trepplein
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| trepplein | CoqGym | |
|---|---|---|
| 2 | 2 | |
| 26 | 370 | |
| - | 2.4% | |
| 0.0 | 3.6 | |
| about 2 years ago | 10 months ago | |
| Scala | Coq | |
| Apache License 2.0 | GNU Lesser General Public License v3.0 only |
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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...
CoqGym
- Lean4 helped Terence Tao discover a small bug in his recent paper
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Discussion Thread
This has been an active area of research for a few years. See for example https://arxiv.org/abs/1905.09381. It's still immature as a field, and most results are essentially "we got basic stuff down but it hasn't gotten powerful enough to prove anything truly challenging" but it definitely exists and is being developed.
What are some alternatives?
hott3 - HoTT in Lean 3
lean - Lean Theorem Prover
scala - Scala 2 compiler and standard library. Bugs at https://github.com/scala/bug; Scala 3 at https://github.com/scala/scala3
coq - Coq is a formal proof management system. It provides a formal language to write mathematical definitions, executable algorithms and theorems together with an environment for semi-interactive development of machine-checked proofs.
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.
lean-chat
Lila - ♞ lichess.org: the forever free, adless and open source chess server ♞ [Moved to: https://github.com/lichess-org/lila]
symmetric_project
cedar-spec - Definitional implementation of Cedar language and utilities for DRT
FStar - A Proof-oriented Programming Language