import Data.Ratio

{- Exercise 8.1 -}

approx :: (Fractional a, Ord a) => a -> a -> (a, Integer)
approx = undefined

{- Exercise 8.2 -} 

data MP = MP String

{- Exercise 8.2.1 -} 

nrmString, negateString :: String -> String 
nrmString = undefined
negateString = undefined

{- Exercise 8.2.2 -} 

instance Show MP where
  show = undefined
instance Eq MP where
  (==) = undefined

{- Exercise 8.2.3 -} 

instance Num MP where
  (+) = undefined
  (*) = undefined
  negate = undefined
  signum = undefined
  abs = undefined
  fromInteger = undefined

fromMP :: MP -> Integer
fromMP = undefined

-- some tests for Exercise 8.2 corresponding to text 
-- provided for convenience only

test82 = test821 && test822 && test823

test821 = test821ex && test821neg "+-++" && test821nrm "+-++"
test821ex =
  (nrmString "+-+-++" == "++") &&
  (nrmString "-+-+--" == "--") &&
  (nrmString "---++-++" == "") &&
  (negateString "+-+-++" == "-+-+--") &&
  (negateString "-+-+--" == "+-+-++")
test821nrm s = let t = nrmString s in nrmString t == t
test821neg s = negateString (negateString s) == s

test822 = ((MP "+-+-+") == (MP "--+++")) &&
  not ((MP "+-+-+") == (MP "")) &&
  (show (MP "+-+-+") == show "+-+-+")
  
three,four,mfive :: MP
three = fromInteger 3
four = fromInteger 4
mfive = fromInteger (-5)

test823 = (fromMP ((three + four) * mfive) == -35) &&
  (fromMP (four * (three + mfive)) == -8)