Currying

In mathematics and computer science, currying is the technique of translating the evaluation of a function that takes multiple arguments (or a tuple of arguments) into evaluating a sequence of functions, each with a single argument. Currying is related to, but not the same as, partial application.

Currying is useful in both practical and theoretical settings. In functional programming languages, and many others, it provides a way of automatically managing how arguments are passed to functions and exceptions. In theoretical computer science, it provides a way to study functions with multiple arguments in simpler theoretical models which provide only one argument. The most general setting for the strict notion of currying and uncurrying is in the closed monoidal categories; this is interesting because it underpins a vast generalization of the Curry–Howard correspondence of proofs and programs to a correspondence with many other structures, including quantum mechanics, cobordisms and string theory. It was introduced by Gottlob Frege, developed by Moses Schönfinkel, and further developed by Haskell Curry.

Uncurrying is the dual transformation to currying, and can be seen as a form of defunctionalization. It takes a function f whose return value is another function g, and yields a new function f′ that takes as parameters the arguments for both f and g, and returns, as a result, the application of f and subsequently, g, to those arguments. The process can be iterated.

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