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Apply is also the name of a special function in many languages, which takes a function and a list, and uses the list as the function's own argument list, as if the function were called with the elements of the list as the arguments.
A higher-order function is a function that takes a function as an argument or returns one as a result. This is commonly used to customize the behavior of a generically defined function, often a looping construct or recursion scheme. Anonymous functions are a convenient way to specify such function arguments. The following examples are in Python 3.
Map is sometimes generalized to accept dyadic (2-argument) functions that can apply a user-supplied function to corresponding elements from two lists. Some languages use special names for this, such as map2 or zipWith. Languages using explicit variadic functions may have versions of map with variable arity to support variable-arity functions ...
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 Python, functions are first-class objects that can be created and passed around dynamically. Python's limited support for anonymous functions is the lambda construct. An example is the anonymous function which squares its input, called with the argument of 5:
Folds can be regarded as consistently replacing the structural components of a data structure with functions and values. Lists, for example, are built up in many functional languages from two primitives: any list is either an empty list, commonly called nil ([]), or is constructed by prefixing an element in front of another list, creating what is called a cons node ( Cons(X1,Cons(X2,Cons ...
In functional programming languages, variadics can be considered complementary to the apply function, which takes a function and a list/sequence/array as arguments, and calls the function with the arguments supplied in that list, thus passing a variable number of arguments to the 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.