Hello everyone! It's well known that Num & Co type classes are not adequate for vectors (I don't mean arrays). I have an idea how to address this problem. Conal Elliott wrote very nice set of type classes for vectors. (Definition below). I used them for some time and quite pleased. Code is concise and readable.
class AdditiveGroup v where zeroV :: v (^+^) :: v -> v -> v negateV :: v -> v
class AdditiveGroup v => VectorSpace v where type Scalar v :: * (*^) :: Scalar v -> v -> v
class VectorSpace v => InnerSpace v where (<.>) :: v -> v -> Scalar v
There are few problems though. Fisrt one is inlining. Functions are not inlined so if client code uses uses stream fusion it breaks. Second is dependecies. Vector-space doesn't have big chain of dependencies. People may be reluctant to use vector-spaces just for API for small packages. My proposal is to split type classes above into separate package which provide only type classes, doesn't have any dependencies. Second point is to lean more on performance side in performance vs elegance. Add INLINE pragmas everywhere (unfortunate feature of stream fusion), move ^-^ to AdditiveGroup with default implementation. I'd like to know opinion of haskellers on this and specifically opinion of Conal Eliott as author and maintainer (I CC'ed him)