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- Fixed-point_combinator abstract "In computer science, a fixed-point combinator (or fixpoint combinator) is a higher-order function y that satisfies the equation, It is so named because, by setting , it represents a solution to the fixed point equation, A fixed point of a function f is a value that doesn't change under the application of the function f. Consider the function . 0 and 1 are fixed points of this function, because and . This function has no other fixed points.A fixed point combinator need not exist for all functions. Also if f is a function of more than 1 parameter, the fixed point of the function need not be a total function.Functions that satisfy the equation for y expand as, A particular implementation of y is Curry's paradoxical combinator Y, represented in Lambda calculus by, This combinator may be used in implementing Curry's paradox. The heart of Curry's paradox is that Lambda calculus is unsound as a deductive system, and the Y combinator demonstrates that by allowing an anonymous expression to represent zero, or even many values. This is inconsistent in mathematical logic.Applied to a function with one variable the Y combinator usually does not terminate. More interesting results are obtained by applying the Y combinator to functions of two or more variables. The second variable may be used as a counter, or index. The resulting function behaves like a while or a for loop in an imperative language.Used in this way the Y combinator implements simple recursion. In the Lambda calculus it is not possible to refer to the definition of a function in a function body. Recursion may only be achieved by passing in a function as a parameter. The Y combinator demonstrates this style of programming.".
- Fixed-point_combinator wikiPageExternalLink y-combinator-in-arc-and-java.html.
- Fixed-point_combinator wikiPageExternalLink 070611.html.
- Fixed-point_combinator wikiPageExternalLink recursive-lambda-expressions.aspx.
- Fixed-point_combinator wikiPageExternalLink YCombinatorExplained.
- Fixed-point_combinator wikiPageExternalLink implementation-of-recursive-fixed-point-y-combinator-in-javascript-for-memoization.
- Fixed-point_combinator wikiPageExternalLink 2897.html.
- Fixed-point_combinator wikiPageExternalLink functional-programming-inada.html.
- Fixed-point_combinator wikiPageExternalLink fixed-point-combinators.html.
- Fixed-point_combinator wikiPageExternalLink Y_combinator.
- Fixed-point_combinator wikiPageExternalLink 154267.
- Fixed-point_combinator wikiPageExternalLink 30896.
- Fixed-point_combinator wikiPageExternalLink BRICS-RS-05-1.pdf.
- Fixed-point_combinator wikiPageExternalLink 2002-10-28-lc.pdf.
- Fixed-point_combinator wikiPageExternalLink Y.
- Fixed-point_combinator wikiPageExternalLink ycomb.html.
- Fixed-point_combinator wikiPageExternalLink ycombinator.shtml.
- Fixed-point_combinator wikiPageExternalLink j05cmp.html.
- Fixed-point_combinator wikiPageExternalLink LambdaCalculus.
- Fixed-point_combinator wikiPageExternalLink YYWorks.ps.
- Fixed-point_combinator wikiPageExternalLink reinvent-y.
- Fixed-point_combinator wikiPageID "150287".
- Fixed-point_combinator wikiPageRevisionID "602855558".
- Fixed-point_combinator hasPhotoCollection Fixed-point_combinator.
- Fixed-point_combinator subject Category:Combinatory_logic.
- Fixed-point_combinator subject Category:Fixed_points_(mathematics).
- Fixed-point_combinator subject Category:Lambda_calculus.
- Fixed-point_combinator subject Category:Mathematics_of_computing.
- Fixed-point_combinator subject Category:Recursion.
- Fixed-point_combinator comment "In computer science, a fixed-point combinator (or fixpoint combinator) is a higher-order function y that satisfies the equation, It is so named because, by setting , it represents a solution to the fixed point equation, A fixed point of a function f is a value that doesn't change under the application of the function f. Consider the function . 0 and 1 are fixed points of this function, because and .".
- Fixed-point_combinator label "Fixed-point combinator".
- Fixed-point_combinator label "Operator paradoksalny".
- Fixed-point_combinator label "Комбинатор неподвижной точки".
- Fixed-point_combinator label "不动点组合子".
- Fixed-point_combinator label "不動点コンビネータ".
- Fixed-point_combinator sameAs 不動点コンビネータ.
- Fixed-point_combinator sameAs Operator_paradoksalny.
- Fixed-point_combinator sameAs m.013bzn.
- Fixed-point_combinator sameAs Q2976255.
- Fixed-point_combinator sameAs Q2976255.
- Fixed-point_combinator wasDerivedFrom Fixed-point_combinator?oldid=602855558.
- Fixed-point_combinator isPrimaryTopicOf Fixed-point_combinator.