src/TwoTuple.hs

   1 -- | Implement ordered pairs all over again for fun (and to make sure
   2 --   that we can manipulate them algebraically). Also require (as
   3 --   opposed to the built-in ordered pairs) that the elements have
   4 --   matching types.
   5 --
   6 module TwoTuple
   7 where
   8
   9 import Vector
  10
  11
  12 data TwoTuple a = TwoTuple a a
  13   deriving (Eq)
  14
  15 instance (Show a) => Show (TwoTuple a) where
  16   show (TwoTuple x y) = "(" ++ (show x) ++ ", " ++ (show y) ++ ")"
  17
  18 instance Functor TwoTuple where
  19   f `fmap` (TwoTuple x1 y1) = TwoTuple (f x1) (f y1)
  20
  21 instance (RealFloat a) => Vector (TwoTuple a) where
  22   -- The standard Euclidean 2-norm. We need RealFloat for the square
  23   -- root.
  24   norm (TwoTuple x1 y1) = fromRational $ toRational (sqrt(x1^2 + y1^2))
  25
  26 -- | It's not correct to use Num here, but I really don't want to have
  27 --   to define my own addition and subtraction.
  28 instance Num a => Num (TwoTuple a) where
  29   -- Standard componentwise addition.
  30   (TwoTuple x1 y1) + (TwoTuple x2 y2) =
  31     TwoTuple (x1 + x2) (y1 + y2)
  32
  33   -- Standard componentwise subtraction.
  34   (TwoTuple x1 y1) - (TwoTuple x2 y2) =
  35     TwoTuple (x1 - x2) (y1 - y2)
  36
  37   -- Left undefined to prevent mistakes. One sane definition
  38   -- would be componentwise multiplication.
  39   (*) _ _ = error "multiplication of vectors is undefined"
  40
  41   abs _ = error "absolute value of vectors is undefined"
  42
  43   signum _ = error "signum of vectors is undefined"
  44
  45   fromInteger x = TwoTuple (fromInteger x) (fromInteger x)