arXiv:2606.03743v1 Announce Type: new Abstract: While Large Language Models (LLMs) have shown strong performance in generating formal proofs, their outputs often remain less readable, modular, maintainable, and reusable than proofs in mature formal mathematics libraries. We argue that this gap stems in part from the compile-first objective implicit in most proof-generation pipelines, which encourages monolithic or ad hoc proof scripts rather than library-quality artifacts. Existing approaches to proof-quality improvement often rely on explicit, computable optimization objectives. In practice,
The proliferation of LLMs capable of generating formal proofs necessitates immediate efforts to refine their outputs for practical, rigorous applications.
Improving the modularity, readability, and reusability of LLM-generated proofs is crucial for their integration into mature formal mathematics and software verification, moving beyond mere generative capability.
The focus in LLM proof generation is shifting from simple 'compile-first' generation to a more sophisticated 'refactor-for-quality' approach, enhancing practical applicability.
- · Formal verification developers
- · AI researchers focusing on proof assistants
- · Software engineering
- · Mathematical research
- · Developers relying solely on raw LLM proof outputs
- · Systems unable to integrate modular proofs
The quality and reliability of AI-assisted formal verification will significantly improve.
This improved reliability could accelerate the adoption of formal methods in critical software and hardware development.
Increased trust in AI-generated formal proofs might eventually lead to autonomous systems capable of self-proving their own correctness or security protocols.
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Read at arXiv cs.AI