let ident = \ x . x;
let true  = \a.\b.a;
let false = \a.\b.b;
let if    = \a.\b.\c.a b c;

let zero = \f.\x.x;
let succ = \n.\f.\x.f (n f x);
let one = succ zero;
let two = succ one;
let three = succ two;
let four = succ three;
let five = succ four;
let six = succ five;
let seven = succ six;
let eight = succ seven;
let nine = succ eight;
let ten = succ nine;
let add = \n.\m.\f.\x.n f (m f x);
let mul = \n.\m.\f.n (m f);
let twenty = add ten ten;
let thirty = add twenty ten;
let fourty = add thirty ten;
let one_hundred = mul ten ten;

let pred = \n.n
        (\p.\x.\y.p (succ x) x)
                (\x.\y.y) zero zero;



if true YES NO;
if false YES NO;

zero;
one;
one_hundred;