Verifying Concurrent Data Structures Using Data-Expansion

Abstract

We present the first thread modular proof of a concurrent binary search tree. This proof tackles the problem of reasoning about complicated thread interferences using thread modular invariants. The key tool in this proof is the Data-Expansion Lemma, a novel lemma that allows us to reason about search operations in any state. We highlight the power of this lemma when combined with our generalized version of the Hindsight Lemma, which enables us to prove linearizability by reasoning about the temporal properties of the operations instead of reasoning about the linearization points directly.

The Data-Expansion Lemma provides an interesting solution to the proof blowup problem when reasoning about concurrent data structures by separating the verification of effectful and effectless operations. We show that our proof methodology is applicable to several algorithms and argue that many advanced concurrent data structures can be easy to verify using thread-modular arguments.