gistfile1.hs

newtype Vector2 a = Vector2 (a, a)

instance Eq a => Eq (Vector2 a) where
  Vector2 x == Vector2 y = x == y

instance Functor Vector2 where
  fmap f (Vector2 (a, b)) = Vector2 (f a, f b)

instance Applicative Vector2 where
  pure x = Vector2 (x, x)
  Vector2 (f, g) <*> Vector2 (x, y) = Vector2 (f x, g y)

instance Foldable Vector2 where
  foldr f z (Vector2 (x, y)) = f y . f a $ z

instance (Eq a, Ord a) => Ord (Vector2 a) where
  compare x y = fold $ compare <$> x <*> y

instance Num a => Num (Vector2 a) where
  Vector2 (a, b) + Vector2 (c, d) = Vector2 (a + c, b + d)
  abs = (abs <$>)
  signum = (signum <$>)
  fromInteger = undefined -- Is there a sensible instance?
  (*) = undefined -- There is no sensible instance for a commutative-associative multiplication *: V x V -> V