Higher-order function

In <a href="/facts/Mathematics/pxTouaz4">mathematics</a> and <a href="/facts/Computer_science/lN3pEyPz">computer science</a>, a higher-order function (HOF) is a <a href="/facts/Function_(mathematics)/CdReEKCh">function</a> that does at least one of the following:
<ul><li>takes one or more functions as arguments (i.e. a <a href="/facts/Procedural_parameter/jAJHk0d3">procedural parameter</a>, which is a <a href="/facts/Parameter_(computer_science)/LcuLbbSq">parameter</a> of a <a href="/facts/Subroutine/9vFJrg0A">procedure</a> that is itself a procedure),</li>
<li>returns a function as its result.</li></ul>
All other functions are first-order functions. In mathematics higher-order functions are also termed <a href="/facts/Operator_(mathematics)/1VWgEdjS">operators</a> or <a href="/facts/Functional_(mathematics)/3Cp3PHBR">functionals</a>. The <a href="/facts/Differential_operator/Nr15J0IE">differential operator</a> in <a href="/facts/Calculus/MEmUTYoz">calculus</a> is a common example, since it maps a function to its <a href="/facts/Derivative/7Ito70Dh">derivative</a>, also a function. Higher-order functions should not be confused with other uses of the word "functor" throughout mathematics, see <a href="/facts/Functor_(disambiguation)/Jb7Bp8NT">Functor (disambiguation)</a>.
In the untyped <a href="/facts/Lambda_calculus/DaD3RuQ4">lambda calculus</a>, all functions are higher-order; in a <a href="/facts/Typed_lambda_calculus/g86GP4uK">typed lambda calculus</a>, from which most <a href="/facts/Functional_programming/cdxqPEIM">functional programming</a> languages are derived, higher-order functions that take one function as argument are values with types of the form 
 
 
 
 (
 
 τ
 
 1
 
 
 →
 
 τ
 
 2
 
 
 )
 →
 
 τ
 
 3
 
 
 
 
 {\displaystyle (\tau _{1}\to \tau _{2})\to \tau _{3}}
 
.

Higher-order function open-in-new

Higher-order function