Abstract
We describe symbol elimination and consequence finding in the first-order theorem prover Vampire for automatic generation of quantified invariants, possibly with quantifier alternations, of loops with arrays. Unlike the previous implementation of symbol elimination in Vampire, our work is not limited to a specific programming language but provides a generic framework by relying on a simple guarded command representation of the input loop. We also improve the loop analysis part in Vampire by generating loop properties more easily handled by the saturation engine of Vampire. Our experiments show that, with our changes, the number of generated invariants is decreased, in some cases, by a factor of 20. We also provide a framework to use our approach to invariant generation in conjunction with pre- and post-conditions of program loops. We use the program specification to find relevant invariants as well as to verify the partial correctness of the loop. As a case study, we demonstrate how symbol elimination in Vampire can be used as an interface for realistic imperative languages, by integrating our tool in the KeY verification system, thus allowing reasoning about loops in Java programs in a fully automated way, without any user guidance.
This work was partially supported by the Wallenberg Academy Fellowship 2014, the Swedish VR grant D0497701 and the Austrian research project FWF S11409-N23.
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- 1.
available at www.cse.chalmers.se/~simrob.
- 2.
More complex Boolean expressions are transformed away by KeY rules.
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We wish to thank Martin Hentschel for his help with KeY.
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Ahrendt , W., Kovács, L., Robillard, S. (2015). Reasoning About Loops Using Vampire in KeY. In: Davis, M., Fehnker, A., McIver, A., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2015. Lecture Notes in Computer Science(), vol 9450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48899-7_30
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