PEP 285: Adding a bool type

[Tim Peters]

[Pearu Peterson]
> Theorem:
> ========
> Assume specification of PEP 285. The following statements hold truth:
>
>   True is One
>
> and
>
>   False is Zero,
>
> where One and Zero represent integers 1 and 0, respectively.

The theorem is false; it would be true if you replaced "is" by "==".

> Proof:
> ------
> According to PEP, True and False are instances of bool that is a
> subclass of int.

True.

> Therefore True and False can be considered as integers

Unclear what that means, exactly.

> and it makes sense to compare them with integers.

Except "is", in terms of which your theorem is stated, is a special kind of
comparison that can reveal non-guaranteed implementation accidents.  To cut
this short, there's no guarantee that even

    0 is 0

returns true, although it *happens* to be true in all implementations of
CPython to date (although for different internal reasons in different
implementations!).  The PEP *does* guarantee that

    True is True
    False is False

are true; that's a stronger guarantee than is made for integers.

> If n is an integer then the following statements hold
>
>   True == n   only if n is 1

Only if you're using a non-Python meaning for "is".  A true statement using
Python meanings would be

    True == n   if and only if   n == 1

Note that this covers cases like

    True == 1.0

too.

> ...