MonadWriter instances for IterT and FreeT

[ekmett]

MonadWriter instances for IterT and FreeT

[fizruk]

I would appreciate if someone proved the implementation wrong/correct or at least pointed to the laws to be considered.

[ekmett]

I'm going to leave this one open until I can get a longer look at it.

[fizruk]

Here is a bunch of "laws":

listen (return a) = return (a, mempty)
listen (tell w) = tell w >> return ((), w)
listen (m >>= k)
  = listen m >>= \(x, w) -> listen (k x) >>= \(y, w') -> return (y, (w <> w'))

pass (return (a, f)) = tell (f mempty) >> return a
pass (tell w >> m) = pass (second (. (w <>)) `liftM` m)
pass (m >>= k)
  = pass ((,const mempty) `liftM` listen m) >>= \(x, w) -> pass (tell w >> k x)

I believe these capture the expectations given that pass is the only way to modify output.

This modification gets rid of Functor constaint and resolves issue (extra delay) with the second law (listen-tell):

instance (MonadWriter w m) => MonadWriter w (IterT m) where
  tell = lift . tell
  listen (IterT m) = IterT $ liftM concat' $ listen (fmap listen `liftM` m)
    where
      concat' (Left  x, w) = Left (x, w)
      concat' (Right y, w) = Right $ second (w <>) <$> y
  pass m = IterT . pass' . runIterT . hoistIterT clean $ listen m
    where
      clean = pass . liftM (\x -> (x, const mempty))
      pass' = join . liftM (either
                             (\((x, f), w) -> tell (f w) >> return (Left x))
                             (return . Right . IterT . pass' . runIterT))

I don't know if this fulfills all of the outlined laws.

[ekmett]

Going through closing out old issues. I have no issue with this instance if you want to add it.

[fizruk]

Sure, will prepare a pull request now.

[fizruk]

Merged in #45.