Order out of Chaos: Proving Linearizability Using Local Views

TL;DR

This paper introduces a unifying proof framework for establishing linearizability of highly concurrent data structures by reasoning about local views and interference-free traversals, simplifying correctness proofs.

Contribution

The paper presents a novel proof method based on local view arguments that unifies and simplifies linearizability proofs for concurrent data structures.

Findings

Framework applies to optimistic self-balancing binary search trees

Framework proves linearizability of Lazy List and lock-free skip list

Simplifies correctness proofs through local view reasoning

Abstract

Proving the linearizability of highly concurrent data structures, such as those using optimistic concurrency control, is a challenging task. The main difficulty is in reasoning about the view of the memory obtained by the threads, because as they execute, threads observe different fragments of memory from different points in time. Until today, every linearizability proof has tackled this challenge from scratch. We present a unifying proof argument for the correctness of unsynchronized traversals, and apply it to prove the linearizability of several highly concurrent search data structures, including an optimistic self-balancing binary search tree, the Lazy List and a lock-free skip list. Our framework harnesses {\em sequential reasoning} about the view of a thread, considering the thread as if it traverses the data structure without interference from other operations. Our key contribution is showing that properties of reachability along search paths can be deduced for concurrent traversals from such interference-free traversals, when certain intuitive conditions are met. Basing the correctness of traversals on such \emph{local view arguments} greatly simplifies linearizability proofs. To apply our framework, the user proves that the data structure satisfies two conditions: (1) acyclicity of the order on memory, even when it is considered across intermediate memory states, and (2) preservation of search paths to locations modified by interfering writes. Establishing the conditions, as well as the full linearizability proof utilizing our proof argument, reduces to simple concurrent reasoning. The result is a clear and comprehensible correctness proof, and elucidates common patterns underlying several existing data structures.