Work · alternatives · 2026
24 alternatives to Formalizing Principia Mathematica using Lean
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…
This project formalizes the first volume of Bertrand Russell's Principia Mathematica using the Lean theorem prover. It translates Russell's mathematical proofs into machine-verifiable code while adhering closely to the… Below are 24 products that do a similar job, ranked by how close each is in meaning and then by launch-day votes.
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Framework for specifying and proving properties—such as robustness, fairness, and interpretability—of machine learning models using Lean 4. - fraware/leanverifier
2025 · github.com · its alternatives →
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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 · its alternatives →
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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 · its alternatives →
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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 · its alternatives →
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Stephen Wolfram's new book on the Wolfram Language
2015 · wolfram.com · its alternatives →
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Hi HN, I turned the freshly published paper “The Constructor Theory of Time” by David Deutsch and Chiara Marletto (arXiv, 13 May 2025) into an executable Python library. What you’ll find • One-to-one translation of the paper’s formalism: Substrates, Attributes, Tasks, Constructors, and task-algebra operators • Possibility / impossibility predicates and counterfactuals encoded exactly as defined • Test suite that mirrors every lemma and example (>95 % coverage, mypy-typed) • Reproductions of key results: time-keeping substrates, irreversibility proofs, quantum branching tasks, and a…
2025 · github.com · its alternatives →
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GitHub: https://www.github.com/fizzbee-io/FizzBee Traditionally, formal methods are used only for highly mission critical systems to validate the software will work as expected before it's built. Recently, every major cloud vendor like AWS, Azure, Mongo DB, confluent, elastic and so on use formal methods to validate their design like the replication algorithm or various protocols doesn't have a design bug. I used TLA+ for billing and usage based metering applications. However, the current formal methods solutions like TLA+, Alloy or P and so on are incredibly complex to…
2024 · fizzbee.io · its alternatives →
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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 · its alternatives →
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We all know Rust's trait system is Turing complete, so tell me, why aren't we exploiting this??? - cofibrant/trait-eval
2020 · github.com · its alternatives →
- 10IA
Hi! We're Amisi and Claude, builders of the i2 language and the i2forge platform. i2 is an (early draft of a) language designed to make formal verification easy for mathematicians. We are launching the language as an open source project today (https://i2lang.org) together with a closed alpha for i2forge. However, we have a publicly accessible demo page which anyone can use, and we would love your feedback. Thanks.
2023 · i2forge.com · its alternatives →
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TypeScript as a proof assistant. GitHub Gist: instantly share code, notes, and snippets.
2025 · gist.github.com · its alternatives →
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Michael Spivak's Calculus formalized in Lean 4: every theorem and every problem of all 30 chapters and 9 appendices, in both the 3rd and 4th editions - stormj-UH/spivak-lean
27d ago · github.com · its alternatives →
- 13
A pipeline that translates Rust GPU code into formal Coq models, as a foundation for memory model proofs - neelsomani/vericuda
2025 · github.com · its alternatives →
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I started writing this book 10 years ago in JavaScript, got through a few chapters (asymptotic notation, basic techniques, start of sorting), and then abandoned it. Recently I picked it back up, converted everything to TypeScript, and used AI (Zenflow [1] + Claude Opus 4.6) to complete the remaining chapters. I provided the structure, direction, and initial chapters; the AI generated the bulk of the remaining content under a spec-driven workflow. The book covers roughly a first 1-2 year CS curriculum: sorting, dynamic programming, graph algorithms, trees, heaps, hash tables, and more. All…
Mar 2026 · amoilanen.github.io · its alternatives →
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"The Bible" of all fundamental algorithms for programming
2015 · amazon.com · its alternatives →
- 16
Hey HN! We built *lapisla*, a theorem proving platform designed to make formal proofs more open and collaborative. We developed a kernel, editor, proof registry, and platform ── all accessible directly in the browser. Why we built this: Existing theorem provers are powerful, but they often feel isolated and difficult to extend. Unlike modern programming languages, which thrive on package managers and shared libraries, theorem proving tools lack a seamless way to integrate others' work. lapisla aims to bridge this gap by: * Offering a verified public proof registry for sharing and discovering…
2025 · github.com · its alternatives →
- 17
Install the Prove Together skill. Your agents pool compute, coordinate on the Ledger, contribute reusable Lean proofs, and build on shared mathematical knowledge.
Sep 2026 · provetogether.ai · its alternatives →
- 18
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 · its alternatives →
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Hey HN, I wanted to share the new online playground for Salt (https://salt-lang.dev/playground/), a sovereign systems language designed for high-performance, distributed workloads where paying an "abstraction tax" is no longer acceptable. We started building Salt to bridge the gap between the raw power of manual pointer arithmetic and the safety guarantees of modern high-level languages. The architecture relies on an MLIR-based backbone and a Z3-powered "formal shadow," and the design is rooted in three main pillars: Fast Enough: The target is to stay within 20% of C's…
Jul 2026 · salt-lang.dev · its alternatives →
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Advancing Formal Mathematical Reasoning via RL
2025 · github.com · its alternatives →
- 21
Contribute to skorotkiewicz/algebruh development by creating an account on GitHub.
Aug 2026 · github.com · its alternatives →
- 22
Everything that would be here is in the README. I hope this gets big, it has tons of potential.
2013 · github.com · its alternatives →
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Automatically interpret and validate nested natural logic arguments based on rules of inference and propositional logic - ParhamP/Natural_Logic_Interpreter
2017 · github.com · its alternatives →
- 24SA
Hey HN, I’m a physicist turned quant. Some friends and I 'built' SymDerive because we wanted a symbolic math library that was "Agent-Native" by design, but still a practical tool for humans. It boils down to two main goals: 1. Agent Reliability: I’ve found that AI agents write much more reliable code when they stick to stateless, functional pipelines (Lisp-style). It keeps them from hallucinating state changes or getting lost in long procedural scripts. I wanted a library that enforces that "Input -> Transform -> Output" flow by default. 2. Easing the transition to Python: For many…
Feb 2026 · its alternatives →
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- Formally verified 3D CSG: Trust 93 lines spec, not 1000 lines AI code alternatives
- Formally verified polygon intersection – Opus 4.8 oneshots, prev failed alternatives
- Talos – Open-source WASM interpreter for Lean alternatives
- An Elementary Introduction to the Wolfram Language alternatives
- Python Simulator of David Deutsch’s “Constructor Theory of Time” alternatives
Ranked by how close each launch is in meaning, then by votes. Prices were read from each product’s own site when checked and can change. Refine with your own description →