class A:
   def __init__(self,a):
     self.a = a
   def __eq__(self, other):
     return self.a == other.a

class B:
   def __init__(self,b):
     self.b = b
   def __eq__(self, other):
     return self.b == other.b

A(1) == B(1)
---> AttributeError: B instance has no attribute a

B(1) == A(1)
---> AttributeError: A instance has no attribute b

 From the above, it seems that Python always uses the function defined
by the class on the LEFT.  However, I don't understand the following then:

A(1) == 3
---> AttributeError: 'int' object has no attribute a

3 == A(1)
---> AttributeError: 'int' object has no attribute a

 class A:
    def __init__(self,a):
      self.a = a
    def __eq__(self, other):
      print "(A) self:%r, other:%r" %(self.__class__, other.__class__)
      return self.a == other.a

 class B:
    def __init__(self,b):
      self.b = b
    def __eq__(self, other):
      print "(B) self:%r, other:%r" %(self.__class__, other.__class__)
      return self.b == other.b

You are correct, Python evaluates the expressions from left to right.

The last of the four tests that you have mentioned is giving you the
trouble, right? Perhaps the solution is to add type-checking to the
__eq__ method?

(untested)
def __eq__(self, other):
  if isinstance(other, int):
    tmp = other
  else:
    tmp = other.a   # (other.b in class B definition)
  return self.a == tmp   # (self.b in class B definition)