diff --git a/arraycontext/impl/numpy/__init__.py b/arraycontext/impl/numpy/__init__.py
index 28910150feb4d0124cd633a00731cb2ff39abf37..7d724b843eb3b2b9799ad61d97bd66c7328b239e 100644
--- a/arraycontext/impl/numpy/__init__.py
+++ b/arraycontext/impl/numpy/__init__.py
@@ -30,15 +30,20 @@ OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
 THE SOFTWARE.
 """
 
-from typing import Any, Dict, Sequence, Union
+from typing import Any, Dict
 
 import numpy as np
 
 import loopy as lp
-from pytools.tag import Tag
+from pytools.tag import ToTagSetConvertible
 
 from arraycontext.container.traversal import rec_map_array_container, with_array_context
-from arraycontext.context import ArrayContext
+from arraycontext.context import (
+    ArrayContext,
+    ArrayOrContainerOrScalar,
+    ArrayOrContainerOrScalarT,
+    NumpyOrContainerOrScalar,
+)
 
 
 class NumpyNonObjectArrayMetaclass(type):
@@ -56,7 +61,7 @@ class NumpyArrayContext(ArrayContext):
 
     .. automethod:: __init__
     """
-    def __init__(self):
+    def __init__(self) -> None:
         super().__init__()
         self._loopy_transform_cache: \
                 Dict[lp.TranslationUnit, lp.TranslationUnit] = {}
@@ -72,18 +77,14 @@ class NumpyArrayContext(ArrayContext):
     def clone(self):
         return type(self)()
 
-    def empty(self, shape, dtype):
-        return np.empty(shape, dtype=dtype)
-
-    def zeros(self, shape, dtype):
-        return np.zeros(shape, dtype)
-
-    def from_numpy(self, np_array: np.ndarray):
-        # Uh oh...
-        return np_array
+    def from_numpy(self,
+                   array: NumpyOrContainerOrScalar
+                   ) -> ArrayOrContainerOrScalar:
+        return array
 
-    def to_numpy(self, array):
-        # Uh oh...
+    def to_numpy(self,
+                 array: ArrayOrContainerOrScalar
+                 ) -> NumpyOrContainerOrScalar:
         return array
 
     def call_loopy(self, t_unit, **kwargs):
@@ -119,11 +120,16 @@ class NumpyArrayContext(ArrayContext):
                          "transform_loopy_program. Sub-classes are supposed "
                          "to implement it.")
 
-    def tag(self, tags: Union[Sequence[Tag], Tag], array):
+    def tag(self,
+            tags: ToTagSetConvertible,
+            array: ArrayOrContainerOrScalarT) -> ArrayOrContainerOrScalarT:
         # Numpy doesn't support tagging
         return array
 
-    def tag_axis(self, iaxis, tags: Union[Sequence[Tag], Tag], array):
+    def tag_axis(self,
+                 iaxis: int, tags: ToTagSetConvertible,
+                 array: ArrayOrContainerOrScalarT) -> ArrayOrContainerOrScalarT:
+        # Numpy doesn't support tagging
         return array
 
     def einsum(self, spec, *args, arg_names=None, tagged=()):