Completeness of Cyclic Proofs for Symbolic Heaps with Inductive Definitions

Separation logic is successful for software verification in both theory and practice. Decision procedure for symbolic heaps is one of the key issues. This paper proposes a cyclic proof system for symbolic heaps with general form of inductive definitions called cone inductive definitions, and shows its soundness and completeness. Cone inductive definitions are obtained from bounded-treewidth inductive definitions by imposing some restrictions for existentials, but they still include a wide class of recursive data structures. The completeness is proved by using a proof search algorithm and it also gives us a decision procedure for entailments of symbolic heaps with cone inductive definitions. The time complexity of the algorithm is nondeterministic double exponential. A prototype system for the algorithm has been implemented and experimental results are also presented.