How can I make a Maybe-Transformer MaybeT into an instance of MonadWriter?

Question

I am trying to build a MaybeT-Transformer Monad, based on the example in the Real World Haskell, Chapter Monad Transformers:

data MaybeT m a = MaybeT { runMT :: m (Maybe a) }

instance (Monad m) => Monad (MaybeT m) where
  m >>= f = MaybeT $ do a <- runMT m
                        case a of 
                            Just x -> runMT (f x)
                            Nothing -> return Nothing
  return a = MaybeT $ return (Just a)

instance MonadTrans MaybeT where
  lift m = MaybeT $ do
                     a <- m
                     return (Just a)

This works fine, but now I want to make MaybeT an instance of MonadWriter:

instance (MonadWriter w m) => MonadWriter w (MaybeT m) where
 tell = lift . tell 
 listen m = MaybeT $ do unwrapped <- listen (runMT m)
                        return (Just unwrapped)

The tell is ok, but I can't get the listen function right. The best I could come up with after 1 1/2 days of constructor origami is the one you see above: unwrapped is supposed to be a tuple of (Maybe a, w), and that I want to wrap up in a Maybe-Type and put the whole thing in an empty MonadWriter.

But the compiler complains with:

Occurs check: cannot construct the infinite type: a = Maybe a
    When generalising the type(s) for `listen'
    In the instance declaration for `MonadWriter w (MaybeT m)'

What am I missing?

Answer 1

listen has type signature

  m a -> m (a, w)

i.e.

 MaybeT m a -> MaybeT m (a, w)

But MaybeT $ listen (runMT m) >>= return . Just has type signature

 MaybeT m a -> MaybeT m (Maybe a, w)

so the infinite type error is raised. You need to convert that unwrapped :: (Maybe a, w) into a Maybe (a, w) to proceed:

listen m = MaybeT $ do (val, wr) <- listen (runMT m)
                    case val of
                        Nothing -> return Nothing
                        Just x  -> return (Just (x, wr))

(BTW, there is an implementation of MaybeT in http://www.haskell.org/haskellwiki/New_monads/MaybeT.)