Fixed-point combinator
In combinatory logic for computer science, a fixed-point combinator (or fixpoint combinator) is a higher-order function (i.e., a function that 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 f i x {\displaystyle \mathrm {fix} } is a fixed-point combinator and the function f {\displaystyle f} has one or more fixed points, then f i x f {\displaystyle \mathrm {fix} \ f} is one of these fixed points, i.e., f i x f = f ( f i x f ) .