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wiki/concepts/Y-Combinator.md
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---
title: "Y Combinator"
type: concept
tags: []
---
## Definition
Y 不动点组合子（Y Combinator），λ 表达式为：Y ≡ λf.(λx.f(x,x))(λx.f(x,x))。用于在 λ-calculus 中表达递归。
## Context
在递归自优化生成系统的 λ-calculus 形式化中，Y 组合子用于表达稳定生成器的自引用本质：
- STEP ≡ λG. (M G) ((O (G I)) Ω)
- G* ≡ Y STEP
这使得生成器被定义为转换生成器的函数的不动点，显式表达了自引用性质。
## Related Concepts
- [[Fixed Point]]
- [[Self-Map]]
- [[Recursive Self-Optimizing Generative Systems]]