lean
DISCONTINUED
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lean | CoqGym | |
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4 | 2 | |
1,915 | 367 | |
- | 4.1% | |
0.0 | 3.6 | |
over 3 years ago | 9 months ago | |
C++ | Coq | |
Apache License 2.0 | GNU Lesser General Public License v3.0 only |
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lean
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How do I get back into math?
However, mathlib makes some weird design choices. For example, (semi)groups are defined using multiplicative notation -- and then immediately followed by an entire section giving the exact same definitions using additive notation! The claimed reason for this is that the more abstract approach is inconvenient for automation. I did it in Coq using the abstract approach, and indeed, noticed that doing so broke automation, which I then worked around in various ways. But it's just weird to me as a mathematician to have additive and multiplicative groups be different objects, so I wouldn't want to do it the Lean way come hell or high water. The Lean approach causes practical difficulties as well: you have to prove every theorem about groups twice. In some cases (e.g. product groups), you have to prove every theorem FOUR times. Ugh.
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?
Agda - Agda is a dependently typed programming language / interactive theorem prover.
FStar - A Proof-oriented Programming Language
Coq-HoTT - A Coq library for Homotopy Type Theory
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.
arend-lib
ttlite - A SuperCompiler for Martin-Löf's Type Theory
trepplein - Lean type-checker written in Scala.
daisy-nfsd - DaisyNFS is an NFS server verified using Dafny and Perennial.
OEISbot - Automatically posts links to OEIS sequences on Reddit
mathlib - Lean 3's obsolete mathematical components library: please use mathlib4
lean-chat
symmetric_project