Why is a method not identical to itself?

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When you ask for an instance attribute which is a function, you get a bound method: a callable object which wraps the function defined in the class and passes the instance as the first argument. In Python 2.x, when you ask for a class attribute which is a function, you get a similar proxy object called an unbound method:

>>> class A:
...     def m():
...         return None
... 
>>> A.m
<unbound method A.m>

This special object is created when you ask for it, and not apparently cached anywhere. That means that when you do

>>> A.m is A.m
False

you are creating two distinct unbound method objects and testing them for identity.

Notice that these work fine:

>>> x = A.m
>>> x is x
True

and

>>> A.m.im_func is A.m.im_func
True

(im_func is the original function which the unbound method object is wrapping.)

In Python 3.x, incidentally, C.m is C.m is True, because the (somewhat pointless) unbound method proxy objects were removed entirely and you just get the original function which you defined.

This is just one example of the very dynamic nature of attribute lookup in Python: when you ask for an attribute of an object, it is possible to run arbitrary code to calculate the value of that attribute. Here’s another example where your test fails in which it is much clearer why:

>>> class ChangingAttribute(object):
...     @property
...     def n(self):
...         self._n += 1
...         return self._n
... 
...     def __init__(self):
...         self._n = 0
... 
>>> foo = ChangingAttribute()
>>> foo.n
1
>>> foo.n
2
>>> foo.n
3
>>> foo.n is foo.n
False
>>> foo.n
6

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