[Haskell-cafe] Applicative but not Monad
Yusaku Hashimoto
nonowarn at gmail.com
Fri Oct 30 13:33:04 EDT 2009
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 <tom.davie at gmail.com> wrote:
> On Fri, Oct 30, 2009 at 5:59 PM, Luke Palmer <lrpalmer at gmail.com> wrote:
>>
>> On Fri, Oct 30, 2009 at 10:39 AM, Tom Davie <tom.davie at gmail.com> wrote:
>> > 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
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