diff --git a/loopy/kernel/array.py b/loopy/kernel/array.py
index 1f10e01a726d5d7e4e0171cb439cb53ab1163e05..5d4240b9ab3e1ce2ad356a93b5e21b3bbf4d499e 100644
--- a/loopy/kernel/array.py
+++ b/loopy/kernel/array.py
@@ -887,6 +887,7 @@ class ArrayBase(ImmutableRecord):
         :class:`pytools.persistent_dict.PersistentDict`.
         """
 
+        key_builder.rec(key_hash, type(self).__name__.encode("utf-8"))
         key_builder.rec(key_hash, self.name)
         key_builder.rec(key_hash, self.dtype)
         self.update_persistent_hash_for_shape(key_hash, key_builder, self.shape)
diff --git a/loopy/tools.py b/loopy/tools.py
index 69a25b375cac5ac519182c71160d4d9b476c4c65..4acea7cff1cc66e1e3860b43895761c67b684e11 100644
--- a/loopy/tools.py
+++ b/loopy/tools.py
@@ -51,7 +51,12 @@ class PersistentHashWalkMapper(LoopyWalkMapper, PersistentHashWalkMapperBase):
     See also :meth:`LoopyKeyBuilder.update_for_pymbolic_expression`.
     """
 
-    # <empty implementation>
+    def map_reduction(self, expr, *args):
+        if not self.visit(expr):
+            return
+
+        self.key_hash.update(type(expr.operation).__name__.encode("utf-8"))
+        self.rec(expr.expr, *args)
 
 
 class LoopyKeyBuilder(KeyBuilderBase):