Are objects with the same id always equal when comparing them with ==?

The paper is right. Consider the following.

class WeirdEquals:
    def __eq__(self, other):
        return False

w = WeirdEquals()
print("id(w) == id(w)", id(w) == id(w))
print("w == w", w == w)

Output is this:

id(w) == id(w) True
w == w False

id(o1) == id(o2) does not imply o1 == o2.

Let’s have a look at this Troll which overrides __eq__ to always return False.

>>> class Troll(object):
...     def __eq__(self, other):
...         return False
... 
>>> a = Troll()
>>> b = a
>>> id(a) == id(b)
True
>>> a == b
False

That being said, there should be very few examples in the standard library where the object-ids match but __eq__ can return False anyway, kudos @MarkMüller for finding a good example.

So either the objects are insane, very special (like nan), or concurrency bites you. Consider this extreme example, where Foo has a more reasonable __eq__ method (which ‘forgets’ to check the ids) and f is f is always True.

import threading

class Foo(object):
    def __init__(self):
        self.x = 1

    def __eq__(self, other):
        return isinstance(other, Foo) and self.x == other.x

f = Foo()

class MutateThread(threading.Thread):
    def run(self):
        while True:
            f.x = 2
            f.x = 1

class CheckThread(threading.Thread):
    def run(self):
        i = 1
        while True:
            if not (f == f):
                print 'loop {0}: f != f'.format(i) 
            i += 1

MutateThread().start()
CheckThread().start()

Output:

$ python eqtest.py
loop 520617: f != f
loop 1556675: f != f
loop 1714709: f != f
loop 2436222: f != f
loop 3210760: f != f
loop 3772996: f != f
loop 5610559: f != f
loop 6065230: f != f
loop 6287500: f != f
...