Finding Loop Invariants for Programs over Arrays Using a Theorem Prover

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.

This research was partly done in the frame of the Transnational Access Programme at RISC, Johannes Kepler University Linz, supported by the European Commission Framework 6 Programme for Integrated Infrastructures Initiatives under the project SCIEnce (contract No 026133). The first author was supported by the Swiss NSF.

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