diff --git a/.basedpyright/baseline.json b/.basedpyright/baseline.json
index b5a86728..534ed9fb 100644
--- a/.basedpyright/baseline.json
+++ b/.basedpyright/baseline.json
@@ -1851,14 +1851,6 @@
             }
         ],
         "./arraycontext/context.py": [
-            {
-                "code": "reportDeprecated",
-                "range": {
-                    "startColumn": 69,
-                    "endColumn": 74,
-                    "lineCount": 1
-                }
-            },
             {
                 "code": "reportAny",
                 "range": {
@@ -1867,14 +1859,6 @@
                     "lineCount": 1
                 }
             },
-            {
-                "code": "reportDeprecated",
-                "range": {
-                    "startColumn": 27,
-                    "endColumn": 32,
-                    "lineCount": 1
-                }
-            },
             {
                 "code": "reportAny",
                 "range": {
@@ -17009,6 +16993,14 @@
                     "lineCount": 1
                 }
             },
+            {
+                "code": "reportInvalidCast",
+                "range": {
+                    "startColumn": 15,
+                    "endColumn": 45,
+                    "lineCount": 1
+                }
+            },
             {
                 "code": "reportUnknownParameterType",
                 "range": {
@@ -19761,6 +19753,46 @@
                     "lineCount": 1
                 }
             },
+            {
+                "code": "reportArgumentType",
+                "range": {
+                    "startColumn": 54,
+                    "endColumn": 63,
+                    "lineCount": 1
+                }
+            },
+            {
+                "code": "reportArgumentType",
+                "range": {
+                    "startColumn": 54,
+                    "endColumn": 63,
+                    "lineCount": 1
+                }
+            },
+            {
+                "code": "reportArgumentType",
+                "range": {
+                    "startColumn": 54,
+                    "endColumn": 63,
+                    "lineCount": 1
+                }
+            },
+            {
+                "code": "reportArgumentType",
+                "range": {
+                    "startColumn": 54,
+                    "endColumn": 63,
+                    "lineCount": 1
+                }
+            },
+            {
+                "code": "reportArgumentType",
+                "range": {
+                    "startColumn": 54,
+                    "endColumn": 63,
+                    "lineCount": 1
+                }
+            },
             {
                 "code": "reportIndexIssue",
                 "range": {
@@ -20265,6 +20297,14 @@
                     "lineCount": 1
                 }
             },
+            {
+                "code": "reportOperatorIssue",
+                "range": {
+                    "startColumn": 21,
+                    "endColumn": 28,
+                    "lineCount": 1
+                }
+            },
             {
                 "code": "reportUnknownLambdaType",
                 "range": {
@@ -20313,6 +20353,22 @@
                     "lineCount": 1
                 }
             },
+            {
+                "code": "reportOperatorIssue",
+                "range": {
+                    "startColumn": 8,
+                    "endColumn": 53,
+                    "lineCount": 1
+                }
+            },
+            {
+                "code": "reportOperatorIssue",
+                "range": {
+                    "startColumn": 8,
+                    "endColumn": 32,
+                    "lineCount": 1
+                }
+            },
             {
                 "code": "reportUnusedExpression",
                 "range": {
@@ -20321,6 +20377,14 @@
                     "lineCount": 1
                 }
             },
+            {
+                "code": "reportOperatorIssue",
+                "range": {
+                    "startColumn": 8,
+                    "endColumn": 27,
+                    "lineCount": 1
+                }
+            },
             {
                 "code": "reportUnusedExpression",
                 "range": {
@@ -20377,6 +20441,22 @@
                     "lineCount": 1
                 }
             },
+            {
+                "code": "reportOperatorIssue",
+                "range": {
+                    "startColumn": 36,
+                    "endColumn": 55,
+                    "lineCount": 1
+                }
+            },
+            {
+                "code": "reportOperatorIssue",
+                "range": {
+                    "startColumn": 32,
+                    "endColumn": 51,
+                    "lineCount": 1
+                }
+            },
             {
                 "code": "reportMissingParameterType",
                 "range": {
@@ -20601,6 +20681,14 @@
                     "lineCount": 1
                 }
             },
+            {
+                "code": "reportOperatorIssue",
+                "range": {
+                    "startColumn": 12,
+                    "endColumn": 21,
+                    "lineCount": 1
+                }
+            },
             {
                 "code": "reportMissingParameterType",
                 "range": {
@@ -21063,22 +21151,6 @@
                     "lineCount": 1
                 }
             },
-            {
-                "code": "reportGeneralTypeIssues",
-                "range": {
-                    "startColumn": 10,
-                    "endColumn": 31,
-                    "lineCount": 1
-                }
-            },
-            {
-                "code": "reportGeneralTypeIssues",
-                "range": {
-                    "startColumn": 14,
-                    "endColumn": 35,
-                    "lineCount": 1
-                }
-            },
             {
                 "code": "reportUnannotatedClassAttribute",
                 "range": {
@@ -21087,22 +21159,6 @@
                     "lineCount": 1
                 }
             },
-            {
-                "code": "reportGeneralTypeIssues",
-                "range": {
-                    "startColumn": 10,
-                    "endColumn": 31,
-                    "lineCount": 1
-                }
-            },
-            {
-                "code": "reportGeneralTypeIssues",
-                "range": {
-                    "startColumn": 14,
-                    "endColumn": 35,
-                    "lineCount": 1
-                }
-            },
             {
                 "code": "reportUnannotatedClassAttribute",
                 "range": {
diff --git a/arraycontext/container/arithmetic.py b/arraycontext/container/arithmetic.py
index 87313fd9..23495c8f 100644
--- a/arraycontext/container/arithmetic.py
+++ b/arraycontext/container/arithmetic.py
@@ -8,6 +8,13 @@
 .. autofunction:: with_container_arithmetic
 
 .. autoclass:: BcastUntilActxArray
+
+References
+----------
+
+.. class:: TypeT
+
+    A type variable with an upper bound of :class:`type`.
 """
 
 
@@ -62,6 +69,8 @@
 
 T = TypeVar("T")
 
+TypeT = TypeVar("TypeT", bound=type)
+
 
 @enum.unique
 class _OpClass(enum.Enum):
@@ -190,7 +199,7 @@ def with_container_arithmetic(
             bcast_numpy_array: bool = False,
             _bcast_actx_array_type: bool | None = None,
             bcast_container_types: tuple[type, ...] | None = None,
-        ) -> Callable[[type], type]:
+        ) -> Callable[[TypeT], TypeT]:
     """A class decorator that implements built-in operators for array containers
     by propagating the operations to the elements of the container.
 
diff --git a/arraycontext/context.py b/arraycontext/context.py
index d064392d..61e338ab 100644
--- a/arraycontext/context.py
+++ b/arraycontext/context.py
@@ -171,12 +171,20 @@
 THE SOFTWARE.
 """
 
+
 from abc import ABC, abstractmethod
 from collections.abc import Callable, Mapping
-from typing import TYPE_CHECKING, Any, Protocol, TypeAlias, TypeVar, Union, overload
+from typing import (
+    TYPE_CHECKING,
+    Any,
+    Literal,
+    Protocol,
+    TypeAlias,
+    TypeVar,
+    overload,
+)
 from warnings import warn
 
-import numpy as np
 from typing_extensions import Self
 
 from pymbolic.typing import Integer, Scalar as _Scalar
@@ -184,6 +192,9 @@
 
 
 if TYPE_CHECKING:
+    import numpy as np
+    from numpy.typing import DTypeLike
+
     import loopy
     from pytools.tag import ToTagSetConvertible
 
@@ -243,6 +254,21 @@ def __rpow__(self, other: Self | ScalarLike) -> Array: ...
     def __truediv__(self, other: Self | ScalarLike) -> Array: ...
     def __rtruediv__(self, other: Self | ScalarLike) -> Array: ...
 
+    def copy(self) -> Self: ...
+
+    @property
+    def real(self) -> Array: ...
+    @property
+    def imag(self) -> Array: ...
+    def conj(self) -> Array: ...
+
+    def astype(self, dtype: DTypeLike) -> Array: ...
+
+    def reshape(self,
+            *shape: int,
+            order: Literal["C"] | Literal["F"]
+        ) -> Array: ...
+
 
 # deprecated, use ScalarLike instead
 Scalar = _Scalar
@@ -287,7 +313,7 @@ def __rtruediv__(self, other: Self | ScalarLike) -> Array: ...
 ContainerOrScalarT = TypeVar("ContainerOrScalarT", bound="ArrayContainer | ScalarLike")
 
 
-NumpyOrContainerOrScalar = Union[np.ndarray, "ArrayContainer", ScalarLike]
+NumpyOrContainerOrScalar: TypeAlias = "np.ndarray | ArrayContainer | ScalarLike"
 
 # }}}
 
@@ -476,7 +502,7 @@ def tag(self,
     @abstractmethod
     def tag_axis(self,
                  iaxis: int, tags: ToTagSetConvertible,
-                 array: ArrayOrContainerOrScalarT) -> ArrayOrContainerOrScalarT:
+                 array: ArrayOrContainerT) -> ArrayOrContainerT:
         """If the array type used by the array context is capable of capturing
         metadata, return a version of *array* in which axis number *iaxis* has
         the *tags* applied. *array* itself is not modified. When working with
@@ -623,7 +649,7 @@ def permits_advanced_indexing(self) -> bool:
 def tag_axes(
         actx: ArrayContext,
         dim_to_tags: Mapping[int, ToTagSetConvertible],
-        ary: ArrayT) -> ArrayT:
+        ary: ArrayOrContainerT) -> ArrayOrContainerT:
     """
     Return a copy of *ary* with the axes in *dim_to_tags* tagged with their
     corresponding tags. Equivalent to repeated application of