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A Simple Abstraction of Arrays and Maps by Program Translation

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Static Analysis (SAS 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9291))

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Abstract

We present an approach for the static analysis of programs handling arrays, with a Galois connection between the semantics of the array program and semantics of purely scalar operations. The simplest way to implement it is by automatic, syntactic transformation of the array program into a scalar program followed analysis of the scalar program with any static analysis technique (abstract interpretation, acceleration, predicate abstraction,...). The scalars invariants thus obtained are translated back onto the original program as universally quantified array invariants. We illustrate our approach on a variety of examples, leading to the “Dutch flag” algorithm.

D. Monniaux—The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007–2013) / ERC Grant Agreement nr. 306595 “STATOR”

F. Alberti—This work has been carried out while the author was affiliated to the Università della Svizzera Italiana and supported by the Swiss National Science Foundation under grant no. P1TIP2_152261.

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Notes

  1. 1.

    [7, 8, 15] http://www.astree.ens.fr, http://absint.de/astree/.

  2. 2.

    Possible since Astrée targets safety-critical embedded systems where array sizes are typically fixed at system design and dynamic memory allocation is prohibited.

  3. 3.

    We have left out, for the sake of brevity, tests for array accesses out of bounds.

  4. 4.

    We implemented a simplification algorithm for quantifier-free Presburger arithmetic inspired by [37] so as to understand the output of Flata and ConcurInterproc.

  5. 5.

    http://cpachecker.sosy-lab.org/.

  6. 6.

    scripts/cpa.sh -predicateAnalysis after preprocessing with assert.h.

  7. 7.

    All timings using one core of a 2.4 GHz Intel ® Core™ i3 running 32-bit Linux.

  8. 8.

    http://pop-art.inrialpes.fr/people/bjeannet/bjeannet-forge/interproc/.

  9. 9.

    http://apron.cri.ensmp.fr/library/.

  10. 10.

    http://pop-art.inrialpes.fr/interproc/concurinterprocweb.cgi.

  11. 11.

    From Presburger arithmetic, a decidable theory.

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Author information

Authors and Affiliations

  1. Université Grenoble Alpes, VERIMAG, 38000, Grenoble, France

    David Monniaux

  2. CNRS, VERIMAG, 38000, Grenoble, France

    David Monniaux

  3. Fondazione Centro San Raffaele, Milan, Italy

    Francesco Alberti

Authors
  1. David Monniaux
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  2. Francesco Alberti
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Correspondence to Francesco Alberti .

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Editors and Affiliations

  1. Université Rennes 1, Rennes, France

    Sandrine Blazy

  2. Inria, Rennes, France

    Thomas Jensen

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Monniaux, D., Alberti, F. (2015). A Simple Abstraction of Arrays and Maps by Program Translation. In: Blazy, S., Jensen, T. (eds) Static Analysis. SAS 2015. Lecture Notes in Computer Science(), vol 9291. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48288-9_13

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