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Fields of Logic and Computation II pp 24–51Cite as

Horn Clause Solvers for Program Verification

Part of the Lecture Notes in Computer Science book series (LNPSE,volume 9300)

Abstract

Automatic program verification and symbolic model checking tools interface with theorem proving technologies that check satisfiability of formulas. A theme pursued in the past years by the authors of this paper has been to encode symbolic model problems directly as Horn clauses and develop dedicated solvers for Horn clauses. Our solvers are called Duality, HSF, SeaHorn, and \(\mu {Z}\) and we have devoted considerable attention in recent papers to algorithms for solving Horn clauses. This paper complements these strides as we summarize main useful properties of Horn clauses, illustrate encodings of procedural program verification into Horn clauses and then highlight a number of useful simplification strategies at the level of Horn clauses. Solving Horn clauses amounts to establishing Existential positive Fixed-point Logic formulas, a perspective that was promoted by Blass and Gurevich.

Keywords

  • Symbolic Model
  • Horn Clause
  • Satisfiability Modulo Theory
  • Proof Rule
  • Constraint Logic Programming

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Fig. 1.
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Fig. 3.

Notes

  1. 1.

    Note that we don’t need the clause \(s(x,y) \rightarrow q(y) \vee r(z)\) to preserve satisfiability because the sub-formula that s(x, y) summarizes is only used in negative scope.

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Authors and Affiliations

  1. Microsoft Research, Redmond, USA

    Nikolaj Bjørner & Ken McMillan

  2. Software Engineering Institute, Pittsburgh, USA

    Arie Gurfinkel

  3. Microsoft Research, Cambridge, UK

    Andrey Rybalchenko

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  1. Nikolaj Bjørner
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  2. Arie Gurfinkel
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  3. Ken McMillan
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  4. Andrey Rybalchenko
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Correspondence to Nikolaj Bjørner .

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Editors and Affiliations

  1. Steklov Mathematical Institute, Moscow, Russia

    Lev D. Beklemishev

  2. University of Michigan, Ann Arbor, Michigan, USA

    Andreas Blass

  3. Tel Aviv University, Tel Aviv, Israel

    Nachum Dershowitz

  4. Universität des Saarlandes, Saarbrücken, Germany

    Bernd Finkbeiner

  5. Microsoft Research, REDMOND, Washington, USA

    Wolfram Schulte

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Bjørner, N., Gurfinkel, A., McMillan, K., Rybalchenko, A. (2015). Horn Clause Solvers for Program Verification. In: Beklemishev, L., Blass, A., Dershowitz, N., Finkbeiner, B., Schulte, W. (eds) Fields of Logic and Computation II. Lecture Notes in Computer Science(), vol 9300. Springer, Cham. https://doi.org/10.1007/978-3-319-23534-9_2

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