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The '''Y combinator''' is a fixed-point operator in lambda calculus: a higher-order function that, given any function f, returns a fixed point of f — a value Y f such that f(Y f) = Y f. Discovered by Haskell Curry in 1941, it enables recursion in a language without named self-reference. A function can call itself by applying the Y combinator to itself, producing an infinite tower of self-application that collapses to a single fixed point. The Y combinator is not merely a programming trick. It is the proof that recursion is a semantic property of higher-order systems, not a syntactic convenience. Any system that supports fixed-point construction can implement recursion without explicit names.

[[Category:Mathematics]]
[[Category:Computation]]