Decidable entailment checking for concurrent separation logic with fractional permissions

Abstract

We propose a subsystem of concurrent separation logic with fractional permissions introduced by Brotherston et al. Separation logic is an extension of Hoare logic that reasons about programs using shared mutable data. Separation logic has separating conjunction asserting that its subformulas hold for separated (disjoint) parts in the heap. Fractional permissions manage access permission of shared resources between concurrent threads. Brotherston et al. introduced an extension of concurrent separation logic with fractional permissions, but they still need to discuss the decidability of logic. The heart of this paper is restricting the formulas of the system to symbolic heaps. We present examples to illustrate that our system is appropriate to prove the entailment for data structures, such as list segments with cycles. We eliminate permissions by normalization, and therefore we can reduce the entailment checking problem to the existing decidable entailment checking.