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A Relational Shape Abstract Domain

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NASA Formal Methods (NFM 2017)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 10227))

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Abstract

Static analyses aim at inferring semantic properties of programs. While many analyses compute an over-approximation of reachable states, some analyses compute a description of the input-output relations of programs. In the case of numeric programs, several analyses have been proposed that utilize relational numerical abstract domains to describe relations. On the other hand, designing abstractions for relations over memory states and taking shapes into account is challenging. In this paper, we propose a set of novel logical connectives to describe such relations, which are inspired by separation logic. This logic can express that certain memory areas are unchanged, freshly allocated, or freed, or that only part of the memory was modified. Using these connectives, we build an abstract domain and design a static analysis that over-approximates relations over memory states containing inductive structures. We implement this analysis and report on the analysis of a basic library of list manipulating functions.

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Acknowledgements

We thank Arlen Cox for fruitful discussions, and Francois Berenger, Huisong Li, Jiangchao Liu and the anonymous reviewers for their comments on an earlier version of this paper. This work has received funding from the European Research Council under the EU’s seventh framework programme (FP7/2007-2013), grant agreement 278673, Project MemCAD, and from Bpifrance, grant agreement P3423-189738, FUI Project P-RC2.

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Authors and Affiliations

  1. CEA, LIST, Software Reliability and Security Laboratory, P.C. 174, 91191, Gif-sur-Yvette, France

    Hugo Illous & Matthieu Lemerre

  2. Inria Paris/CNRS/École Normale Supérieure/PSL Research University, Paris, France

    Hugo Illous & Xavier Rival

Authors
  1. Hugo Illous
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  2. Matthieu Lemerre
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  3. Xavier Rival
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Corresponding author

Correspondence to Hugo Illous .

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Editors and Affiliations

  1. Stanford University, Palo Alto, California, USA

    Clark Barrett

  2. NASA Ames Research Center, Moffett Field, California, USA

    Misty Davies

  3. NASA Ames Research Center, Moffett Field, California, USA

    Temesghen Kahsai

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Illous, H., Lemerre, M., Rival, X. (2017). A Relational Shape Abstract Domain. In: Barrett, C., Davies, M., Kahsai, T. (eds) NASA Formal Methods. NFM 2017. Lecture Notes in Computer Science(), vol 10227. Springer, Cham. https://doi.org/10.1007/978-3-319-57288-8_15

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  • DOI: https://doi.org/10.1007/978-3-319-57288-8_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-57287-1

  • Online ISBN: 978-3-319-57288-8

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