any() and all() on empty list?

[Paul McGuire]

"Steve R. Hastings" <steve at hastings.org> wrote in message
news:pan.2006.03.29.05.32.50.221097 at hastings.org...
> So, Python 2.5 will have new any() and all() functions.
> http://www.python.org/dev/peps/pep-0356/
>
>
> any(seq) returns True if any value in seq evaluates true, False otherwise.
>
> all(seq) returns True if all values in seq evaluate true, False otherwise.
>
> I have a question: what should these functions return when seq is an empty
> list?
>
Here is my attempt at a more formal approach to this question, rather than
just using our intuition.  Unfortunately, following this process proves my
earlier post to be wrong, but, oh well...

Consider two sets A and B where A+B is the union of the two sets.

if any(A+B) = True -> any(A) or any(B) = True
but we cannot assert either any(A)=True or any(B)=True.

if any(A+B) = False -> any(A) = False and any(B) = False.


if all(A+B) = True -> all(A)=True and all(B)=True
if all(A+B) = False -> all(A)=False or all(B)=False
but we cannot assert either all(A)=False or all(B)=False.


Now instead of B, lets add the empty set 0 to A.  We want to come up logic
such that adding the empty set does not change the values of all() or any(),
since A+0=A.

any(A+0) = any(A) or any(0)

any(0) must be False, so that if any(A) is True, any(A+0) is True, and if
any(A) is False, any(A+0) is False.

all(A+0) = all(A) and all(0)

if all(A) is True, all(A+0) is True.
Therefore, all(0) is True.

-- Paul