In Scheme:
(define ncons (λ (a b) (λ(z)((z a)b))))
(define ncar (λ(a) (a (λ(a)(λ(b)a)))))
(define ncdr (λ(a)(a(λ(a)(λ(b)b)))))
car: (λa(a(λa(λba))))
cdr: (λa(a(λa(λbb))))
cons: (λa(λb (λz((za)b))))
For λ, the Jig:
((λa((λd((λc
42 ; place for app
)(λa(λb(λz((za)b))))) ; c cons
)(λa(a(λa(λbb))))) ; d cdr
)(λa(a(λa(λba))))) ; a car
or in new speak:
((λadc.
(d(c 3 6))
)
(λa.(a(λa.(λb.a)))) ; a car
(λa.(a(λa.(λb.b)))) ; d cdr
(λabz.(zab)) ; c cons
)
The following two lines may be substituted for the app line above:
(a((c 3) 6)) -> 3
(d((c 3) 6)) -> 6
This is not yet servicable for lack of a matching null? function
The Mairson list suite goes much father.