It's possible; we can only make a comparison based on those aspects of the design that have been publicly disclosed, so we can only really address the question of MSOL vs. MLTT. Both HMC and Ohad claim to know the answers here, but their answers are in contradiction with each other. Previously I had thought I was able to demonstrate the insufficiency of MSOL but upon closer analysis I realized that my proofs were based on flawed assumptions and misinterpretations. Since coming to this realization, have taken a step back from "pushing the MLTT agenda", and now my goal is simply to play the role of a neutral 3rd party and analyze the validity of these claims, along with carrying out some further research into the strengths and weaknesses of various other logical systems that could potentially be used (mainly just standard systems discussed frequently in academic literature on formal logic, as these have the most metatheoretic results available to aid in the comparisons, and are the most likely systems to be brought up as an actual candidate logic as MSOL and MLTT have). I'll share my results with the community as I go along, on the AutoNomic wiki, though I will warn ahead of time that the explanations will still be very technically involved; it's simply a complex subject.


I'm guessing you mean HMC, myself and the AutoNomic project? Anyway, we were all originally working with Ohad but we split for various reasons, one major factor being Ohad's choice to change the planned logical framework from MLTT to MSOL. The history's all in the thread and the IRC logs, and I don't feel like dragging it up. Tau continued as same name, new design. AutoNomic continued as same design, new name. Adding this question of which logical framework to use has indeed "stalled" at least our side of the project as it's now added the goal of rigorously sorting out the differences between... nearly every standard logical framework presented in academic literature on the subject or in modern use in automated theorem proving and proof-checking, though we are still developing the MLTT-based client in parallel to this for concrete experimentation (and because until our research indicates a flaw in this choice we'll continue under the operating assumption that it will still eventually be the chosen framework). I can't speak to what's going on on the Tau side of things though (from what I understand it's not even publicly disclosed).

Edit to fix grammar mistakes.