Adding more instances to Kleisli: Generic, Monad, etc

[Edward Kmett]

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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