| hott3 | cubical | |
|---|---|---|
| 2 | 3 | |
| 72 | 421 | |
| - | 1.0% | |
| 1.8 | 8.5 | |
| almost 4 years ago | 5 days ago | |
| Lean | Agda | |
| Apache License 2.0 | GNU General Public License v3.0 or later |
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hott3
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The HoTT Game
Lean 3 introduced singleton-elimination which is inconsistent with HoTT. There's a project [0] that uses an attribute to restrict uses of that rule, but it isn't really ergonomic to use.
[0] https://github.com/gebner/hott3
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Homotopy Type Theory
HoTT is somewhat independent of the choice of proof assistant.
Coq: https://github.com/HoTT/HoTT
Lean: https://github.com/gebner/hott3
idk what you mean by "blue screened", or results being on the way. afaict most of the non-foundational work present (what I assume you mean by "results") in these libraries are basic properties of basic mathematical concepts being rebuilt on HoTT.
cubical
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Will Computers Redefine the Roots of Math?
For those interested in formalisation of homotopy type theory, there are several (more or less) active and developed libraries. To mention a few:
UniMath (https://github.com/UniMath/UniMath, mentioned in the article)
Coq-HoTT (https://github.com/HoTT/Coq-HoTT)
agda-unimath (https://unimath.github.io/agda-unimath/)
cubical agda (https://github.com/agda/cubical)
All of these are open to contributions, and there are lots of useful basic things that haven't been done and which I think would make excellent semester projects for a cs/math undergrad (for example).
- Homotopy Type Theory
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Cubical Type Theory?
In the case of transpension, it seems like one of the uses is proving something about a path in inductive types by cases on an abstract point along that path. For instance, right now, the way that you prove that a path in A + B is either a path in A or a path in B is to define a family by cases and then transport like here. But I think transpension might let you just do cases on a formal intermediate point directly, which would be much simpler.
What are some alternatives?
Coq-HoTT - A Coq library for Homotopy Type Theory
template-agda - An Agda template, configured for Gitpod (www.gitpod.io) to give you pre-built, ephemeral development environments in the cloud.
redtt - "Between the darkness and the dawn, a red cube rises!": a proof assistant for cartesian cubical type theory
mathlib - Lean 3's obsolete mathematical components library: please use mathlib4
nqthm - nqthm - the original Boyer-Moore theorem prover, from 1992
trepplein - Lean type-checker written in Scala.
UniMath - This coq library aims to formalize a substantial body of mathematics using the univalent point of view.
Leantime - Leantime is a goals focused project management system for non-project managers. Building with ADHD, Autism, and dyslexia in mind.
lean4 - Lean 4 programming language and theorem prover
pasv - The Pascal-F Verifier