diff --git a/src/awkward/_nplikes/array_module.py b/src/awkward/_nplikes/array_module.py
index 23b1128292..88d5d93de7 100644
--- a/src/awkward/_nplikes/array_module.py
+++ b/src/awkward/_nplikes/array_module.py
@@ -17,7 +17,7 @@
 )
 from awkward._nplikes.placeholder import PlaceholderArray
 from awkward._nplikes.shape import ShapeItem, unknown_length
-from awkward._typing import Any, Final, Literal
+from awkward._typing import Any, cast, Final, Literal, DType
 
 np = NumpyMetadata.instance()
 NUMPY_HAS_NEP_50 = packaging.version.Version(
@@ -37,7 +37,8 @@ def _nplike_concatenate_has_casting(module: Any) -> bool:
 
 
 class ArrayModuleNumpyLike(NumpyLike):
-    known_data: Final = True
+    known_data: Final[bool] = True
+    _module: Any
 
     def prepare_ufunc(self, ufunc: UfuncLike) -> UfuncLike:
         return ufunc
@@ -48,7 +49,7 @@ def asarray(
         self,
         obj,
         *,
-        dtype: numpy.dtype | None = None,
+        dtype: DType | None = None,
         copy: bool | None = None,
     ) -> ArrayLike:
         if isinstance(obj, PlaceholderArray):
@@ -73,7 +74,7 @@ def ascontiguousarray(self, x: ArrayLike) -> ArrayLike:
             return self._module.ascontiguousarray(x)
 
     def frombuffer(
-        self, buffer, *, dtype: np.dtype | None = None, count: ShapeItem = -1
+        self, buffer, *, dtype: DType | None = None, count: ShapeItem = -1
     ) -> ArrayLike:
         if isinstance(buffer, PlaceholderArray):
             raise TypeError("placeholder arrays are not supported in `frombuffer`")
@@ -83,39 +84,43 @@ def from_dlpack(self, x: Any) -> ArrayLike:
         return self._module.from_dlpack(x)
 
     def zeros(
-        self, shape: int | tuple[int, ...], *, dtype: np.dtype | None = None
+        self, shape: ShapeItem | tuple[ShapeItem, ...], *, dtype: DType | None = None
     ) -> ArrayLike:
         return self._module.zeros(shape, dtype=dtype)
 
     def ones(
-        self, shape: int | tuple[int, ...], *, dtype: np.dtype | None = None
+        self, shape: ShapeItem | tuple[ShapeItem, ...], *, dtype: DType | None = None
     ) -> ArrayLike:
         return self._module.ones(shape, dtype=dtype)
 
     def empty(
-        self, shape: int | tuple[int, ...], *, dtype: np.dtype | None = None
+        self, shape: ShapeItem | tuple[ShapeItem, ...], *, dtype: DType | None = None
     ) -> ArrayLike:
         return self._module.empty(shape, dtype=dtype)
 
     def full(
-        self, shape: int | tuple[int, ...], fill_value, *, dtype: np.dtype | None = None
+        self,
+        shape: ShapeItem | tuple[ShapeItem, ...],
+        fill_value,
+        *,
+        dtype: DType | None = None,
     ) -> ArrayLike:
         return self._module.full(shape, fill_value, dtype=dtype)
 
-    def zeros_like(self, x: ArrayLike, *, dtype: np.dtype | None = None) -> ArrayLike:
+    def zeros_like(self, x: ArrayLike, *, dtype: DType | None = None) -> ArrayLike:
         if isinstance(x, PlaceholderArray):
             return self.zeros(x.shape, dtype=dtype or x.dtype)
         else:
             return self._module.zeros_like(x, dtype=dtype)
 
-    def ones_like(self, x: ArrayLike, *, dtype: np.dtype | None = None) -> ArrayLike:
+    def ones_like(self, x: ArrayLike, *, dtype: DType | None = None) -> ArrayLike:
         if isinstance(x, PlaceholderArray):
             return self.ones(x.shape, dtype=dtype or x.dtype)
         else:
             return self._module.ones_like(x, dtype=dtype)
 
     def full_like(
-        self, x: ArrayLike, fill_value, *, dtype: np.dtype | None = None
+        self, x: ArrayLike, fill_value, *, dtype: DType | None = None
     ) -> ArrayLike:
         if isinstance(x, PlaceholderArray):
             return self.full(x.shape, fill_value, dtype=dtype or x.dtype)
@@ -128,7 +133,7 @@ def arange(
         stop: float | int | None = None,
         step: float | int = 1,
         *,
-        dtype: np.dtype | None = None,
+        dtype: DType | None = None,
     ) -> ArrayLike:
         assert not isinstance(start, PlaceholderArray)
         assert not isinstance(stop, PlaceholderArray)
@@ -230,7 +235,7 @@ def _compute_compatible_shape(
     ) -> tuple[ShapeItem, ...]:
         next_shape = list(shape)
         j = None
-        length_factor = 1
+        length_factor: ShapeItem = 1
         for i, item in enumerate(shape):
             if item != -1:
                 length_factor *= item
@@ -313,6 +318,8 @@ def regularize_index_for_length(
 
         Returns regularized index that is guaranteed to be in-bounds.
         """  # We have known length and index
+        length = cast(int, length)
+
         if index < 0:
             index = index + length
 
@@ -429,12 +436,12 @@ def broadcast_to(self, x: ArrayLike, shape: tuple[ShapeItem, ...]) -> ArrayLike:
     def strides(self, x: ArrayLike) -> tuple[ShapeItem, ...]:
         if isinstance(x, PlaceholderArray):
             # Assume contiguous
-            strides = (x.itemsize,)
+            strides: tuple[int, ...] = (x.itemsize,)
             for item in x.shape[-1:0:-1]:
                 strides = (item * strides[0], *strides)
             return strides
 
-        return x.strides
+        return x.strides  # type: ignore[attr-defined]
 
     ############################ ufuncs
 
@@ -517,7 +524,7 @@ def all(
         self,
         x: ArrayLike,
         *,
-        axis: int | tuple[int, ...] | None = None,
+        axis: ShapeItem | tuple[ShapeItem, ...] | None = None,
         keepdims: bool = False,
         maybe_out: ArrayLike | None = None,
     ) -> ArrayLike:
@@ -528,7 +535,7 @@ def any(
         self,
         x: ArrayLike,
         *,
-        axis: int | tuple[int, ...] | None = None,
+        axis: ShapeItem | tuple[ShapeItem, ...] | None = None,
         keepdims: bool = False,
         maybe_out: ArrayLike | None = None,
     ) -> ArrayLike:
@@ -539,7 +546,7 @@ def min(
         self,
         x: ArrayLike,
         *,
-        axis: int | tuple[int, ...] | None = None,
+        axis: ShapeItem | tuple[ShapeItem, ...] | None = None,
         keepdims: bool = False,
         maybe_out: ArrayLike | None = None,
     ) -> ArrayLike:
@@ -550,7 +557,7 @@ def max(
         self,
         x: ArrayLike,
         *,
-        axis: int | tuple[int, ...] | None = None,
+        axis: ShapeItem | tuple[ShapeItem, ...] | None = None,
         keepdims: bool = False,
         maybe_out: ArrayLike | None = None,
     ) -> ArrayLike:
@@ -558,7 +565,7 @@ def max(
         return self._module.max(x, axis=axis, keepdims=keepdims, out=maybe_out)
 
     def count_nonzero(
-        self, x: ArrayLike, *, axis: int | tuple[int, ...] | None = None
+        self, x: ArrayLike, *, axis: ShapeItem | tuple[ShapeItem, ...] | None = None
     ) -> ArrayLike:
         assert not isinstance(x, PlaceholderArray)
         assert isinstance(axis, int) or axis is None
@@ -594,9 +601,9 @@ def astype(
         self, x: ArrayLike, dtype: numpy.dtype, *, copy: bool | None = True
     ) -> ArrayLike:
         assert not isinstance(x, PlaceholderArray)
-        return x.astype(dtype, copy=copy)
+        return x.astype(dtype, copy=copy)  # type: ignore
 
-    def can_cast(self, from_: np.dtype | ArrayLike, to: np.dtype | ArrayLike) -> bool:
+    def can_cast(self, from_: DType | ArrayLike, to: DType | ArrayLike) -> bool:
         return self._module.can_cast(from_, to, casting="same_kind")
 
     @classmethod