wren ng thornton wrote:

...

how, for instance, turn a nested Map like

Map Int (Map Int (Map String Double)

into a "zipped" version. You can't. Or rather, you can't unless you have access to the implementation of the datastructure itself; and Data.Map doesn't provide enough details to do it.

Actually Data.Map does provide enough details: Data.Map is a member of Traversable and anything that supports Traversable (at the very least, provides something like mapM) can be turned into a Zipper. Generically. We do not need to know any details of a data structure (or if it is a data structure: the collection may well be ephemeral, whose elements are computed on the fly). Please see the enclosed code; the code defines a function tmod to interactively traverse the collection, displaying the elements one by one and offering to modify the current element, or quit the traversal. The enclosed code implements the zipper that can only move forward. Chung-chieh Shan has well described how to turn any one-directional zipper into bi-directional. Again generically. http://conway.rutgers.edu/~ccshan/wiki/blog/posts/WalkZip3/ Although the enclosed code demonstrates the possibility of turning a Data.Map into a Zipper, one may wonder about the merits of that endeavour. Data.Map is a very rich data structure, with efficient means to focus on any given element and replace it (e.g., elemAt, replaceAt) and to incrementally deconstruct the map (deleteMax, deleteMin, minView, etc). Triple-nested maps can be processed just as effectively. The case for a tree of maps (which is essentially a file system) is described in http://okmij.org/ftp/Computation/Continuations.html#zipper-fs module ZT where import qualified Data.Traversable as T import Control.Monad.Cont import qualified Data.Map as M -- In the variant Z a k, a is the current, focused value -- evaluate (k Nothing) to move forward -- evaluate (k v) to replace the current value with v and move forward. data Zipper t a = ZDone (t a) | Z a (Maybe a -> Zipper t a) make_zipper :: T.Traversable t => t a -> Zipper t a make_zipper t = reset $ T.mapM f t >>= return . ZDone where f a = shift (\k -> return $ Z a (k . maybe a id)) zip_up :: Zipper t a -> t a zip_up (ZDone t) = t zip_up (Z _ k) = zip_up $ k Nothing reset :: Cont r r -> r reset m = runCont m id shift :: ((a -> r) -> Cont r r) -> Cont r a shift e = Cont (\k -> reset (e k)) -- Tests -- sample collections tmap = M.fromList [ (v,product [1..v]) | v <- [1..10] ] -- extract a few sample elements from the collection trav t = let (Z a1 k1) = make_zipper t (Z a2 k2) = k1 Nothing (Z a3 k3) = k2 Nothing (Z a4 k4) = k3 Nothing in [a1,a3,a4] travm = trav tmap -- Traverse and possibly modify elements of a collection tmod t = loop (make_zipper t) where loop (ZDone t) = putStrLn $ "Done\n: " ++ show t loop (Z a k) = do putStrLn $ "Current element: " ++ show a ask k ask k = do putStrLn "Enter Return, q or the replacement value: " getLine >>= check k check k "" = loop $ k Nothing check k "\r" = loop $ k Nothing check k ('q':_) = loop . ZDone . zip_up $ k Nothing check k s | [(n,_)] <- reads s = loop $ k (Just n) -- replace check k _ = putStrLn "Repeat" >> ask k testm = tmod tmap