How to override comparison operators in Python

Python, like many languages, allows the behavior of operators to be customized using a scheme based on the types of objects they are applied to. The precise rules and intricacies of this customization are fairly involved, though, and most people are unaware
of their full scope. While it is sometimes valuable to be able to control the behavior of an operator to the full extent supported by Python, quite often the complexity which this results in spills over into simpler applications. This is visible as a general
tendency on the part of Python programmers to implement customizations which are correct for the narrow case which they have in mind at the moment, but are incorrect when considered in a broader context. Since many parts of the runtime and standard library
rely on the behavior of these operators, this is a somewhat more egregious than the case of a similar offense made in an application-specific method, where the author can simply claim that behavior beyond what was intended is unsupported and behaves in an
undefined manner.

So, with my long-winded introduction out of the way, here are the basic rules for the customization of ==, !=, <, >, <=, and >=:

• For all six of the above operators, if __cmp__ is defined on the left-hand argument, it is called with the right-hand argument. A result of -1 indicates the LHS is less than the RHS. A result of 0 indicates they are
  equal. A result of 1 indicates the LHS is greater than the RHS.
• For ==, if __eq__ is defined on the left-hand argument, it is called with the right hand argument. A result of True indicates the objects are equal. A result of False indicates they are not equal. A result ofNotImplemented indicates
  that the left-hand argument doesn't know how to test for equality with the given right-hand argument. __eq__ is not used for !=.
• For !=, the special method __ne__ is used. The rules for its behavior are similar to those of __eq__, with the obvious adjustments.
• For <, __lt__ is used. For >, __gt__. For <= and >=, __le__ and __ge__ respectively.

So how should these be applied? This is best explained with an example. While __cmp__ is often useful, I am going to ignore it for the rest of this post, since it is easier to get right, particularly onceNotImplemented (which I will
talk about) is understood.

class A(object):    def __init__(self, foo):        self.foo = foo    def __eq__(self, other):        if isinstance(other, A):            return self.foo == other.foo        return NotImplemented    def __ne__(self, other):        result = self.__eq__(other)        if result is NotImplemented:            return result        return not result

That's it (because I'm not going to define the other four methods to make <, >, <=, and >= work. They follow basically the same rules as __eq__ and __ne__, though). Pretty straightforward, but there are some points which are not always
obvious:

• __eq__ does an isinstance test on its argument. This lets it know if it is dealing with another object which is like itself. In the case of this example, I have implemented A to only know how to compare itself with other
  instances of A. If it is called with something which is not an A, it returns NotImplemented. I'll explain what the consequences of this are below.
• __ne__ is also implemented, but only in terms of __eq__. If you implement __eq__ but not __ne__, then == and != will behave somewhat strangely, since the default implementation
  of __ne__ is based on identity, not the negation of equality. Quite often a class with only __eq__ will appear to work properly with !=, but it fails for various corner-cases (for example, an object which does not compare equal to
  itself, such as NaN).

The major remaining point is NotImplemented: what is that thing? NotImplemented signals to the runtime that it should ask someone else to satisfy the operation. In the expression a == b, if a.__eq__(b)returns NotImplemented,
then Python tries b.__eq__(a). If b knows enough to return True or False, then the expression can succeed. If it doesn't, then the runtime will fall back to the built-in behavior (which is based on identity for == and !=).

Here's another class which customizes equality:

class B(object):    def __init__(self, bar):        self.bar = bar    def __eq__(self, other):        if isinstance(other, B):            return self.bar == other.bar        elif isinstance(other, A):            return self.bar + 3 == other.foo        else:            return NotImplemented    def __ne__(self, other):        result = self.__eq__(other)        if result is NotImplemented:            return result        return not result

Here we have a class which can compare instances of itself to both instances itself and to instances of A. Now, what would happen if we weren't careful about returning NotImplemented at the right times?

One way it might go is...

>>> class A(object):...     def __init__(self, foo):...             self.foo = foo...     def __eq__(self, other):...             return self.foo == other.foo...>>> class B(object):...     def __init__(self, bar):...             self.bar = bar...>>> A(5) == B(6)Traceback (most recent call last):  File "<stdin>", line 1, in ?  File "<stdin>", line 5, in __eq__AttributeError: 'B' object has no attribute 'foo'>>>

Another way it could go is...

>>> class A(object):...     def __init__(self, foo):...             self.foo = foo...     def __eq__(self, other):...             if isinstance(other, A):...                     return self.foo == other.foo...>>> class B(object):...     def __init__(self, bar):...             self.bar = bar...     def __eq__(self, other):...             if isinstance(other, A):...                     return self.bar + 3 == other.foo...             else:...                     return self.bar == other.bar...>>> print A(3) == B(0)None>>> print B(0) == A(3)True>>>

That one's particularly nasty. But here's what we get with correct NotImplemented use:

>>> class A(object):...     def __init__(self, foo):...             self.foo = foo...     def __eq__(self, other):...             if isinstance(other, A):...                     return self.foo == other.foo...             return NotImplemented...>>> class B(object):...     def __init__(self, bar):...             self.bar = bar...     def __eq__(self, other):...             if isinstance(other, A):...                     return self.bar + 3 == other.foo...             elif isinstance(other, B):...                     return self.bar == other.bar...             else:...                     return NotImplemented...>>> print A(3) == B(0)True>>> print B(0) == A(3)True>>>

Ahh, excellent. NotImplemented has uses for other operators in Python as well. For example, if the + override, __add__, returns it, then __radd__ is tried on the right-hand argument. These can be useful as well, though
equality and inequality are by far more common use cases.

If you follow these examples, then in the general case you'll find yourself with more consistently behaving objects. You may even want to implement a mixin which provides the __ne__ implementation (and one of __lt__ or __gt__),
since it gets pretty boring typing that out after a few times.

Of course, there are plenty of special cases where it makes sense to deviate from this pattern. However, they are special. For most objects, this is the behavior you want.

You can read about all the gory details of Python's operator overloading system on the Python website: http://docs.python.org/ref/specialnames.html