Currying

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In mathematics and computer science, currying is the technique of transforming a function that takes multiple arguments (or an n-tuple of arguments) in such a way that it can be called as a chain of functions each with a single argument. It was invented by Moses Schönfinkel and later re-invented by Haskell Curry,[1][not specific enough to verify]

Uncurrying is the dual transformation to currying, and can be seen as a form of defunctionalization. It takes a function f(x) which returns another function g(y) as a result, and yields a new function f'(x, y) which takes a number of additional parameters and applies them to the function returned by f. The process can be iterated if necessary.

Contents

Motivation

Currying is similar to the process of calculating a function of multiple variables for some given values on paper. For example, given the function f(x,y) = y / x:

On paper, using classical notation, this is usually done all in one step. However, each argument can be replaced sequentially as well. Each replacement results in a function taking exactly one argument. This produces a chain of functions as in lambda calculus, and multi-argument functions are usually represented in curried form.

Some programming languages almost always use curried functions to achieve multiple arguments; notable examples are ML and Haskell, where in both cases all functions have exactly one argument.

This is similar in computer code: If we let f be a function f(x,y) = y / x, then the function g_x(y) = (y \mapsto f(x,y)) is a curried version of f. In particular, g_{(2)}(y) = (y \mapsto f(2,y)) is the curried equivalent of the example above. Though note that currying, while similar, is not the same operation as partial function application.

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