Dan Doel schrieb:
On Thursday 20 January 2011 3:26:53 pm Henning Thielemann wrote:
I could define an RApplicative class only if I introduced an auxiliary type, in the example a stream-fusion:Stream. Then I could define a ZipList instance for StorableVector by converting each StorableVector to Stream and the zipped resulting Stream back to StorableVector.
Relating to my other mail, applicatives are already sort of equipped to be restricted, because their category theoretic analogues are lax monoidal functors. However, you need to look at their first-order interface:
unit :: f () pair :: (f a, f b) -> f (a, b)
The Applicative class takes advantage of the existence of exponential objects to provide a nicer interface to program with, but the above is the closer to the category theory. So, we can probably define a restricted applicative like so:
let Suitable identify a monoidal subcategory of Hask, with Suitable () and (Suitable a, Suitable b) => Suitable (a, b) A restricted applicative is a lax monoidal functor from the subcategory to Hask, so:
unit :: f () pair :: (Suitable a, Suitable b) => (f a, f b) -> f (a, b)
Satisfying some coherence conditions. In general, the subcategory needn't have (all) exponential objects, so we cannot provide the Applicative interface. The only problem with this in Haskell might be enforcing the conditions on Suitable.
Translating for me: liftA2 is essentially pair with subsequent fmap. I already though about this and came to the conclusion, that this does not help in my case. A zipWith3 written as pure f <*> storableVectorA <*> storableVectorB <*> storableVectorC would require a Storable instance for pairs. I provided that in storable-tuple, but then it is not efficient to store intermediate pairs in StorableVector. That's why I think that an optimal solution would neither require (Suitable a, Suitable b) => Suitable (a -> b) nor (Suitable a, Suitable b) => Suitable (a, b) but would best have no such constraint at all. Using an intermediate type does not have such an constraint, but unfortunately does not look nice. Maybe I should switch thread topic now ...