables_table: CallablesTable):
+    def get_used_hw_axes(self,
+                         callables_table: CallablesTable) -> tuple[Set[str], Set[str]]:
         """
         Returns a tuple ``group_axes_used, local_axes_used``, where
         ``(group|local)_axes_used`` are :class:`frozenset` of hardware axes
@@ -512,14 +536,18 @@ def get_used_hw_axes(self, callables_table: CallablesTable):
         """
 
     @abstractmethod
-    def generate_preambles(self, target):
+    def generate_preambles(self, target: TargetBase) -> Iterator[str]:
         """
         Yields the target specific preamble.
         """
         raise NotImplementedError()
 
+    # FIXME(pyright): these return types are not correct: see IndexOfCallable.emit_call
     @abstractmethod
-    def emit_call(self, expression_to_code_mapper, expression, target):
+    def emit_call(self,
+                  expression_to_code_mapper: AbstractExpressionToCodeMapper,
+                  expression: p.Call,
+                  target: TargetBase) -> p.Call | p.CallWithKwargs:
         ...
 
     @abstractmethod
@@ -531,29 +559,28 @@ def emit_call_insn(self,
         """
         Returns a tuple of ``(call, assignee_is_returned)`` which is the target
         facing function call that would be seen in the generated code. ``call``
-        is an instance of ``pymbolic.primitives.Call`` ``assignee_is_returned``
-        is an instance of :class:`bool` to indicate if the assignee is returned
+        is an instance of ``pymbolic.primitives.Call`` and ``assignee_is_returned``
+        is a boolean flag used to indicate if the assignee is returned
         by value of C-type targets.
 
-        *Example:* If ``assignee_is_returned=True``, then ``a, b = f(c, d)`` is
+        *Example*: If ``assignee_is_returned=True``, then ``a, b = f(c, d)`` is
             interpreted in the target as ``a = f(c, d, &b)``. If
             ``assignee_is_returned=False``, then ``a, b = f(c, d)`` is interpreted
             in the target as the statement ``f(c, d, &a, &b)``.
         """
 
     @abstractmethod
-    def with_added_arg(self, arg_dtype, arg_descr):
+    def with_added_arg(self, arg_dtype: LoopyType,
+                       arg_descr: ArgDescriptor) -> tuple[InKernelCallable, str]:
         """
         Registers a new argument to the callable and returns the name of the
         argument in the callable's namespace.
         """
 
     @abstractmethod
-    def get_called_callables(
-                             self,
+    def get_called_callables(self,
                              callables_table: CallablesTable,
-                             recursive: bool = True
-                         ) -> frozenset[CallableId]:
+                             recursive: bool = True) -> frozenset[CallableId]:
         """
         Returns a :class:`frozenset` of callable ids called by *self* that are
         resolved via *callables_table*.
@@ -589,15 +616,9 @@ class ScalarCallable(InKernelCallable):
     """
     An abstract interface to a scalar callable encountered in a kernel.
 
-    .. attribute:: name_in_target
-
-        A :class:`str` to denote the name of the function in a
-        :class:`loopy.target.TargetBase` for which the callable is specialized.
-        *None* if the callable is not specialized enough to know its name
-        in target.
-
+    .. autoattribute:: name
+    .. autoattribute:: name_in_target
     .. automethod:: with_types
-
     .. automethod:: with_descrs
 
     .. note::
@@ -605,8 +626,13 @@ class ScalarCallable(InKernelCallable):
         The :meth:`ScalarCallable.with_types` is intended to assist with type
         specialization of the function and sub-classes must define it.
     """
-    name: str
+
+    name: str  # pyright: ignore[reportIncompatibleMethodOverride]
     name_in_target: str | None
+    """A :class:`str` to denote the name of the function in a
+    :class:`loopy.target.TargetBase` for which the callable is specialized.
+    *None* if the callable is not specialized enough to know its name in target.
+    """
 
     def __init__(self,
                  name: str,
@@ -639,45 +665,58 @@ def with_descrs(self,
         return (self.copy(arg_id_to_descr=new_arg_id_to_descr.finish()),
                 clbl_inf_ctx)
 
-    def get_hw_axes_sizes(self, arg_id_to_arg, space, callables_table):
+    @override
+    def get_hw_axes_sizes(self,
+                    arg_id_to_arg: Mapping[int, Expression],
+                    space: isl.Space,
+                    callables_table: CallablesTable,
+                ) -> tuple[Mapping[int, isl.PwAff], Mapping[int, isl.PwAff]]:
         return {}, {}
 
-    def get_used_hw_axes(self, callables_table):
+    @override
+    def get_used_hw_axes(self,
+                         callables_table: CallablesTable) -> tuple[Set[str], Set[str]]:
         return frozenset(), frozenset()
 
-    def is_ready_for_codegen(self):
-
+    @override
+    def is_ready_for_codegen(self) -> bool:
         return (self.arg_id_to_dtype is not None and
                 self.arg_id_to_descr is not None)
 
     # {{{ code generation
 
-    def emit_call(self, expression_to_code_mapper, expression, target):
-
+    @override
+    def emit_call(self,
+                  expression_to_code_mapper: AbstractExpressionToCodeMapper,
+                  expression: p.Call,
+                  target: TargetBase) -> p.Call | p.CallWithKwargs:
         assert self.is_ready_for_codegen()
+        assert self.arg_id_to_dtype is not None
 
         # must have single assignee
         assert len(expression.parameters) == len(self.arg_id_to_dtype) - 1
-        arg_dtypes = tuple(self.arg_id_to_dtype[id] for id in
-                range(len(self.arg_id_to_dtype)-1))
+        arg_dtypes = tuple(self.arg_id_to_dtype[id]
+                          for id in range(len(self.arg_id_to_dtype) - 1))
 
-        par_dtypes = tuple(expression_to_code_mapper.infer_type(par) for par in
-                expression.parameters)
+        par_dtypes = tuple(expression_to_code_mapper.infer_type(par)
+                           for par in expression.parameters)
 
         from loopy.expression import dtype_to_type_context
         # processing the parameters with the required dtypes
         processed_parameters = tuple(
-                expression_to_code_mapper.rec(par,
+                expression_to_code_mapper.rec(
+                    par,
                     dtype_to_type_context(target, tgt_dtype),
                     tgt_dtype)
-                for par, par_dtype, tgt_dtype in zip(
+                for par, _par_dtype, tgt_dtype in zip(
                     expression.parameters,
                     par_dtypes,
                     arg_dtypes, strict=True))
 
-        from pymbolic import var
-        return var(self.name_in_target)(*processed_parameters)
+        assert self.name_in_target is not None
+        return p.Variable(self.name_in_target)(*processed_parameters)
 
+    @override
     def emit_call_insn(self,
                        insn: CallInstruction,
                        target: TargetBase,
@@ -702,11 +741,13 @@ def emit_call_insn(self,
 
             *Example:* ``c, d = f(a, b)`` is returned as ``c = f(a, b, &d)``
         """
+
         from loopy.target.c import CFamilyTarget
         if not isinstance(target, CFamilyTarget):
-            raise NotImplementedError()
+            raise NotImplementedError(
+                f"{type(self).__name__}.emit_call_insn for targets of "
+                f"type {type(target)}")
 
-        from pymbolic import var
         from pymbolic.mapper.stringifier import PREC_NONE
 
         from loopy.expression import dtype_to_type_context
@@ -716,7 +757,6 @@ def emit_call_insn(self,
         assert self.is_ready_for_codegen()
         assert self.arg_id_to_dtype is not None
 
-        ecm = expression_to_code_mapper
         parameters = insn.expression.parameters
         assignees = insn.assignees[1:]
 
@@ -729,10 +769,11 @@ def emit_call_insn(self,
                                 for i, _ in enumerate(assignees))
 
         tgt_parameters: list[Expression] = [
-            ecm(par, PREC_NONE,
+            expression_to_code_mapper(
+                par, PREC_NONE,
                 dtype_to_type_context(target, tgt_dtype),
                 tgt_dtype).expr
-            for par, par_dtype, tgt_dtype in
+            for par, _par_dtype, tgt_dtype in
             zip(parameters, par_dtypes, arg_dtypes, strict=True)]
 
         for a, tgt_dtype in zip(assignees, assignee_dtypes, strict=True):
@@ -740,27 +781,37 @@ def emit_call_insn(self,
                 raise LoopyError("Type Mismatch in function %s. Expected: %s"
                         "Got: %s" % (self.name, tgt_dtype,
                             expression_to_code_mapper.infer_type(a)))
-            tgt_parameters.append(var("&")(ecm(a, PREC_NONE,
-                                               dtype_to_type_context(target,
-                                                                     tgt_dtype),
-                                               tgt_dtype).expr))
+
+            tgt_parameters.append(p.Variable("&")(
+                expression_to_code_mapper(
+                    a, PREC_NONE,
+                    dtype_to_type_context(target, tgt_dtype),
+                    tgt_dtype).expr))
 
         # assignee is returned whenever the size of assignees is non zero.
         first_assignee_is_returned = len(insn.assignees) > 0
 
         assert self.name_in_target
-        return var(self.name_in_target)(*tgt_parameters), first_assignee_is_returned
+        return (p.Variable(self.name_in_target)(*tgt_parameters),
+                first_assignee_is_returned)
 
-    def generate_preambles(self, target):
+    @override
+    def generate_preambles(self, target: TargetBase) -> Iterator[str]:
         return
         yield
 
     # }}}
 
-    def with_added_arg(self, arg_dtype, arg_descr):
+    @override
+    def with_added_arg(self,
+                       arg_dtype: LoopyType,
+                       arg_descr: ArgDescriptor) -> tuple[InKernelCallable, str]:
         raise LoopyError("Cannot add args to scalar callables.")
 
-    def get_called_callables(self, callables_table, recursive=True):
+    @override
+    def get_called_callables(self,
+                             callables_table: CallablesTable,
+                             recursive: bool = True) -> frozenset[CallableId]:
         """
         Returns a :class:`frozenset` of callable ids called by *self*.
         """
@@ -771,10 +822,9 @@ def with_name(self, name: CallableId) -> Self:
         return self
 
     @override
-    def is_type_specialized(self):
+    def is_type_specialized(self) -> bool:
         return (self.arg_id_to_dtype is not None
-                and all(dtype is not None
-                        for dtype in self.arg_id_to_dtype.values()))
+                and all(dtype is not None for dtype in self.arg_id_to_dtype.values()))
 
 # }}}
 
@@ -814,6 +864,7 @@ def __init__(self,
         object.__setattr__(self, "subkernel", subkernel)
 
     @property
+    @override
     def name(self) -> str:
         return self.subkernel.name
 
@@ -824,7 +875,7 @@ def with_types(self,
                ) -> tuple[CallableKernel, CallablesInferenceContext]:
         kw_to_pos, pos_to_kw = get_kw_pos_association(self.subkernel)
 
-        new_args = []
+        new_args: list[KernelArgument] = []
         for arg in self.subkernel.args:
             kw = arg.name
             if kw in arg_id_to_dtype:
@@ -833,8 +884,7 @@ def with_types(self,
                 new_args.append(arg.copy(dtype=arg_id_to_dtype[kw]))
             elif kw_to_pos[kw] in arg_id_to_dtype:
                 # id exists as positional argument
-                new_args.append(arg.copy(
-                    dtype=arg_id_to_dtype[kw_to_pos[kw]]))
+                new_args.append(arg.copy(dtype=arg_id_to_dtype[kw_to_pos[kw]]))
             else:
                 new_args.append(arg)
 
@@ -849,7 +899,7 @@ def with_types(self,
                     pre_specialized_subkernel,
                     clbl_inf_ctx))
 
-        new_arg_id_to_dtype = {}
+        new_arg_id_to_dtype: Mapping[int | str, LoopyType] = {}
         for pos, kw in pos_to_kw.items():
             arg = specialized_kernel.arg_dict[kw]
             if arg.dtype:
@@ -876,8 +926,7 @@ def with_descrs(self,
         kw_to_callee_idx = {arg.name: i
                             for i, arg in enumerate(self.subkernel.args)}
 
-        new_args = self.subkernel.args[:]
-
+        new_args = list(self.subkernel.args)
         for arg_id, descr in new_arg_id_to_descr.items():
             if isinstance(arg_id, int):
                 arg_id = pos_to_kw[arg_id]
@@ -898,6 +947,7 @@ def with_descrs(self,
 
             if (isinstance(descr, ArrayArgDescriptor)
                     and isinstance(callee_arg.shape, tuple)
+                    and descr.shape is not None
                     and len(callee_arg.shape) != len(descr.shape)):
                 raise LoopyError(f"In call to {self.subkernel.name}, '{arg_id}'"
                         " has a dimensionality mismatch, expected "
@@ -943,7 +993,10 @@ def with_descrs(self,
                           arg_id_to_descr=new_arg_id_to_descr.finish()),
                 clbl_inf_ctx)
 
-    def with_added_arg(self, arg_dtype, arg_descr):
+    @override
+    def with_added_arg(self,
+                       arg_dtype: LoopyType,
+                       arg_descr: ArgDescriptor) -> tuple[InKernelCallable, str]:
         var_name = self.subkernel.get_var_name_generator()(based_on="_lpy_arg")
 
         if isinstance(arg_descr, ValueArgDescriptor):
@@ -976,15 +1029,15 @@ def with_added_arg(self, arg_dtype, arg_descr):
 
         else:
             # don't think this should ever be needed
-            raise NotImplementedError("with_added_arg not implemented for array"
-                    " types arguments.")
+            raise NotImplementedError(
+                f"{type(self).__name__}.with_added_arg is not implemented for "
+                f"arguments of type {type(arg_descr)}")
 
-    def with_packing_for_args(self):
+    def with_packing_for_args(self) -> InKernelCallable:
         from loopy.kernel.data import AddressSpace
         _kw_to_pos, pos_to_kw = get_kw_pos_association(self.subkernel)
 
-        arg_id_to_descr = {}
-
+        arg_id_to_descr: Mapping[str | int, ArgDescriptor] = {}
         for pos, kw in pos_to_kw.items():
             arg = self.subkernel.arg_dict[kw]
             arg_id_to_descr[pos] = ArrayArgDescriptor(
@@ -995,13 +1048,20 @@ def with_packing_for_args(self):
         return self.copy(subkernel=self.subkernel,
                 arg_id_to_descr=constantdict(arg_id_to_descr))
 
-    def get_used_hw_axes(self, callables_table):
+    @override
+    def get_used_hw_axes(self,
+                         callables_table: CallablesTable) -> tuple[Set[str], Set[str]]:
         gsize, lsize = self.subkernel.get_grid_size_upper_bounds(callables_table,
                                                                  return_dict=True)
 
         return frozenset(gsize.keys()), frozenset(lsize.keys())
 
-    def get_hw_axes_sizes(self, arg_id_to_arg, space, callables_table):
+    @override
+    def get_hw_axes_sizes(self,
+                    arg_id_to_arg: Mapping[int, Expression],
+                    space: isl.Space,
+                    callables_table: CallablesTable,
+                ) -> tuple[Mapping[int, isl.PwAff], Mapping[int, isl.PwAff]]:
         from loopy.isl_helpers import subst_into_pwaff
         _, pos_to_kw = get_kw_pos_association(self.subkernel)
         gsize, lsize = self.subkernel.get_grid_size_upper_bounds(callables_table,
@@ -1019,28 +1079,43 @@ def get_hw_axes_sizes(self, arg_id_to_arg, space, callables_table):
 
         return gsize, lsize
 
-    def is_ready_for_codegen(self):
+    @override
+    def is_ready_for_codegen(self) -> bool:
         return (self.arg_id_to_dtype is not None
                 and self.arg_id_to_descr is not None)
 
-    def generate_preambles(self, target):
+    @override
+    def generate_preambles(self, target: TargetBase) -> Iterator[str]:
         """ Yields the *target* specific preambles.
         """
         return
         yield
 
-    def emit_call(self, expression_to_code_mapper, expression, target):
-        raise LoopyError("Kernel '{self.name}' cannot be called "
+    @override
+    def emit_call(self,
+                  expression_to_code_mapper: AbstractExpressionToCodeMapper,
+                  expression: p.Call,
+                  target: TargetBase) -> p.Call | p.CallWithKwargs:
+        raise LoopyError(f"Kernel '{self.name}' cannot be called "
                          "from within an expression, use a call statement")
 
-    def emit_call_insn(self, insn, target, expression_to_code_mapper):
+    @override
+    def emit_call_insn(
+                self,
+                insn: CallInstruction,
+                target: TargetBase,
+                expression_to_code_mapper: AbstractExpressionToCodeMapper
+            ) -> tuple[p.Call | p.CallWithKwargs, bool]:
         from loopy.target.c import CFamilyTarget
         if not isinstance(target, CFamilyTarget):
-            raise NotImplementedError()
+            raise NotImplementedError(
+                f"{type(self).__name__}.emit_call_insn for targets of "
+                f"type {type(target)}")
 
         from loopy.kernel.instruction import CallInstruction
 
         assert self.is_ready_for_codegen()
+        assert self.arg_id_to_dtype is not None
         assert isinstance(insn, CallInstruction)
 
         ecm = expression_to_code_mapper
@@ -1077,10 +1152,11 @@ def emit_call_insn(self, insn, target, expression_to_code_mapper):
         return var(self.subkernel.name)(*tgt_parameters), False
 
     @override
-    def get_called_callables(self,
+    def get_called_callables(
+                self,
                 callables_table: CallablesTable,
                 recursive: bool = True
-            ):
+            ) -> frozenset[CallableId]:
         from loopy.kernel.tools import get_resolved_callable_ids_called_by_knl
         return get_resolved_callable_ids_called_by_knl(self.subkernel,
                                                        callables_table,
diff --git a/loopy/transform/callable.py b/loopy/transform/callable.py
index 5e27bf4c1..77b8900b3 100644
--- a/loopy/transform/callable.py
+++ b/loopy/transform/callable.py
@@ -68,8 +68,11 @@
 """
 
 
-def register_callable(translation_unit, function_identifier, callable_,
-        redefining_not_ok=True):
+def register_callable(
+        translation_unit: TranslationUnit,
+        function_identifier: str,
+        callable_: InKernelCallable,
+        redefining_not_ok: bool = True) -> TranslationUnit:
     """
     :param translation_unit: A :class:`loopy.TranslationUnit`.
     :param callable_: A :class:`loopy.InKernelCallable`.
@@ -78,7 +81,6 @@ def register_callable(translation_unit, function_identifier, callable_,
     if isinstance(callable_, LoopKernel):
         callable_ = CallableKernel(callable_)
 
-    from loopy.kernel.function_interface import InKernelCallable
     assert isinstance(callable_, InKernelCallable)
 
     if (function_identifier in translation_unit.callables_table) and (
diff --git a/loopy/typing.py b/loopy/typing.py
index 0a0f847f8..cf3b54356 100644
--- a/loopy/typing.py
+++ b/loopy/typing.py
@@ -67,8 +67,9 @@
     from loopy.types import LoopyType
 
 
-# The Fortran parser may insert dimensions of 'None', but I'd like to phase
+# TODO: Fortran parser may insert dimensions of 'None', but I'd like to phase
 # that out, so we're not encoding that in the type.
+# TODO: ArrayArgDescriptor: also looks for 'None' or 'auto' in the shape
 ShapeType: TypeAlias = tuple[ArithmeticExpression, ...]
 StridesType: TypeAlias = ShapeType
 

From ca2b9ce7a4774ab4c798e5d4b548afa147ce2efe Mon Sep 17 00:00:00 2001
From: Alexandru Fikl <alexfikl@gmail.com>
Date: Thu, 30 Oct 2025 13:33:25 +0200
Subject: [PATCH 05/18] feat(typing): add overloads for
 get_grid_size_upper_bounds

---
 loopy/kernel/__init__.py | 16 ++++++++++++++++
 1 file changed, 16 insertions(+)

diff --git a/loopy/kernel/__init__.py b/loopy/kernel/__init__.py
index b1686bbe0..fa92560ed 100644
--- a/loopy/kernel/__init__.py
+++ b/loopy/kernel/__init__.py
@@ -1073,6 +1073,22 @@ def tup_to_exprs(tup):
 
         return tup_to_exprs(grid_size), tup_to_exprs(group_size)
 
+    @overload
+    def get_grid_size_upper_bounds(self,
+                callables_table: CallablesTable,
+                *,
+                ignore_auto: bool = ...,
+                return_dict: Literal[False] = ...
+            ) -> tuple[tuple[isl.PwAff, ...], tuple[isl.PwAff, ...]]: ...
+
+    @overload
+    def get_grid_size_upper_bounds(self,
+                callables_table: CallablesTable,
+                *,
+                ignore_auto: bool = ...,
+                return_dict: Literal[True]
+            ) -> tuple[dict[int, isl.PwAff], dict[int, isl.PwAff]]: ...
+
     def get_grid_size_upper_bounds(self,
                 callables_table: CallablesTable,
                 ignore_auto: bool = False,

From 8f59b595d35677b08c9d9836c86f5ea13c762808 Mon Sep 17 00:00:00 2001
From: Alexandru Fikl <alexfikl@gmail.com>
Date: Thu, 30 Oct 2025 13:37:48 +0200
Subject: [PATCH 06/18] feat: use more f-strings in function_interface

---
 loopy/kernel/function_interface.py | 13 +++++++------
 1 file changed, 7 insertions(+), 6 deletions(-)

diff --git a/loopy/kernel/function_interface.py b/loopy/kernel/function_interface.py
index a0c0f0d04..f94f48073 100644
--- a/loopy/kernel/function_interface.py
+++ b/loopy/kernel/function_interface.py
@@ -651,8 +651,8 @@ def with_types(self,
                    arg_id_to_dtype: Mapping[int | str, LoopyType],
                    clbl_inf_ctx: CallablesInferenceContext,
                ) -> tuple[ScalarCallable, CallablesInferenceContext]:
-        raise LoopyError("No type inference information present for "
-                "the function %s." % (self.name))
+        raise LoopyError(
+            f"No type inference information present for the function {self.name!r}.")
 
     @override
     def with_descrs(self,
@@ -777,10 +777,11 @@ def emit_call_insn(self,
             zip(parameters, par_dtypes, arg_dtypes, strict=True)]
 
         for a, tgt_dtype in zip(assignees, assignee_dtypes, strict=True):
-            if tgt_dtype != expression_to_code_mapper.infer_type(a):
-                raise LoopyError("Type Mismatch in function %s. Expected: %s"
-                        "Got: %s" % (self.name, tgt_dtype,
-                            expression_to_code_mapper.infer_type(a)))
+            inferred_dtype = expression_to_code_mapper.infer_type(a)
+            if tgt_dtype != inferred_dtype:
+                raise LoopyError(
+                        f"type mismatch in function {self.name!r}: expected "
+                        f"{tgt_dtype} got {inferred_dtype}")
 
             tgt_parameters.append(p.Variable("&")(
                 expression_to_code_mapper(

From a0db40e651b611ea5d3d8f0c503c3ab4c95d8c7f Mon Sep 17 00:00:00 2001
From: Alexandru Fikl <alexfikl@gmail.com>
Date: Thu, 30 Oct 2025 14:13:01 +0200
Subject: [PATCH 07/18] docs: update some refs

---
 loopy/kernel/function_interface.py |  1 +
 loopy/symbolic.py                  | 18 ++++++++++--------
 2 files changed, 11 insertions(+), 8 deletions(-)

diff --git a/loopy/kernel/function_interface.py b/loopy/kernel/function_interface.py
index f94f48073..b11041c70 100644
--- a/loopy/kernel/function_interface.py
+++ b/loopy/kernel/function_interface.py
@@ -58,6 +58,7 @@
 __doc__ = """
 .. autoclass:: GeneratedExpression
 .. autoclass:: AbstractExpressionToCodeMapper
+.. autoclass:: SubstitutionCallable
 .. autoclass:: ArgDescriptor
 .. autoclass:: ValueArgDescriptor
 .. autoclass:: ArrayArgDescriptor
diff --git a/loopy/symbolic.py b/loopy/symbolic.py
index 490f7cc68..c127528b9 100644
--- a/loopy/symbolic.py
+++ b/loopy/symbolic.py
@@ -144,6 +144,8 @@
     :show-inheritance:
 .. autoclass:: RuleArgument
     :show-inheritance:
+.. autoclass:: LinearSubscript
+    :show-inheritance:
 .. autoclass:: ResolvedFunction
     :show-inheritance:
 
@@ -663,8 +665,8 @@ class Literal(LoopyExpressionBase):
     .. note::
 
         Only used in the output of
-        :mod:`loopy.target.c.codegen.expression.ExpressionToCExpressionMapper` (and
-        similar mappers). Not for use in Loopy source representation.
+        :class:`~loopy.target.c.codegen.expression.ExpressionToCExpressionMapper`
+        (and similar mappers). Not for use in Loopy source representation.
 
     .. autoattribute:: s
     """
@@ -679,8 +681,8 @@ class ArrayLiteral(LoopyExpressionBase):
     .. note::
 
         Only used in the output of
-        :mod:`loopy.target.c.codegen.expression.ExpressionToCExpressionMapper` (and
-        similar mappers). Not for use in Loopy source representation.
+        :class:`~loopy.target.c.codegen.expression.ExpressionToCExpressionMapper`
+        (and similar mappers). Not for use in Loopy source representation.
 
     .. autoattribute:: children
     """
@@ -700,8 +702,8 @@ class GroupHardwareAxisIndex(HardwareAxisIndex):
     .. note::
 
         Only used in the output of
-        :mod:`loopy.target.c.expression.ExpressionToCExpressionMapper` (and
-        similar mappers). Not for use in Loopy source representation.
+        :class:`~loopy.target.c.codegen.expression.ExpressionToCExpressionMapper`
+        (and similar mappers). Not for use in Loopy source representation.
 
     .. autoattribute:: axis
     """
@@ -716,8 +718,8 @@ class LocalHardwareAxisIndex(HardwareAxisIndex):
     .. note::
 
         Only used in the output of
-        :mod:`loopy.target.c.expression.ExpressionToCExpressionMapper` (and
-        similar mappers). Not for use in Loopy source representation.
+        :class:`~loopy.target.c.codegen.expression.ExpressionToCExpressionMapper`
+        (and similar mappers). Not for use in Loopy source representation.
 
     .. autoattribute:: axis
     """

From 4cd9833edb18dc23490c119a90c293e08562b3cd Mon Sep 17 00:00:00 2001
From: Alexandru Fikl <alexfikl@gmail.com>
Date: Fri, 31 Oct 2025 12:22:00 +0200
Subject: [PATCH 08/18] feat: remove unused par_dtypes

---
 loopy/kernel/function_interface.py | 12 ++----------
 1 file changed, 2 insertions(+), 10 deletions(-)

diff --git a/loopy/kernel/function_interface.py b/loopy/kernel/function_interface.py
index b11041c70..ca9d1735b 100644
--- a/loopy/kernel/function_interface.py
+++ b/loopy/kernel/function_interface.py
@@ -699,9 +699,6 @@ def emit_call(self,
         arg_dtypes = tuple(self.arg_id_to_dtype[id]
                           for id in range(len(self.arg_id_to_dtype) - 1))
 
-        par_dtypes = tuple(expression_to_code_mapper.infer_type(par)
-                           for par in expression.parameters)
-
         from loopy.expression import dtype_to_type_context
         # processing the parameters with the required dtypes
         processed_parameters = tuple(
@@ -709,9 +706,8 @@ def emit_call(self,
                     par,
                     dtype_to_type_context(target, tgt_dtype),
                     tgt_dtype)
-                for par, _par_dtype, tgt_dtype in zip(
+                for par, tgt_dtype in zip(
                     expression.parameters,
-                    par_dtypes,
                     arg_dtypes, strict=True))
 
         assert self.name_in_target is not None
@@ -761,11 +757,8 @@ def emit_call_insn(self,
         parameters = insn.expression.parameters
         assignees = insn.assignees[1:]
 
-        par_dtypes = tuple(expression_to_code_mapper.infer_type(par)
-                           for par in parameters)
         arg_dtypes = tuple(self.arg_id_to_dtype[i]
                            for i, _ in enumerate(parameters))
-
         assignee_dtypes = tuple(self.arg_id_to_dtype[-i-2]
                                 for i, _ in enumerate(assignees))
 
@@ -774,8 +767,7 @@ def emit_call_insn(self,
                 par, PREC_NONE,
                 dtype_to_type_context(target, tgt_dtype),
                 tgt_dtype).expr
-            for par, _par_dtype, tgt_dtype in
-            zip(parameters, par_dtypes, arg_dtypes, strict=True)]
+            for par, tgt_dtype in zip(parameters, arg_dtypes, strict=True)]
 
         for a, tgt_dtype in zip(assignees, assignee_dtypes, strict=True):
             inferred_dtype = expression_to_code_mapper.infer_type(a)

From d1c8df571f12672896738704dac4e76858be79f0 Mon Sep 17 00:00:00 2001
From: Alexandru Fikl <alexfikl@gmail.com>
Date: Mon, 3 Nov 2025 21:35:53 +0200
Subject: [PATCH 09/18] feat: update InKernelCallable.emit_call types and docs

---
 loopy/kernel/function_interface.py | 67 ++++++++++++++----------------
 loopy/library/function.py          |  4 +-
 2 files changed, 34 insertions(+), 37 deletions(-)

diff --git a/loopy/kernel/function_interface.py b/loopy/kernel/function_interface.py
index ca9d1735b..45b68848f 100644
--- a/loopy/kernel/function_interface.py
+++ b/loopy/kernel/function_interface.py
@@ -42,7 +42,7 @@
     from collections.abc import Iterator, Mapping, Sequence, Set
 
     import islpy as isl
-    from pymbolic.typing import Expression
+    from pymbolic.typing import ArithmeticExpression, Expression
 
     from loopy.kernel import LoopKernel
     from loopy.kernel.instruction import CallInstruction
@@ -543,31 +543,48 @@ def generate_preambles(self, target: TargetBase) -> Iterator[str]:
         """
         raise NotImplementedError()
 
-    # FIXME(pyright): these return types are not correct: see IndexOfCallable.emit_call
     @abstractmethod
     def emit_call(self,
                   expression_to_code_mapper: AbstractExpressionToCodeMapper,
                   expression: p.Call,
-                  target: TargetBase) -> p.Call | p.CallWithKwargs:
-        ...
+                  target: TargetBase) -> ArithmeticExpression:
+        """Generate a target-specific call expression by mapping its arguments
+        to the appropriate data types.
+
+        :arg expression_to_code_mapper: an instance of
+            ``loopy.symbolic.IdentityMapper``
+            responsible mapping the arguments (see
+            :meth:`~loopy.target.c.codegen.expression.ExpressionToCExpressionMapper`).
+        """
 
     @abstractmethod
     def emit_call_insn(self,
                        insn: CallInstruction,
                        target: TargetBase,
                        expression_to_code_mapper: AbstractExpressionToCodeMapper,
-                   )  -> tuple[p.Call | p.CallWithKwargs, bool]:
+                   )  -> tuple[ArithmeticExpression, bool]:
         """
         Returns a tuple of ``(call, assignee_is_returned)`` which is the target
         facing function call that would be seen in the generated code. ``call``
-        is an instance of ``pymbolic.primitives.Call`` and ``assignee_is_returned``
-        is a boolean flag used to indicate if the assignee is returned
-        by value of C-type targets.
-
-        *Example*: If ``assignee_is_returned=True``, then ``a, b = f(c, d)`` is
-            interpreted in the target as ``a = f(c, d, &b)``. If
-            ``assignee_is_returned=False``, then ``a, b = f(c, d)`` is interpreted
-            in the target as the statement ``f(c, d, &a, &b)``.
+        is (usually) an instance of :class:`pymbolic.primitives.Call` and
+        ``assignee_is_returned`` is a boolean flag used to indicate if the
+        assignee is returned by value of C-type targets.
+
+        .. note::
+
+            *Example*: If ``assignee_is_returned=True``, then ``a, b = f(c,
+            d)`` is interpreted in the target as ``a = f(c, d, &b)``. If
+            ``assignee_is_returned=False``, then ``a, b = f(c, d)`` is
+            interpreted in the target as the statement ``f(c, d, &a, &b)``.
+
+        :arg expression_to_code_mapper: an instance of
+            ``loopy.symbolic.IdentityMapper`` responsible for code mapping
+            from :mod:`loopy` syntax to the *target syntax* (see
+            :meth:`~loopy.target.c.codegen.expression.ExpressionToCExpressionMapper`).
+
+        :returns: a tuple of the call to be generated and an instance of
+            :class:`bool` whether the first assignee is a part of the LHS in
+            the assignment instruction
         """
 
     @abstractmethod
@@ -690,7 +707,7 @@ def is_ready_for_codegen(self) -> bool:
     def emit_call(self,
                   expression_to_code_mapper: AbstractExpressionToCodeMapper,
                   expression: p.Call,
-                  target: TargetBase) -> p.Call | p.CallWithKwargs:
+                  target: TargetBase) -> ArithmeticExpression:
         assert self.is_ready_for_codegen()
         assert self.arg_id_to_dtype is not None
 
@@ -718,27 +735,7 @@ def emit_call_insn(self,
                        insn: CallInstruction,
                        target: TargetBase,
                        expression_to_code_mapper: AbstractExpressionToCodeMapper,
-                   )  -> tuple[p.Call | p.CallWithKwargs, bool]:
-        """
-        :arg insn: An instance of :class:`loopy.kernel.instructions.CallInstruction`.
-        :arg target: An instance of :class:`loopy.target.TargetBase`.
-        :arg expression_to_code_mapper: An instance of :class:`IdentityMapper`
-            responsible for code mapping from :mod:`loopy` syntax to the
-            **target syntax**.
-
-        :returns: A tuple of the call to be generated and an instance of
-            :class:`bool` whether the first assignee is a part of the LHS in
-            the assignment instruction.
-
-        .. note::
-
-            The default implementation returns the first assignees and the
-            references of the rest of the assignees are appended to the
-            arguments of the call.
-
-            *Example:* ``c, d = f(a, b)`` is returned as ``c = f(a, b, &d)``
-        """
-
+                   )  -> tuple[ArithmeticExpression, bool]:
         from loopy.target.c import CFamilyTarget
         if not isinstance(target, CFamilyTarget):
             raise NotImplementedError(
diff --git a/loopy/library/function.py b/loopy/library/function.py
index 5b89fc95e..df17e5a95 100644
--- a/loopy/library/function.py
+++ b/loopy/library/function.py
@@ -129,8 +129,8 @@ def get_loopy_callables() -> CallablesTable:
     category are --
 
     - reductions leading to function calls like ``argmin``, ``argmax``.
-    - callables that have a predefined meaning in :mod:`loo.py` like
-      ``make_tuple``, ``index_of``, ``indexof_vec``.
+    - callables that have a predefined meaning in :mod:`loopy` like
+      ``make_tuple``, ``indexof``, ``indexof_vec``.
     """
     return constantdict({
             "make_tuple": MakeTupleCallable(name="make_tuple"),

From d0fb33c716fc63b4e1cbbe6ec41e65c9c2921358 Mon Sep 17 00:00:00 2001
From: Andreas Kloeckner <inform@tiker.net>
Date: Tue, 4 Nov 2025 12:59:31 -0600
Subject: [PATCH 10/18] Add a TypeContext type alias

---
 loopy/expression.py      | 19 ++++++++++---------
 loopy/target/__init__.py |  7 ++++++-
 loopy/target/opencl.py   |  7 ++++---
 loopy/target/pyopencl.py | 11 ++++++-----
 4 files changed, 26 insertions(+), 18 deletions(-)

diff --git a/loopy/expression.py b/loopy/expression.py
index 390198799..2278d89f0 100644
--- a/loopy/expression.py
+++ b/loopy/expression.py
@@ -1,7 +1,5 @@
 from __future__ import annotations
 
-from pymbolic import ArithmeticExpression
-
 
 __copyright__ = "Copyright (C) 2012-15 Andreas Kloeckner"
 
@@ -24,11 +22,12 @@
 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
 THE SOFTWARE.
 """
-from typing import TYPE_CHECKING, cast
+from typing import TYPE_CHECKING, Literal, TypeAlias, cast
 
 import numpy as np
 
 import pymbolic.primitives as p
+from pymbolic import ArithmeticExpression
 from pymbolic.mapper import Mapper
 
 from loopy.codegen import UnvectorizableError
@@ -41,13 +40,15 @@
     from loopy.symbolic import LinearSubscript, Reduction
 
 
-# type_context may be:
-# - "i" for integer -
-# - "f" for single-precision floating point
-# - "d" for double-precision floating point
-# or None for 'no known context'.
+TypeContext: TypeAlias = Literal[
+    "f",  # single-precision floating point
+    "d",  # double-precision floating point
+    "i",  # integer
+    "b",  # boolean
+] | None  # "no known context"
+
 
-def dtype_to_type_context(target, dtype) -> str | None:
+def dtype_to_type_context(target, dtype) -> TypeContext:
     from loopy.types import NumpyType
 
     if dtype.is_integral():
diff --git a/loopy/target/__init__.py b/loopy/target/__init__.py
index 673a46d4d..8cde975ec 100644
--- a/loopy/target/__init__.py
+++ b/loopy/target/__init__.py
@@ -58,6 +58,7 @@
 
     from loopy.codegen import CodeGenerationState, PreambleInfo
     from loopy.codegen.result import CodeGenerationResult
+    from loopy.expression import TypeContext
     from loopy.kernel import LoopKernel
     from loopy.target.c import DTypeRegistry
     from loopy.target.execution import ExecutorBase
@@ -331,7 +332,11 @@ def process_ast(self, node: ASTType):
 # {{{ dummy host ast builder
 
 class _DummyExpressionToCodeMapper:
-    def rec(self, expr, prec, type_context=None, needed_dtype=None):
+    def rec(self,
+            expr,
+            prec,
+            type_context: TypeContext | None = None,
+            needed_dtype=None):
         return ""
 
     __call__ = rec
diff --git a/loopy/target/opencl.py b/loopy/target/opencl.py
index 7e2b136b8..30e84d9ba 100644
--- a/loopy/target/opencl.py
+++ b/loopy/target/opencl.py
@@ -62,6 +62,7 @@
 
     from loopy.codegen import CodeGenerationState
     from loopy.codegen.result import CodeGenerationResult
+    from loopy.expression import TypeContext
     from loopy.kernel.instruction import Assignable, VarAtomicity
     from loopy.translation_unit import CallablesInferenceContext
 
@@ -582,10 +583,10 @@ def wrap_in_typecast(self, actual_type, needed_dtype, s):
 
         return super().wrap_in_typecast(actual_type, needed_dtype, s)
 
-    def map_group_hw_index(self, expr, type_context):
+    def map_group_hw_index(self, expr, type_context: TypeContext):
         return var("gid")(expr.axis)
 
-    def map_local_hw_index(self, expr, type_context):
+    def map_local_hw_index(self, expr, type_context: TypeContext):
         return var("lid")(expr.axis)
 
 # }}}
@@ -845,7 +846,7 @@ def emit_atomic_init(self,
                 lhs_expr: Assignable,
                 rhs_expr: Expression,
                 lhs_dtype: AtomicType,
-                rhs_type_context: str | None) -> Generable:
+                rhs_type_context: TypeContext | None) -> Generable:
         # for the CL1 flavor, this is as simple as a regular update with whatever
         # the RHS value is...
 
diff --git a/loopy/target/pyopencl.py b/loopy/target/pyopencl.py
index 9b5295d63..e8a1629bd 100644
--- a/loopy/target/pyopencl.py
+++ b/loopy/target/pyopencl.py
@@ -78,6 +78,7 @@
 
     from loopy.codegen import CodeGenerationState
     from loopy.codegen.result import CodeGenerationResult
+    from loopy.expression import TypeContext
     from loopy.kernel import LoopKernel
     from loopy.target.pyopencl_execution import PyOpenCLExecutor
     from loopy.translation_unit import (
@@ -257,7 +258,7 @@ def wrap_in_typecast(self, actual_type, needed_type, s):
             return super().wrap_in_typecast(actual_type, needed_type, s)
 
     @override
-    def map_sum(self, expr: p.Sum, type_context: str) -> Expression:
+    def map_sum(self, expr: p.Sum, type_context: TypeContext) -> Expression:
         # I've added 'type_context == "i"' because of the following
         # idiotic corner case: Code generation for subscripts comes
         # through here, and it may involve variables that we know
@@ -369,7 +370,7 @@ def binary_tree_add(start, end):
                 return complex_sum
 
     @override
-    def map_product(self, expr: p.Product, type_context: str) -> Expression:
+    def map_product(self, expr: p.Product, type_context: TypeContext) -> Expression:
         # I've added 'type_context == "i"' because of the following
         # idiotic corner case: Code generation for subscripts comes
         # through here, and it may involve variables that we know
@@ -443,7 +444,7 @@ def binary_tree_mul(start, end):
                 return complex_prd
 
     @override
-    def map_quotient(self, expr: p.Quotient, type_context: str):
+    def map_quotient(self, expr: p.Quotient, type_context: TypeContext):
         n_dtype = self.infer_type(expr.numerator).numpy_dtype
         d_dtype = self.infer_type(expr.denominator).numpy_dtype
         tgt_dtype = self.infer_type(expr)
@@ -467,7 +468,7 @@ def map_quotient(self, expr: p.Quotient, type_context: str):
                     self.rec(expr.denominator, type_context, tgt_dtype))
 
     @override
-    def map_constant(self, expr: object, type_context: str):
+    def map_constant(self, expr: object, type_context: TypeContext):
         if isinstance(expr, (complex, np.complexfloating)):
             try:
                 dtype = expr.dtype
@@ -494,7 +495,7 @@ def map_constant(self, expr: object, type_context: str):
         return super().map_constant(expr, type_context)
 
     @override
-    def map_power(self, expr: p.Power, type_context: str):
+    def map_power(self, expr: p.Power, type_context: TypeContext):
         tgt_dtype = self.infer_type(expr)
         base_dtype = self.infer_type(expr.base)
         exponent_dtype = self.infer_type(expr.exponent)

From 5b544ce840190014ae5871a0963cc16e3c61664f Mon Sep 17 00:00:00 2001
From: Andreas Kloeckner <inform@tiker.net>
Date: Tue, 4 Nov 2025 13:00:20 -0600
Subject: [PATCH 11/18] IdentityMapperMixin: separate out map_rule_argument

---
 loopy/symbolic.py | 8 +++++---
 1 file changed, 5 insertions(+), 3 deletions(-)

diff --git a/loopy/symbolic.py b/loopy/symbolic.py
index c127528b9..e0139cffa 100644
--- a/loopy/symbolic.py
+++ b/loopy/symbolic.py
@@ -178,7 +178,7 @@ def map_array_literal(self, expr: ArrayLiteral,
         return type(expr)(tuple(self.rec(ch, *args, **kwargs)
                                 for ch in expr.children))
 
-    def map_group_hw_index(self, expr: GroupHardwareAxisIndex | RuleArgument,
+    def map_group_hw_index(self, expr: GroupHardwareAxisIndex,
                            *args: P.args, **kwargs: P.kwargs) -> Expression:
         return expr
 
@@ -256,10 +256,12 @@ def map_type_cast(self, expr: TypeCast,
 
         return type(expr)(expr.type, new_child)
 
+    def map_rule_argument(self, expr: RuleArgument,
+                           *args: P.args, **kwargs: P.kwargs) -> Expression:
+        return expr
+
     map_linear_subscript: Callable[Concatenate[Self, LinearSubscript, P],
                                    Expression] = IdentityMapperBase.map_subscript
-    map_rule_argument: Callable[Concatenate[Self, RuleArgument, P],
-                                Expression] = map_group_hw_index
     map_fortran_division: Callable[Concatenate[Self, FortranDivision, P],
                                    Expression] = IdentityMapperBase.map_quotient
 

From 955f6a612d6e4fb24f9504d5eb967a1b62122bc4 Mon Sep 17 00:00:00 2001
From: Andreas Kloeckner <inform@tiker.net>
Date: Tue, 4 Nov 2025 13:00:39 -0600
Subject: [PATCH 12/18] LinearSubscript: index is arithmetic

---
 loopy/symbolic.py | 10 +++++++---
 1 file changed, 7 insertions(+), 3 deletions(-)

diff --git a/loopy/symbolic.py b/loopy/symbolic.py
index e0139cffa..94cb92030 100644
--- a/loopy/symbolic.py
+++ b/loopy/symbolic.py
@@ -940,7 +940,7 @@ class LinearSubscript(LoopyExpressionBase):
     .. autoattribute:: index
     """
     aggregate: Expression
-    index: Expression
+    index: ArithmeticExpression
 
     def __post_init__(self) -> None:
         warn("LinearSubscript is deprecated "
@@ -1965,9 +1965,13 @@ def parse_postfix(self,
         if pstate.next_tag() is _open_dbl_bracket and min_precedence < _PREC_CALL:
             pstate.advance()
             pstate.expect_not_end()
+            subscript = self.parse_expression(pstate)
+            if not p.is_arithmetic_expression(subscript):
+                raise LoopyError("subscript in linear subscript "
+                                 "must be of arithmetic type")
             left_exp = LinearSubscript(
-                        left_exp,
-                        self.parse_expression(pstate))
+                        left_exp, subscript,
+                        )
             pstate.expect(_closebracket)
             pstate.advance()
             pstate.expect(_closebracket)

From 6bdf67c82c8ae8b461b6fa159d3f3ae654564a36 Mon Sep 17 00:00:00 2001
From: Andreas Kloeckner <inform@tiker.net>
Date: Tue, 4 Nov 2025 13:05:06 -0600
Subject: [PATCH 13/18] Code gen for SubArrayRef: handle empty subscript

x-ref: https://github.com/inducer/pymbolic/pull/224
---
 loopy/symbolic.py                    | 2 ++
 loopy/target/c/codegen/expression.py | 7 +++++--
 2 files changed, 7 insertions(+), 2 deletions(-)

diff --git a/loopy/symbolic.py b/loopy/symbolic.py
index 94cb92030..b62f2c1e4 100644
--- a/loopy/symbolic.py
+++ b/loopy/symbolic.py
@@ -1072,6 +1072,8 @@ def _get_lower_bound(iname: str) -> int:
             for swept_iname in sar.swept_inames}
 
     result = EvaluatorWithDeficientContext(swept_inames_to_zeros)(sar.subscript)
+    # assert isinstance(result, p.Subscript)
+    # pending https://github.com/inducer/pymbolic/pull/224
     assert isinstance(result, (p.Variable, p.Subscript))
 
     return result
diff --git a/loopy/target/c/codegen/expression.py b/loopy/target/c/codegen/expression.py
index af50df89f..7c2de567a 100644
--- a/loopy/target/c/codegen/expression.py
+++ b/loopy/target/c/codegen/expression.py
@@ -232,8 +232,11 @@ def map_tagged_variable(self, expr, type_context):
     @override
     def map_sub_array_ref(self, expr, type_context):
         from loopy.symbolic import get_start_subscript_from_sar
-        return var("&")(self.rec(get_start_subscript_from_sar(expr, self.kernel),
-            type_context))
+        if not expr.subscript.index_tuple:
+            return var("&")(self.rec(expr.subscript.aggregate, type_context))
+        else:
+            return var("&")(self.rec(get_start_subscript_from_sar(expr, self.kernel),
+                type_context))
 
     @override
     def map_subscript(self, expr, type_context):

From 0ae2bcd821aef76fbb74ec6d13938b87aae1a026 Mon Sep 17 00:00:00 2001
From: Andreas Kloeckner <inform@tiker.net>
Date: Tue, 4 Nov 2025 13:06:25 -0600
Subject: [PATCH 14/18] Code gen for expressions: more types

---
 loopy/target/c/codegen/expression.py | 118 +++++++++++++++++++--------
 1 file changed, 84 insertions(+), 34 deletions(-)

diff --git a/loopy/target/c/codegen/expression.py b/loopy/target/c/codegen/expression.py
index 7c2de567a..1d75ccd94 100644
--- a/loopy/target/c/codegen/expression.py
+++ b/loopy/target/c/codegen/expression.py
@@ -23,7 +23,7 @@
 THE SOFTWARE.
 """
 
-from typing import TYPE_CHECKING
+from typing import TYPE_CHECKING, cast
 
 import numpy as np
 from typing_extensions import override
@@ -46,8 +46,14 @@
 )
 
 from loopy.diagnostic import LoopyError
-from loopy.expression import dtype_to_type_context
-from loopy.symbolic import IdentityMapper
+from loopy.expression import TypeContext, dtype_to_type_context
+from loopy.symbolic import (
+    GroupHardwareAxisIndex,
+    IdentityMapper,
+    LocalHardwareAxisIndex,
+    ResolvedFunction,
+    SubArrayRef,
+)
 from loopy.target.c import CExpression
 from loopy.type_inference import TypeInferenceMapper, TypeReader
 from loopy.types import LoopyType, NumpyType
@@ -55,6 +61,9 @@
 
 
 if TYPE_CHECKING:
+    from pymbolic.typing import ArithmeticExpression
+
+    from loopy import LinearSubscript, LoopKernel, TaggedVariable
     from loopy.codegen import CodeGenerationState
     from loopy.symbolic import TypeCast
 
@@ -68,7 +77,7 @@
 
 # {{{ Loopy expression to C expression mapper
 
-class ExpressionToCExpressionMapper(IdentityMapper[[str]]):
+class ExpressionToCExpressionMapper(IdentityMapper[[TypeContext]]):
     """
     Mapper that converts a loopy-semantic expression to a C-semantic expression
     with typecasts, appropriate arithmetic semantic mapping, etc.
@@ -81,6 +90,12 @@ class ExpressionToCExpressionMapper(IdentityMapper[[str]]):
           expected type for untyped expressions such as python scalars. The
           type of the expressions takes precedence over *type_context*.
     """
+    kernel: LoopKernel
+    codegen_state: CodeGenerationState
+    type_inf_mapper: TypeInferenceMapper
+    allow_complex: bool
+    fortran_abi: bool
+
     def __init__(self,
                  codegen_state: CodeGenerationState,
                  fortran_abi: bool = False,
@@ -142,7 +157,7 @@ def wrap_in_typecast(self,
     @override
     def rec(self,
             expr: Expression,
-            type_context: str | None = None,
+            type_context: TypeContext = None,
             needed_type: LoopyType | None = None) -> Expression:
         result = super().rec(expr, type_context)
 
@@ -171,7 +186,7 @@ def __call__(self,  # pyright: ignore[reportIncompatibleMethodOverride]
     # }}}
 
     @override
-    def map_variable(self, expr, type_context):
+    def map_variable(self, expr: p.Variable, type_context: TypeContext):
         from loopy.kernel.data import AddressSpace, ValueArg
 
         def postproc(x):
@@ -226,11 +241,11 @@ def postproc(x):
         return postproc(var(expr.name))
 
     @override
-    def map_tagged_variable(self, expr, type_context):
+    def map_tagged_variable(self, expr: TaggedVariable, type_context: TypeContext):
         return var(expr.name)
 
     @override
-    def map_sub_array_ref(self, expr, type_context):
+    def map_sub_array_ref(self, expr: SubArrayRef, type_context: TypeContext):
         from loopy.symbolic import get_start_subscript_from_sar
         if not expr.subscript.index_tuple:
             return var("&")(self.rec(expr.subscript.aggregate, type_context))
@@ -239,8 +254,8 @@ def map_sub_array_ref(self, expr, type_context):
                 type_context))
 
     @override
-    def map_subscript(self, expr, type_context):
-        def base_impl(expr, type_context):
+    def map_subscript(self, expr: p.Subscript, type_context: TypeContext):
+        def base_impl(expr, type_context: TypeContext):
             return self.rec(expr.aggregate, type_context)[self.rec(expr.index, "i")]
 
         def make_var(name):
@@ -261,7 +276,8 @@ def make_var(name):
         from loopy.kernel.array import get_access_info
         from loopy.symbolic import simplify_using_aff
         index_tuple = tuple(
-                simplify_using_aff(self.kernel, idx) for idx in expr.index_tuple)
+                simplify_using_aff(self.kernel, cast("ArithmeticExpression", idx))
+                for idx in expr.index_tuple)
 
         access_info = get_access_info(self.kernel, ary, index_tuple,
                 lambda expr: evaluate(expr, self.codegen_state.var_subst_map),
@@ -335,7 +351,7 @@ def make_var(name):
             raise AssertionError()
 
     @override
-    def map_linear_subscript(self, expr, type_context):
+    def map_linear_subscript(self, expr: LinearSubscript, type_context: TypeContext):
         from pymbolic.primitives import Variable
         if not isinstance(expr.aggregate, Variable):
             raise RuntimeError("linear indexing on non-variable: %s"
@@ -369,7 +385,11 @@ def map_linear_subscript(self, expr, type_context):
     def make_subscript(self, array, base_expr, subscript):
         return base_expr[subscript]
 
-    def _map_integer_div_operator(self, base_func_name, op_func, expr, type_context):
+    def _map_integer_div_operator(self,
+                base_func_name: str,
+                op_func,
+                expr: p.QuotientBase,
+                type_context: TypeContext):
         from loopy.symbolic import get_dependencies
         iname_deps = get_dependencies(expr) & self.kernel.all_inames()
         domain = self.kernel.get_inames_domain(iname_deps)
@@ -394,7 +414,7 @@ def _map_integer_div_operator(self, base_func_name, op_func, expr, type_context)
         result_dtype = self.infer_type(expr)
         suffix = result_dtype.numpy_dtype.type.__name__
 
-        def seen_func(name):
+        def seen_func(name: str):
             from loopy.codegen import SeenFunction
             self.codegen_state.seen_functions.add(
                     SeenFunction(
@@ -419,13 +439,13 @@ def seen_func(name):
                     self.rec(expr.denominator, "i"))
 
     @override
-    def map_floor_div(self, expr, type_context):
+    def map_floor_div(self, expr: p.FloorDiv, type_context: TypeContext):
         import operator
         return self._map_integer_div_operator(
                 "loopy_floor_div", operator.floordiv, expr, type_context)
 
     @override
-    def map_remainder(self, expr, type_context):
+    def map_remainder(self, expr: p.Remainder, type_context: TypeContext):
         tgt_dtype = self.infer_type(expr)
         if tgt_dtype.is_complex():
             raise RuntimeError("complex remainder not defined")
@@ -435,7 +455,7 @@ def map_remainder(self, expr, type_context):
                 "loopy_mod", operator.mod, expr, type_context)
 
     @override
-    def map_if(self, expr, type_context):
+    def map_if(self, expr: p.If, type_context: TypeContext):
         from loopy.types import to_loopy_type
         result_type = self.infer_type(expr)
         return type(expr)(
@@ -446,10 +466,12 @@ def map_if(self, expr, type_context):
                 )
 
     @override
-    def map_comparison(self, expr, type_context):
+    def map_comparison(self, expr: p.Comparison, type_context: TypeContext):
         inner_type_context = dtype_to_type_context(
                 self.kernel.target,
-                self.infer_type(expr.left - expr.right))
+                self.infer_type(
+                                cast("ArithmeticExpression", expr.left)
+                                - cast("ArithmeticExpression", expr.right)))
 
         return type(expr)(
                     self.rec(expr.left, inner_type_context),
@@ -457,11 +479,14 @@ def map_comparison(self, expr, type_context):
                     self.rec(expr.right, inner_type_context))
 
     @override
-    def map_type_cast(self, expr: TypeCast, type_context: str | None) -> Expression:
+    def map_type_cast(self,
+                expr: TypeCast,
+                type_context: TypeContext | None
+            ) -> Expression:
         return self.rec(expr.child, type_context, expr.type)
 
     @override
-    def map_constant(self, expr, type_context):
+    def map_constant(self, expr: object, type_context: TypeContext):
         from loopy.symbolic import Literal
 
         if isinstance(expr, (complex, np.complexfloating)):
@@ -470,7 +495,7 @@ def map_constant(self, expr, type_context):
             iota = p.Variable("I" if "I" not in self.kernel.all_variable_names()
                     else "_Complex_I")
             return real + imag*iota
-        elif np.isnan(expr):
+        elif np.isnan(expr):  # pyright: ignore[reportCallIssue, reportArgumentType]
             from warnings import warn
             warn("Encountered 'bare' floating point NaN value. Since NaN != NaN,"
                  " this leads to problems with cache retrieval."
@@ -480,9 +505,9 @@ def map_constant(self, expr, type_context):
             from pymbolic.primitives import NaN
             data_type = expr.dtype.type if isinstance(expr, np.generic) else None
             return self.map_nan(NaN(data_type), type_context)
-        elif np.isneginf(expr):
+        elif np.isneginf(expr):  # pyright: ignore[reportCallIssue, reportArgumentType]
             return -p.Variable("INFINITY")
-        elif np.isinf(expr):
+        elif np.isinf(expr):  # pyright: ignore[reportCallIssue, reportArgumentType]
             return p.Variable("INFINITY")
         elif isinstance(expr, np.generic):
             # Explicitly typed: Generated code must reflect type exactly.
@@ -512,7 +537,7 @@ def map_constant(self, expr, type_context):
                 raise LoopyError("do not know how to generate code for "
                         "constant of numpy type '%s'" % type(expr).__name__)
 
-        elif np.isfinite(expr):
+        elif np.isfinite(expr):  # pyright: ignore[reportCallIssue]
             if type_context == "f":
                 return Literal(repr(float(expr))+"f")
             elif type_context == "d":
@@ -529,7 +554,8 @@ def map_constant(self, expr, type_context):
                              "for constant '%s'" % expr)
 
     @override
-    def map_call(self, expr, type_context):
+    def map_call(self, expr: p.Call, type_context: TypeContext):
+        assert isinstance(expr.function, (p.Variable, ResolvedFunction))
         return (
                 self.codegen_state.callables_table[
                     expr.function.name].emit_call(
@@ -539,14 +565,18 @@ def map_call(self, expr, type_context):
 
     # {{{ deal with complex-valued variables
 
-    def map_quotient(self, expr, type_context):
+    @override
+    def map_quotient(self,
+                expr: p.Quotient,
+                type_context: TypeContext
+            ) -> ArithmeticExpression:
         n_dtype = self.infer_type(expr.numerator).numpy_dtype
         d_dtype = self.infer_type(expr.denominator).numpy_dtype
 
-        num = self.rec(expr.numerator, type_context)
+        num = self.rec_arith(expr.numerator, type_context)
 
         # analogous to ^{-1}
-        denom = self.rec(expr.denominator, type_context)
+        denom = self.rec_arith(expr.denominator, type_context)
 
         if (n_dtype.kind not in "fc"
                 and d_dtype.kind not in "fc"):
@@ -561,7 +591,7 @@ def map_quotient(self, expr, type_context):
         return type(expr)(num, denom)
 
     @override
-    def map_power(self, expr, type_context):
+    def map_power(self, expr: p.Power, type_context: TypeContext):
         tgt_dtype = self.infer_type(expr)
         base_dtype = self.infer_type(expr.base)
         exponent_dtype = self.infer_type(expr.exponent)
@@ -604,14 +634,18 @@ def map_power(self, expr, type_context):
     # }}}
 
     @override
-    def map_group_hw_index(self, expr, type_context):
+    def map_group_hw_index(self,
+                expr: GroupHardwareAxisIndex,
+                type_context: TypeContext):
         raise LoopyError("plain C does not have group hw axes")
 
     @override
-    def map_local_hw_index(self, expr, type_context):
+    def map_local_hw_index(self,
+                expr: LocalHardwareAxisIndex,
+                type_context: TypeContext):
         raise LoopyError("plain C does not have local hw axes")
 
-    def map_nan(self, expr, type_context):
+    def map_nan(self, expr: p.NaN, type_context: TypeContext):
         from loopy.types import NumpyType
         if expr.data_type is None:
             if type_context == "f":
@@ -645,7 +679,7 @@ def map_nan(self, expr, type_context):
 
 # {{{ C expression to code mapper
 
-class CExpressionToCodeMapper(Mapper):
+class CExpressionToCodeMapper(Mapper[str, [int]]):
 
     # {{{ helpers
 
@@ -741,6 +775,7 @@ def map_min(self, expr, enclosing_prec):
 
     map_max = map_min
 
+    @override
     def map_if(self, expr, enclosing_prec):
         from pymbolic.mapper.stringifier import PREC_CALL, PREC_NONE
 
@@ -755,6 +790,7 @@ def map_if(self, expr, enclosing_prec):
 
         return f"({cond_} ? {then_} : {else_})"
 
+    @override
     def map_comparison(self, expr, enclosing_prec):
         from pymbolic.mapper.stringifier import PREC_COMPARISON
 
@@ -767,26 +803,31 @@ def map_comparison(self, expr, enclosing_prec):
     def map_literal(self, expr, enclosing_prec):
         return expr.s
 
+    @override
     def map_left_shift(self, expr, enclosing_prec):
         return self.parenthesize_if_needed(
             self.join_rec(" << ", (expr.shiftee, expr.shift), PREC_SHIFT),
             enclosing_prec, PREC_SHIFT)
 
+    @override
     def map_right_shift(self, expr, enclosing_prec):
         return self.parenthesize_if_needed(
             self.join_rec(" >> ", (expr.shiftee, expr.shift), PREC_SHIFT),
             enclosing_prec, PREC_SHIFT)
 
+    @override
     def map_logical_not(self, expr, enclosing_prec):
         return self.parenthesize_if_needed(
                 "!" + self.rec(expr.child, PREC_UNARY),
                 enclosing_prec, PREC_UNARY)
 
+    @override
     def map_logical_and(self, expr, enclosing_prec):
         return self.parenthesize_if_needed(
                 self.join_rec(" && ", expr.children, PREC_LOGICAL_AND),
                 enclosing_prec, PREC_LOGICAL_AND)
 
+    @override
     def map_logical_or(self, expr, enclosing_prec):
         mapped_children = []
         from pymbolic.primitives import LogicalAnd
@@ -802,26 +843,31 @@ def map_logical_or(self, expr, enclosing_prec):
             result = "(%s)" % result
         return result
 
+    @override
     def map_bitwise_not(self, expr, enclosing_prec):
         return self.parenthesize_if_needed(
                 "~" + self.rec(expr.child, PREC_UNARY),
                 enclosing_prec, PREC_UNARY)
 
+    @override
     def map_bitwise_and(self, expr, enclosing_prec):
         return self.parenthesize_if_needed(
                 self.join_rec(" & ", expr.children, PREC_BITWISE_AND),
                 enclosing_prec, PREC_BITWISE_AND)
 
+    @override
     def map_bitwise_or(self, expr, enclosing_prec):
         return self.parenthesize_if_needed(
                 self.join_rec(" | ", expr.children, PREC_BITWISE_OR),
                 enclosing_prec, PREC_BITWISE_OR)
 
+    @override
     def map_bitwise_xor(self, expr, enclosing_prec):
         return self.parenthesize_if_needed(
                 self.join_rec(" ^ ", expr.children, PREC_BITWISE_XOR),
                 enclosing_prec, PREC_BITWISE_XOR)
 
+    @override
     def map_sum(self, expr, enclosing_prec):
         from pymbolic.mapper.stringifier import PREC_SUM
 
@@ -831,6 +877,7 @@ def map_sum(self, expr, enclosing_prec):
 
     multiplicative_primitives = (p.Product, p.Quotient, p.FloorDiv, p.Remainder)
 
+    @override
     def map_product(self, expr, enclosing_prec):
         force_parens_around = (p.Quotient, p.FloorDiv, p.Remainder)
 
@@ -854,12 +901,15 @@ def _map_division_operator(self, operator, expr, enclosing_prec):
                 # start-of-comment in C.
                 enclosing_prec, PREC_PRODUCT)
 
+    @override
     def map_quotient(self, expr, enclosing_prec):
         return self._map_division_operator("/", expr, enclosing_prec)
 
+    @override
     def map_floor_div(self, expr, enclosing_prec):
         return self._map_division_operator("/", expr, enclosing_prec)
 
+    @override
     def map_remainder(self, expr, enclosing_prec):
         return self._map_division_operator("%", expr, enclosing_prec)
 

From 97914622a28a47bd2205ed7bf7ce685ed7f0c6b3 Mon Sep 17 00:00:00 2001
From: Andreas Kloeckner <inform@tiker.net>
Date: Tue, 4 Nov 2025 13:06:35 -0600
Subject: [PATCH 15/18] Misc type fixes

---
 loopy/kernel/function_interface.py | 13 ++++++++-----
 loopy/symbolic.py                  |  8 ++++----
 loopy/target/__init__.py           |  2 +-
 loopy/target/c/__init__.py         |  4 ++--
 loopy/target/ispc.py               |  1 +
 loopy/target/pyopencl.py           | 12 +++++++++---
 loopy/transform/loop_fusion.py     |  7 ++++---
 7 files changed, 29 insertions(+), 18 deletions(-)

diff --git a/loopy/kernel/function_interface.py b/loopy/kernel/function_interface.py
index 45b68848f..7f84bcce1 100644
--- a/loopy/kernel/function_interface.py
+++ b/loopy/kernel/function_interface.py
@@ -24,7 +24,7 @@
 """
 from abc import ABC, abstractmethod
 from dataclasses import dataclass, replace
-from typing import TYPE_CHECKING, Any, Protocol, TypeVar
+from typing import TYPE_CHECKING, Any, Protocol, TypeVar, cast
 from warnings import warn
 
 from constantdict import constantdict
@@ -44,6 +44,7 @@
     import islpy as isl
     from pymbolic.typing import ArithmeticExpression, Expression
 
+    from loopy.codegen import CodeGenerationState
     from loopy.kernel import LoopKernel
     from loopy.kernel.instruction import CallInstruction
     from loopy.target import TargetBase
@@ -186,7 +187,7 @@ def depends_on(self) -> frozenset[str]:
             dep_mapper = DependencyMapper(composite_leaves=False)
             for axis_len in self.shape:
                 if axis_len not in [None, auto]:
-                    result |= dep_mapper(axis_len)
+                    result |= cast("set[p.Variable]", dep_mapper(axis_len))
 
         if self.dim_tags:
             for dim_tag in self.dim_tags:
@@ -323,6 +324,8 @@ class AbstractExpressionToCodeMapper(Protocol):
     .. automethod:: infer_type
     .. automethod:: __call__
     """
+    kernel: LoopKernel
+    codegen_state: CodeGenerationState
 
     def infer_type(self, expr: Expression) -> LoopyType: ...
 
@@ -529,7 +532,7 @@ def get_hw_axes_sizes(self,
 
     @abstractmethod
     def get_used_hw_axes(self,
-                         callables_table: CallablesTable) -> tuple[Set[str], Set[str]]:
+                         callables_table: CallablesTable) -> tuple[Set[int], Set[int]]:
         """
         Returns a tuple ``group_axes_used, local_axes_used``, where
         ``(group|local)_axes_used`` are :class:`frozenset` of hardware axes
@@ -693,7 +696,7 @@ def get_hw_axes_sizes(self,
 
     @override
     def get_used_hw_axes(self,
-                         callables_table: CallablesTable) -> tuple[Set[str], Set[str]]:
+                         callables_table: CallablesTable) -> tuple[Set[int], Set[int]]:
         return frozenset(), frozenset()
 
     @override
@@ -1041,7 +1044,7 @@ def with_packing_for_args(self) -> InKernelCallable:
 
     @override
     def get_used_hw_axes(self,
-                         callables_table: CallablesTable) -> tuple[Set[str], Set[str]]:
+                         callables_table: CallablesTable) -> tuple[Set[int], Set[int]]:
         gsize, lsize = self.subkernel.get_grid_size_upper_bounds(callables_table,
                                                                  return_dict=True)
 
diff --git a/loopy/symbolic.py b/loopy/symbolic.py
index b62f2c1e4..e1a4abe4c 100644
--- a/loopy/symbolic.py
+++ b/loopy/symbolic.py
@@ -1325,14 +1325,14 @@ def rename_subst_rules_in_instructions(
 
 
 class SubstitutionRuleMappingContext:
-    old_subst_rules: dict[str, SubstitutionRule]
+    old_subst_rules: Mapping[str, SubstitutionRule]
     make_unique_var_name: Callable[[str], str]
 
     subst_rule_registry: dict[Expression, tuple[str, Sequence[str], Expression]]
     subst_rule_old_names: dict[Expression, list[str]]
 
     def __init__(self,
-                 old_subst_rules: dict[str, SubstitutionRule],
+                 old_subst_rules: Mapping[str, SubstitutionRule],
                  make_unique_var_name: Callable[[str], str]) -> None:
         self.old_subst_rules = old_subst_rules
         self.make_unique_var_name = make_unique_var_name
@@ -1648,12 +1648,12 @@ class RuleAwareSubstitutionMapper(RuleAwareIdentityMapper[[]]):
         renaming mandated by the rule expression divergences.
     """
 
-    subst_func: Callable[[Expression], Expression | None]
+    subst_func: Callable[[p.AlgebraicLeaf], Expression | None]
     _within: StackMatch
 
     def __init__(self,
                  rule_mapping_context: SubstitutionRuleMappingContext,
-                 subst_func: Callable[[Expression], Expression | None],
+                 subst_func: Callable[[p.AlgebraicLeaf], Expression | None],
                  within: StackMatch) -> None:
         super().__init__(rule_mapping_context)
 
diff --git a/loopy/target/__init__.py b/loopy/target/__init__.py
index 8cde975ec..5c147c0f6 100644
--- a/loopy/target/__init__.py
+++ b/loopy/target/__init__.py
@@ -298,7 +298,7 @@ def emit_sequential_loop(self,
             ) -> ASTType:
         raise NotImplementedError()
 
-    def emit_unroll_hint(self, value):
+    def emit_unroll_hint(self, value: int | None):
         raise NotImplementedError()
 
     @property
diff --git a/loopy/target/c/__init__.py b/loopy/target/c/__init__.py
index dcf60f977..e9a297cc3 100644
--- a/loopy/target/c/__init__.py
+++ b/loopy/target/c/__init__.py
@@ -752,7 +752,7 @@ def with_types(self,
                 self.copy(arg_id_to_dtype=constantdict(arg_num_to_dtype)),
                 clbl_inf_ctx)
 
-    def generate_preambles(self, target):
+    def generate_preambles(self, target: CFamilyTarget):
         if self.name_in_target.startswith("lpy_max"):
             dtype = self.arg_id_to_dtype[-1]
             ctype = target.dtype_to_typename(dtype)
@@ -1425,7 +1425,7 @@ def emit_sequential_loop(self,
         else:
             return loop
 
-    def emit_unroll_hint(self, value):
+    def emit_unroll_hint(self, value) -> Generable:
         from cgen import Pragma
         if value:
             return Pragma(f"unroll {value}")
diff --git a/loopy/target/ispc.py b/loopy/target/ispc.py
index 86ac3a916..3fe9b7d9c 100644
--- a/loopy/target/ispc.py
+++ b/loopy/target/ispc.py
@@ -176,6 +176,7 @@ def map_subscript(self, expr, type_context):
 
                 from loopy.kernel.array import get_access_info
 
+                assert p.is_arithmetic_expression(expr.index)
                 access_info = get_access_info(self.kernel, ary, expr.index,
                     lambda expr: evaluate(expr, self.codegen_state.var_subst_map),
                     self.codegen_state.vectorization_info)
diff --git a/loopy/target/pyopencl.py b/loopy/target/pyopencl.py
index e8a1629bd..b0a1b8079 100644
--- a/loopy/target/pyopencl.py
+++ b/loopy/target/pyopencl.py
@@ -168,7 +168,7 @@ def with_types(self,
                 name_in_target=self.name_in_target).with_types(
                         arg_id_to_dtype, clbl_inf_ctx)
 
-    def generate_preambles(self, target):
+    def generate_preambles(self, target: PyOpenCLTarget):
         name = self.name_in_target
         if (name.startswith("_lpy_real")
                 or name.startswith("_lpy_conj")
@@ -284,7 +284,10 @@ def map_sum(self, expr: p.Sum, type_context: TypeContext) -> Expression:
             for child in expr.children:
                 rhs_is_complex = self.infer_type(child).is_complex()
                 if rhs_is_complex:
-                    child_val = self.rec_arith(child, type_context, tgt_dtype)
+                    # FIXME: Yes, rec_arith isn't supposed to take the extra
+                    # argument, but it passes it through to rec(), which does.
+                    # Kinda ugly, I agree. -AK
+                    child_val = self.rec_arith(child, type_context, tgt_dtype)  # pyright: ignore[reportCallIssue]
                 else:
                     child_val = self.rec_arith(child, type_context)
 
@@ -393,7 +396,10 @@ def map_product(self, expr: p.Product, type_context: TypeContext) -> Expression:
             for child in expr.children:
                 rhs_is_complex = self.infer_type(child).is_complex()
                 if rhs_is_complex:
-                    child_val = self.rec_arith(child, type_context, tgt_dtype)
+                    # FIXME: Yes, rec_arith isn't supposed to take the extra
+                    # argument, but it passes it through to rec(), which does.
+                    # Kinda ugly, I agree. -AK
+                    child_val = self.rec_arith(child, type_context, tgt_dtype)  # pyright: ignore[reportCallIssue]
                 else:
                     child_val = self.rec_arith(child, type_context)
 
diff --git a/loopy/transform/loop_fusion.py b/loopy/transform/loop_fusion.py
index 8de5047a2..d318a5455 100644
--- a/loopy/transform/loop_fusion.py
+++ b/loopy/transform/loop_fusion.py
@@ -42,6 +42,7 @@
     RuleAwareIdentityMapper,
     SubstitutionRuleMappingContext,
 )
+from loopy.typing import InameStr
 
 
 if TYPE_CHECKING:
@@ -50,7 +51,7 @@
     from loopy.kernel.instruction import InstructionBase
     from loopy.match import RuleStack
     from loopy.schedule.tools import LoopNestTree
-    from loopy.typing import InameStr, InameStrSet, InsnId
+    from loopy.typing import InameStrSet, InsnId
 
 
 __doc__ = """
@@ -675,7 +676,7 @@ def _fuse_sequential_loops_within_outer_loops(
 
 
 @final
-class ReductionLoopInserter(RuleAwareIdentityMapper[[]]):
+class ReductionLoopInserter(RuleAwareIdentityMapper[[frozenset[InameStr]]]):
     """
     Main mapper used by :func:`_add_reduction_loops_in_partial_loop_nest_tree`.
     """
@@ -753,7 +754,7 @@ def map_reduction(self,
 
         assert not (outer_redn_inames & redn_inames)
         return super().map_reduction(
-            expr, expn_state, outer_redn_inames=(outer_redn_inames | redn_inames)
+            expr, expn_state, (outer_redn_inames | redn_inames)
         )
 
 

From 65df8274de87436d4933f004ab54d26de47b5404 Mon Sep 17 00:00:00 2001
From: Andreas Kloeckner <inform@tiker.net>
Date: Tue, 4 Nov 2025 13:31:11 -0600
Subject: [PATCH 16/18] IdentityMapperMixin: positional-only expr

---
 loopy/symbolic.py | 24 ++++++++++++------------
 1 file changed, 12 insertions(+), 12 deletions(-)

diff --git a/loopy/symbolic.py b/loopy/symbolic.py
index e1a4abe4c..ba6d71a80 100644
--- a/loopy/symbolic.py
+++ b/loopy/symbolic.py
@@ -169,28 +169,28 @@
 # {{{ mappers with support for loopy-specific primitives
 
 class IdentityMapperMixin(Mapper[Expression, P]):
-    def map_literal(self, expr: Literal,
+    def map_literal(self, expr: Literal, /,
                     *args: P.args, **kwargs: P.kwargs) -> Expression:
         return expr
 
-    def map_array_literal(self, expr: ArrayLiteral,
+    def map_array_literal(self, expr: ArrayLiteral, /,
                           *args: P.args, **kwargs: P.kwargs) -> Expression:
         return type(expr)(tuple(self.rec(ch, *args, **kwargs)
                                 for ch in expr.children))
 
-    def map_group_hw_index(self, expr: GroupHardwareAxisIndex,
+    def map_group_hw_index(self, expr: GroupHardwareAxisIndex, /,
                            *args: P.args, **kwargs: P.kwargs) -> Expression:
         return expr
 
-    def map_local_hw_index(self, expr: LocalHardwareAxisIndex,
+    def map_local_hw_index(self, expr: LocalHardwareAxisIndex, /,
                            *args: P.args, **kwargs: P.kwargs) -> Expression:
         return expr
 
-    def map_loopy_function_identifier(self, expr: FunctionIdentifier,
+    def map_loopy_function_identifier(self, expr: FunctionIdentifier, /,
                                       *args: P.args, **kwargs: P.kwargs) -> Expression:
         return expr
 
-    def map_reduction(self, expr: Reduction,
+    def map_reduction(self, expr: Reduction, /,
                       *args: P.args, **kwargs: P.kwargs) -> Expression:
         mapped_inames = [self.rec(p.Variable(iname), *args, **kwargs)
                          for iname in expr.inames]
@@ -213,12 +213,12 @@ def map_reduction(self, expr: Reduction,
                 new_expr,
                 allow_simultaneous=expr.allow_simultaneous)
 
-    def map_tagged_variable(self, expr: TaggedVariable,
+    def map_tagged_variable(self, expr: TaggedVariable, /,
                             *args: P.args, **kwargs: P.kwargs) -> Expression:
         # leaf, doesn't change
         return expr
 
-    def map_type_annotation(self, expr: TypeAnnotation,
+    def map_type_annotation(self, expr: TypeAnnotation, /,
                             *args: P.args, **kwargs: P.kwargs) -> Expression:
         new_child = self.rec(expr.child, *args, **kwargs)
 
@@ -227,7 +227,7 @@ def map_type_annotation(self, expr: TypeAnnotation,
 
         return type(expr)(expr.type, new_child)
 
-    def map_sub_array_ref(self, expr: SubArrayRef,
+    def map_sub_array_ref(self, expr: SubArrayRef, /,
                           *args: P.args, **kwargs: P.kwargs) -> Expression:
         new_inames = self.rec(expr.swept_inames, *args, **kwargs)
         new_subscript = self.rec(expr.subscript, *args, **kwargs)
@@ -242,12 +242,12 @@ def map_sub_array_ref(self, expr: SubArrayRef,
 
         return SubArrayRef(cast("tuple[p.Variable, ...]", new_inames), new_subscript)
 
-    def map_resolved_function(self, expr: ResolvedFunction,
+    def map_resolved_function(self, expr: ResolvedFunction, /,
                               *args: P.args, **kwargs: P.kwargs) -> Expression:
         # leaf, doesn't change
         return expr
 
-    def map_type_cast(self, expr: TypeCast,
+    def map_type_cast(self, expr: TypeCast, /,
                       *args: P.args, **kwargs: P.kwargs) -> Expression:
         new_child = self.rec(expr.child, *args, **kwargs)
 
@@ -256,7 +256,7 @@ def map_type_cast(self, expr: TypeCast,
 
         return type(expr)(expr.type, new_child)
 
-    def map_rule_argument(self, expr: RuleArgument,
+    def map_rule_argument(self, expr: RuleArgument, /,
                            *args: P.args, **kwargs: P.kwargs) -> Expression:
         return expr
 

From 01e5054def87d770e433dfccb4895f83243f49fd Mon Sep 17 00:00:00 2001
From: Andreas Kloeckner <inform@tiker.net>
Date: Tue, 4 Nov 2025 13:32:43 -0600
Subject: [PATCH 17/18] Reduction code gen: fail for non-C targets

---
 loopy/library/reduction.py | 8 ++++++++
 1 file changed, 8 insertions(+)

diff --git a/loopy/library/reduction.py b/loopy/library/reduction.py
index 1c21885b9..cc7c56593 100644
--- a/loopy/library/reduction.py
+++ b/loopy/library/reduction.py
@@ -1,5 +1,7 @@
 from __future__ import annotations
 
+from loopy.target.c import CFamilyTarget
+
 
 __copyright__ = "Copyright (C) 2012 Andreas Kloeckner"
 
@@ -786,6 +788,9 @@ def with_descrs(self, arg_id_to_descr, callables_table):
 class ArgExtOpCallable(ReductionCallable):
 
     def generate_preambles(self, target):
+        if not isinstance(target, CFamilyTarget):
+            raise NotImplementedError("non-C code generation for SegmentOpCallable")
+
         op = self.name.reduction_op  # pylint: disable=no-member
         scalar_dtype = self.arg_id_to_dtype[-1]
         index_dtype = self.arg_id_to_dtype[-2]
@@ -822,6 +827,9 @@ def generate_preambles(self, target):
 class SegmentOpCallable(ReductionCallable):
 
     def generate_preambles(self, target):
+        if not isinstance(target, CFamilyTarget):
+            raise NotImplementedError("non-C code generation for SegmentOpCallable")
+
         op = self.name.reduction_op  # pylint: disable=no-member
         scalar_dtype = self.arg_id_to_dtype[-1]
         segment_flag_dtype = self.arg_id_to_dtype[-2]

From bff59f2a4f61d28453d861efd2e7b4e9ab8d6892 Mon Sep 17 00:00:00 2001
From: Andreas Kloeckner <inform@tiker.net>
Date: Tue, 4 Nov 2025 13:39:26 -0600
Subject: [PATCH 18/18] Update baseline

---
 .basedpyright/baseline.json | 32890 ++++++++++++----------------------
 1 file changed, 11277 insertions(+), 21613 deletions(-)

diff --git a/.basedpyright/baseline.json b/.basedpyright/baseline.json
index 35dbcbcab..83cdce81c 100644
--- a/.basedpyright/baseline.json
+++ b/.basedpyright/baseline.json
@@ -2141,14 +2141,6 @@
                     "lineCount": 1
                 }
             },
-            {
-                "code": "reportUnknownParameterType",
-                "range": {
-                    "startColumn": 33,
-                    "endColumn": 39,
-                    "lineCount": 1
-                }
-            },
             {
                 "code": "reportMissingParameterType",
                 "range": {
@@ -2180,14 +2172,6 @@
                     "endColumn": 24,
                     "lineCount": 1
                 }
-            },
-            {
-                "code": "reportUnknownMemberType",
-                "range": {
-                    "startColumn": 6,
-                    "endColumn": 26,
-                    "lineCount": 1
-                }
             }
         ],
         "./examples/python/find-centers.py": [
@@ -6177,30 +6161,6 @@
                     "lineCount": 1
                 }
             },
-            {
-                "code": "reportGeneralTypeIssues",
-                "range": {
-                    "startColumn": 27,
-                    "endColumn": 65,
-                    "lineCount": 1
-                }
-            },
-            {
-                "code": "reportUnknownArgumentType",
-                "range": {
-                    "startColumn": 44,
-                    "endColumn": 45,
-                    "lineCount": 1
-                }
-            },
-            {
-                "code": "reportUnknownArgumentType",
-                "range": {
-                    "startColumn": 44,
-                    "endColumn": 45,
-                    "lineCount": 1
-                }
-            },
             {
                 "code": "reportUnknownMemberType",
                 "range": {
@@ -6793,14 +6753,6 @@
                     "lineCount": 1
                 }
             },
-            {
-                "code": "reportGeneralTypeIssues",
-                "range": {
-                    "startColumn": 43,
-                    "endColumn": 81,
-                    "lineCount": 1
-                }
-            },
             {
                 "code": "reportUnknownArgumentType",
                 "range": {
@@ -7837,22 +7789,6 @@
                     "lineCount": 1
                 }
             },
-            {
-                "code": "reportUnknownMemberType",
-                "range": {
-                    "startColumn": 37,
-                    "endColumn": 60,
-                    "lineCount": 1
-                }
-            },
-            {
-                "code": "reportUnknownArgumentType",
-                "range": {
-                    "startColumn": 37,
-                    "endColumn": 75,
-                    "lineCount": 1
-                }
-            },
             {
                 "code": "reportUnknownMemberType",
                 "range": {
@@ -8057,14 +7993,6 @@
                     "lineCount": 8
                 }
             },
-            {
-                "code": "reportUnknownMemberType",
-                "range": {
-                    "startColumn": 21,
-                    "endColumn": 63,
-                    "lineCount": 1
-                }
-            },
             {
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@@ -21399,14 +21327,6 @@
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@@ -32586,74 +32506,82 @@
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@@ -32666,194 +32594,196 @@
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@@ -32861,388 +32791,396 @@
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@@ -33252,88 +33190,88 @@
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@@ -33341,55 +33279,63 @@
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                 "code": "reportUnknownParameterType",
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                 "code": "reportMissingParameterType",
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@@ -33397,199 +33343,199 @@
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@@ -33597,262 +33543,270 @@
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@@ -33860,240 +33814,240 @@
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@@ -34101,833 +34055,839 @@
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@@ -34935,23 +34895,23 @@
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@@ -34959,7 +34919,23 @@
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@@ -34967,7 +34943,15 @@
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@@ -34975,7 +34959,23 @@
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@@ -34983,7 +34983,7 @@
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@@ -35047,7 +35047,7 @@
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@@ -35055,7 +35055,7 @@
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@@ -35063,175 +35063,175 @@
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@@ -35239,79 +35239,79 @@
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@@ -35319,7 +35319,7 @@
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@@ -35327,23 +35327,23 @@
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@@ -35351,7 +35351,7 @@
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@@ -35359,7 +35359,7 @@
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@@ -35367,7 +35367,7 @@
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@@ -35375,23 +35375,31 @@
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@@ -35406,40 +35414,56 @@
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@@ -35524,577 +35556,563 @@
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@@ -38280,31 +38256,31 @@
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@@ -38312,120 +38288,128 @@
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@@ -39449,334 +39449,334 @@
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@@ -39784,56 +39784,48 @@
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@@ -39841,7 +39833,7 @@
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@@ -39849,206 +39841,230 @@
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@@ -40121,79 +40137,87 @@
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@@ -40201,286 +40225,286 @@
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@@ -40488,133 +40512,125 @@
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@@ -40622,530 +40638,524 @@
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@@ -52832,7 +43042,7 @@
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@@ -53320,7 +43510,7 @@
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@@ -53328,207 +43518,207 @@
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@@ -53536,287 +43726,263 @@
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@@ -55446,281 +45622,281 @@
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@@ -55728,184 +45904,176 @@
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@@ -55929,7 +46097,7 @@
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@@ -55937,15 +46105,39 @@
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@@ -55961,7 +46153,15 @@
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@@ -55974,81 +46174,81 @@
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@@ -56056,32 +46256,40 @@
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@@ -56089,223 +46297,223 @@
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@@ -56313,182 +46521,182 @@
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@@ -56497,39 +46705,47 @@
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@@ -58817,47 +49057,55 @@
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@@ -58865,304 +49113,326 @@
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@@ -59170,16 +49440,16 @@
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@@ -59187,39 +49457,39 @@
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@@ -59227,7 +49497,7 @@
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@@ -59235,39 +49505,39 @@
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@@ -59275,1175 +49545,1191 @@
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@@ -60451,7 +50737,7 @@
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@@ -60739,239 +51065,231 @@
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@@ -60979,7 +51297,7 @@
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@@ -60987,63 +51305,63 @@
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@@ -61051,100 +51369,100 @@
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@@ -61154,512 +51472,496 @@
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@@ -62579,7 +52921,7 @@
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@@ -62587,143 +52929,143 @@
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@@ -64106,32 +54416,40 @@
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@@ -64139,7 +54457,7 @@
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@@ -64266,7 +54584,7 @@
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@@ -64275,7 +54593,7 @@
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@@ -67487,7 +57893,7 @@
                 "code": "reportUnknownParameterType",
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@@ -67495,38 +57901,46 @@
                 "code": "reportMissingParameterType",
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-                    "endColumn": 37,
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                     "lineCount": 1
                 }
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+                    "endColumn": 50,
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+            },
+            {
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             {
                 "code": "reportUnknownParameterType",
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@@ -67534,352 +57948,376 @@
             {
                 "code": "reportUnknownParameterType",
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             {
                 "code": "reportUnusedParameter",
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             {
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             {
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+                "code": "reportUnusedParameter",
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             },
             {
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+                "code": "reportUnknownParameterType",
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@@ -67887,359 +58325,359 @@
                 "code": "reportUnknownParameterType",
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-                    "endColumn": 27,
+                    "endColumn": 30,
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             },
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             {
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+                "code": "reportUnusedParameter",
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@@ -78434,314 +68506,66 @@
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