Alternatives
Products that do what Sostactic – polynomial inequalities using sums-of-squares in Lean does
Current support for nonlinear inequalities in Lean is quite limited. This package attempts to solve this. It contains a collection of Lean4 tactics for proving polynomial inequalities via sum-of-squares (SOS) decompositions, powered by a Python backend. You can use it via Python or Lean. These tactics are significantly more powerful than `nlinarith` and `positivity` -- i.e., they can prove inequalities they cannot. In theory, they can be used to prove any of the following types of statements - prove that a polynomial is nonnegative globally - prove that a polynomial is nonnegative over a…
- 1FP
This project aims to formalize the first volume of Prof. Bertrand Russell’s Principia Mathematica using the Lean theorem prover. Throughout the formalization, I tried to rigorously follow Prof. Russell’s proof, with no or little added statements from my side, which were only necessary for the formalization but not the logical argument. Should you notice any inaccuracy (even if it does not necessarily falsify the proof), please let me know as I would like to proceed with the same spirit of rigour. Before starting this project, I had already found Prof. Elkind’s formalization of the Principia…
2025 · github.com
- 2IM
I've been studying interval arithmetic for the past few weeks and it's a really interesting field because while there is a ton of super interesting research published over the past decades, it has never really gotten the recognition that it deserves, IMO. One reason for this is that standard interval arithmetic has really poor handling of division by intervals containing zero. If you compute 1 / [-1, 2] in regular interval arithmetic, you get either [-∞, +∞], or you have to say that the operation is undefined. Both solutions are virtually useless. The real answer of course is [-∞, -1] U…
Apr 2026 · victorpoughon.github.io
- 3LP
I formalized the Single Source of Truth (SSOT) principle in Lean 4 (~2.1k LOC, zero sorry) and proved two core results: Structural SSOT is achievable only when a language provides definition-time hooks and runtime introspection. Macros/codegen (before definition) and reflection (after definition) are insufficient. These requirements are derived, not chosen: because structural facts are fixed at definition, derivation must occur at definition time and be introspectable to verify DOF = 1. Would appreciate review, critique, or independent checking of the Lean scripts.
Jan 2026 · zenodo.org
- 4AM
2012 · github.com
- 5
To my knowledge, this is the first formally verified implementation of a 3D constructive solid geometry (CSG) operation: mesh intersection, implemented in Lean 4 and verified against a concise specification that pins down the surface of the resulting mesh exactly and guarantees practical well-formedness conditions on the triangulation. This project is also an experiment in avoiding having to trust AI-generated code. A human reviewer only needs to read 93 lines of formal specification and run the Lean checker to certify the correctness of the kernel, skipping the intricate 1000+ lines of…
Jul 2026 · github.com
- 6RL
Integrate is a fast, small, lightweight Rust library for performing numerical integration of real-valued functions. It is designed to integrate functions, providing a simple and efficient way to approximate definite integrals using various numerical methods. Integrate supports a variety of numerical integration techniques: - Newton-Cotes methods: - Rectangle Rule. - Trapezoidal Rule. - Simpson's Rule. - Newton's 3/8 Rule. - Gauss quadrature methods: - Gauss-Legendre. - Gauss-Laguerre. - Gauss-Hermite. - Gauss-Chebyshev First Kind. - Gauss-Chebyshev Second Kind. - Adaptive Methods: -…
2024 · github.com
- 7FV
2025 · github.com
- 8FV
To my knowledge, this is the first formally verified implementation of an intersection algorithm for polygons. The experience of working with AI agents on this project changed a lot with recent model releases, as I describe in the readme. Opus 4.8 is able to provide algorithm implementation with formal proof in one shot, whereas previous models required me to provide proof strategies in multiple steps. Trust in the correctness comes entirely from the Lean checker and human review of a small specification, not from the LLM. Also check out the web demo built around the verified core linked in…
Jun 2026 · github.com
- 9GC
Achieved a new world record in verifying the Goldbach Conjecture using grid computing, by extending the verification up to 4 quadrillion (4×10¹⁸) + 70 trillion (7×10¹³). My grid computing system - Gridbach is a cloud-based distributed computing system accessible from any PC or smartphone. It requires no login or app installation. The high-performance WASM (WebAssembly) binary code is downloaded as browser content, enabling computation on the user’s browser. [Website] https://gridbach.com/ [Medium]…
2025 · medium.com
- 10TJ
2023 · totaljs.com
- 11TO
At Cajal (YC W26) we’re excited to share Talos (https://github.com/cajal-technologies/talos), an open source framework for formal verification of WebAssembly modules in Lean. AI is now writing tons of the code that gets pushed to production. As code generation gets cheaper, verification becomes the bottleneck. We believe in a future where every piece of software comes with a mathematical proof that it does what its author intended - in doing so, eliminating many classes of exploits. Talos is part of the foundation for that. Talos provides a Wasm interpreter optimized for…
Jun 2026 · github.com
- 12AU
2017 · github.com
- 13AN
2018 · github.com
- 14AS
2021 · github.com
- 15AD
Greetings! A 2.5 weekends project to teach myself newer Python features (>= 3.10). Conditions are written as Lambda expressions that annotate parameters and return types, and coexist with type annotations. Symbols to share values between conditions are also supported to a limited extend.
2022 · github.com
- 16
Zero-Knowledge Proofs (ZKPs) let an untrusted proved show that computation was executed correctly without revealing the inputs to the verifier. However to prove anything, the computation first has to be expressed as a circuit: a system of polynomial equations (constraints) over a finite field. Circuits are the assembly language of zk and every constraint costs prover (and sometimes verifier) time, so production circuits are aggressively hand-optimized. Over the last months, we have been experimenting with writing formal specifications instead and letting LLMs produce the circuits: as long as…
Jul 2026 · zk.golf
- 17AJ
2015 · algebra.js.org
- 18
Contribute to skorotkiewicz/algebruh development by creating an account on GitHub.
29d ago · github.com
- 19IP
2017 · duetosymmetry.com
- 20VA
Wrote this to learn more about the `chumsky` parser combinator library, rustyline, and the `ariadne` error reporting crate. Such a nice DX combo for writing new languages. Still a work in progress, but I thought I'd share :)
2025 · github.com
- 21SA
Hi everyone, I’m a student with a strong interest in computer science and complexity theory. Recently, I worked on a manuscript attempting to prove that P ≠ NP. I know how this sounds — it’s one of the hardest and most debated problems in CS, and many have tried and failed. I don’t claim to have the final answer, but I believe the approach I used might at least offer some fresh perspective or provoke useful critique. The idea involves geometric separation between deterministic and nondeterministic computation, using high-dimensional lattice constructions and some physics-inspired intuition.…
2025 · zenodo.org
- 22EG
2022 · hackage.haskell.org
- 23LS
I'm excited to introduce a new beta version of LIPS Scheme. The most important features of this
21d ago · lips.js.org
- 24CJ
2015 · github.com
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