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International Conference on Integrated Formal Methods

IFM 2022: Integrated Formal Methods pp 86–105Cite as

Certified Verification of Relational Properties

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13274))

Abstract

The use of function contracts to specify the behavior of functions often remains limited to the scope of a single function call. Relational properties link several function calls together within a single specification. They can express more advanced properties of a given function, such as non-interference, continuity, or monotonicity. They can also relate calls to different functions, for instance, to show that an optimized implementation is equivalent to its original counterpart. However, relational properties cannot be expressed and verified directly in the traditional setting of modular deductive verification. Self-composition has been proposed to overcome this limitation, but it requires complex transformations and additional separation hypotheses for real-life languages with pointers. We propose a novel approach that is not based on code transformation and avoids those drawbacks. It directly applies a verification condition generator to produce logical formulas that must be verified to ensure a given relational property. The approach has been fully formalized and proved sound in the Coq proof assistant.

Part of this work was funded by the AESC project supported by the Ministry of Science, Research and Arts Baden-Württemberg (Ref: 33-7533.-9-10/20/1).

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Notes

  1. 1.

    Termination can be assumed (partial correctness) or proved separately (full correctness) in a well-known way [15]; for the purpose of this paper we can assume it.

  2. 2.

    The Coq development is at https://github.com/lyonel2017/Relational-Spec, where the version corresponding to this paper is tagged iFM2022.

  3. 3.

    https://formal.kastel.kit.edu/projects/improve/reve/.

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Author information

Authors and Affiliations

  1. Karlsruhe Institute of Technology, Karlsruhe, Germany

    Lionel Blatter

  2. Université Paris-Saclay, CEA, List, 91120, Palaiseau, France

    Nikolai Kosmatov & Virgile Prevosto

  3. Thales Research and Technology, 91120, Palaiseau, France

    Nikolai Kosmatov

  4. CentraleSupélec, Université Paris-Saclay, 91190, Gif-sur-Yvette, France

    Pascale Le Gall

Authors
  1. Lionel Blatter
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  2. Nikolai Kosmatov
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  3. Virgile Prevosto
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  4. Pascale Le Gall
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Corresponding author

Correspondence to Nikolai Kosmatov .

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Editors and Affiliations

  1. ISTI-CNR, Pisa, Italy

    Maurice H. ter Beek

  2. Maynooth University, Maynooth, Ireland

    Rosemary Monahan

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Blatter, L., Kosmatov, N., Prevosto, V., Le Gall, P. (2022). Certified Verification of Relational Properties. In: ter Beek, M.H., Monahan, R. (eds) Integrated Formal Methods. IFM 2022. Lecture Notes in Computer Science, vol 13274. Springer, Cham. https://doi.org/10.1007/978-3-031-07727-2_6

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  • DOI: https://doi.org/10.1007/978-3-031-07727-2_6

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