2 research outputs found

    Separation Logic with Linearly Compositional Inductive Predicates and Set Data Constraints

    Full text link
    We identify difference-bound set constraints (DBS), an analogy of difference-bound arithmetic constraints for sets. DBS can express not only set constraints but also arithmetic constraints over set elements. We integrate DBS into separation logic with linearly compositional inductive predicates, obtaining a logic thereof where set data constraints of linear data structures can be specified. We show that the satisfiability of this logic is decidable. A crucial step of the decision procedure is to compute the transitive closure of DBS-definable set relations, to capture which we propose an extension of quantified set constraints with Presburger Arithmetic (RQSPA). The satisfiability of RQSPA is then shown to be decidable by harnessing advanced automata-theoretic techniques.Comment: 31 pages, 2 figures, SOFSEM 2019, to appea

    Go with the Flow: Compositional Abstractions for Concurrent Data Structures (Extended Version)

    Full text link
    Concurrent separation logics have helped to significantly simplify correctness proofs for concurrent data structures. However, a recurring problem in such proofs is that data structure abstractions that work well in the sequential setting are much harder to reason about in a concurrent setting due to complex sharing and overlays. To solve this problem, we propose a novel approach to abstracting regions in the heap by encoding the data structure invariant into a local condition on each individual node. This condition may depend on a quantity associated with the node that is computed as a fixpoint over the entire heap graph. We refer to this quantity as a flow. Flows can encode both structural properties of the heap (e.g. the reachable nodes from the root form a tree) as well as data invariants (e.g. sortedness). We then introduce the notion of a flow interface, which expresses the relies and guarantees that a heap region imposes on its context to maintain the local flow invariant with respect to the global heap. Our main technical result is that this notion leads to a new semantic model of separation logic. In this model, flow interfaces provide a general abstraction mechanism for describing complex data structures. This abstraction mechanism admits proof rules that generalize over a wide variety of data structures. To demonstrate the versatility of our approach, we show how to extend the logic RGSep with flow interfaces. We have used this new logic to prove linearizability and memory safety of nontrivial concurrent data structures. In particular, we obtain parametric linearizability proofs for concurrent dictionary algorithms that abstract from the details of the underlying data structure representation. These proofs cannot be easily expressed using the abstraction mechanisms provided by existing separation logics.Comment: This is an extended version of a POPL 2018 conference pape
    corecore