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@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@gmail.com> wrote:
Agreed, that would be a great addition.

On Thu, Jun 4, 2020, 8:31 AM Simon Jakobi <simon.jakobi@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@gmail.com>:
>
> David is right. This can't happen, unfortunately
>
> On Thu, Jun 4, 2020, 12:48 AM David Feuer <david.feuer@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@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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