On scoring builtin functions

Question

Suppose there's a challenge which can be solved completely by a builtin function, and functions are allowed. Note that as of writing the standard loophole for builtins is heavily disputed, but let's just assume that the poster explicitly allowed builtins since that's not the point of this question.

Which of the following submissions would be valid? To give a more concrete example, let's say the task was adding a list of numbers.

                   0 bytes, since the user can use the function already
sum                3 bytes, an expression which evaluations to a function
s=sum              5 bytes, aliasing the builtin
lambda L:sum(L)    15 bytes, an explicit unnamed function

Similarly, if the task was to multiply two numbers, would the following be valid? Or rather, is it possible that the following is only valid in languages which treat operators in a certain way?

*                  1 byte, multiplication operator

(For context, this question was inspired by the Calculate Standard Deviation question)

Answer 1

Code that purports to define a function should only be accepted if it actually causes the function to be defined. That is, the function should not be defined before/without that code running.

Accordingly, the empty string is not a valid function answer. s=sum is valid because it defines a function s that did not exist before. sum and lambda L:sum(L) are valid because expressions that evaluate to a function are an accepted answer form. However, an unnamed expression may only be used if the entire answer is the expression; it may not be part of a larger program. * is not a valid answer in Python because it is neither an expression nor any other kind of executable code.

Answer 2

Since feersum edited his answer and the edit conflicts with the common interpretation of the text (which is how we've been doing things since that answer was posted), I'll repost the text of his answer prior to the edit so that we still have an answer here reflecting that practice.

Code that purports to define a function should only be accepted if it actually causes the function to be defined. That is, the function should not be defined before/without that code running.

Accordingly, the empty string is not a valid function answer. s=sum is valid because it defines a function s that did not exist before. sum and lambda L:sum(L) are valid because expressions that evaluate to a function are an accepted answer form. * is not a valid answer in Python because it is neither an expression nor any other kind of executable code.

It is acceptable to post a defined function along with an import, such as the pseudocode import math; sum. (This is what was declined by the edit.)

Answer 3

For challenges that accept functions as answers, a submission should be valid if after being run, there exists a function that does exactly as the challenge asks.

Thus, the zero byte submission is valid, if the builtin function accepts input in a way that perfectly conforms to the challenge specifications; if it is even slightly different (such as taking extra parameters), then the zero byte submission is invalid.