any() and all() on empty list?
Tim Peters
tim.peters at gmail.com
Wed Mar 29 08:46:39 CEST 2006
[Steve R. Hastings]
> 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, from the current development trunk, is what they _do_ return:
Python 2.5a0 (trunk:43410M, Mar 28 2006, 16:42:49) ...
Type "help", "copyright", "credits" or "license" for more information.
>>> any([])
False
>>> all([])
True
> Here is Guido's original article where he suggested any() and all():
> http://www.artima.com/weblogs/viewpost.jsp?thread=98196
>
> He offered this sample code for the semantics of any() and all():
>
>
>
> def any(S):
> for x in S:
> if x:
> return True
> return False
>
> def all(S):
> for x in S:
> if not x:
> return False
> return True
>
> ...
>|
> I'm completely on board with the semantics for any(). But all() bothers
> me. If all() receives an empty list, it will return True,
Yes.
> and I don't like that.
Tough ;-)
> To me, all() should be a more restrictive function than any(),
> and it bothers me to see a case where any() returns False but all()
> returns True.
There are deeper principles at work: so that endcases work out as
smoothly as possible, a "reduction" function applied to an empty
collection always arranges to return the identity element for the
reduction operation. This is the reason that sum([]) returns 0, for
example: 0 is the identity element for addition, meaning that x+0=x
for all x.
Other useful identities follow from this, and from the associativity
of most reduction operations. For example, sum(seq) = sum(seq[:i]) +
sum(seq[i:]) for any i >= 0, even if i is such that one (or both!) of
the slices on the right-hand side is empty. That wouldn't be true if
sum([]) were not 0, and arranging to make it true saves programmers
from having to deal with some otherwise special cases.
The reduction operation for any() is logical-or, and False is the
identity element for logical-or: x logical-or False = x for all
Boolean x.
Likewise the reduction operation for all() is logical-and, and True is
the identity element for that: x logical-and True = x for all Boolean
x.
Examples of other useful identities that follow from picking the
identity elements in the empty case, which hold even if `seq` is
empty:
any(seq) = not all(not x for x in seq)
all(seq) = not any(not x for x in seq)
> In the all() example, if there *are* no values in S, then none of the
> values can be != 0, and IMHO all() should return False.
That would break everything mentioned above. Think of it another way:
if all(seq) is false, shouldn't it be the case that you can point to
a specific element in seq that is false? After all (pun intended
;-)), if it's not the case that all x in seq are true, it must be the
case that some x in seq is false. But if seq is empty, there is no x
in seq that's either true or false, and in particular there's no x in
seq that's false. Since we can't exhibit an x in seq such that x is
false, saying that all(seq) is false would be very surprising to you
on some other day ;-)
> Therefore, I propose that all() should work as if it were written this way:
>
> def all(S):
> ret_val = False
>
> for x in S:
> ret_val = True
> if not x:
> return False
>
> return ret_val
>
>
> Comments?
That won't happen, for three reasons: several were given above; this
is also the convention used for universal and existential quantifiers
applied to empty sets in mathematical logic (and for much the same
reasons there); and it matches prior art in the ABC language (which is
one of Python's predecessors, and which had direct syntactic support
for universal and existential quantifiers in Boolean expressions).
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