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

[Alexey Khudyakov]

On 24.10.2010 01:19, Daniel Peebles wrote:
> Just out of curiosity, why do you (and many others I've seen with
> similar proposals) talk about additive monoids? are they somehow
> fundamentally different from multiplicative monoids? Or is it just a
> matter of notation? When I was playing with building an algebraic
> hierarchy, I picked a "neutral" operator for my monoids (I actually
> started at magma, but it's the same thing) and then introduced the
> addition and multiplication distinction at semirings, as it seemed
> pointless to distinguish them until you have a notion of a distributive
> law between the two.
>
I'm not sure that I understood your question completely. But I think it 
happens naturally. Authors of such proposals just don't think about 
monoids and abstract algebra. They think about R^n. It appears quite 
frequently (well it depends on domain) and Num&Co is useless. Proposals 
are born out of that frustration.

Probably people who do care about distinction between additive and 
multiplicative monoids don't face that problem or it's