Fixed point combinators

Fixed point M is a fixed point of F if F M =β M for example, every term M is a fixed point of I.

Fixed point combinator Y is a fixed point combinator if F M =β M (F M) for every λ-term F

examples:

• Curry’s — Y = λf.(λx.f (x x)) (λx.f (x x))
• Turing’s — (λx.λy.(x x y)) (λx.λy.y (x x y))