points.hs

{-# LANGUAGE GeneralizedNewtypeDeriving #-}

type CGFloat = Double

data CGPoint = CGPoint { x :: CGFloat, y :: CGFloat } deriving (Eq, Show)

instance Num CGPoint where
  (CGPoint x y) + (CGPoint x' y') = CGPoint { x = x+x', y = y+y' }
  (CGPoint x y) * (CGPoint x' y') = CGPoint { x = x*x', y = y*y' }
  (CGPoint x y) - (CGPoint x' y') = CGPoint { x = x-x', y = y-y' }
  abs (CGPoint x y) = CGPoint { x = abs x, y = abs y}
  signum = undefined
  fromInteger = undefined

class (Show a, Num a) => IsPoint a where
  zero :: a
  distance :: a -> a -> CGFloat

instance IsPoint CGPoint where
  zero = CGPoint 0 0
  distance = undefined -- blah blah blah

newtype NaturalPoint = NaturalPoint CGPoint
  deriving (Show, Eq, Num, IsPoint) -- we inherit the definitions of equality, numeric operations, and those defined in the IsPoint class

newtype UnscaledPoint = UnscaledPoint CGPoint
  deriving (Show, Eq, Num, IsPoint)

newtype ScaledPoint = ScaledPoint CGPoint
  deriving (Show, Eq, Num, IsPoint)