diff --git a/pytools/__init__.py b/pytools/__init__.py
index 6eb69004..77fca6bf 100644
--- a/pytools/__init__.py
+++ b/pytools/__init__.py
@@ -1385,7 +1385,7 @@ def indices_in_shape(shape):
 
 
 def generate_nonnegative_integer_tuples_below(
-        n: tuple[int, ...] | int, length: int | None = None, least: int = 0
+        n: Sequence[int] | int, length: int | None = None, least: int = 0
         ) -> Iterator[tuple[int, ...]]:
     """n may be a sequence, in which case length must be None."""
     if length is None:
@@ -1477,7 +1477,10 @@ def generate_all_integer_tuples_below(
         n, length, least_abs))
 
 
-class _ConcatenableSequence(Protocol):
+T_co = TypeVar("T_co", covariant=True)
+
+
+class _ConcatenableSequence(Generic[T_co], Protocol):
     """
     A protocol that supports the following:
 
@@ -1494,10 +1497,13 @@ def __add__(self, other: Self) -> Self:
     def __len__(self) -> int:
         ...
 
+    def __iter__(self) -> Iterator[T_co]:
+        ...
+
 
 def generate_permutations(
-            original: _ConcatenableSequence
-        ) -> Iterator[_ConcatenableSequence]:
+            original: _ConcatenableSequence[T]
+        ) -> Iterator[_ConcatenableSequence[T]]:
     """Generate all permutations of the list *original*.
 
     Nicked from http://aspn.activestate.com/ASPN/Cookbook/Python/Recipe/252178
@@ -1512,8 +1518,8 @@ def generate_permutations(
 
 
 def generate_unique_permutations(
-            original: _ConcatenableSequence
-        ) -> Iterator[_ConcatenableSequence]:
+            original: _ConcatenableSequence[T]
+        ) -> Iterator[_ConcatenableSequence[T]]:
     """Generate all unique permutations of the list *original*.
 
     Note that, unlike for :func:`generate_permutations`, *original* must be a