diff --git a/loopy/symbolic.py b/loopy/symbolic.py
index 55658f696..4a67d69f5 100644
--- a/loopy/symbolic.py
+++ b/loopy/symbolic.py
@@ -931,8 +931,8 @@ def is_tuple_typed(self) -> bool:
         return self.operation.arg_count > 1
 
     @cached_property
-    def inames_set(self) -> set[str]:
-        return set(self.inames)
+    def inames_set(self) -> frozenset[str]:
+        return frozenset(self.inames)
 
 
 @p.expr_dataclass()