Re: [Haskell-cafe] Applicative but not Monad

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:

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