cubical
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| cubical | redtt | |
|---|---|---|
| 3 | 2 | |
| 420 | 199 | |
| 2.1% | 0.5% | |
| 8.6 | 0.0 | |
| 8 days ago | about 2 years ago | |
| Agda | OCaml | |
| GNU General Public License v3.0 or later | Apache License 2.0 |
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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.
redtt
What are some alternatives?
Coq-HoTT - A Coq library for Homotopy Type Theory
cooltt - 😎TT
hott3 - HoTT in Lean 3
sml-redprl - The People's Refinement Logic
nqthm - nqthm - the original Boyer-Moore theorem prover, from 1992
Agda - Agda is a dependently typed programming language / interactive theorem prover.
UniMath - This coq library aims to formalize a substantial body of mathematics using the univalent point of view.
mathlib - Lean 3's obsolete mathematical components library: please use mathlib4
pasv - The Pascal-F Verifier