Add instance Monad ZipList

[Zemyla]

Here's my thoughts on why it's impossible:

ZipList is basically ReaderT Natural Maybe with the requirement that
  f m === Nothing -> forall n > m. f n === Nothing

The Applicative and Alternative instances are derived straightforwardly in
this manner and satisfy the requirements, but there is no way to verify the
requirement for the Monad instance. I'm pretty sure that this:
  ZipList [0..] >>= (\n -> if even n then pure (div n 2) else empty)
would produce nonsense no matter the definition of (>>=).

On Thu, Jun 4, 2020, 10:57 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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