Re: [Haskell-cafe] Applicative but not Monad

If you use a monad instance for ZipLists as follows: instance Monad ZipList where return x = ZipList $ repeat x ZipList [] >>= _ = ZipList [] xs >>= f = diagonal $ fmap f xs (where diagonal pulls out the diagonal elements of a ziplist of ziplists) It will satisfy all the monad laws _except_ when the function f (in xs >>= f) returns ziplists of different length depending on the value passed to it. If f always returns lists of the same length, the monad laws should still hold even if the lists are not infinite in length. I have a fixed size list type (http://github.com/jvranish/FixedList) that uses an instance like this and it always satisfies the monad laws since the length of the list can be determined from the type so f is forced to always return the same size of list. I hope that helps things make sense :) - Job On Fri, Oct 30, 2009 at 1:33 PM, Yusaku Hashimoto wrote:

Thanks for fast replies! Examples you gave explain why all Applicatives are not Monads to me.

And I tried to rewrite Bob's Monad instance for ZipList with (>>=).

import Control.Applicative

instance Monad ZipList where return = ZipList . return (ZipList []) >>= _ = ZipList [] (ZipList (a:as)) >>= f = zlHead (f a) `zlCons` (ZipList as >>= f)

zlHead :: ZipList a -> a zlHead (ZipList (a:_)) = a zlCons :: a -> ZipList a -> ZipList a zlCons a (ZipList as) = ZipList $ a:as zlTail :: ZipList a -> ZipList a zlTail (ZipList (_:as)) = ZipList as

I understand if this instance satisfies the laws, we can replace <$> with `liftM` and <*> and `ap`. And I found a counterexample (correct me if I'm wrong).

*Main Control.Monad> getZipList $ (*) <$> ZipList [1,2] <*> ZipList [3,4,5] [3,8] *Main Control.Monad> getZipList $ (*) `liftM` ZipList [1,2] `ap` ZipList [3,4,5] [3,6]

Cheers, -~nwn

On Sat, Oct 31, 2009 at 2:06 AM, Tom Davie wrote:

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On Fri, Oct 30, 2009 at 5:59 PM, Luke Palmer wrote:

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On Fri, Oct 30, 2009 at 10:39 AM, Tom Davie

wrote:

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Of note, there is a sensible monad instance for zip lists which I *think* agrees with the Applicative one, I don't know why they're not monads: instance Monad (ZipList a) where return = Ziplist . return join (ZipList []) = ZipList [] join (ZipList (a:as)) = zlHead a `zlCons` join (map zlTail as)

IIRC, that doesn't satisfy the associativity law, particularly when you are joining a list of lists of different lengths. 2 minutes of experimenting failed to find me the counterexample though.

Cool, thanks Luke, that explains why this is available in Stream, but not in ZipList too. Bob _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe

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