module Data.ForeignNat.Impl where

data Nat = Zero | Suc Nat
data Divides = Divides

unpack :: Nat -> Integer
unpack Zero = 0
unpack (Suc n) = 1 + (unpack n)

pack :: Integer -> Nat
pack 0 = Zero
pack n = Suc $ pack (n-1)
                 
mul :: Nat -> Nat -> Nat
n `mul` m = pack $ (unpack n) * (unpack m)

divide :: Nat -> Nat -> Nat
n `divide` m = pack $ (unpack n) `div` (unpack m)

modulo :: Nat -> Nat -> Nat               
n `modulo` m = pack $ (unpack n) `mod` (unpack m)
               
divides :: Nat -> Nat -> Bool
n `divides` m = (unpack n) `mod` (unpack m) == 0

instance Show Nat where
    show = show . unpack