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| hott3 | Coq-HoTT | |
|---|---|---|
| 2 | 4 | |
| 72 | 1,211 | |
| - | 0.4% | |
| 1.8 | 9.8 | |
| over 3 years ago | 4 days ago | |
| Lean | Coq | |
| Apache License 2.0 | GNU General Public License v3.0 or later |
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For example, an activity of 9.0 indicates that a project is amongst the top 10% of the most actively developed projects that we are tracking.
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.
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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.
Coq-HoTT
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What do we mean by "the foundations of mathematics"?
https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_t... :
> * Today, Zermelo–Fraenkel set theory [ZFC], with the historically controversial axiom of choice (AC) included, is the standard form of axiomatic set theory and as such is the most common* foundation of mathematics.
Foundation of mathematics: https://en.wikipedia.org/wiki/Foundations_of_mathematics
Implementation of mathematics in set theory:
> The implementation of a number of basic mathematical concepts is carried out in parallel in ZFC (the dominant set theory) and in NFU, the version of Quine's New Foundations shown to be consistent by R. B. Jensen in 1969 (here understood to include at least axioms of Infinity and Choice).
> What is said here applies also to two families of set theories: on the one hand, a range of theories including Zermelo set theory near the lower end of the scale and going up to ZFC extended with large cardinal hypotheses such as "there is a measurable cardinal"; and on the other hand a hierarchy of extensions of NFU which is surveyed in the New Foundations article. These correspond to different general views of what the set-theoretical universe is like
IEEE-754 specifies that float64s have ±infinity and specify ZeroDivisionError. Symbolic CAS with MPFR needn't be limited to float64s.
HoTT in CoQ: Coq-HoTT: https://github.com/HoTT/Coq-HoTT
leanprover-community/mathlib4//
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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).
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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.
What are some alternatives?
lean - Lean Theorem Prover
cubical - An experimental library for Cubical Agda
Agda - Agda formalisation of the Introduction to Homotopy Type Theory
cubicaltt - Experimental implementation of Cubical Type Theory
mathlib - Lean 3's obsolete mathematical components library: please use mathlib4
trepplein - Lean type-checker written in Scala.
template-agda - An Agda template, configured for Gitpod (www.gitpod.io) to give you pre-built, ephemeral development environments in the cloud.
Leantime - Leantime is a goals focused project management system for non-project managers. Building with ADHD, Autism, and dyslexia in mind.
TypeTopology - Logical manifestations of topological concepts, and other things, via the univalent point of view.
UniMath - This coq library aims to formalize a substantial body of mathematics using the univalent point of view.