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I have a nested function as follow:

def make_adder(n):
    def add(x):
        return x + n
    return add
>>> plus_3 = make_adder(3)
>>> plus_5 = make_adder(5)
>>> plus_3(4) 7
>>> plus_5(4) 9

What's the formal names of make_adder and add?
Can I call them 'outer function' and 'inner function'?

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  • $\begingroup$ I can't think of a completely standard term, but I believe your terms (outer/inner) are sometimes used. I think I also heard top-level/nested function, and global/local function. None of these term properly "scale" to multiple nestings, though. $\endgroup$ – chi Nov 29 '17 at 17:39
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A function that either takes a function as argument or returns a function as result is called a High Order Function in functional programming. Your function make_adder is doing the latter.

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One specific name for that kind of construct is "closure". That term specifically refers to a situation where the inner function uses variables from the outer function's "enclosing" namespace.

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  • $\begingroup$ That term is uses for so many different things, it hardly qualifies as "formal". $\endgroup$ – Raphael Nov 30 '17 at 7:57

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