Baking the Y Combinator from Scratch: Part 1 - The Fixpoint Combinator

This post delves into the Y combinator, a mathematical construct that implements recursion in functional languages without explicit self-reference. It begins by explaining fixed points, then progressively derives the formula for the Y combinator, explaining its self-replicating mechanism. Through analysis of the Ω combinator, the author shows how the Y combinator avoids infinite nesting by self-replication at runtime. The post also briefly introduces lambda calculus and formal systems, laying the groundwork for a deeper understanding of the Y combinator in later parts.