Editing First-class function (section)

== Type theory ==
{{main|Function type}}
In [[type theory]], the type of functions accepting values of type ''A'' and returning values of type ''B'' may be written as ''A'' → ''B'' or ''B''<sup>''A''</sup>. In the [[Curry–Howard correspondence]], [[function type]]s are related to [[logical implication]]; lambda abstraction corresponds to discharging hypothetical assumptions and function application corresponds to the [[modus ponens]] inference rule. Besides the usual case of programming functions, type theory also uses first-class functions to model [[associative array]]s and similar [[data structure]]s.

In [[category theory|category-theoretical]] accounts of programming, the availability of first-class functions corresponds to the [[closed category]] assumption. For instance, the [[simply typed lambda calculus]] corresponds to the internal language of [[Cartesian closed category|Cartesian closed categories]].