On Mon, Apr 05, 2004 at 01:59:18PM +0200, Henning Thielemann wrote:
In addition I separated a class VectorSpacePure from the VectorSpace class that contains the operations that don't need the scalar type 'a', i.e. 'zero' and 'add'.
I called this class 'Additive' in my old proposal to revamp the numeric hierarchy of the basic Prelude, and made 'Num' inherit from it: http://www.haskell.org/pipermail/haskell-cafe/2001-February/001632.html (Perhaps I should revive this proposal. I have been using a newer version in my own programs, but I didn't see a way to actually get it widely adopted. In particular, the design I proposed is somewhat annoying to use because there's no defaulting and you have to add an explicit type whenever you raise a number to an explicit integer power.)
Further I swapped consistently 'a' and 'v' in the class definition and in the quantity data type, i.e. "class VectorSpace a v" and "data Quantity a v". I suppose that it will more oftenly be necessary to say something about the vectors that can built from a certain scalar (i.e. Quantity a) rather than about the scalar types that can be the base of a vector type.
Yes, that's a good choice.
By the way, depending how you resolve the issue above, you might want instead
instance (RealFloat a, VectorSpace b a) => VectorSpace [b] a where ...
That's really a nice generalization! With the specialised instances for Float and Double as shown above this works. Now I can built VectorSpace over several levels, e.g. a list of complex numbers as vectors with respect to real numbers. But it prohibits functional dependency, right?
No, it shouldn't, if you do it right.
Functional dependency would probably allow the compiler to detect which scalar type is associated with an vector and thus the compiler wouldn't ask me to tell it explicitly all the time.
Yes. That's what you want if you only have one scalar type for a given vector space.
Maybe a type class like the VectorSpace finds the way to a revised version of Prelude?
I didn't include it in my proposal, because it uses multi-parameter type classes, which are not in nhc, for instance. I don't know that it should be in the Prelude, but in the standard library. There are a few design issues, as you noticed; it's particularly annoying that you can't easily right 'instance (Num a) => VectorSpace a a'. Peace, Dylan