Add an extra class to Control.Applicative.Alternative
Doaitse Swierstra
doaitse at swierstra.net
Wed Apr 30 09:58:11 UTC 2014
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 Objection withdrawn.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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