I've written a small proof of concept that seems to work just fine (but, of course, there may be errors), that you can find
here: https://gist.github.com/m-alvarez/b1e42b7b42cbeed7d1f0

It seems to be solid enough to pass the tests that Octachron tried, but there probably are some other corner cases for which
it breaks down. Otherwise, it would be interesting to coalesce both representations, using Octachron's idea of row types instead
of tuples to have extensible dimensional analysis, where each part of the program can introduce its own dimensions.