-- | Implement ordered pairs all over again for fun (and to make sure
--   that we can manipulate them algebraically).
--
module TwoTuple
where

data TwoTuple a = TwoTuple a a
  deriving (Eq, Show)

instance Functor TwoTuple where
  f `fmap` (TwoTuple x1 y1) = TwoTuple (f x1) (f y1)


instance Num a => Num (TwoTuple a) where
  -- Standard componentwise addition.
  (TwoTuple x1 y1) + (TwoTuple x2 y2) =
    TwoTuple (x1 + x2) (y1 + y2)

  -- Standard componentwise subtraction.
  (TwoTuple x1 y1) - (TwoTuple x2 y2) =
    TwoTuple (x1 - x2) (y1 - y2)

  -- Left undefined to prevent mistakes. One sane definition
  -- would be componentwise multiplication.
  (*) _ _ = error "multiplication of vectors is undefined"

  abs _ = error "absolute value of vectors is undefined"

  signum _ = error "signum of vectors is undefined"

  fromInteger x = TwoTuple (fromInteger x) (fromInteger x)