--------------------
-- Base conversions for numerals

unfoldl p f a x = if p x then a else unfoldl p f (y:a) r
                  where (r,y) = f x

sumProd b n m = n * b + m

contract b = foldl          (sumProd b)  0
expand   b = unfoldl (==0) (`divMod` b) []

number b = contract b . map digitToInt
string b = map intToDigit  .  expand b

[ (bin, unbin), (dec, undec), (hex, unhex) ] 
  = map base [2, 10, 16]
    where base b = (string b, number b)



--------------------
-- unfoldr from the List module

unfoldr f b = case f b of
                Nothing    -> []
                Just (a,b') -> a : unfoldr f b'


unfold :: (b -> Bool) -> (b -> a) -> (b -> b) -> b -> [a] 
unfold p h g b = if p b
                    then h b : unfold p h g (g b)
                    else []