This is a description of a puzzle that I think could use a better solution. But I’m missing the pieces.
I think that there’s a clear mathematical side to the problem in whole, but the rest of it is like a production of a typesetting system or something else that requires creativity. How do you extend the set of rules such that the type promotion still forms a lattice, and that the extensions people can introduce are meaningful for solving their problems?
It would be surprising if someone figures this out. It may require that I’ll play with lattices a bit more and actually experiment with it a whole lot. But maybe there are some people who are smarter than me and see a solution to this straight away. You don’t know if you don’t try showing it to them.