Decision Procedure for Entailment of Symbolic Heaps with Arrays

Abstract: This paper gives a decision procedure for the validity of en- tailment of symbolic heaps in separation logic with Presburger arithmetic and arrays. The correctness of the decision procedure is proved under the condition that sizes of arrays in the succedent are not existentially bound. This condition is independent of the condition proposed by the CADE-2017 paper by Brotherston et al, namely, one of them does not imply the other. For improving efficiency of the decision procedure, some techniques are also presented. The main idea of the decision procedure is a novel translation of an entailment of symbolic heaps into a formula in Presburger arithmetic, and to combine it with an external SMT solver. This paper also gives experimental results by an implementation, which shows that the decision procedure works efficiently enough to use.