{-# OPTIONS -XTemplateHaskell -XMultiParamTypeClasses #-}
import UpdatableViewStub 

data Bin = Z | O deriving Eq -- Zero or One 

incr' [] = [O]
incr' (O:x) = Z:incr' x 
incr' (Z:x) = O:x 

decr' []  = []
decr' [O] = []
decr' (Z:x) = (O:decr' x)
decr' (O:x) = Z:x


{-# LINE 16 "../examples/msblsb.hs" #-}
data MSB = MSB [Bin] deriving Eq 

{-# LINE 29 "../examples/msblsb.hs" #-}
data LSB = LSB [Bin] deriving Eq 

instance UpdatableView (LSB ) (MSB ) where 
{-# LINE 52 "../examples/msblsb.hs" #-}
    view = $(foldT ''LSB) (reverseB) >>>> $(toC 'MSB)


zero :: MSB 
zero = 
  let
    zero = LSB []
  in (toView :: (LSB) ->  (MSB )) zero
incr :: MSB -> MSB 
incr = 
  let
    incr (LSB x) = LSB $ incr' x 
  in (toView :: (LSB -> LSB ) ->  (MSB -> MSB )) incr
-- :: cr (MSB x) = MSB $ reverse $ incr' (reverse x))
decr :: MSB -> MSB
decr = 
  let
    decr (LSB x) = LSB $ decr' x 
  in (toView :: (LSB -> LSB) ->  (MSB -> MSB)) decr
-- :: cr (LSB x) = LSB $ reverse $ decr' $ reverse x 
isZero :: MSB -> Bool 
isZero = 
  let
    isZero (LSB [])    = True 
    isZero (LSB (Z:x)) = isZero (LSB x)
    isZero _           = False
  in (toView :: (LSB -> Bool ) ->  (MSB -> Bool )) isZero
binFromInteger :: Integer -> MSB
binFromInteger = 
  let
    binFromInteger n = LSB $ f n 
      where 
        f 0 = []
        f n = if n `mod` 2 == 0 then Z:f (n `div` 2)
              else                 O:f (n `div` 2)
  in (toView :: (Integer -> LSB ) ->  (Integer -> MSB)) binFromInteger
{-# LINE 54 "../examples/msblsb.hs" #-}
instance Show MSB where 
    show n = show (f n)
        where f n | isZero n  = 0 
                  | otherwise = 1 + f (decr n)


instance Num MSB where
    (+) = add 
    (*) = mul 
    fromInteger = binFromInteger 
    abs = id 
    signum n | isZero n  = 0 
             | otherwise = 1 
    



normal :: MSB -> MSB 
normal (MSB x) = MSB (normal' x)
    where 
      normal' []     = []
      normal' (O:x)  = O:x 
      normal' (Z:x)  = normal' x 



add :: MSB -> MSB -> MSB 
add x y | isZero x  = y 
        | otherwise = add (decr x) (incr y)


mul :: MSB -> MSB -> MSB 
mul x y | isZero x  = zero
        | otherwise = add y (mul (decr x) y)