[Haskell-cafe] vector-space and standard API for vectors

[Conal Elliott]

> Vector (Complex a) is a vector with respect to both 'a' and 'Complex a'.

Even worse, () is a vector w.r.t. *every* scalar type.

On Sat, Oct 30, 2010 at 3:07 AM, Henning Thielemann <
schlepptop at henning-thielemann.de> wrote:

> wren ng thornton schrieb:
> > On 10/22/10 8:46 AM, Alexey Khudyakov wrote:
> >> 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
> >> [...]
> >> I'd like to know opinion of haskellers on this and specifically opinion
> >> of Conal Eliott as author and maintainer (I CC'ed him)
>
> Looks like you are about to re-implement numeric-prelude. :-)
>
> > Just my standard complaint: lack of support for semirings, modules, and
> > other simple/general structures. How come everyone's in such a hurry to
> > run off towards Euclidean spaces et al.?
> >
> > I'd rather see,
> >
> >     class Additive v where -- or AdditiveMonoid, if preferred
> >         zeroV :: v
> >         (^+^) :: v -> v -> v
> >
> >     class Additive v => AdditiveGroup v where
> >         negateV :: v -> v
> >
> >     type family Scalar :: * -> *
>
> Vector (Complex a) is a vector with respect to both 'a' and 'Complex a'.
>
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