Fixed-point combinator

Higher-order function Y for which Y f = f (Y f) / From Wikipedia, the free encyclopedia

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In combinatory logic for computer science, a fixed-point combinator (or fixpoint combinator),[1]:p.26 is a higher-order function (i.e. a function which takes a function as argument) that returns some fixed point (a value that is mapped to itself) of its argument function, if one exists.

Formally, if is a fixed-point combinator and the function has one or more fixed points, then is one of these fixed points, i.e.

Fixed-point combinators can be defined in the lambda calculus and in functional programming languages and provide a means to allow for recursive definitions.

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