Causal Linearizability: Compositionality for Partially Ordered Executions

In the interleaving model of concurrency, where events are totally ordered, linearizability is compositional: the composition of two linearizable objects is guaranteed to be linearizable. However, linearizability is not compositional when events are only partially ordered, as in many weak-memory models that describe multicore memory systems. In this paper, we present causal linearizability, a correctness condition for concurrent objects implemented in weak-memory models. We abstract from the details of specific memory models by defining our condition using Lamport's execution structures. We apply our condition to the C11 memory model, providing a correctness condition for C11 objects. We develop a proof method for verifying objects implemented in C11 and related models. Our method is an adaptation of simulation-based methods, but in contrast to other such methods, it does not require that the implementation totally order its events. We also show that causal linearizability reduces to linearizability in the totally ordered case.