M2F scales autoformalization from isolated theorems to machine-checked Lean projects

M2F first translates long mathematical documents into dependency-ordered Lean declaration skeletons and repairs project-level structural inconsistencies, then freezes statement signatures and iteratively closes proof holes using verifier feedback.

What happened?

The M2F paper reported a two-stage statement-compilation and proof-repair pipeline that converted 479 pages of real- and convex-analysis material into a 153,853-line Lean project and achieved 96% proof success on FATE-H in its fully automatic setting; generated Lean code was released publicly.

M2F first translates long mathematical documents into dependency-ordered Lean declaration skeletons and repairs project-level structural inconsistencies, then freezes statement signatures and iteratively closes proof holes using verifier feedback. The companion ReasBook repository exposes generated formalizations from textbooks and research papers.

Why it matters

Project-scale autoformalization changes the unit of automation from one problem at a time to coherent mathematical literature with shared definitions and dependencies, a prerequisite for turning large informal corpora into reusable formal libraries.

Significance rationale: M2F moved automated formalization from single theorem statements toward dependency-aware, document- and project-scale Lean generation, addressing imports, declarations, proof holes and whole-project compilation as one workflow.

Historical context

Primary evidence

Evidence & status at a glance

Significance
H2 · Field milestone
Verification
Paper released
Evidence level
E3 · Inspectable artifact
AI role
Autonomous primary role
Formal assurance
Machine-checked

How should these labels be read? →

Contribution & verification

Mathematical novelty
Tooling only
Interface
Informal, Formal, Hybrid
AI contribution
The system automatically translates statements, repairs declarations and closes proof holes while using Lean toolchain feedback to accept or reject project edits.
Human contribution
Researchers designed the staged formalization pipeline, prepared source documents and evaluation protocol, and report human checks for whether extracted natural-language theorems and their formal statements align with the original mathematics.
Verification
Paper released · E3 · Inspectable artifact · Machine-checked
Last reviewed
2026-09-11

Technical details

Systems
m2f, reasbook, lean
Organizations
peking-university
Problems
project-scale-autoformalization, mathematical-literature-formalization
Methods
autoformalization, dependency-ordering, verifier-guided-repair, proof-repair, lean

Sources & artifacts

Verification history

  • 2026-02-19 · Paper released · E2 · Research record

    The arXiv paper introduced M2F and reported project-scale formalization and FATE-H results.

  • 2026-09-11 · Paper released · E3 · Inspectable artifact

    The public M2F and ReasBook repositories expose the framework, examples and generated Lean projects. Machine-checked refers to Lean compilation and proof checking in the released workflow; it does not establish independent semantic review of every generated formalization.

Corrections

No corrections recorded.