Why Python built in "all" function returns True for empty iterables?

Question

I know it has a good reason, but I want to know what reason?

>>> print all([])
True

If all() is intended to check if every item on iterable evaluates to "True", and we know empty lists are evaluated to False

>>> bool([])
False

So why the all() returns True for empty lists?

< edit >

I already read the docs, and I know the implementation

 def all(iterable):
    for element in iterable:
        if not element:
            return False
    return True

But the question is why not?

def all(iterable):
    if not iterable:
        return False
    for element in iterable:
        if not element:
            return False
    return True

There is a logic on this? if you have a list of done-tasks

today_todo_status = [task.status for task in my_todo if task.date == today]
can_i_go_home = all(today_todo_status)

Ok, on the above hypothetical example it really makes sense, if I have no tasks, so I can go home.

But there are other cases and I dont think all() was made for todo lists.. LOL

< /edit >

Answer 1

This is expressed as "For all X in S, X is true". If S is empty, there are no X. However, the truth statement remains True, because for all X, X was true... there just aren't any X!

Here is a explanation using logic.

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, let's add the empty set Ø 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+Ø=A.

any(A+Ø) = any(A) or any(Ø)

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

all(A+Ø) = all(A) and all(Ø)

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

Answer 2

all() (documented to "Return True if all elements of the iterable are true (or if the iterable is empty).") is equivalent to the following:

def all(iterable):
    for element in iterable:
        if not element:
            return False
    return True

Since there are no elements, it will skip the loop and return True.

Answer 3

Suppose all([]) is False.

Then, for all non empty list A, all(A + []) should be also False as

all(A + []) = all(A) and all([])
            = all(A) and False
            = False

Since A + [] = A, we know

all(A + []) = all(A) for any non empty list A

But, all(A) could be True (e.g., A = [True])

Hence,

for all non empty list A, all(A + []) should be also False

This contradicts. As a result, the first assumption is wrong and

all([]) is True