Division by two

div2.hs

-- div2.hs

data Nat = Zero | Succ Nat
    deriving (Show)

zero  = Zero
one   = Succ zero
two   = Succ one
three = Succ two
four  = Succ three
five  = Succ four

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

main :: IO ()
main = do
    let v = map div2 [zero, one, two, three, four, five]
    mapM_ print v

{- Output:
 -
 - Zero
 - Zero
 - Succ Zero
 - Succ Zero
 - Succ (Succ Zero)
 - Succ (Succ Zero)
 -}

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