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Certifying a Termination Criterion Based on Graphs, without Graphs

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Theorem Proving in Higher Order Logics (TPHOLs 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5170))

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Abstract

Although graphs are very common in computer science, they are still very difficult to handle for proof assistants as proving properties of graphs may require heavy computations. This is a problem when it comes to issues such as the certification of a proof of well-foundedness, since premises of generic theorems involving graph properties may be at least as difficult to prove as their conclusion. We define a framework and propose an original approach based on both shallow and deep embeddings for the mechanical certification of these kinds of proofs without the help of any graph library. This framework actually avoids concrete models of graphs and handles those implicitly. We illustrate this approach on a powerful refinement of the dependency pairs approach for proving termination. This refinement makes heavy use of graph analysis and our technique is powerful enough to deal efficiently –and with full automation– with graphs containing thousands of arcs, as they may occur in practice.

Work partially supported by A3PAT project of the French ANR (ANR-05-BLAN-0146-01).

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Author information

Authors and Affiliations

  1. Cédric – CNAM, Paris, France

    Pierre Courtieu

  2. Cédric – ENSIIE, Évry, France

    Julien Forest & Xavier Urbain

Authors
  1. Pierre Courtieu
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  2. Julien Forest
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  3. Xavier Urbain
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Editor information

Editors and Affiliations

  1. Department of Electrical and Computer Engineering, Concordia University, 1455 de Maisonneuve Blvd. W, H3G 1M8, Montreal, Quebec, Canada

    Otmane Ait Mohamed

  2. National Institute of Aerospace, 100 Exploration Way, VA 23666, Hampton, USA

    César Muñoz

  3. Dept. of Electrical & Computer Engineering, Concordia University, 1455 de Maisonette W, H3G 1M8, Montreal, Quebec, Canada

    Sofiène Tahar

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Courtieu, P., Forest, J., Urbain, X. (2008). Certifying a Termination Criterion Based on Graphs, without Graphs. In: Mohamed, O.A., Muñoz, C., Tahar, S. (eds) Theorem Proving in Higher Order Logics. TPHOLs 2008. Lecture Notes in Computer Science, vol 5170. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71067-7_17

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  • DOI: https://doi.org/10.1007/978-3-540-71067-7_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-71065-3

  • Online ISBN: 978-3-540-71067-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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