higher-order function first-order function

Higher-order function

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Not to be confused with Functor (category theory).

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In mathematics and computer
science, a higher-order function (also functional, functional form or functor) is a function that
does at least one of the following:
takes one or more functions as arguments (i.e., procedural
parameters),
returns a function as its result.[disputed – discuss]
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.
In the untyped lambda calculus,
all functions are higher-order; in a typed lambda calculus, from which most functional
programming languages are derived, higher-order functions that take one function as argument are values with types of the form {\displaystyle
(\tau _{1}\to \tau _{2})\to \tau _{3}}

.

General examples[edit]

The 

map

 function,
found in many functional programming languages, is one example of a higher-order function. It takes as arguments a function f and a list of elements, and as the result, returns a new list with f applied to each element from the list. Another
very common kind of higher-order function in those languages which support them are sorting functions which take a comparison function as a parameter, allowing the programmer to separate the sorting algorithm from the comparisons of the items being sorted.
The C standard function 

qsort

 is
an example of this.

Other examples of higher-order functions include fold, function
composition, and integration.

Direct support[edit]

The examples are not intended to compare and contrast programming languages, but to serve as examples of higher-order function syntax

In the following examples, the higher-order function 

twice

 takes a function, and applies the function
to some value twice. If 

twice

 has to be applied several times for the same 

f

 it
preferably should return a function rather than a value. This is in line with the "don't
repeat yourself" principle.

Python[edit]

Further information: Python (programming language)

>>> def twice(function):
...     return lambda x: function(function(x))

>>> def f(x):
...     return x + 3

>>> g = twice(f)

>>> print g(7)
13

JavaScript[edit]

Further information: JavaScript

var twice = function(f, v) {
return f(f(v));
};

var f = function(v) {
return v + 3;
};

console.log(twice(f, 7)); // 13

Go[edit]

Further information: Go (programming language)

func twice(f func(int) int, v int) int {
return f(f(v))
}

func main() {
f := func(v int) int {
return v + 3
}
twice(f, 7) // returns 13
}