diff --git a/loopy/library/reduction.py b/loopy/library/reduction.py
index 865ed1d66fd060716743b0c8ee499c3b05f017cb..650d1e45218ff21a8140288cb3e84762b98046ef 100644
--- a/loopy/library/reduction.py
+++ b/loopy/library/reduction.py
@@ -40,6 +40,14 @@ class ReductionOperation(object):
     def neutral_element(self, dtype, inames):
         raise NotImplementedError
 
+    def __hash__(self):
+        # Force subclasses to override
+        raise NotImplementedError
+
+    def __eq__(self, other):
+        # Force subclasses to override
+        raise NotImplementedError
+
     def __call__(self, dtype, operand1, operand2, inames):
         raise NotImplementedError
 
@@ -142,6 +150,12 @@ class _ArgExtremumReductionOperation(ReductionOperation):
     def neutral_element(self, dtype, inames):
         return ArgExtFunction(self, dtype, "init", inames)()
 
+    def __hash__(self):
+        return hash(type(self))
+
+    def __eq__(self, other):
+        return type(self) == type(other)
+
     def __call__(self, dtype, operand1, operand2, inames):
         iname, = inames