Reformalization Study of Jordan Curve Theorem in Proof Assistants
Summary
This paper presents a case study in reformalization, where formal proofs from one proof assistant are translated into another. It reports three reformalizations of the Jordan Curve Theorem from Mizar to Lean, HOL Light to Lean, and HOL Light to Agda, analyzing pipeline design choices.
Why it matters
Professionals in software engineering, formal verification, and AI for mathematics can gain insights into the challenges and methodologies for translating and verifying complex proofs across different formal systems, improving reliability and interoperability.
How to implement this in your domain
- 1Explore tools and techniques for autoformalization or reformalization to translate mathematical specifications or proofs between different formal systems.
- 2Investigate the use of proof assistants (e.g., Lean, Agda) for formal verification of critical software components or algorithms.
- 3Contribute to or utilize open-source efforts aimed at building bridges between different formal verification ecosystems.
- 4Consider the implications of formal proof interoperability for developing highly reliable AI systems that require mathematical guarantees.
Who benefits
Key takeaways
- Reformalization involves translating formal proofs between different proof assistants.
- The Jordan Curve Theorem serves as a complex case study for this process.
- Pipeline design choices are critical for practical reformalization tasks.
- This research contributes to improving interoperability and accessibility in formal mathematics.
Original post by Simon Guilloud, Sankalp Gambhir, Samuel Chassot
"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…"
View on XOriginally posted by Simon Guilloud, Sankalp Gambhir, Samuel Chassot on X · view source
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