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In many programming languages, map is a higher-order function that applies a given function to each element of a collection, e.g. a list or set, returning the results in a collection of the same type. It is often called apply-to-all when considered in functional form.
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).
Map (higher-order function) O. Outer product; P. Prefix sum; S. Segmented scan This page was last edited on 29 March 2013, at 01:42 (UTC). Text is available under ...
Higher-order programming is a style of computer programming that uses software components, like functions, modules or objects, as values. It is usually instantiated with, or borrowed from, models of computation such as lambda calculus which make heavy use of higher-order functions. A programming language can be considered higher-order if ...
First-class functions are a necessity for the functional programming style, in which the use of higher-order functions is a standard practice. A simple example of a higher-ordered function is the map function, which takes, as its arguments, a function and a list, and returns the list formed by applying the function to each member of the list.
In functional programming, fold (also termed reduce, accumulate, aggregate, compress, or inject) refers to a family of higher-order functions that analyze a recursive data structure and through use of a given combining operation, recombine the results of recursively processing its constituent parts, building up a return value.
Higher-order Voronoi diagrams also subdivide space. Higher-order Voronoi diagrams can be generated recursively. To generate the n th-order Voronoi diagram from set S, start with the (n − 1) th-order diagram and replace each cell generated by X = {x 1, x 2, ..., x n−1} with a Voronoi diagram generated on the set S − X.
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