Higher order

In mathematics and computer science, a higher-order function is a function that does at least one of the following:

takes one or more functions as arguments (i.e. procedural parameters),
returns a function as its result.All other functions are first-order functions. In mathematics higher-order functions are also termed operators or 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).
In the untyped lambda calculus, all functions are higher-order; in a typed lambda calculus, from which most functional programming 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}}
.

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