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How Fitting is Your Abstract Domain?

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Static Analysis (SAS 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14284))

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Abstract

Abstract interpretation offers sound and decidable approximations for undecidable queries related to program behavior. The effectiveness of an abstract domain is entirely reliant on the abstract domain itself, and the worst-case scenario is when the abstract interpreter provides a response of “don’t know", indicating that anything could happen during runtime. Conversely, a desirable outcome is when the abstract interpreter provides information that exceeds a specified level of precision, resulting in a more precise answer. The concept of completeness relates to the level of precision that is forfeited when performing computations within the abstract domain. Our focus is on the domain’s ability to express program behaviour, which we refer to as adequacy. In this paper, we present a domain refinement strategy towards adequacy and a simple sound proof system for adequacy, designed to determine whether an abstract domain is capable of providing satisfactory responses to specified program queries. Notably, this proof system is both language and domain agnostic, and can be readily incorporated to support static program analysis.

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Notes

  1. 1.

    By \(\le _{{\tiny \textsf{A}}}\) we denote the partial order relation on \(\textsf{A}\).

  2. 2.

    Similarly to what happens with completeness, adequacy of any sound abstract operator implies the adequacy of the best correct approximation.

  3. 3.

    Where \(\textsf{max}\) extracts the upper bounds from a set.

  4. 4.

    Let us recall that \(\mathcal{M}\) is the Moore closure, namely the operator closing a set by concrete greatest lower bound, hence making a set a Moore family.

  5. 5.

      is introduced by \(\boxplus \) in \({ Sign}''\).

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Authors and Affiliations

  1. Department of Computer Science, University of Arizona Tucson, Tucson, USA

    Roberto Giacobazzi

  2. Computer Science Department, University of Verona, Verona, Italy

    Isabella Mastroeni & Elia Perantoni

Authors
  1. Roberto Giacobazzi
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  2. Isabella Mastroeni
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  3. Elia Perantoni
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Corresponding author

Correspondence to Isabella Mastroeni .

Editor information

Editors and Affiliations

  1. U. Politécnica de Madrid (UPM) and IMDEA Software Institute, Pozuelo de Alarcón, Madrid, Spain

    Manuel V. Hermenegildo

  2. U. Politécnica de Madrid (UPM) and IMDEA Software Institute, Pozuelo de Alarcon, Spain

    José F. Morales

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Giacobazzi, R., Mastroeni, I., Perantoni, E. (2023). How Fitting is Your Abstract Domain?. In: Hermenegildo, M.V., Morales, J.F. (eds) Static Analysis. SAS 2023. Lecture Notes in Computer Science, vol 14284. Springer, Cham. https://doi.org/10.1007/978-3-031-44245-2_14

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  • DOI: https://doi.org/10.1007/978-3-031-44245-2_14

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