{-# LANGUAGE FlexibleInstances #-}

-- | The 'Vector' class represents elements of a normed vector
--   space. We define instances for all common numeric types.
module Vector
where

import Data.Number.BigFloat

class Vector a where
  norm :: RealFrac b => a -> b

-- Define instances for common numeric types.
instance Vector Integer where
  norm = fromInteger

instance Vector Rational where
  norm = fromRational

instance Epsilon e => Vector (BigFloat e) where
  norm = fromRational . toRational

instance Vector Double where
  norm = fromRational . toRational