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 data TwoTuple a = TwoTuple a a
   8   deriving (Eq, Show)
   9
  10 instance Functor TwoTuple where
  11   f `fmap` (TwoTuple x1 y1) = TwoTuple (f x1) (f y1)
  12
  13
  14 instance Num a => Num (TwoTuple a) where
  15   -- Standard componentwise addition.
  16   (TwoTuple x1 y1) + (TwoTuple x2 y2) =
  17     TwoTuple (x1 + x2) (y1 + y2)
  18
  19   -- Standard componentwise subtraction.
  20   (TwoTuple x1 y1) - (TwoTuple x2 y2) =
  21     TwoTuple (x1 - x2) (y1 - y2)
  22
  23   -- Left undefined to prevent mistakes. One sane definition
  24   -- would be componentwise multiplication.
  25   (*) _ _ = error "multiplication of vectors is undefined"
  26
  27   abs _ = error "absolute value of vectors is undefined"
  28
  29   signum _ = error "signum of vectors is undefined"
  30
  31   fromInteger x = TwoTuple (fromInteger x) (fromInteger x)