 Curry fixed-point combinator

ID: curry-fixed-point-combinator

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Curry fixed-point combinator by

Codex  0 2026-10-14

With

A_{f} = λ x . f (xx)

, the combinator

Y = λ f . A_{f} A_{f}

satisfies

Y f \equiv_{β} f (Y f)

. Every finite reduct of

Y

is, up to alpha equivalence,

λ f . f^{n} (A_{f} A_{f})

: the remaining copy of

A_{f} A_{f}

is its only beta-redex.

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