Yeah I tried applicative, but saw that the <*> operator didn't do what I want with lists, and started looking elsewhere.
I didn't even see the ZipList! Actually the other problem is that the data structure that I'm using won't support pure, so no Applicative :(
Though for a generic zip, Applicative may be the better general purpose way to go.

I didn't see TypeCompose and category-extras either those look pretty sweet :)
Those would have worked. But I think I in my case, my version is a bit more general.

Thanks for the input!
It has been very enlightening. :)

Hmmm I also should have pulled the zips out of the typeclass:

class (Foldable f) => Zippable f where
  fmaps :: (Foldable g) => g (a -> b) -> f a -> f b
  fmaps' :: [a -> b] -> f a -> f b -- to save a step on instance implementation
 
  fmaps fs a = fmaps' (toList fs) a
  fmaps' fs a = fmaps fs a
 
zipWith :: (Zippable f) => (a -> b -> c) -> f a -> f b -> f c
zipWith f a b = fmaps (fmap f a) b
zip :: (Zippable f) => f a -> f b -> f (a, b)
zip a b = zipWith (,) a b
unzip :: (Functor f) => f (a, b) -> (f a, f b)
unzip a = (fmap fst a, fmap snd a)
 
instance Zippable [] where
  fmaps' (fx:fs) (x:xs) = fx x : fmaps' fs xs
  fmaps' _       _      = []

On Thu, Jul 16, 2009 at 8:40 PM, Ryan Ingram <ryani.spam@gmail.com> 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@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