Currying is the technique of emulating multiple-parametered functions with higher-order functions. The notion is that a function of n arguments can be thought of as a function of 1 argument that maps to a function of n-1 arguments. A curried function is a function represented by currying, e.g.


For conciseness, the mapping operator is usually considered right-associative, so one could drop the parentheses in the expression above and write f:ABC instead.

In contrast, an uncurried function is usually specified as a mapping from a Cartesian product, such as


The term currying is derived from the name of Haskell Curry, a 20th-century logician. However, Curry was not the first person to discover this notion, as it was first introduced by Gottlob Frege in 1893 and expanded by Moses Schönfinkel in the 1920s. Hence the notion is sometimes referred to as schönfinkeling.

From the perspective of category theoryMathworldPlanetmathPlanetmathPlanetmathPlanetmath, currying can be thought of as exploiting the fact that -×B and Hom(B,-) are adjoint functorsMathworldPlanetmathPlanetmathPlanetmath on 𝐒𝐞𝐭. That is, for each set B, there is a natural equivalence


defined by sending a map f:(A×B)C to the map νf:AHom(B,C). For each aA, νf(a):BC is the map defined by νf(a)(b)=f(a,b).

Title currying
Canonical name Currying
Date of creation 2013-03-22 12:33:35
Last modified on 2013-03-22 12:33:35
Owner mps (409)
Last modified by mps (409)
Numerical id 8
Author mps (409)
Entry type Definition
Classification msc 68Q01
Synonym schönfinkeling
Synonym schönfinkelization
Related topic HigherOrderFunction
Defines curried function
Defines uncurried function