Re: Add instance Monad ZipList

4 Jun 2020

      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...

*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  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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Re: Add instance Monad ZipList

Carter Schonwald