Add an extra class to Control.Applicative.Alternative
Edward Kmett
ekmett at gmail.com
Wed Apr 30 13:50:47 UTC 2014
A few thoughts:
* Splittable has been used as a name historically for splitting random
number generators and the like, so the name conflict (especially from
somewhere so prominent) would be unfortunate. That can of course be fixed
by a simple bikeshedding exercise.
* You should be able to implement this in one pass. e.g. f a -> Either a (f
a) rather than as two combinators, but it isn't clear to me what the
getNonPure branch can do other than return the original when the scan fails
or some partially zonked/expanded version of it.
* Personally, I'm rather hesitant, as there are a lot of points in the
design space and it isn't apparent how to implement/lift it for instance
over any of the monad transformers we have, so it is the kind of class that
lifting it too high up the import hierarchy will lead to users being forced
to write orphans, when they disagree about whether, say writer (mempty, a)
should be an effect or not or if you should be have instance (Monad m,
Splittable m, Eq s) => Splittable (StateT s m).
* The lack of any constraints on `f` tying it to anything else in
Control.Applicative gives me pause. Without any relationship to other types
it is harder to specify the laws and make them feel coherent rather than
bolted on.
Off the cuff, I'm currently -1 on this proposal, almost entirely because of
the concern I'd have that pushing it too far up the class hierarchy
actually invites a worse experience due to orphans than leaving it closer
to the use site where such ambiguous cases can be resolved unilaterally by
the author or ignored as irrelevant by them safely.
-Edward
On Wed, Apr 30, 2014 at 5:58 AM, Doaitse Swierstra <doaitse at swierstra.net>wrote:
> In the package uu-interleaved I introduce a new class
>
> class Splittable f where
> getNonPure :: f a -> Maybe (f a)Source
> getPure :: f a -> Maybe aSource
>
> which I use for splitting an applicative value into its pure and its
> non-pure part. This is then used in the rest of this package to define
> (non-ambiguous) interleaved structures (as a generalisation of permuted
> structures).
>
> My feeling that this class should be better located in
> Control.Applicative.Alternative.
>
> If you agree what are the steps to be taken?
>
> Doaitse
>
>
>
>
>
>
>
> On 01 Nov 2013, at 14:08 , Twan van Laarhoven <twanvl at gmail.com> wrote:
>
> > On 01/11/13 12:44, Nathan van Doorn wrote:
> >> Firstly, I don't see how IO is relevant here, it has neither a MonadPlus
> >> instance nor an Alternative instance.
> >
> > You are right. I thought it was an instance with mzero=fail "foo" and
> mplus=catch. But I was apparently mistaken. Objection withdrawn.
> >
> >> Secondly, the MonadPlus laws are documented in Control.Monad to be:
> >>
> >> mzero >>= f = mzero
> >> v >> mzero = mzero
> >
> > I missed them, because they are written in the documentation of mzero
> rather than the documentation of the class where I expected them.
> >
> >> Thirdly, the monoid laws are already documented. (<|>) must be "An
> associative
> >> binary operation", and empty "The identity of <|>". These are exactly
> the monoid
> >> laws. Perhaps they should be made more explicit, but that is a
> different issue.
> >
> > Missed this as well.
> >
> >> Fourthly, [] fulfils neither the left-distribution law or the
> left-catch law,
> >> and I doubt many people would be happy to lose []'s MonadPlus instance.
> >
> > List does satisfy left distribution:
> >
> > λ> (,) <$> ([1,2] <|> [3]) <*> [4,5]
> > [(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)]
> > λ> (,) <$> [1,2] <*> [4,5] <|> (,) <$> [3] <*> [4,5]
> > [(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)]
> > λ> quickCheck (\x y z -> ((,) <$> (x <|> y :: [Int]) <*> (z :: [Int]))
> > == (((,) <$> x <*> z) <|> ((,) <$> y <*> z)))
> > +++ OK, passed 100 tests.
> >
> > See also http://www.haskell.org/haskellwiki/MonadPlus. Then law which
> it doesn't is right distribution.
> >
> > Consider Maybe. it does satisfies left catch but not left distribution
> for MonadPlus. Since
> > mplus (Just False >>= guard) (Just True >>= guard) = Just ()
> > while
> > mplus (Just False) (Just True) >>= guard = Nothing
> >
> > But for Alternative, you can't have the failure of the second argument
> of (<*>) depend on the first. So Maybe *does* satisfy left distribution for
> Alternative. IMO that makes it a good candidate law.
> >
> >
> > Twan
> >
> >> I believe I have addressed all your issues. If I've missed something,
> please
> >> point it out to me.
> >>
> >> Nathan.
> >>
> >>
> >> On 1 November 2013 12:09, Twan van Laarhoven <twanvl at gmail.com
> >> <mailto:twanvl at gmail.com>> wrote:
> >>
> >> On 01/11/13 11:42, Nathan van Doorn wrote:
> >>
> >> Proposal: add the following laws to the documentation of
> >> Control.Applicative.__Alternative:
> >>
> >> * empty <*> a = empty
> >> * f <*> empty = empty
> >>
> >> > These laws correspond to the laws given in MonadPlus- if you take
> mzero =
> >> > empty and ap = (<*>), the ones in MonadPlus imply these- and I
> don't think
> >> > this proposal should be too controversial.
> >>
> >> As far as I can see, the documentation for MonadPlus does not
> specify these
> >> laws anywhere [1,2].
> >>
> >> Consider the IO monad. These laws claim that
> >>
> >> launchMissiles *> fail "empty" = fail "empty"
> >>
> >> This is clearly *not* true.
> >>
> >> --
> >>
> >> If we add laws, I think we should first consider the much more
> reasonable
> >> monoid laws
> >>
> >> identity
> >> empty <|> a = a
> >> a <|> empty = a
> >> associativity:
> >> (a <|> b) <|> c = a <|> (b <|> c)
> >>
> >> In the MonadPlus world, the controversial part is the choice between
> >>
> >> left distribution
> >> (f <|> g) <*> a = (f <*> a) <|> (g <*> a)
> >>
> >> or
> >>
> >> left catch
> >> pure a <|> b = pure a
> >>
> >> Your proposal would be
> >>
> >> left zero
> >>
> >> empty <*> a = empty
> >> right zero
> >>
> >> f <*> empty = empty
> >>
> >> And as mentioned above, right zero is problematic. The fmap version
> should
> >> be okay though
> >>
> >> map zero
> >> f <$> empty = empty
> >>
> >>
> >> Twan
> >>
> >> [1]
> >>
> http://hackage.haskell.org/__package/base-4.6.0.1/docs/__Control-Monad.html#t:MonadPlus
> >> <
> http://hackage.haskell.org/package/base-4.6.0.1/docs/Control-Monad.html#t:MonadPlus
> >
> >> [2] http://www.haskell.org/__haskellwiki/MonadPlus
> >> <http://www.haskell.org/haskellwiki/MonadPlus>
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