Adding more instances to Kleisli: Generic, Monad, etc

[Fumiaki Kinoshita]

I see... Thanks for the explanation, I updated the patch.

2019年4月4日(木) 4:46 Edward Kmett <ekmett at gmail.com>:

> The issue is that you can't prove that whicher set of MonadPlus laws you
> are using _follows_ from whichever set of Alternative laws you are using.
>
> This discussion is somewhat hampered by neither one having a well-written
> set of laws, because we use MonadPlus in two or three mutually incompatible
> ways and for the most part "it just works" so people don't notice.
>
> Consider the space of laws mentioned in:
>
> https://wiki.haskell.org/MonadPlus_reform_proposal
>
> These don't necessarily follow from any of the popular Alternative law
> proposals.
>
> Left Zero:
>
> On the Applicative side you can do more to explore the tree, can "run"
> effects right to left, etc.
>
> We have a _left_ zero law for a monadplus:
>
> mzero >>= f = mzero
>
> but not a right one, just because of the existence of the function space
> in (>>=) that we can't see through
>
> (do putStrLn "die"; mzero) /= mzero
>
> But nothing keeps us from seeing through an (*>) to count up something on
> the right. Control.Applicative.Backwards exists and would satisfy a "right
> zero" law if the original satisfied a left zero law.
>
> Left Distribution:
>
> Similarly, you can imagine a data type that is Alternative and also a
> Monad, but where
>
> mplus a b >>= k = mplus (a >>= k) (b >>= k)
>
>
> fails to hold in the left distributive style, and it also fails to be in
> the left catch style.
>
> Without _retiring_ MonadPlus, we should at least use it consistently to
> imply the requirement of this sort of extra structure, even if it is
> ambiguous what that structure should be.
>
> -Edward
>
> On Wed, Apr 3, 2019 at 3:16 AM Fumiaki Kinoshita <fumiexcel at gmail.com>
> wrote:
>
>> I'm not quite sure what the point of MonadPlus is; the default
>> definitions are the Alternative methods. Would we ever want to have
>> MonadPlus different from Alternative?
>>
>> 2019年4月2日(火) 13:44 David Feuer <david.feuer at gmail.com>:
>>
>>> I think the MonadPlus instance should probably have a MonadPlus
>>> constraint, since MonadPlus makes a sort of statement about the interaction
>>> between >>= and mplus, even if it's a bit of an ambiguous one.
>>>
>>> On Tue, Apr 2, 2019, 12:30 AM Fumiaki Kinoshita <fumiexcel at gmail.com>
>>> wrote:
>>>
>>>> This is another part of
>>>> https://gitlab.haskell.org/ghc/ghc/merge_requests/644, which is
>>>> presumably much less controversial:
>>>>
>>>> Generic (Kleisli m a b)
>>>> Functor m => Functor (Kleisli m a)
>>>> Applicative m => Applicative (Kleisli m a)
>>>> Alternative m => Alternative (Kleisli m a)
>>>> Monad m => Monad (Kleisli m a)
>>>> (Alternative m, Monad m) => MonadPlus (Kleisli m a)
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