Constants and their operators such as
ints 0, 1,2, ..., +, -, ...,
Booleans true, false, and, or, not, ...,
Lists, nil, cons, hd, tl, null, etc.,
can all be defined in λ calculus,

The examples
can be run interactively using the FORM below

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 by the fixed-point Y combinator}