[Haskell-cafe] Why is there no Zippable class? Would this work?

[Dan Weston]

Way cool. I have gained newfound respect for what I don't know. :)

Can there ever be more than one (observably different) valid definition 
of pure for a given <*> that obeys all the laws? I would imagine that 
there could be at most one.

Dan

Ryan Ingram wrote:
> (I'm going to play fast and loose with constructors for this post,
> treating MyList and ZipList as if they were [])
> 
> On Thu, Jul 16, 2009 at 4:10 PM, Dan Weston<westondan at imageworks.com> wrote:
>> -- different from [], sum rather than product
>> instance Applicative MyList where
>>  pure x = x ::: Nil
>>  (<*>) (f ::: fs) (x ::: xs) = f x ::: (fs <*> xs)
>>  (<*>) _ _ = Nil
> 
> Unfortunately, this instance doesn't fulfill this Applicative law:
>      pure id <*> f = f
> 
> pure id <*> [1,2,3]
> = [id] <*> [1,2,3]
> = [id 1]
> = [1]
> 
> Fortunately, the solution already exists in Control.Applicative:
> 
>> -- | Lists, but with an 'Applicative' functor based on zipping, so that
>> --
>> -- @f '<$>' 'ZipList' xs1 '<*>' ... '<*>' 'ZipList' xsn = 'ZipList' (zipWithn f xs1 ... xsn)@
>> --
>> newtype ZipList a = ZipList { getZipList :: [a] }
>>
>> instance Functor ZipList where
>>         fmap f (ZipList xs) = ZipList (map f xs)
>>
>> instance Applicative ZipList where
>>         pure x = ZipList (repeat x)
>>         ZipList fs <*> ZipList xs = ZipList (zipWith id fs xs)
> 
> In this case:
> 
> pure id <*> [1,2,3]
> = [id, id, ...] <*> [1,2,3]
> = [id 1, id 2, id 3]
> = [1,2,3]
> 
>   -- ryan
> 
>