Higher-order functionIn mathematics and computer science, a higher-order function (HOF) is a function that does at least one of the following: takes one or more functions as arguments (i.e. a procedural parameter, which is a parameter of a procedure that is itself a procedure), returns a function as its result. 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.
Fold (higher-order function)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. Typically, a fold is presented with a combining function, a top node of a data structure, and possibly some default values to be used under certain conditions.
Filter (higher-order function)In functional programming, filter is a higher-order function that processes a data structure (usually a list) in some order to produce a new data structure containing exactly those elements of the original data structure for which a given predicate returns the boolean value true. In Haskell, the code example filter even [1..10] evaluates to the list 2, 4, ..., 10 by applying the predicate even to every element of the list of integers 1, 2, ...
Return statementIn computer programming, a return statement causes execution to leave the current subroutine and resume at the point in the code immediately after the instruction which called the subroutine, known as its return address. The return address is saved by the calling routine, today usually on the process's call stack or in a register. Return statements in many programming languages allow a function to specify a return value to be passed back to the code that called the function.
Map (higher-order function)In many programming languages, map is the name of 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. The concept of a map is not limited to lists: it works for sequential containers, tree-like containers, or even abstract containers such as futures and promises. Suppose we have a list of integers [1, 2, 3, 4, 5] and would like to calculate the square of each integer.
