Rabbit-hole #6: The Sage Bird -- Y Combinators in an Eager Array Language
A technical blog post deriving the Y combinator as a composition of combinator birds in an array language, and examining how eager evaluation changes fixed-point recursion compared with the usual lazy telling.
This post works through the Y combinator using Raymond Smullyan's combinatory-logic birds, showing it as a composition of three simpler combinators that reduces to the classical lambda-calculus form and satisfies the usual fixed-point equation. It then applies this to a recursive factorial function to demonstrate the combinator in practice.
The post examines what changes when the same construction runs in sw-MLPL, an eager array language in the APL lineage, rather than a lazy language, since the classical Y combinator's self-application does not terminate under eager evaluation, and discusses what the APL tradition does instead to get recursion without it. It links to a live in-browser demo of the combinators, to Smullyan's book To Mock a Mockingbird as background reading, and to the relevant lesson and source file in the author's own study repository.