[Moved to haskell-cafe] At 20:40 04/06/03 +0200, Tomasz Zielonka wrote:

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I'm trying to figure if there's any way I can use (say) monads to

collect > > > values from a Functor. > > > > > > For example, suppose I have a tree of some values that supports fmap, is > > > there any way I can use the fmap function to collect a list of all the node > > > values? > > > > No, you need a fold to do that.

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Or a variant of Functor constructor class that I have proposed some time ago on comp.lang.functional:

class FunctorM t where fmapM :: Monad m => (a -> m b) -> (t a -> m (t b)) fmapM_ :: Monad m => (a -> m b) -> (t a -> m ()) fmapM_ f t = fmapM f t >> return ()

instance FunctorM [] where fmapM = mapM fmapM_ = mapM_

I've done a little playing with this, which seems to work on a small scale, and am just wanting to check if I am properly understanding your idea... 'Arc' is a small part of a data structure I am playing with, which is currently a Functor. I've made this an instance of FunctorM, defining fmapM which has some recognizable similarity with fmap. Finally, there's a monad type CollectNodes using Control.Monad.State and constructor function mungeNode to actually apply the transformation and collect results. It seems to work -- is this roughly what you envisaged? [[ -- spike-FunctorM.hs import Control.Monad.State class FunctorM t where fmapM :: Monad m => (a -> m b) -> (t a -> m (t b)) fmapM_ :: Monad m => (a -> m b) -> (t a -> m ()) fmapM_ f t = fmapM f t >> return () data Arc lb = Arc { asubj, apred, aobj :: lb } deriving (Eq, Show) instance Functor Arc where fmap f (Arc s p o) = Arc (f s) (f p) (f o) instance FunctorM Arc where -- fmapM :: (lb -> m l2) -> Arc lb -> m (Arc l2) fmapM f (Arc s p o) = do { s' <- f s ; p' <- f p ; o' <- f o ; return $ Arc s' p' o' } -- CollectNodes a b is a state transformer on a state of -- type '[a]', which additionally returns a value of type 'b'. type CollectNodes a b = State [a] b -- constructor State { runState :: (s -> (a, s)) } -- runState :: State s a -> s -> (a, s) -- evalState :: State s a -> s -> a -- execState :: State s a -> s -> s -- mapState :: ((a, s) -> (b, s)) -> State s a -> State s b -- withState :: (s -> s) -> State s a -> State s a -- instance MonadState s (State s) -- get :: m s -- (CollectNodes a b) [a] -- put :: s -> m () -- modify :: (MonadState s m) => (s -> s) -> m () -- gets :: (MonadState s m) => (s -> a) -> m a mungeNode :: lb -> CollectNodes lb (Maybe lb) mungeNode lab = do { modify (lab:) -- accumulate labels ; return (Just lab) -- return modified label } a1 = Arc "s1" "p1" "o1" r1 = runState ( fmapM mungeNode a1 ) [] ]] I think, but haven't worked out the details, that one could define fmap in terms of fmapM. (I read somewhere about an identity Monad, but can't recall the reference -- I think that might do it.) I'm also harbouring a suspiscion that this FunctorM framework might be subsumed by gmap and friends, but I'll leave that for another day. #g ------------------- Graham Klyne PGP: 0FAA 69FF C083 000B A2E9 A131 01B9 1C7A DBCA CB5E