src/TwoTuple.hs

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