On 7 September 2010 12:18, wren ng thornton
On 9/6/10 2:35 AM, Ivan Lazar Miljenovic wrote:
Well, if we consider what this does, pure is equivalent to singleton for container types. The actual definition of pure (or any other aspect of Pointed) doesn't require Functor; however there are properties for types that are instances of Functor and Pointed.
Right, that's what I was meaning to highlight. If we were doing this in Coq, for example, then not having Functor as a superclass of Pointed would mean that we'd need a third class PointedFunctor which has both as superclasses. In Haskell, since we don't have proofs, PointedFunctor wouldn't have any methods and would therefore just be unnecessary complication. Though this raises the question of which one makes more sense to keep around: Pointed (with no superclass), or PointedFunctor.
So, from a proof/testing POV having Functor as a superclass is nice; from an implementation POV it doesn't seem to be needed.
Though, again, I wonder what the use case would be. Your example of singleton collections doesn't seem quite right. I'd expect the singleton functions to obey various "spatial" laws (i.e., module-like or vector space-like laws). For example,
union (singleton a) x = insert a x
This isn't exactly like Applicative because 'a' is an element instead of a function. And it's not quite like Alternative either, since it only requires union to be a semigroup instead of a monoid.
Well, I think the ability to create singleton values is a nice function to abstract away into a type class. Whether we can prove something or not is, however, a different story.
Perhaps this just means that union/insert should be part of some other class.
That is part of the plan (I'm tentatively calling the class with the "insert" method "Buildable" or "Extendable"); this means that if a type is an instance of Monoid (for mempty), Buildable/whatever (for insert) and Foldable (for foldr), then we can possibly define a build-fusion rule (note: I dont' think this will work on Sets, etc. unless we have some way of guarantee-ing that the folding function is strictly monotonic). Note also that we can then define that singleton = flip insert mempty (but in general this might not be ideal; Sets, for example, don't have the Ord constraint for singleton).
Of course, I'd expect singleton to obey the pointed law as well, so that other class would (most likely) be a subclass of pointed functors. In any case, it does mean there's something of a mismatch between singleton vs return/pure/point/unit.
Not quite sure what you mean by a "mis-match" -- Ivan Lazar Miljenovic Ivan.Miljenovic@gmail.com IvanMiljenovic.wordpress.com