```{-# LANGUAGE MultiParamTypeClasses, FlexibleInstances #-}
-----------------------------------------------------------------------------------------
-- |
-- Module      :  FRP.Yampa.Point2
-- Copyright   :  (c) Antony Courtney and Henrik Nilsson, Yale University, 2003
--
-- Maintainer  :  nilsson@cs.yale.edu
-- Stability   :  provisional
-- Portability :  non-portable (GHC extensions)
--
-- 2D point abstraction (R^2).
--
-- ToDo: Deriving Show, or provide dedicated show instance?
--
-----------------------------------------------------------------------------------------

module FRP.Yampa.Point2 (
-- module AFRPVectorSpace,
-- module AFRPAffineSpace,
-- module AFRPVector2,
Point2(..),	-- Non-abstract, instance of AffineSpace
point2X,	-- :: RealFloat a => Point2 a -> a
point2Y	-- :: RealFloat a => Point2 a -> a
) where

import FRP.Yampa.VectorSpace ()
import FRP.Yampa.AffineSpace
import FRP.Yampa.Vector2
import FRP.Yampa.Forceable

------------------------------------------------------------------------------
-- 2D point, constructors and selectors.
------------------------------------------------------------------------------

data RealFloat a => Point2 a = Point2 !a !a deriving (Eq, Show)

point2X :: RealFloat a => Point2 a -> a
point2X (Point2 x _) = x

point2Y :: RealFloat a => Point2 a -> a
point2Y (Point2 _ y) = y

------------------------------------------------------------------------------
-- Affine space instance
------------------------------------------------------------------------------

instance RealFloat a => AffineSpace (Point2 a) (Vector2 a) a where
origin = Point2 0 0

(Point2 x y) .+^ v = Point2 (x + vector2X v) (y + vector2Y v)

(Point2 x y) .-^ v = Point2 (x - vector2X v) (y - vector2Y v)

(Point2 x1 y1) .-. (Point2 x2 y2) = vector2 (x1 - x2) (y1 - y2)

------------------------------------------------------------------------------
-- Forceable instance
------------------------------------------------------------------------------

instance RealFloat a => Forceable (Point2 a) where
force = id
```