2017
DOI: 10.1007/s10703-017-0289-4
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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 p… Show more

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Cited by 21 publications
(40 citation statements)
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“…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 .…”
Section: Satisfiability Of Slid S Lc Rp Smentioning
confidence: 99%
“…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 .…”
Section: Satisfiability Of Slid S Lc Rp Smentioning
confidence: 99%
“…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.…”
Section: Related Workmentioning
confidence: 99%
“…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.…”
Section: Related Workmentioning
confidence: 99%
“…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.…”
Section: Introductionmentioning
confidence: 99%