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Compositional entailment checking for a fragment of separation logic

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Abstract

We present a decision procedure for checking entailment between separation logic formulas with inductive predicates specifying complex data structures corresponding to finite nesting of various kinds of singly linked lists: acyclic or cyclic, nested lists, skip lists, etc. The decision procedure is compositional in the sense that it reduces the problem of checking entailment between two arbitrary formulas to the problem of checking entailment between a formula and an atom. Subsequently, in case the atom is a predicate, we reduce the entailment to testing membership of a tree derived from the formula in the language of a tree automaton derived from the predicate. The procedure is later also extended to doubly linked lists. We implemented this decision procedure and tested it successfully on verification conditions obtained from programs using both singly and doubly linked nested lists as well as skip lists.

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Notes

  1. Our former work [9] does not include this constraint, thus the procedure proposed was incomplete.

  2. Points-to edges are depicted as simple lines, predicate edges as double lines, and disequality edges as dotted lines. For readability, we omit some of the labelling with existentially-quantified variables and some of the disequality edges in the normalised graphs.

  3. Note that in the example in Fig. 8, we performed some manual minimisation of the result.

  4. Our experiments were performed on a PC with an Intel Core 2 Duo @2.53 GHz processor and 4 GiB DDR3 @1067 MHz running a virtual machine with Fedora 20 (64-bit).

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Acknowledgements

This work was supported by the French ANR project Vecolib, the Czech Science Foundation (Projects 14-11384S and 16-175385), the EU/Czech IT4Innovations Excellence in Science Project LQ1602, and by the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation programme (Grant Agreement No. 678177).

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Authors and Affiliations

  1. IRIF, University Paris Diderot and CNRS, 8 place Aurélie Nemours, 75013, Paris, France

    Constantin Enea & Mihaela Sighireanu

  2. FIT, IT4I Centre of Excellence, Brno University of Technology, Božetěchova 2, 61266, Brno, Czech Republic

    Ondřej Lengál & Tomáš Vojnar

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  1. Constantin Enea
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  2. Ondřej Lengál
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  3. Mihaela Sighireanu
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  4. Tomáš Vojnar
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Correspondence to Ondřej Lengál.

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Enea, C., Lengál, O., Sighireanu, M. et al. Compositional entailment checking for a fragment of separation logic. Form Methods Syst Des 51, 575–607 (2017). https://doi.org/10.1007/s10703-017-0289-4

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