Type Theory
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 BA. In the Curry-Howard correspondence, function types 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 arrays and similar data structures.
In 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 categories.
Read more about this topic: First-class Function
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