ProofWala: Multilingual Proof Data Synthesis and Theorem-Proving
This addresses the challenge of limited transferability in neural theorem-proving for researchers and practitioners in automated reasoning, though it is incremental as it builds on existing methods for data synthesis and evaluation.
The paper tackles the problem of neural theorem-proving being restricted to specific interactive proof assistants (ITPs) by introducing ProofWala, a multilingual framework that enables cross-lingual transfer between Coq and Lean, resulting in a model trained on mixed data outperforming single-ITP models on the prove-at-k metric.
Neural networks have shown substantial promise at automatic theorem-proving in interactive proof assistants (ITPs) like Lean and Coq. However, most neural theorem-proving models are restricted to specific ITPs, leaving out opportunities for cross-lingual $\textit{transfer}$ between ITPs. We address this weakness with a multilingual proof framework, ${\rm P{\small ROOF}W{\small ALA}}$, that allows a standardized form of interaction between neural theorem-provers and two established ITPs (Coq and Lean). It enables the collection of multilingual proof step data -- data recording the result of proof actions on ITP states -- for training neural provers. ${\rm P{\small ROOF}W{\small ALA}}$ allows the systematic evaluation of a model's performance across different ITPs and problem domains via efficient parallel proof search algorithms. We show that multilingual training enabled by ${\rm P{\small ROOF}W{\small ALA}}$ can lead to successful transfer across ITPs. Specifically, a model trained on a mix of ${\rm P{\small ROOF}W{\small ALA}}$-generated Coq and Lean data outperforms Lean-only and Coq-only models on the standard prove-at-$k$ metric. We open source all code including code for the ${\rm P{\small ROOF}W{\small ALA}}$ Framework (https://github.com/trishullab/proof-wala), and the Multilingual ITP interaction framework (https://github.com/trishullab/itp-interface).