src/Normed.hs

   1 {-# LANGUAGE FlexibleInstances #-}
   2
   3 -- | The 'Normed' class represents elements of a normed vector
   4 --   space. We define instances for all common numeric types.
   5 module Normed
   6 where
   7
   8 import Data.Number.BigFloat
   9
  10 class Normed a where
  11   norm_p :: (Integral c, RealFrac b) => c -> a -> b
  12   norm_infty :: RealFrac b => a -> b
  13
  14 -- Define instances for common numeric types.
  15 instance Normed Integer where
  16   norm_p _ = fromInteger
  17   norm_infty = fromInteger
  18
  19 instance Normed Rational where
  20   norm_p _ = fromRational
  21   norm_infty = fromRational
  22
  23 instance Epsilon e => Normed (BigFloat e) where
  24   norm_p _ = fromRational . toRational
  25   norm_infty = fromRational . toRational
  26
  27 instance Normed Double where
  28   norm_p _ = fromRational . toRational
  29   norm_infty = fromRational . toRational