ProofWala: A Framework for Multilingual Proof Data Synthesis and Theorem-Proving

ProofWala is an open-source multilingual proof engineering framework that enables neural theorem proving across multiple interactive theorem provers like Lean 4 and Rocq through unified infrastructure. The framework demonstrates that cross-lingual training across different proof assistants improves performance on mathematical proof tasks, with significant gains shown in Lean Mathlib and domain-specific applications.

ProofWala addresses a critical infrastructure gap in the theorem-proving ecosystem by providing standardized tooling for extracting and analyzing proof data across multiple languages and proof assistants. Traditional approaches required assistant-specific solutions oriented toward single-file execution, creating bottlenecks for large-scale research and parallel experimentation. The framework's core innovation—itp-interface—abstracts away language-specific complexities while maintaining semantic fidelity through meta-programmed interaction layers that operate at tactic and declaration levels.

The research demonstrates practical benefits of multilingual proof training, a concept gaining momentum as AI systems tackle increasingly complex mathematical problems. By enabling knowledge transfer between Lean and Rocq ecosystems, ProofWala shows that cross-domain learning improves generalization capabilities. This has implications for developing more robust automated reasoning systems that can leverage diverse proof methodologies and mathematical formalizations.

For the broader AI and mathematics communities, this work provides essential infrastructure for scaling neural theorem proving research. Developers working on machine learning for formal verification can now operate at repository scale rather than file scale, dramatically expanding experimental scope. The open-source release of both the framework and trained models accelerates community-wide progress by reducing barriers to entry for researchers building theorem-proving systems.

The framework's unified pipeline across multiple proof assistants signals a maturing ecosystem where interoperability becomes increasingly valued. As neural approaches to theorem proving advance, standardized infrastructure like ProofWala becomes more critical for benchmarking progress and enabling reproducible research across institutions.

• →ProofWala enables programmatic interaction with multiple interactive theorem provers through a unified itp-interface library supporting Lean 4 and Rocq.
• →Multilingual proof training across different theorem-proving languages demonstrates statistically significant improvements on established benchmarks like Lean Mathlib.
• →The framework supports repository-scale analysis and parallel proof search, overcoming file-level limitations of existing theorem-proving infrastructure.
• →Cross-lingual transfer learning shows consistent upward trends, indicating mathematical knowledge generalizes across different formal proof systems.
• →Full open-source release across two repositories accelerates neural theorem-proving research and lowers barriers for AI community participation.