Add instance Monad ZipList

[Carter Schonwald]

ONe point worth mentioning, is that for *sized* lists, I believe a ziplist
monad instance *is* possible? I think ?
i have an example of the functor/ applicative sized list stuff here
https://github.com/wellposed/numerical/blob/master/src/Numerical/Array/Shape.hs#L252-L271

*i believe* the way to write the monad instance would be to implement a
join :: SizedLIst n (SizedList n a) -> SizedList n a
that picks the diagonal. But i could be wrong? it wasn't a priority for me
at the time, but would that "diagonal" / trace be the right way to induce a
bind?

On Thu, Jun 4, 2020 at 4:04 PM Roman Cheplyaka <roma at ro-che.info> wrote:

> On 04/06/2020 09.53, Dannyu NDos 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
>
> While others have commented on the general feasibility of the idea, the
> problem with this specific instance is that it appears to violate the
> associativity law:
>
> % ./ziplist --smallcheck-depth=3
>
> Monad laws
>   Right identity: OK
>     21 tests completed
>   Left identity:  OK
>     98 tests completed
>   Associativity:  FAIL (0.04s)
>     there exist {True->ZipList {getZipList = [True]};False->ZipList
> {getZipList = [False,True]}} {True->ZipList {getZipList =
> [True,True]};False->ZipList {getZipList = []}} ZipList {getZipList =
> [True,False]} such that
>       condition is false
>
> 1 out of 3 tests failed (0.05s)
>
>
> Here's the code I used for testing:
>
> {-# LANGUAGE ScopedTypeVariables, FlexibleInstances, MultiParamTypeClasses
> #-}
> import Control.Applicative
> import Control.Monad
> import Data.List
> import Data.Maybe
> import Test.SmallCheck.Series
> import Test.Tasty
> import Test.Tasty.SmallCheck
>
> 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 Serial m a => Serial m (ZipList a) where
>   series = ZipList <$> series
>
> main = defaultMain $ testGroup "Monad laws"
>   [ testProperty "Right identity" $ \(z :: ZipList Int) ->
>       (z >>= return) == z
>   , testProperty "Left identity" $ \(b :: Bool) (f :: Bool -> ZipList
> Bool) ->
>       (return b >>= f) == f b
>   , testProperty "Associativity" $
>       \(f1 :: Bool -> ZipList Bool)
>        (f2 :: Bool -> ZipList Bool)
>        (z :: ZipList Bool) ->
>          (z >>= (\x -> f1 x >>= f2)) == ((z >>= f1) >>= f2)
>   ]
>
> Roman
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