Editing Higher-order function (section)

{{Short description|Function that takes one or more functions as an input or that outputs a function}}{{More sources|date=November 2024}}{{Distinguish|Functor{{!}}Functor (category theory)}}In [[mathematics]] and [[computer science]], a '''higher-order function''' ('''HOF''') is a [[function (mathematics)|function]] that does at least one of the following:
* takes one or more functions as arguments (i.e. a [[procedural parameter]], which is a [[Parameter (computer science)|parameter]] of a [[Subroutine|procedure]] that is itself a procedure),
* returns a function as its result.
All other functions are ''first-order functions''. In mathematics higher-order functions are also termed ''[[operator (mathematics)|operators]]'' or ''[[functional (mathematics)|functionals]]''. The [[differential operator]] in [[calculus]] is a common example, since it maps a function to its [[derivative]], also a function. Higher-order functions should not be confused with other uses of the word "functor" throughout mathematics, see [[Functor (disambiguation)]].

In the untyped [[lambda calculus]], all functions are higher-order; in a [[typed lambda calculus]], from which most [[functional programming]] languages are derived, higher-order functions that take one function as argument are values with types of the form <math>(\tau_1\to\tau_2)\to\tau_3</math>.