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).
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