K = \ x y . x
S = \ f g x . f x (g x)
I = S K K

Dot = \ f g x . f (g x)
Flip = \ f x y . f y x

True = K
Not = Flip
False = Not True

If = I

Zero = \ s z . z
Succ = \ n . \ s z . n s (s z)

IsZero = \ n . n (K False) True

Add = \ m n . \ s z . m s (n s z)
Mul = \ m n . \ s z . m (n s) z
Pow = \ m n . \ s z . n m s z

One = Succ Zero
Two = Succ One
Three = Succ Two

Tup = \ x y . \ p . p x y
Fst = \ t . t K
Snd = \ t . t (Flip K)

Fac = \ n . Snd (n (\ t . t (\ x y . Tup (Succ x) (Mul x y))) (Tup One One))