Today I learned how the rich comparison protocol and, in particular, how eq works behind the scenes.

Rich comparison

Prelude

The rich comparisons are just the comparison operators we are used to: <, <=, ==, >=, >, and !=.

Much like other pieces of Python syntax, using these operators actually calls dunder methods behind the scenes. In this short article I'll write about == and its corresponding __eq__ dunder method.

The __eq__ dunder method is responsible for telling Python objects if they are, or are not, equal to each other:

>>> class Person:
...     def __init__(self, name):
...         self.name = name
...     def __eq__(self, other):
...         return self.name == other.name
...
>>> Person("Rodrigo") == Person("Jack")
False
>>> Person("Rodrigo") == Person("Rodrigo")
True

In the example above, we make it so that any two Person instances with the same name are “equal”.

What's interesting is that object implements its version of __eq__, and it's more or less equivalent to the following:

class object:
    def __eq__(self, other):
        return True if self is other else NotImplemented

This means that, by default, objects you create will only be “equal” to each other when they are the same object:

>>> class Obj:
...     pass
...
>>> o1 = Obj(); o2 = Obj()
>>> o1 == o1
True
>>> o1 == o2
False
>>> o1 is o1
True
>>> o1 is o2
False

But why does object.__eq__ return NotImplemented instead of False when the objects are not the same?

That has to do with how the rich comparison protocol actually works.

In general, the code a == b calls a.__eq__(b). But if a.__eq__(b) returns NotImplemented, then b.__eq__(a) is called. That's why object.__eq__ returns NotImplemented: to give a chance to the other object to do its own comparison.

This makes sense: for example, you might create your own objects that you'd like to be able to compare to the built-in types. Now, obviously the built-in types won't be able to compare themselves to your custom objects, but your objects can implement __eq__ and that will suffice!

Comparisons return Booleans and methods return NotImplemented

All of the above makes a lot of sense. At least, it made to me. What threw me off was this excerpt from the REPL:

>>> 3 == "3"
False
>>> (3).__eq__("3")
NotImplemented
>>> "3".__eq__(3)
NotImplemented

As we can see, 3 == "3" obviously returns False, as we all expect. However, explicitly calling the __eq__ method of int with the string returns NotImplemented, and similar when we call str's __eq__ method!

In English, it looks like this is what's happening:

• int says “I don't know how to compare myself to strings”;
• at which point, Python says “fine, let's try to compare strings to ints instead”; and then
• str says “I don't know how to compare myself to ints”.

Even after all this, we can clearly see that 3 and "3" were successfully compared (and the final result is False).

After reading the docs on rich comparisons a couple of times (ok, a couple dozen times), and after taking a look at Brett Cannon's blog post on rich comparisons, I eventually ended up staring at the C code that solves my conundrum:

== is special-cased

== and != never fail. What this means is that they always return a Boolean value!

So, in a way, the C code special-cases this!

If a == or != comparison ends up at a NotImplemented, then the C code itself will return an appropriate Boolean value.

It's these lines of code that matter:

    /* If neither object implements it, provide a sensible default
       for == and !=, but raise an exception for ordering. */
    switch (op) {
    case Py_EQ:
        res = (v == w) ? Py_True : Py_False;
        break;

If the comparison operator (op) is the equality, we return True or False according to whether the C objects representing the two operands are the same or not.

Immediately above this special case, we can see the C code that handles the rich comparison protocol, which is responsible for, for example, checking b.__eq__(a) when a.__eq__(b) fails for a == b.

That's it for now! Stay tuned and I'll see you around!

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References

• CPython source code on GitHub, https://github.com/python/cpython [last accessed 03-11-2021];
• Python 3 Docs, The Python Language Reference, Data model, rich comparisons https://docs.python.org/3/reference/datamodel.html#object.lt [last accessed 03-11-2021];
• “Unravelling rich comparison operators”, Brett Cannon, https://snarky.ca/unravelling-rich-comparison-operators/ [last accessed 03-11-2021];