Compositional entailment checking for a fragment of separation logic

Abstract

We present a decision procedure for checking entailment between separation logic formulas with inductive predicates specifying complex data structures corresponding to finite nesting of various kinds of singly linked lists: acyclic or cyclic, nested lists, skip lists, etc. The decision procedure is compositional in the sense that it reduces the problem of checking entailment between two arbitrary formulas to the problem of checking entailment between a formula and an atom. Subsequently, in case the atom is a predicate, we reduce the entailment to testing membership of a tree derived from the formula in the language of a tree automaton derived from the predicate. The procedure is later also extended to doubly linked lists. We implemented this decision procedure and tested it successfully on verification conditions obtained from programs using both singly and doubly linked nested lists as well as skip lists.

Separation Logic with Linearly Compositional Inductive Predicates and Set Data Constraints

“…The satisfiability problem is to decide whether there is a state (an assignmentheap pair) satisfying φ for a given SLID S LC rP s formula φ. We shall follow the approach adopted in [12,15], i.e., to construct Abspφq, an abstraction of φ that is equisatisfiable to φ. The key ingredient of the construction is to compute the transitive closure of the data constraints extracted from the inductive rule of P .…”

A Decidable Fragment in Separation Logic with Inductive Predicates and Arithmetic

“…Several decidable fragments were proposed with some restrictions over either shape of inductive predicates, or arithmetic, or satisfiability queries. Proposals in [2,21,9,13,5,11,17,29] 5 presented decision procedures for fragments including inductive predicates with heap properties, pure equalities but without arithmetic. Initial attempts like [2,21,9] focus only on linked lists.…”

“…Smallfoot [2] exploits the small model property of linked lists. SPEN [11] enhances the decidable fragment above with nested lists and skip lists. [13] extends the decidable fragment with tree structures.…”

Decision Procedure for Entailment of Symbolic Heaps with Arrays

“…Inductive definitions in a symbolic-heap system is important, since they can describe recursive data structures such as lists and trees. Symbolic-heap systems with inductive predicates have been studied intensively [2,3,1,6,11,13,14,15,16,21]. Berdine et al [2,3] introduced a symbolic-heap system with hard-coded list and tree predicates, and showed the decidability of its entailment problem.…”