arXiv:2607.01734v1 Announce Type: new Abstract: We present a case study in reformalization, a variant of autoformalization in which the input proof is not natural language but a formal development in a different proof assistant. Concretely, we report three reformalizations of the Jordan Curve Theorem: from Mizar to Lean, from HOL Light to Lean, and from HOL Light to Agda. We analyse the results and identify pipeline design choices that matter for practical reformalization tasks.
The proliferation of various formal proof assistants has created a need for methods to automatically translate and verify proofs across different systems, driving the exploration of 'reformalization' techniques like the one presented.
Advanced automated formal verification, as demonstrated by reformalization, is critical for ensuring the correctness and trustworthiness of increasingly complex AI systems and other critical software infrastructure.
The ability to reformalize proofs between different formal systems could streamline the development and verification of highly reliable software and AI, reducing human error and increasing interoperability of formal methods.
- · Formal verification developers
- · AI safety researchers
- · High-assurance software industry
- · Proof assistant communities
- · Manual proof assistants (relative to automated methods)
- · Organizations with fragmented formal verification efforts
This research provides a case study for improving the portability and reusability of formal proofs across different proof environments.
Improved reformalization techniques could lead to more robust and easily verifiable AI models, enhancing trust in their outputs and decisions.
A future with widely adopted and interconnected formal verification systems could fundamentally change how critical software and AI are designed, tested, and certified, impacting standards and regulatory frameworks.
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Read at arXiv cs.AI