diff --git a/arraycontext/impl/pytato/utils.py b/arraycontext/impl/pytato/utils.py
index affa1da3..e50207af 100644
--- a/arraycontext/impl/pytato/utils.py
+++ b/arraycontext/impl/pytato/utils.py
@@ -23,7 +23,7 @@
 """
 
 from collections.abc import Mapping
-from typing import TYPE_CHECKING, Any
+from typing import TYPE_CHECKING, Any, cast
 
 from pytato.array import (
     AbstractResultWithNamedArrays,
@@ -71,7 +71,7 @@ def map_data_wrapper(self, expr: DataWrapper) -> Array:
         self.bound_arguments[name] = expr.data
         return make_placeholder(
                     name=name,
-                    shape=tuple(self.rec(s) if isinstance(s, Array) else s
+                    shape=tuple(cast(Array, self.rec(s)) if isinstance(s, Array) else s
                                 for s in expr.shape),
                     dtype=expr.dtype,
                     axes=expr.axes,
@@ -87,7 +87,7 @@ def map_placeholder(self, expr: Placeholder) -> Array:
 
 def _normalize_pt_expr(
         expr: DictOfNamedArrays
-        ) -> tuple[AbstractResultWithNamedArrays, Mapping[str, Any]]:
+        ) -> tuple[Array | AbstractResultWithNamedArrays, Mapping[str, Any]]:
     """
     Returns ``(normalized_expr, bound_arguments)``.  *normalized_expr* is a
     normalized form of *expr*, with all instances of