How should functions be tested for equality or identity?

Python doesn't keep a canonical foo.bar object for every instance foo of class Foo. Instead, a method object is created when Python evaluates foo.bar. Thus,

foo.bar is not foo.bar

As for ==, things get messy. Python 3.8 fixed method comparison so two methods are equal if they represent the same method of the same object, but on lower versions, the behavior is inconsistent.

Python has a surprisingly large number of method object types, depending on whether the method was implemented in Python or one of the several ways methods can be implemented in C. Before Python 3.8, these method object types respond to == differently:

• For methods written in Python, == compares the methods' __func__ and __self__ attributes, returning True if the method objects represent methods implemented by the same function and bound to equal objects, rather than the same object. Thus, x.foo == y.foo will be True if x == y and foo is written in Python.
• For most "special" methods (__eq__, __repr__, etc.), if they're implemented in C, Python compares __self__ and an internal thing analogous to __func__, again returning True if the methods have the same implementation and are bound to equal objects.
• For other methods implemented in C, Python does what you'd actually expect, returning True if the method objects represent the same method of the same object.

Thus, if you run the following code on a Python version below 3.8:

class Foo(object):
    def __eq__(self, other):
        return True if isinstance(other, Foo) else NotImplemented
    def foo(self):
        pass

print(Foo().foo == Foo().foo)
print([].__repr__ == [].__repr__)
print([].append == [].append)

You get the following bizarre output:

True
True
False

To get the Python 3.8 semantics on lower versions, you can use

meth1.__self__ is meth2.__self__ and meth1 == meth2

tldr: Methods are descriptors, which is why this can happen. Use == if you really need to compare for equality.

is (in effect) tests for equality of id. So let's check that out:

>>> id(foo.bar)
4294145364L
>>> id(foo.bar)
4294145364L
>>> id(foo.bar)
4294145364L
>>> b = foo.bar
>>> id(foo.bar)
4293744796L
>>> id(foo.bar)
4293744796L
>>> b()
>>> id(foo.bar)
4293744796L
>>> b = 1
>>> id(foo.bar)
4294145364L
>>> type(foo.bar)
<type 'instancemethod'>
>>>

So, the immediate cause is that the expression foo.bar intermittently returns a different object.

If you do need to check for equality, just use ==. However, we all want to get to the bottom of this.

>>> foo.__dict__['bar']
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
KeyError: 'bar'
>>> Foo.__dict__['bar']
<function bar at 0xffe2233c>
>>> getattr(foo, 'bar')
<bound method Foo.bar of <__main__.Foo object at 0xffe2f9ac>>
>>> foo.bar
<bound method Foo.bar of <__main__.Foo object at 0xffe2f9ac>>
>>>

It looks like there's something special about bound methods.

>>> type(foo.bar)
<type 'instancemethod'>
>>> help(type(foo.bar))
Help on class instancemethod in module __builtin__:

class instancemethod(object)
 |  instancemethod(function, instance, class)
 |
 |  Create an instance method object.
 |
 |  Methods defined here:
 |
 |  __call__(...)
 |      x.__call__(...) <==> x(...)
 |
 |  __cmp__(...)
 |      x.__cmp__(y) <==> cmp(x,y)
 |
 |  __delattr__(...)
 |      x.__delattr__('name') <==> del x.name
 |
 |  __get__(...)
 |      descr.__get__(obj[, type]) -> value
 |
 |  __getattribute__(...)
 |      x.__getattribute__('name') <==> x.name
 |
 |  __hash__(...)
 |      x.__hash__() <==> hash(x)
 |
 |  __repr__(...)
 |      x.__repr__() <==> repr(x)
 |
 |  __setattr__(...)
 |      x.__setattr__('name', value) <==> x.name = value
 |
 |  ----------------------------------------------------------------------
 |  Data descriptors defined here:
 |
 |  __func__
 |      the function (or other callable) implementing a method
 |
 |  __self__
 |      the instance to which a method is bound; None for unbound methods
 |
 |  im_class
 |      the class associated with a method
 |
 |  im_func
 |      the function (or other callable) implementing a method
 |
 |  im_self
 |      the instance to which a method is bound; None for unbound methods
 |
 |  ----------------------------------------------------------------------
 |  Data and other attributes defined here:
 |
 |  __new__ = <built-in method __new__ of type object>
 |      T.__new__(S, ...) -> a new object with type S, a subtype of T

Now, notice this lists a __get__ method. That means the instancemethod object is a descriptor. As per http://docs.python.org/2/reference/datamodel.html#implementing-descriptors the expression foo.bar returns the result of (getattr(foo,'bar').__get__(foo). And that is why this value can change.

As to why it does change, I can't tell you, except that it is likely an implementation detail.