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Abstract Interpretation as Automated Deduction

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Automated Deduction - CADE-25 (CADE 2015)

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Abstract

Algorithmic deduction and abstract interpretation are two widely used and successful approaches to implementing program verifiers. A major impediment to combining these approaches is that their mathematical foundations and implementation approaches are fundamentally different. This paper presents a new, logical perspective on abstract interpreters that perform reachability analysis using non-relational domains. We encode reachability of a location in a control-flow graph as satisfiability in a monadic, second-order logic parameterized by a first-order theory. We show that three components of an abstract interpreter, the lattice, transformers and iteration algorithm, represent a first-order, substructural theory, parametric deduction and abduction in that theory, and second-order constraint propagation.

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Author information

Authors and Affiliations

  1. Google Inc., San Francisco, USA

    Vijay D’Silva

  2. École Normale Supérieure, Paris, France

    Caterina Urban

Authors
  1. Vijay D’Silva
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  2. Caterina Urban
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Corresponding author

Correspondence to Caterina Urban .

Editor information

Editors and Affiliations

  1. University of Ottawa, Ottawa, Canada

    Amy P. Felty

  2. University of Innsbruck, Innsbruck, Austria

    Aart Middeldorp

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D’Silva, V., Urban, C. (2015). Abstract Interpretation as Automated Deduction. In: Felty, A., Middeldorp, A. (eds) Automated Deduction - CADE-25. CADE 2015. Lecture Notes in Computer Science(), vol 9195. Springer, Cham. https://doi.org/10.1007/978-3-319-21401-6_31

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  • DOI: https://doi.org/10.1007/978-3-319-21401-6_31

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-21400-9

  • Online ISBN: 978-3-319-21401-6

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