Haskell Natural Numbers

Nat.hs

-- Natural Numbers

data Nat = Zero | Succ Nat

instance Show Nat where
         show Zero     = "Zero"
         show (Succ m) = printf "Succ (%s)" (show m)

nat2int :: Nat -> Int
nat2int Zero = 0
nat2int (Succ n) = 1 + nat2int n

int2nat :: Int -> Nat
int2nat 0 = Zero
int2nat n = Succ (int2nat (n-1))

add' :: Nat -> Nat -> Nat
add' Zero n = n
add' (Succ m) n = Succ (add' m n)

-- addNat :: Nat -> Nat -> Nat
-- addNat m n = int2nat (nat2int m + nat2int n)