{-# LANGUAGE FlexibleContexts           #-}
{-# LANGUAGE GeneralizedNewtypeDeriving #-}
{-# LANGUAGE NoMonomorphismRestriction  #-}
{-# LANGUAGE StandaloneDeriving         #-}
import           Control.Lens

import           Data.Ratio

newtype Bits = Bits Rational deriving (Show,Eq, Num, Fractional)

newtype Bytes = Bytes Rational deriving (Show,Eq, Num, Fractional )

newtype Kilo a = Kilo a deriving Show

deriving instance Num a => Num (Kilo a)

deriving instance Fractional a => Fractional (Kilo a)

type Mega a  = Kilo (Kilo  a)
type Giga a  = Kilo (Mega  a)


bits :: Iso' Bytes Bits
bits = iso (\(Bytes s) -> Bits $ 8 * s) (\(Bits s) -> Bytes $ s / 8)

k :: (Fractional a, Num a) => Iso' (Kilo a) a
k = iso (\(Kilo s) -> 1000 * s) (\s -> Kilo $ s / 1000)

m = k . k

g = k . m

kb :: (Fractional a, Num a) => Iso' (Kilo a) a
kb = iso (\(Kilo s) -> 1024 * s) (\s -> Kilo $ s / 1024)

mb = kb . kb

gb = kb . mb