Alright, I return from the land of transformers with a solution:


import Control.Monad.Trans.Class
import Control.Monad.Trans.Maybe

main = sequenceMTAll (lst' >>= map (getB' >=> getC'))

lst' = lift lst :: MaybeT m [a]
getB' = MaybeT . getMB
getC' = lift . getC

sequenceMTAll :: (Monad m) => [MaybeT m a] -> m [a]
sequenceMTAll (x:xs) = do
    y <- runMaybeT x
    case y of
      Nothing -> sequenceMTAll xs
      Just z -> sequenceMTAll xs >>= return . (z:)
sequenceMTAll [] = return []


(Of course in real code I'd just modify lst, getMB, getC, etc. to fit the new types. The crux here is sequenceMTAll.)

Am I abusing Maybe too much?

Mike S Craig
(908) 328 8030


On Thu, Sep 15, 2011 at 1:15 AM, Brent Yorgey <byorgey@seas.upenn.edu> wrote:
On Wed, Sep 14, 2011 at 09:21:04PM -0400, Michael Craig wrote:
> Brent: Thanks for reminding me about (>=>). Far more readable! But regarding
> the sequence thing: I can think of all sorts of reasons why we'd want to do
> a single traversal. How about when lst is long or infinite? In general, it's
> more useful to produce output incrementally than all at once at the
> end.

Yes, producing output incrementally is great!  My point is that
usually laziness will take care of it for you, without having to
worry about it specifically.

In this particular case, most monads will not actually allow
incremental processing anyway.  For example, suppose m = Maybe.  Then
when mapping getMB over lst, any particular element could cause the
whole computation to fail.  So we cannot output anything based on the
first elements in the list until we have processed the entire list,
because until we get to the very end of the list we do not know
whether to begin by outputting 'Just' or 'Nothing'.

-Brent

>
> Mike S Craig
> (908) 328 8030
>
>
> On Wed, Sep 14, 2011 at 8:18 PM, Brent Yorgey <byorgey@seas.upenn.edu>wrote:
>
> > On Wed, Sep 14, 2011 at 06:48:29PM -0400, Michael Craig wrote:
> > > Say we've got these types
> > >
> > > lst :: m [a]
> > > getMB :: a -> m (Maybe b)
> > > getC :: b -> m c
> > >
> > > and we want to map getMB and getC over the elements of lst, all the while
> > > discarding elements x where getMB x == Nothing.
> > >
> > > (This could be generalized more by replacing Maybe with some monad m',
> > but
> > > let's run with Maybe because it's easy to talk about.)
> > >
> > > The best I've got (after some help on IRC) is this not-so-easy-to-read
> > > oneliner:
> > >
> > > lst >>= (\x -> mapM (liftM (liftM getC) (getMB x)) >>= sequence
> > > . catMaybes
> >
> > How about this:
> >
> >  lst >>= (mapM getMB >=> (return . catMaybes) >=> mapM getC)
> >
> > Everyone always forgets about (>=>).
> >
> > > This is hard to read, but it's also bad because we run sequence twice
> > (once
> > > inside of mapM). If we want to do multiple things to each element of lst,
> > it
> > > would be nice to process each element completely before moving on to the
> > > next.
> >
> > I wouldn't worry about running sequence twice.  Processing things by
> > chaining whole-structure transformations is the Haskell Way (tm).  All
> > that business about "doing only one traversal" is for people
> > programming in strict languages to worry about. The compiler can often
> > turn a chain of wholesale transformations into a single traversal
> > anyway.  In short, I see no particular reason why it is "nice" to
> > process each element completely before moving on.  Isn't it nicer to
> > be able to think in a more modular style?
> >
> > -Brent
> >
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