For faster navigation, this Iframe is preloading the Wikiwand page for Function application.

Function application

From Wikipedia, the free encyclopedia

This article does not cite any sources. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.Find sources: "Function application" – news · newspapers · books · scholar · JSTOR (January 2009) (Learn how and when to remove this template message)

In mathematics, function application is the act of applying a function to an argument from its domain so as to obtain the corresponding value from its range. In this sense, function application can be thought of as the opposite of function abstraction.


Function application is usually depicted by juxtaposing the variable representing the function with its argument encompassed in parentheses. For example, the following expression represents the application of the function ƒ to its argument x.

In some instances, a different notation is used where the parentheses aren't required, and function application can be expressed just by juxtaposition. For example, the following expression can be considered the same as the previous one:

The latter notation is especially useful in combination with the currying isomorphism. Given a function , its application is represented as by the former notation and (or with the argument written with the less common angle brackets) by the latter. However, functions in curried form can be represented by juxtaposing their arguments: , rather than . This relies on function application being left-associative.

As an operator

Function application can be trivially defined as an operator, called apply or , by the following definition:

The operator may also be denoted by a backtick (`).

If the operator is understood to be of low precedence and right-associative, the application operator can be used to cut down on the number of parentheses needed in an expression. For example;

can be rewritten as:

However, this is perhaps more clearly expressed by using function composition instead:

or even:

if one considers to be a constant function returning .

Other instances

Function application in the lambda calculus is expressed by β-reduction.

The Curry–Howard correspondence relates function application to the logical rule of modus ponens.

See also

{{bottomLinkPreText}} {{bottomLinkText}}
Function application
Listen to this article

This browser is not supported by Wikiwand :(
Wikiwand requires a browser with modern capabilities in order to provide you with the best reading experience.
Please download and use one of the following browsers:

This article was just edited, click to reload
This article has been deleted on Wikipedia (Why?)

Back to homepage

Please click Add in the dialog above
Please click Allow in the top-left corner,
then click Install Now in the dialog
Please click Open in the download dialog,
then click Install
Please click the "Downloads" icon in the Safari toolbar, open the first download in the list,
then click Install

Install Wikiwand

Install on Chrome Install on Firefox
Don't forget to rate us

Tell your friends about Wikiwand!

Gmail Facebook Twitter Link

Enjoying Wikiwand?

Tell your friends and spread the love:
Share on Gmail Share on Facebook Share on Twitter Share on Buffer

Our magic isn't perfect

You can help our automatic cover photo selection by reporting an unsuitable photo.

This photo is visually disturbing This photo is not a good choice

Thank you for helping!

Your input will affect cover photo selection, along with input from other users.