| trepplein | hott3 | |
|---|---|---|
| 2 | 2 | |
| 26 | 72 | |
| - | - | |
| 0.0 | 1.8 | |
| about 2 years ago | almost 4 years ago | |
| Scala | Lean | |
| Apache License 2.0 | Apache License 2.0 |
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trepplein
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Automated Theorem Provers?
The default kernel used is fairly large, since it does some optimisations for interactivity. However there are 3 independent checkers for Lean's output format, https://github.com/gebner/trepplein, https://github.com/leanprover/lean/tree/master/src/checker and https://github.com/leanprover/tc . They're all fairly small, with leanchecker being less than 1000 loc.
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Formalising Mathematics: An Introduction
Lean allows for third party type checkers. There are relatively small alternative type checkers for Lean, e.g. [1].
Lean's power lies in its elaborator that breaks down complex tactic-based proofs to a core proof language. This elaboration process can be extended with custom tactics, making it way more powerful than metamath.
[1] https://github.com/gebner/trepplein/tree/master/src/main/sca...
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.
What are some alternatives?
CoqGym - A Learning Environment for Theorem Proving with the Coq proof assistant
Coq-HoTT - A Coq library for Homotopy Type Theory
scala - Scala 2 compiler and standard library. Bugs at https://github.com/scala/bug; Scala 3 at https://github.com/scala/scala3
template-agda - An Agda template, configured for Gitpod (www.gitpod.io) to give you pre-built, ephemeral development environments in the cloud.
holbert - A graphical interactive proof assistant designed for education
mathlib - Lean 3's obsolete mathematical components library: please use mathlib4
Play - The Community Maintained High Velocity Web Framework For Java and Scala.
Leantime - Leantime is a goals focused project management system for non-project managers. Building with ADHD, Autism, and dyslexia in mind.
Lila - ♞ lichess.org: the forever free, adless and open source chess server ♞ [Moved to: https://github.com/lichess-org/lila]
cubical - An experimental library for Cubical Agda
lean4 - Lean 4 programming language and theorem prover