Use case for reflection non law abiding Eqs

gistfile1.hs

{-# LANGUAGE FlexibleContexts  #-}
{-# LANGUAGE ScopedTypeVariables  #-}
{-# LANGUAGE UndecidableInstances  #-}
{-# LANGUAGE GeneralizedNewtypeDeriving  #-}
{-# LANGUAGE StandaloneDeriving  #-}
module Approx where
import Data.Reflection
import Data.Proxy
import Foreign.Storable

newtype Approx s = Approx { unApprox :: Double } 
  deriving (Num, Show, Read, Storable) 

deriving instance Reifies s Double => Ord        (Approx s)
deriving instance Reifies s Double => Fractional (Approx s)
deriving instance Reifies s Double => Real       (Approx s)
deriving instance Reifies s Double => RealFrac   (Approx s)
deriving instance Reifies s Double => Floating   (Approx s)
deriving instance Reifies s Double => RealFloat  (Approx s)
deriving instance Reifies s Double => Enum       (Approx s)

mkApprox :: p s -> Double -> Approx s
mkApprox _ = Approx

-- replace with something like one of the anwsers in 
-- http://stackoverflow.com/questions/17333/most-effective-way-for-float-and-double-comparison
instance Reifies s Double => Eq (Approx s) where
  Approx x == Approx y = abs (y - x) < reflect (Proxy :: Proxy s)