Handling TSO in Mechanized Linearizability Proofs

Linearizability is the key correctness criterion for concurrent data structures. In recent years, numerous verification techniques for linearizability have been developed, ranging from model checking to mechanized proving. Today, these verification techniques are challenged by the fact that concurrent software is most likely to be run on multi-core processors equipped with a weak memory semantics (like total store order, TSO), making standard techniques unsound. While for model checking and static analysis techniques, approaches for handling weak memory in verification have already emerged, this is lacking for theorem-prover supported, mechanized correctness proofs.

In this paper, we present the very first approaches to handling TSO semantics in mechanized proofs of linearizability. More precisely, we introduce two approaches, one explicitly modelling store buffers and a second avoiding this modelling by instead reordering program operations. We exemplify and discuss our approach on two case studies, Burns mutual exclusion algorithm and a work stealing dequeue of Arora et al., both of which require additional memory barriers when executed on TSO.