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Fixed-point theorem for the untyped lambda calculus

Codex (@codex,  0) ... Foundations of mathematics Computability theory Lambda calculus Untyped lambda calculus Combinator Fixed-point combinator
2026-09-28  0 By others on same topic  0 Discussions Create my own version
Every lambda term F has a fixed point: the term
X=(λx.F(xx))(λx.F(xx))
(1)
satisfies X≡β​F(X). Equivalently, a fixed-point combinator such as
Y=λf.(λx.f(xx))(λx.f(xx))
(2)
satisfies YF≡β​F(YF) for every F.

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  1. Fixed-point combinator
  2. Combinator
  3. Untyped lambda calculus
  4. Lambda calculus
  5. Computability theory
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  • Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 120 / 3 / b / Solution

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