Add instance Monad ZipList

[Gershom B]

I know of counterexamples that show why the “obvious” instances don’t work. One nice one is here:

https://www.reddit.com/r/haskell/comments/nfyvy/instance_monad_ziplist_where/c38x9q9?utm_source=share&utm_medium=web2x

But I don’t know of a simple full proof of why no such instance is possible. My guess would be that we should consider the action of the operations on lengths of lists, and show that the requirements for monad and ziplist conflict.

-g
On Jun 4, 2020, 11:57 AM -0400, David Feuer <david.feuer at gmail.com>, wrote:
> To add documentation, we need an explanation of *why* it's impossible.
>
> > On Thu, Jun 4, 2020, 11:35 AM chessai . <chessai1996 at gmail.com> wrote:
> > > Agreed, that would be a great addition.
> > >
> > > > On Thu, Jun 4, 2020, 8:31 AM Simon Jakobi <simon.jakobi at googlemail.com> wrote:
> > > > > This sounds worth documenting though.
> > > > >
> > > > > Dannyu, would you be interested in updating the ZipList docs to say
> > > > > why it doesn't have a Monad instance?
> > > > >
> > > > > Cheers,
> > > > > Simon
> > > > >
> > > > > Am Do., 4. Juni 2020 um 17:21 Uhr schrieb chessai . <chessai1996 at gmail.com>:
> > > > > >
> > > > > > David is right. This can't happen, unfortunately
> > > > > >
> > > > > > On Thu, Jun 4, 2020, 12:48 AM David Feuer <david.feuer at gmail.com> wrote:
> > > > > >>
> > > > > >> I don't remember why right now, but it's moderately well-known that there is no possible Monad instance compatible with the Applicative instance for ZipList. See the answers to https://stackoverflow.com/questions/6463058/help-on-writing-the-colist-monad-exercise-from-an-idioms-intro-paper by pigworker (Conor McBride) and C. A. McCann.
> > > > > >>
> > > > > >> On Thu, Jun 4, 2020, 2:53 AM Dannyu NDos <ndospark320 at gmail.com> wrote:
> > > > > >>>
> > > > > >>> instance Monad ZipList where
> > > > > >>>     ZipList [] >>= _ = ZipList []
> > > > > >>>     ZipList (x:xs) >>= f = ZipList $ do
> > > > > >>>         let ZipList y' = f x
> > > > > >>>         guard (not (null y'))
> > > > > >>>         let ZipList ys = ZipList xs >>= ZipList . join . maybeToList . fmap snd . uncons . getZipList . f
> > > > > >>>         head y' : ys
> > > > > >>>
> > > > > >>> instance MonadFail ZipList where
> > > > > >>>     fail _ = empty
> > > > > >>>
> > > > > >>> instance MonadPlus ZipList
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