Currying explained

curry.md

In the following, let’s define sum as

sum = function (a, b, c) a + b +c

Because base::sum’s definition involves ..., which would make the following explanation unnecessarily complex.

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Partial function application takes a function f with n formal parameters and m=1…n arguments, and fixes some of f formal parameters by filling them in, thereby reducing f’s arity to n−m.

f = partial(sum, 1)
f()
f(2, 3)

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Currying takes a function f with n formal parameters and produces a recursive nesting of n functions, each taking 1 formal parameter. Recursively calling all these functions is then identical to calling the original function:

g = curry(sum)
g()
g(1)(2)(3)

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6

Conversely, uncurry reverses a currying:

foo = function (a)
    function (b)
        function (c)
            a + b + c

foo(1)(2)(3)

bar = uncurry(foo)
bar(1, 2, 3)

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