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 .
12-484: [REDACTED] Look up application or applications in Wiktionary, the free dictionary. Application may refer to: Mathematics and computing [ edit ] Application software , computer software designed to help the user to perform specific tasks Application layer , an abstraction layer that specifies protocols and interface methods used in
24-423: A communications network Function application , in mathematics and computer science Processes and documents [ edit ] Application for employment , a form or forms that an individual seeking employment must fill out College application , the process by which prospective students apply for entry into a college or university Patent application , a document filed at a patent office to support
36-423: A communications network Function application , in mathematics and computer science Processes and documents [ edit ] Application for employment , a form or forms that an individual seeking employment must fill out College application , the process by which prospective students apply for entry into a college or university Patent application , a document filed at a patent office to support
48-439: 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
60-849: The argument ⟨ x , y ⟩ ∈ X × Y {\displaystyle \langle x,y\rangle \in X\times Y} written with the less common angle brackets) by the latter. However, functions in curried form f : X → ( Y → Z ) {\displaystyle f:X\to (Y\to Z)} can be represented by juxtaposing their arguments: f x y {\displaystyle f\;x\;y} , rather than f ( x ) ( y ) {\displaystyle f(x)(y)} . This relies on function application being left-associative . Function application can be trivially defined as an operator , called apply or $ {\displaystyle \$ } , by
72-476: 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 x {\displaystyle x} to be
84-409: The 💕 [REDACTED] Look up application or applications in Wiktionary, the free dictionary. Application may refer to: Mathematics and computing [ edit ] Application software , computer software designed to help the user to perform specific tasks Application layer , an abstraction layer that specifies protocols and interface methods used in
96-419: The grant of a patent Other uses [ edit ] Application (virtue) , a characteristic encapsulated in diligence Topical application , the spreading or putting of medication to body surfaces See also [ edit ] All pages with titles containing application Apply Topics referred to by the same term [REDACTED] This disambiguation page lists articles associated with
108-419: The grant of a patent Other uses [ edit ] Application (virtue) , a characteristic encapsulated in diligence Topical application , the spreading or putting of medication to body surfaces See also [ edit ] All pages with titles containing application Apply Topics referred to by the same term [REDACTED] This disambiguation page lists articles associated with
120-594: The same as the previous one: The latter notation is especially useful in combination with the currying isomorphism. Given a function f : ( X × Y ) → Z {\displaystyle f:(X\times Y)\to Z} , its application is represented as f ( x , y ) {\displaystyle f(x,y)} by the former notation and f ( x , y ) {\displaystyle f\;(x,y)} (or f ⟨ x , y ⟩ {\displaystyle f\;\langle x,y\rangle } with
132-467: The title Application . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Application&oldid=1252174476 " Category : Disambiguation pages Hidden categories: Short description is different from Wikidata All article disambiguation pages All disambiguation pages application From Misplaced Pages,
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#1732765950925144-480: The title Application . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Application&oldid=1252174476 " Category : Disambiguation pages Hidden categories: Short description is different from Wikidata All article disambiguation pages All disambiguation pages Function application Function application
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