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Formal Proofs of Tarjan’s Strongly Connected Components Algorithm in Why3, Coq and Isabelle

Authors: Ran Chen, Cyril Cohen, Jean-Jacques Lévy, Stephan Merz, and Laurent Théry

Published in: LIPIcs, Volume 141, 10th International Conference on Interactive Theorem Proving (ITP 2019)


Abstract
Comparing provers on a formalization of the same problem is always a valuable exercise. In this paper, we present the formal proof of correctness of a non-trivial algorithm from graph theory that was carried out in three proof assistants: Why3, Coq, and Isabelle.

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Ran Chen, Cyril Cohen, Jean-Jacques Lévy, Stephan Merz, and Laurent Théry. Formal Proofs of Tarjan’s Strongly Connected Components Algorithm in Why3, Coq and Isabelle. In 10th International Conference on Interactive Theorem Proving (ITP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 141, pp. 13:1-13:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{chen_et_al:LIPIcs.ITP.2019.13,
  author =	{Chen, Ran and Cohen, Cyril and L\'{e}vy, Jean-Jacques and Merz, Stephan and Th\'{e}ry, Laurent},
  title =	{{Formal Proofs of Tarjan’s Strongly Connected Components Algorithm in Why3, Coq and Isabelle}},
  booktitle =	{10th International Conference on Interactive Theorem Proving (ITP 2019)},
  pages =	{13:1--13:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-122-1},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{141},
  editor =	{Harrison, John and O'Leary, John and Tolmach, Andrew},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2019.13},
  URN =		{urn:nbn:de:0030-drops-110683},
  doi =		{10.4230/LIPIcs.ITP.2019.13},
  annote =	{Keywords: Mathematical logic, Formal proof, Graph algorithm, Program verification}
}
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