Qué (quién) es curried function - definición

In mathematics and computer science, currying is the technique of translating the evaluation of a function that takes multiple arguments into evaluating a sequence of functions, each with a single argument. For example, currying a function ${\displaystyle f}$ that takes three arguments creates a nested unary function ${\displaystyle g}$, so that the code

${\displaystyle {\text{let }}x=f(a,b,c)}$

gives ${\displaystyle x}$ the same value as the code

${\displaystyle {\begin{aligned}{\text{let }}h=g(a)\\{\text{let }}i=h(b)\\{\text{let }}x=i(c),\end{aligned}}}$

or called in sequence,

${\displaystyle {\text{let }}x=g(a)(b)(c).}$

In a more mathematical language, a function that takes two arguments, one from ${\displaystyle X}$ and one from ${\displaystyle Y}$, and produces outputs in ${\displaystyle Z,}$ by currying is translated into a function that takes a single argument from ${\displaystyle X}$ and produces as outputs functions from ${\displaystyle Y}$ to ${\displaystyle Z.}$ This is a natural one-to-one correspondence between these two types of functions, so that the sets together with functions between them form a Cartesian closed category. The currying of a function with more than two arguments can then be defined by induction. 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, which 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 ${\displaystyle f}$ whose return value is another function ${\displaystyle g}$, and yields a new function ${\displaystyle f'}$ that takes as parameters the arguments for both ${\displaystyle f}$ and ${\displaystyle g}$, and returns, as a result, the application of ${\displaystyle f}$ and subsequently, ${\displaystyle g}$, to those arguments. The process can be iterated.