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.

• Type: Conference
• Year: 2009
• Where: FASE
• Authors: Laura Kovács, Andrei Voronkov
• Keywords: FASE 2009, Invariants Containing Alternations, Loop Invariants, Software Engineering, Update Predicates