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@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).