Lambda Calculus Fixed-Point Operator Y (lazy)

The fixed-point operator (paradoxical combinator, Y combinator) such that Y F = F(Y F): 

let Y = lambda G. (lambda g. G(g g)) (lambda g. G(g g))

in let F = lambda f. lambda n. if n=0 then 1 else n*f(n-1)

in Y F 10

{ Factorial via Y }
Note that
Y F = (λ g. F(g g)) (λ g. F(g g))
= (λ h. F(h h)) (λ g. F(g g))  – α conv. (name change)
= F ((λ g. F(g g)) (λ g. F(g g)))  – β redn  (substitution)
= F (Y F)



And Y even applies to data structures 

let Y = lambda G. (lambda g. G(g g)) (lambda g. G(g g))

in Y (lambda L. 1::L)

{ 1::1::1:: ...   via Y }
It is a good idea to print only a finite part of the result.