Function type

In computer science, a function type (also arrow type or exponential) is the type of a variable or parameter to which a function has or can be assigned, or an argument or result type of a higher-order function taking or returning a function.

A function type depends on the type of the parameters and the result type of the function (it, or more accurately the unapplied type constructor · → ·, is a higher-kinded type). In theoretical settings and languages where functions are defined in curried form, such as the simply typed lambda calculus, a function type depends on exactly two types, the domain A and the range B. Here a function type is often denoted A → B, following mathematical convention, or B^A, based on the fact that there exist exactly B^A (exponentially many) set-theoretic functions mapping A to B.

The function type can be considered to be a special case of the dependent product type. Among other properties, the dependent product type encompasses the idea of a polymorphic function.