Simple natural number type

div2.hs

-- div2.hs

data Nat = Zero | Succ Nat
    deriving (Eq, Ord)

instance Show Nat where
  show a = show $ fromEnum a

instance Num Nat where
  a + Succ b = Succ a + b
  a + Zero = a
  Succ a - Succ b = a - b
  a - Zero = a
  Zero - _ = Zero
  fromInteger n = (iterate Succ Zero) !! (fromInteger n)
  
instance Enum Nat where
  succ a = Succ a
  pred (Succ a) = a
  toEnum n = fromInteger $ toInteger n
  fromEnum Zero = 0
  fromEnum (Succ a) = 1 + fromEnum a

div2 :: Nat -> Nat
div2 Zero = Zero
div2 (Succ Zero) = Zero
div2 (Succ (Succ n)) = Succ (div2 n)

main :: IO ()
main = do
    let v = take 6 $ map div2 [0..]
    mapM_ print v

{- Output:
 -
 - 0
 - 0
 - 1
 - 1
 - 2
 - 2
 -}