cubicaltt VS anders

- cubicialtt a programming language based on cubical type theory in which univalence from homotopy type theory isn't an axiom but a theorem

If you’re interested in programming languages specifically, the current state of the art is called Cubical Type Theory. CuTT has lots of flavours and the community hasn’t coalesced around a single design. The paper I personally found easiest to digest was the “ABCFHL” paper, but I’d recommend reading it alongside the original CCHM paper. None of the publications made an ounce of sense to me until after I’d digested Favonia’s YouTube channel, Mortberg’s lecture notes and this other series of lectures from Harper (particularly the final one).

I updated the blog post to include some people in academia who contributed. I've been interacting with Kent Palmer and Sylvester James Gates, Jr. The latter held lectures about the philosophy of mathematics. I've been using work inspired by Vladimir Voevodsky, e.g. cubicaltt (https://github.com/mortberg/cubicaltt), which is also performed by academics.

Anders is HoTT theorem prover based on: classical MLTT-80 with 0, 1, 2, W types; CCHM in CHM flavour as cubical type system with hcomp/trans Kan operations; HTS sctrict equality on pretypes; de Rham stack modality primitives. We tend not to touch HIT yet, instead we will try to express as much HIT as possible through Coequlizer and HubSpokes Disc in the style of HoTT/Coq homotopy library and Three-HIT theorem. Written in OCaml https://github.com/groupoid/anders