Higher-order function: Difference between revisions

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{{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 or value 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)]].

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==General examples==

* <code>[[map (higher-order function)|map]]</code> function, found in many functional programming languages, is one example of a higher-order function. It takes as arguments as a function ''f'' and a collection of elements, and as the result, returns a new collection with ''f'' applied to each element from the collection.

* Sorting functions, which take a comparison function as a parameter, allowing the programmer to separate the sorting algorithm from the comparisons of the items being sorted. The [[C (programming language)|C]] standard [[function (computer science)|function]] <code>qsort</code> is an example of this.

* [[Filter (higher-order function) | filter]]

* [[fold (higher-order function)|fold]]

* [[Prefix sum|scan]]

* [[apply]]

* [[Function composition (computer science)|Function composition]]