{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/rm-p-small-roof-w-small-ala-multilingual","title":"ProofWala: Multilingual Proof Data Synthesis and Theorem-Proving","arxiv_id":"2502.04671","date":"2025-02-07","proceeding":null,"authors":["Amitayush Thakur","George Tsoukalas","Greg Durrett","Swarat Chaudhuri"],"abstract":"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).","url_abs":"https://arxiv.org/abs/2502.04671v2","url_pdf":"https://arxiv.org/pdf/2502.04671v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"rm-p-small-roof-w-small-ala-multilingual","repo_url":"https://github.com/trishullab/itp-interface","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"rm-p-small-roof-w-small-ala-multilingual","repo_url":"https://github.com/trishullab/proof-wala","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[{"task_slug":"automated-theorem-proving","task_name":"Automated Theorem Proving"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2502.04671","atlas_url":"https://app.syntology.ai/?focus=2502.04671","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2502.04671"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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