Philippa Gardner

Siddharth Krishna, from the Courant Institute of Mathematical Sciences, NYU, visited the group this week to talk about his work on the verification of concurrent data structures.

Siddharth is a PhD student in the Computer Science Department of New York University, working on Formal Verification and Machine Learning under the supervision of Thomas Wies. Siddharth gave a talk based on his forthcoming paper on Flow Interfaces: Go with the Flow: Compositional Abstractions for Concurrent Data Structures, joint work with Dennis Shasha and Thomas Wies, to appear at POPL 2018.

The abstract of the talk is:

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, such as inductive predicates, 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.