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

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 ${\displaystyle (\tau _{1}\to \tau _{2})\to \tau _{3}}$.

The examples are not intended to compare and contrast programming languages, but to serve as examples of higher-order function syntax

In the following examples, the higher-order function twice takes a function, and applies the function to some value twice. If twice has to be applied several times for the same f it preferably should return a function rather than a value. This is in line with the "don't repeat yourself" principle.

Or in a tacit manner:

Using std::function in C++11:

Or, with generic lambdas provided by C++14: