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DOI: 10.4230/LIPIcs.ITP.2022.3

Candle: A Verified Implementation of HOL Light

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

Published in: LIPIcs, Volume 237, 13th International Conference on Interactive Theorem Proving (ITP 2022)

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.

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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)

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@InProceedings{abrahamsson_et_al:LIPIcs.ITP.2022.3,
  author =	{Abrahamsson, Oskar and Myreen, Magnus O. and Kumar, Ramana and Sewell, Thomas},
  title =	{{Candle: A Verified Implementation of HOL Light}},
  booktitle =	{13th International Conference on Interactive Theorem Proving (ITP 2022)},
  pages =	{3:1--3:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-252-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{237},
  editor =	{Andronick, June and de Moura, Leonardo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2022.3},
  URN =		{urn:nbn:de:0030-drops-167126},
  doi =		{10.4230/LIPIcs.ITP.2022.3},
  annote =	{Keywords: Prover soundness, Higher-order logic, Interactive theorem proving}
}

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Candle: A Verified Implementation of HOL Light

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