{-# OPTIONS_GHC -fno-warn-tabs -fno-warn-orphans #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE IncoherentInstances #-}

module Math.Vector where


data Vec2 a = Vec2 a a deriving (Read, Show, Eq, Ord)

instance Functor Vec2 where
  fmap f (Vec2 x y) = Vec2 (f x) (f y)

instance Applicative Vec2 where
  pure a = Vec2 a a
  (Vec2 f g) <*> (Vec2 x y) = Vec2 (f x) (g y)

instance Foldable Vec2 where
	foldr f a (Vec2 x y) = f x $ f y $ a


class (Foldable v, Applicative v) => Vector v

instance Vector Vec2

instance (Vector v, Num a) => Num (v a) where
  v + v2 = pure (+) <*> v <*> v2
  v - v2 = pure (-) <*> v <*> v2
  v * v2 = pure (*) <*> v <*> v2
  signum v = pure signum <*> v
  abs v = pure abs <*> v
  fromInteger i = pure (fromInteger i)


--dot :: (Vector v, Num a, Num (v a)) => v a -> v a -> a -- works without IncoherentInstances
dot :: (Vector v, Num a) => v a -> v a -> a
dot v v2 = sum $ v*v2