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Candle: A Verified Implementation of HOL Light

Authors Oskar Abrahamsson, Magnus O. Myreen, Ramana Kumar, Thomas Sewell



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Author Details

Oskar Abrahamsson
  • Chalmers University of Technology, Gothenburg, Sweden
Magnus O. Myreen
  • Chalmers University of Technology, Gothenburg, Sweden
Ramana Kumar
  • London, UK
Thomas Sewell
  • University of Cambridge, UK

Acknowledgements

We want to thank Freek Wiedijk and Yong Kiam Tan. We are grateful for Freek Wiedijk’s question at ITP'11. Following a presentation about the verification of a runtime for Milawa [Magnus O. Myreen and Jared Davis, 2011] at ITP'11, Wiedijk asked: "Can you do the same for HOL Light, please?" Wiedijk’s question can be seen as the seed that set us thinking about the possibility of a verified HOL Light implementation and eventually lead us to construct the verified Candle ITP, presented in this paper. We want to thank Yong Kiam Tan for helping with some proofs involving the the CakeML type inferencer. These proofs were part of the proof of safety of CakeML’s new read-eval-print loop.

Cite AsGet BibTex

Oskar Abrahamsson, Magnus O. Myreen, Ramana Kumar, and Thomas Sewell. Candle: A Verified Implementation of HOL Light. In 13th International Conference on Interactive Theorem Proving (ITP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 237, pp. 3:1-3:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.ITP.2022.3

Abstract

This paper presents a fully verified interactive theorem prover for higher-order logic, more specifically: a fully verified clone of HOL Light. Our verification proof of this new system results in an end-to-end correctness theorem that guarantees the soundness of the entire system down to the machine code that executes at runtime. Our theorem states that every exported fact produced by this machine-code program is valid in higher-order logic. Our implementation consists of a read-eval-print loop (REPL) that executes the CakeML compiler internally. Throughout this work, we have strived to make the REPL of the new system provide a user experience as close to HOL Light’s as possible. To this end, we have, e.g., made the new system parse the same variant of OCaml syntax as HOL Light. All of the work described in this paper has been carried out in the HOL4 theorem prover.

Subject Classification

ACM Subject Classification
  • Software and its engineering → Software verification
Keywords
  • Prover soundness
  • Higher-order logic
  • Interactive theorem proving

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References

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