Applicative and Functor

[Ross Paterson]

On Mon, Mar 06, 2006 at 12:36:01PM -0800, Ashley Yakeley wrote:
> 3. Making Functor and Foldable superclasses of Traversable, and getting 
> rid of fmapDefault and foldMapDefault.

If you have the superclasses, the defaults are more useful, for people
who only want to define Traversable.

> You might also consider:
> 
> 4. Adding a method to "class Traversable t" (with a default implementation):
> 
>   toList :: t a -> [a]

It's in Data.Foldable, but as a function, not a method:

toList :: Foldable t => t a -> [a]
#ifdef __GLASGOW_HASKELL__
toList t = build (\ c n -> foldr c n t)
#else
toList = foldr (:) []
#endif

> 5. Renaming pure as returnA and <*> as apA. Only it looks like your 
> Arrows stole returnA.

I rather like <*>, which comes from Doaitse Swierstra's parsing
combinators.

> If Functor is a superclass of Traversable, is it better to have traverse 
> and mapM as the methods, or sequence and sequenceA?

sequence(A) would be the categorical way, but it's often more efficient
to define traverse/mapM, particularly for non-regular types.

> What's your "instance Applicative []"? Does it use repeat and zapp, or 
> is it the "list of successes" (which would be compatible with "instance 
> Monad []")?

It matches the monad instance.  There's a newtype ZipList for the other one.