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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.
Apply is also a continuous function in homotopy theory, and, indeed underpins the entire theory: it allows a homotopy deformation to be viewed as a continuous path in the space of functions. Likewise, valid mutations (refactorings) of computer programs can be seen as those that are "continuous" in the Scott topology .
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. For a language to support map, it must support passing a function as an argument.
In computer science, functional programming is a programming paradigm where programs are constructed by applying and composing functions. It is a declarative programming paradigm in which function definitions are trees of expressions that map values to other values, rather than a sequence of imperative statements which update the running state ...
For a given instance of the map class the keys must be of the same base type. The same must be true for all of the values. Although std::map is typically implemented using a self-balancing binary search tree, C++11 defines a second map called std::unordered_map, which has the algorithmic
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.
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In this example, itself becomes a function, that takes as an argument, and returns a function that maps each to . The proper notation for expressing this is verbose. The function f {\displaystyle f} belongs to the set of functions ( X × Y ) → Z . {\displaystyle (X\times Y)\to Z.}