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Top 8 lean4 Open-Source Projects
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Lean is free and open source and nothing to do with MS. Check out https://lean-lang.org/ and https://github.com/leanprover/lean4 -- no mention of MS or MSR (where de Moura was where he developed Lean 3 and started on Lean 4).
Project mention: A Linear Algebra Trick for Computing Fibonacci Numbers Fast | news.ycombinator.com | 2023-11-06We essentially implemented this matrix version in Lean/mathlib to both compute the fibonacci number and generate an efficient proof for the calculation.
https://github.com/leanprover-community/mathlib4/blob/master...
In practice this isn't very useful (the definition of Nat.fib unfolds quick enough and concrete large fibonacci numbers don't often appear in proofs) but still it shaves a bit of time off the calculation and the proof verification.
Project mention: New Foundations is consistent – a difficult mathematical proof proved using Lean | news.ycombinator.com | 2024-04-23Then it's time to update your LLM reading!
https://leandojo.org/
Project mention: Macro-ts: TypeScript compiler with typesafe syntactic macros (2022) | news.ycombinator.com | 2023-05-30Lean4 manages to pull off changing the parser on the fly at compile time. You can add new productions, add new syntax node types, and add new tokens. Then define macros or code to process the additional syntax. Here is a sample I found that adds a simple JSX-like syntax starting around line 93 and then uses it at line 169:
https://github.com/leanprover/lean4/blob/master/tests/playgr...
I believe most of the language is defined this way, although it is pre-compiled.
For more details see the lean4 metaprogramming book: https://github.com/arthurpaulino/lean4-metaprogramming-book
Project mention: Functional Programming in Lean – a book on using Lean 4 to write programs | news.ycombinator.com | 2023-05-29Lean is currently moving to the 4th iteration which is the first intended to be a general-purpose programming language. It "is currently being released as milestone releases towards a first stable release". For now the main goal is to port mathlib to the new version, and then they will concentrate on the compiler. So it is not production ready. But that doesn't mean it is not suitable for building any programs now. There is a simple raytracer written in Lean [1]. I have built a chip8 interpreter with it and the only problem was the lack of an ecosystem, meaning I had to build the necessary libraries myself.
Now it has a RC GC and boxes everything >= 64 bits, and as the compiler isn't polished it is probably significantly slower. In the referenced raytracer repo you can find rendering time compared to the C implementation (Lean is 25x slower, but that was a year ago).
[1] https://github.com/kmill/lean4-raytracer
Project mention: New Foundations is consistent – a difficult mathematical proof proved using Lean | news.ycombinator.com | 2024-04-23But like, you can look at what parts of Mathlib this development imports, it's mainly stuff imported by files in this subdirectory https://github.com/leanprover-community/con-nf/tree/main/Con... , and it's pretty basic things: the definition of a permutation, a cardinal number etc. Almost all of these are things that would feature in the first one or two years of an undergraduate math degree (from just quickly scanning it, the most advanced thing I could see is the definition of cofinality of ordinals). It seems practically impossible to me that someone would make a mistake when e.g. defining what a group is, in a way subtle enough to later break this advanced theorem. If you think that people could mess up that, then all of math would be in doubt.
NOTE:
The open source projects on this list are ordered by number of github stars.
The number of mentions indicates repo mentiontions in the last 12 Months or
since we started tracking (Dec 2020).
lean4 related posts
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The Fermat's Last Theorem Project
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Dafny is a verification-aware programming language
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New Foundations is consistent – a difficult mathematical proof proved using Lean
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The Mechanics of Proof
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Natural Deduction in Logic (2015)
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LeanDojo: Theorem Proving with Retrieval-Augmented Language Models
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LeanDojo: Theorem Proving with Retrieval-Augmented Language Models
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A note from our sponsor - InfluxDB
www.influxdata.com | 1 May 2024
Index
What are some of the best open-source lean4 projects? This list will help you:
| Project | Stars | |
|---|---|---|
| 1 | lean4 | 3,739 |
| 2 | mathlib4 | 837 |
| 3 | LeanCopilot | 796 |
| 4 | std4 | 197 |
| 5 | lean4-metaprogramming-book | 195 |
| 6 | lean4-raytracer | 113 |
| 7 | lean4-mode | 54 |
| 8 | con-nf | 52 |
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