-- -*- haskell -*-

class Show a => Point a where
    translate :: a -> Double -> a
    my_length :: a -> Double
    pack :: a -> Packed_point
    pack = Packed_point

data Packed_point = forall a. Point a => Packed_point a

data Point2d = Point2d(Double, Double) deriving Show
data Point3d = Point3d(Double, Double, Double) deriving Show

instance Point Point2d where
    translate (Point2d(x1, y1)) x2 = Point2d(x1 + x2, y1)
    my_length (Point2d(x, y)) = sqrt (x * x + y * y)

instance Point Point3d where
    translate (Point3d(x1, y1, z1)) x2 = Point3d(x1 + x2, y1, z1)
    my_length (Point3d(x, y, z)) = sqrt (x * x + y * y + z * z)

instance Show Packed_point where
    show (Packed_point p) = show p

instance Point Packed_point where
    translate (Packed_point p) x = Packed_point(translate p x)
    my_length (Packed_point p) = my_length p
    pack = id

get_z (Point3d(_, _, z)) = z


p2d = Point2d(3, 4)
p3d = Point3d(1, 2, 2)

l = [ pack p2d, pack p3d ]

test p = (my_length p, translate p 1)

main = print (test p2d, test p3d, map my_length l,

              -- after translate, we still have a Point3d
	      get_z (translate p3d 1)) -- get_z (translate p2d 1) is not accepted