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

Abstract

Neural approaches to theorem proving require robust infrastructure for interfacing with interactive theorem provers (ITPs), extracting structured proof data, and executing proof search at scale. However, existing tooling is often assistant-specific and oriented toward file-level execution, making repository-scale analysis and parallel experimentation challenging. We present ProofWala, a multilingual proof engineering framework built around \texttt{itp-interface}, a reusable library for programmatic interaction with ITPs. For Lean 4, we implement a meta-programmed interaction layer executing inside the elaborator, enabling semantically faithful tactic-level tracing alongside declaration- and dependency-level extraction across entire repositories. This design extends beyond traditional REPL-style interaction by supporting project-wide analysis, environment cloning, and pooled execution of proof states. The same interface abstraction supports multiple versions of Rocq, yielding a unified cross-assistant pipeline. Built on this infrastructure, ProofWala provides standardized multilingual proof datasets, model training utilities, and parallel proof search algorithms. Using the framework, we demonstrate that multilingual training across Lean and Rocq enables cross-lingual and cross-domain transfer. We observe statistically significant improvements on Lean Mathlib and in domain adaptation (CategoryTheory), while other settings exhibit consistent upward trends. We open-source the full framework, parallel proof search module, datasets, and models across two repositories: ProofWala (https://github.com/trishullab/proof-wala) and the itp-interface library (https://github.com/trishullab/itp-interface).