 Fixed-point combinator

An untyped lambda term $Y$ is a fixed-point combinator when $Yf{\equiv }_{\beta }f(Yf)$ for every term $f$.

A **fixed-point combinator** is a higher-order function that computes the fixed point of other functions. In simpler terms, it allows you to find a point that satisfies the condition \( f(x) = x \) for a given function \( f \). This concept is particularly important in functional programming, recursion, and lambda calculus, where named functions may not always be available due to the nature of the constructs used.