Main.hs

module Main where
import           Prelude                           hiding ( subtract )

main :: IO ()
main = do
  print zero
  print one
  print two
  print three
  print four
  print five

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

instance Ord Nat where
  compare Zero     Zero     = EQ
  compare Zero     _        = LT
  compare _        Zero     = GT
  compare (Succ x) (Succ y) = compare x y

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

toInt :: Nat -> Int
toInt Zero     = 0
toInt (Succ x) = 1 + toInt x

fromInt :: Int -> Maybe Nat
fromInt i | i < 0     = Nothing
          | otherwise = Just $ fromInt' i
 where
  fromInt' 0  = Zero
  fromInt' i' = Succ $ fromInt' (i' - 1)

plus :: Nat -> Nat -> Nat
plus x        Zero = x
plus Zero     x    = x
plus (Succ x) y    = Succ (plus x y)

times :: Nat -> Nat -> Nat
times _        Zero       = Zero
times Zero     _          = Zero
times (Succ x) z@(Succ y) = Succ (y `plus` (x `times` z))

subtract :: Nat -> Nat -> Maybe Nat
subtract Zero     Zero     = Just Zero
subtract Zero     _        = Nothing
subtract succ     Zero     = Just succ
subtract (Succ x) (Succ y) = subtract x y