[Haskell-cafe] writing a function to make a correspondance between type-level integers and value-level integers

[TP]

Thanks Oleg,

I have discovered geometric algebra some months ago. There is a textbook on 
the topic:

http://eu.wiley.com/WileyCDA/WileyTitle/productCd-0470941634.html

It seems very interesting, but I have not currently the time to make a 
detailed comparison with vector/tensor algebra. Moreover I have not your 
level of knowledge in Haskell/Standard ML and type theory, so I have already 
a lot of work. However, for sure this is something I will do in the few next 
years, because I think that notations are very important in physics and 
mathematics: it is of huge interest to have a condensed and easy to remember 
notation; still better if it is easily extended to higher dimensions/orders 
(unfortunately, generally these notations are not taught at university).

Regards,

TP


oleg at okmij.org wrote:

> Well, I guess you might be interested in geometric algebra then
>         http://dl.acm.org/citation.cfm?id=1173728
> because Geometric Algebra is a quite more principled way of doing
> component-free calculations. See also the web page of the author
>         http://staff.science.uva.nl/~fontijne/
> 
> Geigen seems like a nice DSL that could well be embedded in Haskell.
> 
> Anyway, the reason I pointed out Vectro is that it answers your
> question about reifying and reflecting type-level integers (by means
> of a type class).