-- | A simple library for representing shapes as type classes.
module ShapeClass where

import Numeric (sqrt)


-- A type class for shapes that defines all the things shapes can do
-- (again, like an interface in Java).
class Shape s where
  area      :: s -> Float
  perimeter :: s -> Float


-- Adding our two initial shapes.

type Radius = Float
type Length = Float
type Width  = Float

data Circle    = Circle Radius          deriving (Eq,Show)
data Rectangle = Rectangle Length Width deriving (Eq,Show)

instance Shape Circle where
  area      (Circle r) = pi * r * r
  perimeter (Circle r) = 2 * pi * r

instance Shape Rectangle where
  area      (Rectangle l w) = l * w
  perimeter (Rectangle l w) = 2 * l + 2 * w


-- And now adding a new shape is a modular extension.

data Triangle = Triangle Length Width
  deriving (Eq,Show)

instance Shape Triangle where
  area      (Triangle l w) = (l * w) / 2
  perimeter (Triangle l w) = l + w + sqrt (l * l + w * w)

-- Add a combined shape

data SideBySide a b = SideBySide a b
  deriving (Eq,Show)

instance (Shape a, Shape b) => Shape (SideBySide a b) where
  area      (SideBySide s1 s2) = area s1 + area s2
  perimeter (SideBySide s1 s2) = undefined  -- ???


-- To add a new function, we might do something like this.

class Shape s => ExtShape s where
  diameter :: s -> Float

instance ExtShape Circle where
  diameter (Circle r) = 2 * r

instance ExtShape Rectangle where
  diameter (Rectangle l w) = sqrt (l*l + w*w)

instance ExtShape Triangle where
  diameter (Triangle l) = l