Editing Functional programming (section)

=== First-class and higher-order functions ===
{{main|First-class function|Higher-order function}}

[[Higher-order function]]s are functions that can either take other functions as arguments or return them as results. In calculus, an example of a higher-order function is the [[differential operator]] <math>d/dx</math>, which returns the [[derivative]] of a function <math>f</math>.

Higher-order functions are closely related to [[first-class function]]s in that higher-order functions and first-class functions both allow functions as arguments and results of other functions. The distinction between the two is subtle: "higher-order" describes a mathematical concept of functions that operate on other functions, while "first-class" is a computer science term for programming language entities that have no restriction on their use (thus first-class functions can appear anywhere in the program that other first-class entities like numbers can, including as arguments to other functions and as their return values).

Higher-order functions enable [[partial application]] or [[currying]], a technique that applies a function to its arguments one at a time, with each application returning a new function that accepts the next argument. This lets a programmer succinctly express, for example, the [[successor function]] as the addition operator partially applied to the [[natural number]] one.