zero = \s z -> z
suc  = \n s z -> s (n s z)

n0 = zero
n1 = suc n0
n2 = suc n1
n3 = suc n2
n4 = suc n3
n5 = suc n4
n6 = suc n5

n10 = mul n2 n5
n20 = mul n10 n2

fix = \f -> (\x -> f (x x)) (\x -> f (x x))

fst (P x y) = x
snd (P x y) = y

pred n = snd (natrec (P n0 n0) (\p -> P (suc (fst p)) (fst p)) n)

natrec = \z s n -> n s z

add n m = natrec m suc n
mul n m = natrec zero (add m) n
sub n m = natrec n pred m

div = fix (\d n m ->
    if (less n m)
       zero
       (suc (d (sub n m) m))
    )

mod = fix (\d n m ->
    if (less n m)
       n
       (d (sub n m) m)
    )

fac = fix (\f n ->
    if (nonZero n)
       (mul n (fac (pred n)))
       n1
    )

if True  = \x y -> x
if False = \x y -> y

nonZero = \n -> n (\x -> True) False
isZero = \n -> n (\x -> False) True

less = \n m -> nonZero (sub m n)

decimal = fix (\dec n ->
    if (isZero n)
       (\x -> x)
       (dec (div n n10) (digit (mod n n10)))
    )

inc D0 = D1
inc D1 = D2
inc D2 = D3
inc D3 = D4
inc D4 = D5
inc D5 = D6
inc D6 = D7
inc D7 = D8
inc D8 = D9

digit = natrec D0 inc

main = decimal (fac n4)