diff --git a/doc/conf.py b/doc/conf.py
index 1c69ebfa6..6966a6062 100644
--- a/doc/conf.py
+++ b/doc/conf.py
@@ -46,8 +46,13 @@
 
 sys._BUILDING_SPHINX_DOCS = True
 
+
 nitpick_ignore_regex = [
     ["py:class", r"numpy.(u?)int[\d]+"],
     ["py:class", r"numpy.bool_"],
     ["py:class", r"typing_extensions(.+)"],
+    ["py:class", r"P\.args"],
+    ["py:class", r"P\.kwargs"],
+    ["py:class", r"lp\.LoopKernel"],
+    ["py:class", r"_dtype_any"],
 ]
diff --git a/pyproject.toml b/pyproject.toml
index 6b5563242..665a83d81 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -62,6 +62,7 @@ extend-select = [
     "NPY",   # numpy
     "RUF",
     "UP",
+    "TC",
 ]
 extend-ignore = [
   "E226",
diff --git a/pytato/analysis/__init__.py b/pytato/analysis/__init__.py
index a274a335a..9f4c4bf54 100644
--- a/pytato/analysis/__init__.py
+++ b/pytato/analysis/__init__.py
@@ -26,7 +26,6 @@
 THE SOFTWARE.
 """
 
-from collections.abc import Mapping
 from typing import TYPE_CHECKING, Any
 
 from loopy.tools import LoopyKeyBuilder
@@ -47,12 +46,14 @@
     Stack,
 )
 from pytato.function import Call, FunctionDefinition, NamedCallResult
-from pytato.loopy import LoopyCall
 from pytato.transform import ArrayOrNames, CachedWalkMapper, Mapper
 
 
 if TYPE_CHECKING:
+    from collections.abc import Mapping
+
     from pytato.distributed.nodes import DistributedRecv, DistributedSendRefHolder
+    from pytato.loopy import LoopyCall
 
 __doc__ = """
 .. currentmodule:: pytato.analysis
diff --git a/pytato/array.py b/pytato/array.py
index 1661e6e2d..064a98b4d 100644
--- a/pytato/array.py
+++ b/pytato/array.py
@@ -405,7 +405,7 @@ def _dataclass_setstate(self, state):
 
     # {{{ assign mapper_method
 
-    mm_cls = cast(type[_HasMapperMethod], cls)
+    mm_cls = cast("type[_HasMapperMethod]", cls)
 
     snake_clsname = _CAMEL_TO_SNAKE_RE.sub("_", mm_cls.__name__).lower()
     default_mapper_method_name = f"map_{snake_clsname}"
@@ -804,7 +804,7 @@ def conj(self) -> ArrayOrScalar:
 
     def __abs__(self) -> Array:
         import pytato as pt
-        return cast(Array, pt.abs(self))
+        return cast("Array", pt.abs(self))
 
     def __pos__(self) -> Array:
         return self
@@ -1755,7 +1755,7 @@ def shape(self) -> ShapeType:
                        for i_basic_idx in i_basic_indices)
 
         adv_idx_shape = get_shape_after_broadcasting([
-            cast(Array | Integer, not_none(self.indices[i_idx]))
+            cast("Array | Integer", not_none(self.indices[i_idx]))
             for i_idx in i_adv_indices])
 
         # type-ignored because mypy cannot figure out basic-indices only refer
@@ -1803,7 +1803,7 @@ def shape(self) -> ShapeType:
                    for i_basic_idx in i_basic_indices)
 
         adv_idx_shape = get_shape_after_broadcasting([
-            cast(Array | Integer, not_none(self.indices[i_idx]))
+            cast("Array | Integer", not_none(self.indices[i_idx]))
             for i_idx in i_adv_indices])
 
         # type-ignored because mypy cannot figure out basic-indices only refer slices
@@ -2037,7 +2037,7 @@ def matmul(x1: Array, x2: Array) -> Array:
     if x1.ndim == x2.ndim == 1:
         return pt.sum(x1 * x2)
     elif x1.ndim == 1:
-        return cast(Array, pt.dot(x1, x2))
+        return cast("Array", pt.dot(x1, x2))
     elif x2.ndim == 1:
         x1_indices = index_names[:x1.ndim]
         return pt.einsum(f"{x1_indices}, {x1_indices[-1]} -> {x1_indices[:-1]}",
@@ -2370,7 +2370,7 @@ def full(shape: ConvertibleToShape, fill_value: Scalar | prim.NaN,
     else:
         fill_value = conv_dtype.type(fill_value)
 
-    return IndexLambda(expr=cast(ArithmeticExpression, fill_value),
+    return IndexLambda(expr=cast("ArithmeticExpression", fill_value),
                        shape=shape, dtype=conv_dtype,
                        bindings=immutabledict(),
                        tags=_get_default_tags(),
diff --git a/pytato/cmath.py b/pytato/cmath.py
index d7900ed66..ec981aa32 100644
--- a/pytato/cmath.py
+++ b/pytato/cmath.py
@@ -57,14 +57,13 @@
 # }}}
 
 
-from typing import cast
+from typing import TYPE_CHECKING, cast
 
 import numpy as np
 from immutabledict import immutabledict
 
 import pymbolic.primitives as prim
 from pymbolic import Scalar, var
-from pymbolic.typing import Expression
 
 from pytato.array import (
     Array,
@@ -78,6 +77,10 @@
 from pytato.scalar_expr import SCALAR_CLASSES
 
 
+if TYPE_CHECKING:
+    from pymbolic.typing import Expression
+
+
 def _apply_elem_wise_func(inputs: tuple[ArrayOrScalar, ...],
                           func_name: str,
                           ret_dtype: _dtype_any | None = None,
@@ -88,7 +91,7 @@ def _apply_elem_wise_func(inputs: tuple[ArrayOrScalar, ...],
             np_func_name = func_name
 
         np_func = getattr(np, np_func_name)
-        return cast(ArrayOrScalar, np_func(*inputs))
+        return cast("ArrayOrScalar", np_func(*inputs))
 
     if not inputs:
         raise ValueError("at least one argument must be present")
@@ -233,7 +236,7 @@ def imag(x: ArrayOrScalar) -> ArrayOrScalar:
         result_dtype = np.empty(0, dtype=x_dtype).real.dtype
     else:
         if np.isscalar(x):
-            return cast(Scalar, x_dtype.type(0))
+            return cast("Scalar", x_dtype.type(0))
         else:
             assert isinstance(x, Array)
             import pytato as pt
diff --git a/pytato/codegen.py b/pytato/codegen.py
index aa26e48a9..d08445517 100644
--- a/pytato/codegen.py
+++ b/pytato/codegen.py
@@ -38,8 +38,7 @@
 """
 
 import dataclasses
-from collections.abc import Mapping
-from typing import Any
+from typing import TYPE_CHECKING, Any
 
 from immutabledict import immutabledict
 
@@ -57,10 +56,8 @@
     SizeParam,
     make_dict_of_named_arrays,
 )
-from pytato.function import NamedCallResult
 from pytato.loopy import LoopyCall
 from pytato.scalar_expr import IntegralScalarExpression, is_integral_scalar_expression
-from pytato.target import Target
 from pytato.transform import (
     ArrayOrNames,
     CachedWalkMapper,
@@ -70,6 +67,13 @@
 from pytato.transform.lower_to_index_lambda import ToIndexLambdaMixin
 
 
+if TYPE_CHECKING:
+    from collections.abc import Mapping
+
+    from pytato.function import NamedCallResult
+    from pytato.target import Target
+
+
 SymbolicIndex: TypeAlias = tuple[IntegralScalarExpression, ...]
 
 
diff --git a/pytato/distributed/execute.py b/pytato/distributed/execute.py
index 2630a76c1..3be65c76b 100644
--- a/pytato/distributed/execute.py
+++ b/pytato/distributed/execute.py
@@ -34,28 +34,30 @@
 """
 
 import logging
-from collections.abc import Hashable, Mapping
 from typing import TYPE_CHECKING, Any
 
 import numpy as np
 
 from pytato.array import make_dict_of_named_arrays
-from pytato.distributed.nodes import DistributedRecv, DistributedSend
-from pytato.distributed.partition import (
-    DistributedGraphPart,
-    DistributedGraphPartition,
-    PartId,
-)
 from pytato.scalar_expr import INT_CLASSES
-from pytato.target import BoundProgram
 
 
 logger = logging.getLogger(__name__)
 
 
 if TYPE_CHECKING:
+    from collections.abc import Hashable, Mapping
+
     import mpi4py.MPI
 
+    from pytato.distributed.nodes import DistributedRecv, DistributedSend
+    from pytato.distributed.partition import (
+        DistributedGraphPart,
+        DistributedGraphPartition,
+        PartId,
+    )
+    from pytato.target import BoundProgram
+
 
 # {{{ generate_code_for_partition
 
@@ -134,7 +136,7 @@ def execute_distributed_partition(
     context: dict[str, Any] = input_args.copy()
 
     pids_to_execute = set(partition.parts)
-    pids_executed = set()
+    pids_executed: set[PartId] = set()
     recv_names_completed = set()
     send_requests = []
 
diff --git a/pytato/distributed/partition.py b/pytato/distributed/partition.py
index ca817ad85..c929f750c 100644
--- a/pytato/distributed/partition.py
+++ b/pytato/distributed/partition.py
@@ -88,7 +88,6 @@
     DistributedSend,
     DistributedSendRefHolder,
 )
-from pytato.function import FunctionDefinition, NamedCallResult
 from pytato.scalar_expr import SCALAR_CLASSES
 from pytato.transform import ArrayOrNames, CachedWalkMapper, CombineMapper, CopyMapper
 
@@ -96,6 +95,8 @@
 if TYPE_CHECKING:
     import mpi4py.MPI
 
+    from pytato.function import FunctionDefinition, NamedCallResult
+
 
 @dataclasses.dataclass(frozen=True)
 class CommunicationOpIdentifier:
@@ -350,7 +351,7 @@ def rec(self, expr: ArrayOrNames) -> ArrayOrNames:
             if name is not None:
                 return self._get_placeholder_for(name, expr)
 
-        return cast(ArrayOrNames, super().rec(expr))
+        return cast("ArrayOrNames", super().rec(expr))
 
     def _get_placeholder_for(self, name: str, expr: Array) -> Placeholder:
         placeholder = self.partition_input_name_to_placeholder.get(name)
@@ -820,7 +821,7 @@ def find_distributed_partition(
             raise comm_batches_or_exc
 
         comm_batches = cast(
-                Sequence[Set[CommunicationOpIdentifier]],
+                "Sequence[Set[CommunicationOpIdentifier]]",
                 comm_batches_or_exc)
 
     # }}}
@@ -921,7 +922,7 @@ def find_distributed_partition(
                 ary: max(
                         (comm_id_to_part_id[
                             _recv_to_comm_id(local_rank,
-                                            cast(DistributedRecv, recvd_ary))]
+                                            cast("DistributedRecv", recvd_ary))]
                         for recvd_ary in recvd_array_dep_mapper(ary)),
                         default=-1)
                 for ary in mso_arrays
diff --git a/pytato/distributed/verify.py b/pytato/distributed/verify.py
index 84d8a21ed..5e8aa526d 100644
--- a/pytato/distributed/verify.py
+++ b/pytato/distributed/verify.py
@@ -38,11 +38,8 @@
 
 import dataclasses
 import logging
-from collections.abc import Sequence
 from typing import TYPE_CHECKING, Any
 
-import numpy as np
-
 from pymbolic.mapper.optimize import optimize_mapper
 
 from pytato.array import (
@@ -51,7 +48,6 @@
     ShapeType,
     make_dict_of_named_arrays,
 )
-from pytato.distributed.nodes import CommTagType, DistributedRecv
 from pytato.distributed.partition import (
     CommunicationOpIdentifier,
     DistributedGraphPartition,
@@ -64,7 +60,12 @@
 
 
 if TYPE_CHECKING:
+    from collections.abc import Sequence
+
     import mpi4py.MPI
+    import numpy as np
+
+    from pytato.distributed.nodes import CommTagType, DistributedRecv
 
 
 # {{{ data structures
diff --git a/pytato/equality.py b/pytato/equality.py
index 831dc49a6..1ef2a88ed 100644
--- a/pytato/equality.py
+++ b/pytato/equality.py
@@ -25,7 +25,6 @@
 THE SOFTWARE.
 """
 
-from collections.abc import Callable
 from typing import TYPE_CHECKING, Any
 
 from pytools import memoize_method
@@ -50,11 +49,13 @@
     SizeParam,
     Stack,
 )
-from pytato.function import Call, FunctionDefinition, NamedCallResult
 
 
 if TYPE_CHECKING:
+    from collections.abc import Callable
+
     from pytato.distributed.nodes import DistributedRecv, DistributedSendRefHolder
+    from pytato.function import Call, FunctionDefinition, NamedCallResult
     from pytato.loopy import LoopyCall, LoopyCallResult
 
 __doc__ = """
diff --git a/pytato/loopy.py b/pytato/loopy.py
index 5bb86fcd1..de4c26506 100644
--- a/pytato/loopy.py
+++ b/pytato/loopy.py
@@ -27,9 +27,9 @@
 
 
 import dataclasses
-from collections.abc import Iterable, Iterator, Mapping, Sequence
 from numbers import Number
 from typing import (
+    TYPE_CHECKING,
     Any,
 )
 
@@ -58,6 +58,10 @@
 )
 
 
+if TYPE_CHECKING:
+    from collections.abc import Iterable, Iterator, Mapping, Sequence
+
+
 __doc__ = r"""
 .. currentmodule:: pytato.loopy
 
diff --git a/pytato/pad.py b/pytato/pad.py
index 588070d0f..43ddc4b1d 100644
--- a/pytato/pad.py
+++ b/pytato/pad.py
@@ -1,5 +1,12 @@
 """
 .. autofunction:: pad
+
+Cross-references
+----------------
+
+.. class:: Integer
+
+    See :mod:`pymbolic.typing`.
 """
 from __future__ import annotations
 
@@ -7,20 +14,24 @@
 __copyright__ = "Copyright (C) 2023 Kaushik Kulkarni"
 
 import collections.abc as abc
-from collections.abc import Sequence
-from typing import Any
+from typing import TYPE_CHECKING, Any
 
 import numpy as np
 
 import pymbolic.primitives as prim
 from pymbolic import Scalar
-from pymbolic.typing import Integer
 from pytools import UniqueNameGenerator
 
 from pytato.array import Array, IndexLambda
 from pytato.scalar_expr import INT_CLASSES
 
 
+if TYPE_CHECKING:
+    from collections.abc import Sequence
+
+    from pymbolic.typing import Integer
+
+
 def _get_constant_padded_idx_lambda(
     array: Array,
     pad_widths: Sequence[tuple[Integer, Integer]],
diff --git a/pytato/raising.py b/pytato/raising.py
index 7b1a6bc09..13efb737c 100644
--- a/pytato/raising.py
+++ b/pytato/raising.py
@@ -1,19 +1,16 @@
 from __future__ import annotations
 
-from collections.abc import Mapping, Sequence
 from dataclasses import dataclass
 from enum import Enum, auto, unique
-from typing import Any
+from typing import TYPE_CHECKING, Any
 
 import numpy as np
 from immutabledict import immutabledict
 
 import pymbolic.primitives as p
-from pymbolic.typing import Scalar
 
 from pytato.array import Array, ArrayOrScalar, IndexLambda, ShapeType
 from pytato.diagnostic import UnknownIndexLambdaExpr
-from pytato.reductions import ReductionOperation
 from pytato.scalar_expr import (
     SCALAR_CLASSES,
     IdentityMapper,
@@ -28,6 +25,14 @@
 )
 
 
+if TYPE_CHECKING:
+    from collections.abc import Mapping, Sequence
+
+    from pymbolic.typing import Scalar
+
+    from pytato.reductions import ReductionOperation
+
+
 __doc__ = """
 
 .. autoclass:: HighLevelOp
diff --git a/pytato/reductions.py b/pytato/reductions.py
index e5dc8d817..0d2c5fc1e 100644
--- a/pytato/reductions.py
+++ b/pytato/reductions.py
@@ -30,8 +30,7 @@
 
 
 from abc import ABC, abstractmethod
-from collections.abc import Mapping, Sequence
-from typing import Any
+from typing import TYPE_CHECKING, Any
 
 import numpy as np
 from immutabledict import immutabledict
@@ -43,6 +42,10 @@
 from pytato.scalar_expr import INT_CLASSES, Reduce, ScalarExpression
 
 
+if TYPE_CHECKING:
+    from collections.abc import Mapping, Sequence
+
+
 # {{{ docs
 
 __doc__ = """
diff --git a/pytato/scalar_expr.py b/pytato/scalar_expr.py
index 2e66828cd..e74007c0f 100644
--- a/pytato/scalar_expr.py
+++ b/pytato/scalar_expr.py
@@ -134,7 +134,7 @@ def map_reduce(self,
                    expr: Reduce,
                    *args: P.args, **kwargs: P.kwargs) -> Expression:
         return Reduce(
-                      cast(ArithmeticExpression,
+                      cast("ArithmeticExpression",
                            self.rec(expr.inner_expr, *args, **kwargs)),
                       expr.op,
                       immutabledict({
@@ -148,7 +148,7 @@ def map_reduce(self,
     def map_type_cast(self,
                 expr: TypeCast, *args: P.args, **kwargs: P.kwargs) -> Expression:
         return TypeCast(expr.dtype,
-                        cast(ArithmeticExpression,
+                        cast("ArithmeticExpression",
                              self.rec(expr.inner_expr, *args, **kwargs)))
 
 
diff --git a/pytato/stringifier.py b/pytato/stringifier.py
index 6b50d67f1..f2e7f066b 100644
--- a/pytato/stringifier.py
+++ b/pytato/stringifier.py
@@ -26,7 +26,7 @@
 """
 
 import dataclasses
-from typing import Any, cast
+from typing import TYPE_CHECKING, Any, cast
 
 import numpy as np
 from immutabledict import immutabledict
@@ -41,11 +41,14 @@
     IndexLambda,
     ReductionDescriptor,
 )
-from pytato.function import Call, FunctionDefinition
-from pytato.loopy import LoopyCall
 from pytato.transform import Mapper
 
 
+if TYPE_CHECKING:
+    from pytato.function import Call, FunctionDefinition
+    from pytato.loopy import LoopyCall
+
+
 __doc__ = """
 .. currentmodule:: pytato.stringifier
 
@@ -90,7 +93,7 @@ def map_foreign(self, expr: Any, depth: int) -> str:
                     + ", ".join(f"{key!r}: {self.rec(val, depth)}"
                                 for key, val
                                 in sorted(expr.items(),
-                                          key=lambda k_x_v: cast(str, k_x_v[0])))
+                                          key=lambda k_x_v: cast("str", k_x_v[0])))
                     + "}")
         elif isinstance(expr, frozenset | set):
             return "{" + ", ".join(self.rec(el, depth) for el in expr) + "}"
diff --git a/pytato/tags.py b/pytato/tags.py
index 8a7c8d3e7..e0a98b7da 100644
--- a/pytato/tags.py
+++ b/pytato/tags.py
@@ -19,13 +19,17 @@
 .. autoclass:: InlineCallTag
 """
 
-from collections.abc import Hashable
 from dataclasses import dataclass
 from traceback import FrameSummary, StackSummary
+from typing import TYPE_CHECKING
 
 from pytools.tag import Tag, UniqueTag, tag_dataclass
 
 
+if TYPE_CHECKING:
+    from collections.abc import Hashable
+
+
 # {{{ pre-defined tag: ImplementationStrategy
 
 @tag_dataclass
diff --git a/pytato/target/__init__.py b/pytato/target/__init__.py
index 6e3e1480e..57ab3940b 100644
--- a/pytato/target/__init__.py
+++ b/pytato/target/__init__.py
@@ -33,9 +33,12 @@
 .. autoclass:: BoundProgram
 """
 
-from collections.abc import Mapping
 from dataclasses import dataclass
-from typing import Any
+from typing import TYPE_CHECKING, Any
+
+
+if TYPE_CHECKING:
+    from collections.abc import Mapping
 
 
 class Target:
diff --git a/pytato/target/loopy/__init__.py b/pytato/target/loopy/__init__.py
index cf8d57a51..c6568ba58 100644
--- a/pytato/target/loopy/__init__.py
+++ b/pytato/target/loopy/__init__.py
@@ -50,7 +50,6 @@
 """
 
 import sys
-from collections.abc import Callable, Mapping
 from dataclasses import dataclass, field
 from functools import cached_property
 from typing import TYPE_CHECKING, Any
@@ -64,6 +63,12 @@
 from pytato.target import BoundProgram, Target
 
 
+if TYPE_CHECKING:
+    from collections.abc import Callable, Mapping
+
+    import pyopencl
+
+
 class ImplSubstitution(ImplementationStrategy):
     """
     An :class:`~pytato.tags.ImplementationStrategy` that lowers the array
@@ -75,7 +80,7 @@ class ImplSubstitution(ImplementationStrategy):
 if getattr(sys, "_BUILDING_SPHINX_DOCS", False) or TYPE_CHECKING:
     # Avoid import unless building docs to avoid creating a hard
     # dependency on pyopencl, when Loopy can run fine without.
-    import pyopencl
+    pass
 
 
 class LoopyTarget(Target):
diff --git a/pytato/target/loopy/codegen.py b/pytato/target/loopy/codegen.py
index ca9ae482d..528de5d0e 100644
--- a/pytato/target/loopy/codegen.py
+++ b/pytato/target/loopy/codegen.py
@@ -28,15 +28,13 @@
 import sys
 from abc import ABC, abstractmethod
 from collections.abc import Mapping
+from typing import TYPE_CHECKING
 
 import islpy as isl
 
 import loopy as lp
 import pymbolic.primitives as prim
-import pytools
 from pymbolic import ArithmeticExpression, var
-from pymbolic.typing import Expression
-from pytools.tag import Tag
 
 import pytato.reductions as red
 import pytato.scalar_expr as scalar_expr
@@ -59,8 +57,6 @@
     normalize_outputs,
     preprocess,
 )
-from pytato.function import Call, NamedCallResult
-from pytato.loopy import LoopyCall
 from pytato.scalar_expr import (
     INT_CLASSES,
     ScalarExpression,
@@ -73,16 +69,26 @@
     Named,
     PrefixNamed,
 )
-from pytato.target import BoundProgram
 from pytato.target.loopy import ImplSubstitution, LoopyPyOpenCLTarget, LoopyTarget
 from pytato.transform import Mapper
 
 
+if TYPE_CHECKING:
+    import pyopencl
+    import pytools
+    from pymbolic.typing import Expression
+    from pytools.tag import Tag
+
+    from pytato.function import Call, NamedCallResult
+    from pytato.loopy import LoopyCall
+    from pytato.target import BoundProgram
+
+
 # set in doc/conf.py
 if getattr(sys, "_BUILDING_SPHINX_DOCS", False):
     # Avoid import unless building docs to avoid creating a hard
     # dependency on pyopencl, when Loopy can run fine without.
-    import pyopencl
+    from pytools.tag import Tag  # noqa: TC001
 
 __doc__ = """
 .. autoclass:: PersistentExpressionContext
diff --git a/pytato/target/python/__init__.py b/pytato/target/python/__init__.py
index 8a85405b3..7fbee4e59 100644
--- a/pytato/target/python/__init__.py
+++ b/pytato/target/python/__init__.py
@@ -37,16 +37,19 @@
 """
 
 from abc import ABC, abstractmethod
-from collections.abc import Callable, Mapping
 from dataclasses import dataclass
 from functools import cached_property
-from typing import Any
+from typing import TYPE_CHECKING, Any
 
 import numpy as np
 
 from pytato.target import BoundProgram, Target
 
 
+if TYPE_CHECKING:
+    from collections.abc import Callable, Mapping
+
+
 # {{{ abstract types
 
 class PythonTarget(Target, ABC):
diff --git a/pytato/target/python/jax.py b/pytato/target/python/jax.py
index 2e9350625..efe691ac9 100644
--- a/pytato/target/python/jax.py
+++ b/pytato/target/python/jax.py
@@ -26,13 +26,18 @@
 """
 
 import ast
-from collections.abc import Mapping
+from typing import TYPE_CHECKING
 
-from pytato.array import Array, DictOfNamedArrays
 from pytato.target.python import BoundJAXPythonProgram, JAXPythonTarget
 from pytato.target.python.numpy_like import generate_numpy_like
 
 
+if TYPE_CHECKING:
+    from collections.abc import Mapping
+
+    from pytato.array import Array, DictOfNamedArrays
+
+
 __doc__ = """
 .. autofunction:: generate_jax
 """
diff --git a/pytato/target/python/numpy_like.py b/pytato/target/python/numpy_like.py
index 28f3f0fc4..0c9bd413c 100644
--- a/pytato/target/python/numpy_like.py
+++ b/pytato/target/python/numpy_like.py
@@ -28,8 +28,8 @@
 import ast
 import os
 import sys
-from collections.abc import Callable, Iterable, Mapping
 from typing import (
+    TYPE_CHECKING,
     TypedDict,
     TypeVar,
     cast,
@@ -72,11 +72,16 @@
     ReductionOperation,
     SumReductionOperation,
 )
-from pytato.target.python import BoundPythonProgram, NumpyLikePythonTarget
 from pytato.transform import CachedMapper
 from pytato.utils import are_shape_components_equal, get_einsum_specification
 
 
+if TYPE_CHECKING:
+    from collections.abc import Callable, Iterable, Mapping
+
+    from pytato.target.python import BoundPythonProgram, NumpyLikePythonTarget
+
+
 T = TypeVar("T")
 
 
@@ -410,7 +415,7 @@ def _map_index_base(self, expr: IndexBase) -> str:
             default=-1,
             pred=lambda i: not (isinstance(expr.indices[i], NormalizedSlice)
                                 and _is_slice_trivial(
-                                        cast(NormalizedSlice, expr.indices[i]),
+                                        cast("NormalizedSlice", expr.indices[i]),
                                         expr.array.shape[i]))
         )
 
diff --git a/pytato/transform/__init__.py b/pytato/transform/__init__.py
index 4c5d4a0f1..393583037 100644
--- a/pytato/transform/__init__.py
+++ b/pytato/transform/__init__.py
@@ -28,11 +28,12 @@
 """
 import dataclasses
 import logging
-from collections.abc import Callable, Hashable, Iterable, Mapping
 from typing import (
+    TYPE_CHECKING,
     Any,
     Generic,
     ParamSpec,
+    TypeAlias,
     TypeVar,
     cast,
 )
@@ -78,7 +79,11 @@
 from pytato.tags import ImplStored
 
 
-ArrayOrNames = Array | AbstractResultWithNamedArrays
+if TYPE_CHECKING:
+    from collections.abc import Callable, Hashable, Iterable, Mapping
+
+
+ArrayOrNames: TypeAlias = Array | AbstractResultWithNamedArrays
 MappedT = TypeVar("MappedT",
                   Array, AbstractResultWithNamedArrays, ArrayOrNames)
 TransformMapperResultT = TypeVar("TransformMapperResultT",  # used in TransformMapper
@@ -131,6 +136,8 @@
 Internal stuff that is only here because the documentation tool wants it
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
 
+.. class:: ArrayOrNames
+
 .. class:: MappedT
 
     A type variable representing the input type of a :class:`Mapper`.
@@ -143,6 +150,9 @@
 
     A type variable representing the result type of a :class:`Mapper`.
 
+.. class:: Scalar
+
+    See :data:`pymbolic.Scalar`.
 """
 
 transform_logger = logging.getLogger(__file__)
@@ -211,7 +221,7 @@ def rec(self, expr: ArrayOrNames, *args: P.args, **kwargs: P.kwargs) -> ResultT:
                 return self.map_foreign(expr, *args, **kwargs)
 
         assert method is not None
-        return cast(ResultT, method(expr, *args, **kwargs))
+        return cast("ResultT", method(expr, *args, **kwargs))
 
     def __call__(self,
                  expr: ArrayOrNames, *args: P.args, **kwargs: P.kwargs) -> ResultT:
@@ -1572,7 +1582,7 @@ def map_and_copy(expr: MappedT,
         Uses :class:`CachedMapAndCopyMapper` under the hood and because of its
         caching nature each node is mapped exactly once.
     """
-    return cast(MappedT, CachedMapAndCopyMapper(map_fn)(expr))
+    return cast("MappedT", CachedMapAndCopyMapper(map_fn)(expr))
 
 
 def materialize_with_mpms(expr: DictOfNamedArrays) -> DictOfNamedArrays:
diff --git a/pytato/transform/calls.py b/pytato/transform/calls.py
index 74945a4d4..bc3d69909 100644
--- a/pytato/transform/calls.py
+++ b/pytato/transform/calls.py
@@ -29,7 +29,8 @@
 THE SOFTWARE.
 """
 
-from collections.abc import Mapping
+
+from typing import TYPE_CHECKING
 
 from pytato.array import (
     AbstractResultWithNamedArrays,
@@ -42,6 +43,10 @@
 from pytato.transform import ArrayOrNames, CopyMapper
 
 
+if TYPE_CHECKING:
+    from collections.abc import Mapping
+
+
 # {{{ inlining
 
 class PlaceholderSubstitutor(CopyMapper):
diff --git a/pytato/transform/einsum_distributive_law.py b/pytato/transform/einsum_distributive_law.py
index 0d9a6076f..7a23518c6 100644
--- a/pytato/transform/einsum_distributive_law.py
+++ b/pytato/transform/einsum_distributive_law.py
@@ -35,14 +35,11 @@
 
 
 import dataclasses
-from collections.abc import Callable, Mapping
-from typing import cast
+from typing import TYPE_CHECKING, cast
 
 import numpy as np
 from immutabledict import immutabledict
 
-from pytools.tag import Tag
-
 from pytato.array import (
     Array,
     AxesT,
@@ -59,7 +56,6 @@
     Roll,
     Stack,
 )
-from pytato.raising import HighLevelOp
 from pytato.transform import (
     MappedT,
     TransformMapperWithExtraArgs,
@@ -67,6 +63,14 @@
 from pytato.utils import are_shapes_equal
 
 
+if TYPE_CHECKING:
+    from collections.abc import Callable, Mapping
+
+    from pytools.tag import Tag
+
+    from pytato.raising import HighLevelOp
+
+
 class EinsumDistributiveLawDescriptor:
     """
     Abstract-type that informs :func:`apply_distributive_property_to_einsums`
@@ -358,4 +362,4 @@ def apply_distributive_property_to_einsums(
         True
     """
     mapper = EinsumDistributiveLawMapper(how_to_distribute)
-    return cast(MappedT, mapper(expr, None))
+    return cast("MappedT", mapper(expr, None))
diff --git a/pytato/transform/lower_to_index_lambda.py b/pytato/transform/lower_to_index_lambda.py
index dd8f6babd..e952e4e9e 100644
--- a/pytato/transform/lower_to_index_lambda.py
+++ b/pytato/transform/lower_to_index_lambda.py
@@ -31,7 +31,6 @@
 from dataclasses import dataclass
 from typing import TYPE_CHECKING, Any, TypeVar, cast
 
-import numpy as np
 from immutabledict import immutabledict
 
 import pymbolic.primitives as prim
@@ -61,6 +60,10 @@
 from pytato.transform import Mapper
 
 
+if TYPE_CHECKING:
+    import numpy as np
+
+
 ToIndexLambdaT = TypeVar("ToIndexLambdaT", Array, AbstractResultWithNamedArrays)
 
 
@@ -443,7 +446,7 @@ def map_contiguous_advanced_index(self,
                               for i, idx_expr in enumerate(expr.indices)
                               if isinstance(idx_expr, (Array, *INT_CLASSES)))
         adv_idx_shape = get_shape_after_broadcasting([
-                    cast(Array | int | np.integer[Any], expr.indices[i_idx])
+                    cast("Array | int | np.integer[Any]", expr.indices[i_idx])
                     for i_idx in i_adv_indices])
 
         vng = UniqueNameGenerator()
@@ -511,7 +514,7 @@ def map_non_contiguous_advanced_index(
                               for i, idx_expr in enumerate(expr.indices)
                               if isinstance(idx_expr, (Array, *INT_CLASSES)))
         adv_idx_shape = get_shape_after_broadcasting([
-            cast(Array | int | np.integer[Any], expr.indices[i_idx])
+            cast("Array | int | np.integer[Any]", expr.indices[i_idx])
             for i_idx in i_adv_indices])
 
         vng = UniqueNameGenerator()
@@ -622,7 +625,7 @@ def map_axis_permutation(self, expr: AxisPermutation) -> IndexLambda:
             indices[to_index] = prim.Variable(f"_{from_index}")
 
         index_expr = prim.Variable("_in0")[
-            cast(tuple[ArithmeticExpression], tuple(indices))]
+            cast("tuple[ArithmeticExpression]", tuple(indices))]
 
         return IndexLambda(expr=index_expr,
                            shape=self._rec_shape(expr.shape),
diff --git a/pytato/transform/metadata.py b/pytato/transform/metadata.py
index 139b7bf5b..130db8b7a 100644
--- a/pytato/transform/metadata.py
+++ b/pytato/transform/metadata.py
@@ -40,7 +40,6 @@
 
 
 import logging
-from collections.abc import Collection, Mapping
 from typing import (
     TYPE_CHECKING,
     Any,
@@ -73,7 +72,6 @@
 )
 from pytato.diagnostic import UnknownIndexLambdaExpr
 from pytato.distributed.nodes import DistributedRecv, DistributedSendRefHolder
-from pytato.function import NamedCallResult
 from pytato.raising import (
     BinaryOp,
     BroadcastOp,
@@ -92,6 +90,9 @@
 
 
 if TYPE_CHECKING:
+    from collections.abc import Collection, Mapping
+
+    from pytato.function import NamedCallResult
     from pytato.loopy import LoopyCall
 
 
@@ -416,7 +417,7 @@ def map_contiguous_advanced_index(self,
                                             for i_idx in i_basic_indices
                                             if i_idx > i_adv_indices[-1]])
 
-        indirection_arrays: list[Array] = cast(list[Array],
+        indirection_arrays: list[Array] = cast("list[Array]",
                                                [expr.indices[i_idx]
                                                 for i_idx in i_adv_indices
                                                 if isinstance(expr.indices[i_idx],
diff --git a/pytato/transform/remove_broadcasts_einsum.py b/pytato/transform/remove_broadcasts_einsum.py
index a9997162a..8c7c224fb 100644
--- a/pytato/transform/remove_broadcasts_einsum.py
+++ b/pytato/transform/remove_broadcasts_einsum.py
@@ -97,6 +97,6 @@ def rewrite_einsums_with_no_broadcasts(expr: MappedT) -> MappedT:
         alter its value.
     """
     mapper = EinsumWithNoBroadcastsRewriter()
-    return cast(MappedT, mapper(expr))
+    return cast("MappedT", mapper(expr))
 
 # vim:fdm=marker
diff --git a/pytato/utils.py b/pytato/utils.py
index 7fa60569e..aedd0dc05 100644
--- a/pytato/utils.py
+++ b/pytato/utils.py
@@ -22,8 +22,8 @@
 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
 THE SOFTWARE.
 """
-from collections.abc import Callable, Iterable, Sequence
 from typing import (
+    TYPE_CHECKING,
     Any,
     TypeVar,
     cast,
@@ -36,7 +36,6 @@
 import pymbolic.primitives as prim
 from pymbolic import ArithmeticExpression, Bool, Scalar
 from pytools import UniqueNameGenerator
-from pytools.tag import Tag
 
 from pytato.array import (
     AdvancedIndexInContiguousAxes,
@@ -64,6 +63,12 @@
 from pytato.transform import CachedMapper
 
 
+if TYPE_CHECKING:
+    from collections.abc import Callable, Iterable, Sequence
+
+    from pytools.tag import Tag
+
+
 __doc__ = """
 Helper routines
 ---------------
@@ -534,7 +539,7 @@ def _index_into(
                    + (slice(None, None, None),) * (ary.ndim - len(indices) + 1)
                    + indices[ellipsis_pos+1:])
 
-    indices = cast(tuple[int, slice, "Array", None], indices)
+    indices = cast("tuple[int, slice, Array, None]", indices)
 
     # }}}
 
diff --git a/pytato/visualization/dot.py b/pytato/visualization/dot.py
index f505c900a..7e685aba9 100644
--- a/pytato/visualization/dot.py
+++ b/pytato/visualization/dot.py
@@ -29,7 +29,6 @@
 
 import dataclasses
 import html
-from collections.abc import Callable, Mapping
 from functools import partial
 from typing import (
     TYPE_CHECKING,
@@ -38,7 +37,6 @@
 
 from pytools import UniqueNameGenerator
 from pytools.codegen import remove_common_indentation
-from pytools.tag import Tag
 
 from pytato.array import (
     AbstractResultWithNamedArrays,
@@ -60,13 +58,17 @@
     PartId,
 )
 from pytato.function import Call, FunctionDefinition, NamedCallResult
-from pytato.loopy import LoopyCall
 from pytato.tags import FunctionIdentifier
 from pytato.transform import ArrayOrNames, CachedMapper, InputGatherer
 
 
 if TYPE_CHECKING:
+    from collections.abc import Callable, Mapping
+
+    from pytools.tag import Tag
+
     from pytato.distributed.nodes import DistributedSendRefHolder
+    from pytato.loopy import LoopyCall
 
 
 __doc__ = """
diff --git a/pytato/visualization/fancy_placeholder_data_flow.py b/pytato/visualization/fancy_placeholder_data_flow.py
index f3ffe430b..3d06309fd 100644
--- a/pytato/visualization/fancy_placeholder_data_flow.py
+++ b/pytato/visualization/fancy_placeholder_data_flow.py
@@ -5,9 +5,8 @@
 """
 from __future__ import annotations
 
-from collections.abc import Collection
 from dataclasses import dataclass
-from typing import Any
+from typing import TYPE_CHECKING, Any
 
 from pytools import UniqueNameGenerator
 
@@ -27,6 +26,10 @@
 from pytato.transform import CachedMapper
 
 
+if TYPE_CHECKING:
+    from collections.abc import Collection
+
+
 # {{{ Graph node colors
 
 PLACEHOLDER_COLOR = "lightgrey"
diff --git a/test/testlib.py b/test/testlib.py
index 02e76ad9a..36857197b 100644
--- a/test/testlib.py
+++ b/test/testlib.py
@@ -2,29 +2,34 @@
 
 import operator
 import random
-import types
-from collections.abc import Callable, Sequence
-from typing import Any
+from typing import TYPE_CHECKING, Any
 
 import numpy as np
 
-import pyopencl as cl
 from pytools.tag import Tag
 
 import pytato as pt
-from pytato.array import (
-    Array,
-    AxisPermutation,
-    Concatenate,
-    DataWrapper,
-    Placeholder,
-    Reshape,
-    Roll,
-    Stack,
-)
 from pytato.transform import Mapper
 
 
+if TYPE_CHECKING:
+    import types
+    from collections.abc import Callable, Sequence
+
+    import pyopencl as cl
+
+    from pytato.array import (
+        Array,
+        AxisPermutation,
+        Concatenate,
+        DataWrapper,
+        Placeholder,
+        Reshape,
+        Roll,
+        Stack,
+    )
+
+
 # {{{ tools for comparison to numpy
 
 class NumpyBasedEvaluator(Mapper[Any, []]):
@@ -296,7 +301,7 @@ def make_dws_placeholder(expr: pt.transform.ArrayOrNames
             else:
                 return expr
 
-        dag = cast(pt.DictOfNamedArrays,
+        dag = cast("pt.DictOfNamedArrays",
                    pt.transform.map_and_copy(dag, make_dws_placeholder))
 
     return dag