facebookresearch/atlas-lean

ATLAS – Autoformalized Textbook Library At Scale

What it is – ATLAS is a research‑grade library of mathematics formalised in the Lean 4 proof assistant. The codebase contains a handful of Lean packages that extend the core mathematical library (Mathlib) with new theorems and definitions extracted from undergraduate and graduate textbooks. The formalisation work is driven by an auto‑formalisation pipeline (AutoformBot) that uses large language models to translate textbook statements and proofs into Lean code.

Why it matters – Formalised mathematics lets both humans and machines reason about mathematical results with absolute certainty. By automatically turning textbook material into reusable Lean libraries, ATLAS aims to accelerate the creation of large, high‑quality formal libraries that can be used for:

• Verified research in analysis, algebra, geometry, topology, probability, statistics, and theoretical computer science.
• Training and evaluating AI systems that assist with theorem proving.
• Building a shared repository of machine‑checkable mathematics that can be referenced across projects.

Key components

Component	Role
MathlibExt/	New, fully proved extensions to the standard Mathlib library.
MathlibExtTest/	Tests, benchmarks and diagnostics for the extensions in MathlibExt.
CSLibExt/	Formalised computer‑science results built on top of MathlibExt.
CSLibExtTest/	Tests and diagnostics for the computer‑science extensions.
WantedExt/	A placeholder for important results that have been identified but not yet formalised.

The repository also ships a scripts/ folder with a check.sh script that runs the full validation suite for the root Lake package.

How to get started

1. Install Lean 4 (v4.34.1 or newer) and the Lake build tool.
2. Clone the repo and run the root checks:

   scripts/check.sh
   

3. Explore the libraries by opening the .lean files in any Lean‑compatible editor (e.g., VS Code with the Lean extension).
4. For the original, larger collection of formalised textbooks, switch to the archived v1/ directory and build with:

   cd v1
   lake build
   

   The v1 release also includes evaluation reports, documentation, and a companion research paper.

Status – The current repository holds the scaffolding for ATLAS v2, which is under active development. The earlier v1 release is archived but fully functional and documented.

License – New contributions are under the Apache 2.0 license; the archived v1/ code remains under its original license.

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ATLAS is a genuine research project at the intersection of formal methods and AI‑driven automation, not a tutorial list or a trivial demo.