(en.wikipedia.org) Fixed-point combinator - Wikipedia

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In combinatory logic for computer science, a fixed-point combinator (or fixpoint combinator) 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 \(\text{fix}\) is a fixed-point combinator and the function \(f\) has one or more fixed points, then \(\text{fix}f\) is one of these fixed points, i.e.

\(f(\text{fix}f) = \text{fix}f.\)

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