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DOI: 10.4230/LIPIcs.ITP.2019.32
Characteristic Formulae for Liveness Properties of Non-Terminating CakeML Programs

Authors: Johannes Åman Pohjola, Henrik Rostedt, and Magnus O. Myreen

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

Abstract
There are useful programs that do not terminate, and yet standard Hoare logics are not able to prove liveness properties about non-terminating programs. This paper shows how a Hoare-like programming logic framework (characteristic formulae) can be extended to enable reasoning about the I/O behaviour of programs that do not terminate. The approach is inspired by transfinite induction rather than coinduction, and does not require non-terminating loops to be productive. This work has been developed in the HOL4 theorem prover and has been integrated into the ecosystem of proof tools surrounding the CakeML programming language.
Cite as

Johannes Åman Pohjola, Henrik Rostedt, and Magnus O. Myreen. Characteristic Formulae for Liveness Properties of Non-Terminating CakeML Programs. In 10th International Conference on Interactive Theorem Proving (ITP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 141, pp. 32:1-32:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{amanpohjola_et_al:LIPIcs.ITP.2019.32,
  author =	{\r{A}man Pohjola, Johannes and Rostedt, Henrik and Myreen, Magnus O.},
  title =	{{Characteristic Formulae for Liveness Properties of Non-Terminating CakeML Programs}},
  booktitle =	{10th International Conference on Interactive Theorem Proving (ITP 2019)},
  pages =	{32:1--32:19},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2019.32},
  URN =		{urn:nbn:de:0030-drops-110872},
  doi =		{10.4230/LIPIcs.ITP.2019.32},
  annote =	{Keywords: Program verification, non-termination, liveness, Hoare logic}
}
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