What is "higher-order function"

n. (context computer science English) A function that takes one or more functions as an input, and returns a function as a result.

In mathematics and computer science, a higher-order function (also functional, functional form or functor) 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 known as operators or functionals. The differential operator in calculus is a common example, since it maps a function to its derivative, also a function.

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 → τ) → τ.