On Mon, Jul 28, 2003 at 11:59:48AM +1000, Andrew J Bromage wrote: > G'day all. > > On Fri, Jul 25, 2003 at 03:48:15PM -0400, Dylan Thurston wrote: > > > Another approach is to make Universe a multi-parameter type class: > > > > class (RealFrac a, Floating a) => Universe u a | u -> a where > > distanceVector :: u -> Vector a -> Vector a -> Vector a > > ... > > Actually, this is a nice way to represent vector spaces, too: > > class (Num v, Fractional f) => VectorSpace vs v f | vs -> v f where > scale :: vs -> f -> v -> v > innerProduct :: vs -> v -> v -> f > > The reason why you may want to do this is that you may in general want > different inner products on the same vectors, which result in different > vector spaces.
Hmm, that's an interesting technique, which I'll have to try out; there
are several instances where you want different versions of the same
structure on some elements. This is an interesting alternative to
newtype wrapping or some such.
However, I would be sure to distinguish between an inner product space
and a vector space. A vector space has only the 'scale' operation above
(beyond the +, -, and 0 from Num); you will rarely want to have
different versions of the scale operation for a given set of vectors and
base field. An inner product space has the 'innerProduct' operation you
mention; as you say, there is very frequently more than one interesting
inner product.
Peace,
Dylan
pgp00000.pgp
Description: PGP signature
