Fixed-Point Combinator

combinators

Definition

Fixed-Point Combinator

A fixed-point combinator is a higher-order function that, when applied to any function $f$, returns a fixed point of $f$. Let’s call a fixed point combinator $\mathbf{Y}$. According to the rules of lambda calculus (beta reduction,) it must satisfy: the property:

$$\mathbf{Y}f=f(\mathbf{Y}f)$$