Numerals in Positional Notation   [14]

Abstracting from the numeric structure

Unfortunately, the "abstract" function we have defined is restricted to working on integers (or at least numbers): it takes a numeric "seed" and grows it into a list of results, by breaking off a piece to put in the list (here also a number) and then continuing on with some new "seed" value.

But to make the function truly useful, we will want to generalize from the case of a numeric seed to allow any type of seed. We can do this by adding a predicate that tells us when to stop (for numbers, this might be when we reach zero, but not necessarily).

str b = unfoldl (`divMod` b) []

unfoldl f a 0 = a
unfoldl f a n = unfoldl f (r:a) m
                where (m,r) = f n

str b = unfoldl (==0) (`divMod` b)

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

Notes

• the type of our unfoldl function is now generalized as follows:

  unfoldl :: (a -> (a,b)) -> a -> [b]