Finding Loop Invariants for Programs over Arrays Using a Theorem Prover

  • Authors:

  • Laura Kovács;Andrei Voronkov

  • Affiliations:

  • EPFL,;University of Manchester,

  • Venue:
  • FASE '09 Proceedings of the 12th International Conference on Fundamental Approaches to Software Engineering: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009
  • Year:
  • 2009

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Abstract

We present a new method for automatic generation of loop invariants for programs containing arrays. Unlike all previously known methods, our method allows one to generate first-order invariants containing alternations of quantifiers. The method is based on the automatic analysis of the so-called update predicates of loops. An update predicate for an array A expresses updates made to A . We observe that many properties of update predicates can be extracted automatically from the loop description and loop properties obtained by other methods such as a simple analysis of counters occurring in the loop, recurrence solving and quantifier elimination over loop variables. We run the theorem prover Vampire on some examples and show that non-trivial loop invariants can be generated.