diff --git a/src/primitives.py b/src/primitives.py
index f4003b0b6b5affe8ac4a936f27cf1f17ca45ad05..2caec17f547af34ff4415e1f62a9d6ed7a7c3ebd 100644
--- a/src/primitives.py
+++ b/src/primitives.py
@@ -9,9 +9,6 @@ class Expression(object):
     Expression objects are immutable.
     """
 
-    def __ne__(self, other):
-        return not self.__eq__(other)
-
     def __add__(self, other):
         if not is_valid_operand(other):
             return NotImplemented
@@ -136,13 +133,44 @@ class Expression(object):
 
         return "%s(%s)" % (self.__class__.__name__, initargs_str)
 
+    # hashable interface ------------------------------------------------------
+    def __eq__(self, other):
+        """Provides equality testing with quick positive and negative paths
+        based on L{id} and L{__hash__}().
+
+        Subclasses should generally not override this method, but instead 
+        provide an implementation of L{is_equal}.
+        """
+        if id(self) == id(other):
+            return True
+        elif hash(self) != hash(other):
+            return False
+        else:
+            return self.is_equal(other)
+
+    def __ne__(self, other):
+        return not self.__eq__(other)
+
     def __hash__(self):
+        """Provides caching for hash values.
+
+        Subclasses should generally not override this method, but instead 
+        provide an implementation of L{get_hash}.
+        """
         try:
             return self.hash_value
         except AttributeError:
             self.hash_value = self.get_hash()
             return self.hash_value
 
+    # hashable backend --------------------------------------------------------
+    def is_equal(self, other):
+        return NotImplemented
+
+    def get_hash(self, other):
+        raise NotImplementedError
+
+
 
 
 
@@ -188,7 +216,7 @@ class Variable(Leaf):
         else:
             return NotImplemented
 
-    def __eq__(self, other):
+    def is_equal(self, other):
         return (isinstance(other, Variable) 
                 and self.name == other.name)
 
@@ -206,7 +234,7 @@ class Call(AlgebraicLeaf):
     def __getinitargs__(self):
         return self.function, self.parameters
 
-    def __eq__(self, other):
+    def is_equal(self, other):
         return isinstance(other, Call) \
                and (self.function == other.function) \
                and (self.parameters == other.parameters)
@@ -228,7 +256,7 @@ class Subscript(AlgebraicLeaf):
     def __getinitargs__(self):
         return self.aggregate, self.index
 
-    def __eq__(self, other):
+    def is_equal(self, other):
         return isinstance(other, Subscript) \
                and (self.aggregate == other.aggregate) \
                and (self.index == other.index)
@@ -250,7 +278,7 @@ class Lookup(AlgebraicLeaf):
     def __getinitargs__(self):
         return self.aggregate, self.name
 
-    def __eq__(self, other):
+    def is_equal(self, other):
         return isinstance(other, Lookup) \
                and (self.aggregate == other.aggregate) \
                and (self.name == other.name)
@@ -273,7 +301,7 @@ class Sum(Expression):
     def __getinitargs__(self):
         return self.children
 
-    def __eq__(self, other):
+    def is_equal(self, other):
         return (isinstance(other, Sum) 
                 and (set(self.children) == set(other.children)))
 
@@ -331,7 +359,7 @@ class Product(Expression):
     def __getinitargs__(self):
         return self.children
 
-    def __eq__(self, other):
+    def is_equal(self, other):
         return (isinstance(other, Product) 
                 and (set(self.children) == set(other.children)))
 
@@ -388,7 +416,7 @@ class Quotient(Expression):
     def den(self):
         return self.denominator
 
-    def __eq__(self, other):
+    def is_equal(self, other):
         from pymbolic.rational import Rational
         return isinstance(other, (Rational, Quotient)) \
                and (self.numerator == other.numerator) \
@@ -414,7 +442,7 @@ class Power(Expression):
     def __getinitargs__(self):
         return self.base, self.exponent
 
-    def __eq__(self, other):
+    def is_equal(self, other):
         return isinstance(other, Power) \
                and (self.base == other.base) \
                and (self.exponent == other.exponent)