On Sun, May 26, 2013 at 3:57 AM, Petr Pudlák
I think you hit the nail on the head here. The only places when I missed something like Pointed were when I wanted to abstract building some kind of collection (Set / [] / Seq / ...). They're all monoids, but you need some way how to construct singleton collections. Having MonoidOver would solve precisely this problem. I'd certainly prefer something like this over Pointed.
One point in Pointed's favor is that it lets one express "affine traversals" -- that is, a function with a type like "Pointed f => (a -> f b) -> T a -> f (T b)". This is like a traversal -- traverse :: Applicative f => (a -> f b) -> T a -> f (T b) for some Traversable T -- but guarantees that it traverses either 0 or 1 elements, rather than 0-or-more. With a Pointed superclass for Applicative an affine traversal can automatically be used as a regular traversal. I don't know that this is worth adding a superclass for -- certainly it should be a separate proposal -- but it's useful for some code, e.g. lens, to get stronger type guarantees. Shachaf