Because I’m not sure if I’m going to use Github in the future, instead of contributing to the em repository, I attach here the actual version of the em rewrite system paper. You know how it is: more you write, less goes into the final result.
The goal is to build a lambda calculus style version of emergent algebras, so that emergent algebras become a semantic for this system. One of the problems is that emergent algebras are partly algebraic and partly topological, involving uniform convergence and uniform continuity. But on the other side all this topological frame is not really needed, hence let’s pass it to the semantic side and see what we really have: the em.
The paper is not finished, it still needs developments:
- booleans and naturals encodings
- the sym rewrite and symmetric space like naturals
- the sym and the convex rewrites are a fork for two kinds of numbers, this needs to be explored more [update: no, I proved that (convex) implies (sym) and that (convex) is far more rigid than (sym) because it leads only to commutative stuff, but it’s nice to know, because it gives a sort of axiomatization of FinVect and classical calculus starting from rewrites on trees, no modules, no fields, everything gets constructed from trees.]
Another interesting thing is Victor Maia absal-ex repository. He continues his abstract algorithm explorations. The rewrites are close but not the same as mine, on the contrary his buffer representation of graphs is essentially what I do in needs, see also chemlambda strings for non tehnical explanations. I have the needs algorithm (libraries not public in needs repository) and the theoretical treatment, as a permutation rewrite machine, since a year, maybe one day I’ll post them if you are interested and motivate me to do it. Victor has superb programming skills and I wish him the best in his independent research work, looking forward to see how the abstract algorithm develops further.
And I’m really curious what King is cooking in the RKoD-web repository. He’s the guy who did chemlambda-hask version in Haskell of chemlambda, he’s highly gifted and very young, watch him doing stuff!