Add instance Monad ZipList
David Feuer
david.feuer at gmail.com
Thu Jun 4 23:49:53 UTC 2020
Yes, for length-indexed lists that's fine, basically a special case of
Reader.
On Thu, Jun 4, 2020, 7:48 PM Carter Schonwald <carter.schonwald at gmail.com>
wrote:
> 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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