A Generic Specification Framework for Weakly Consistent Replicated Data Types

Burckhardt et al. proposed a formal specification framework for eventually consistent replicated data types, denoted $(vis, ar)$, based on the notions of visibility and arbitration relations. However, being specific to eventually consistent systems, this framework has two limitations. First, it does not cover non-convergent consistency models since arbitration $ar$ is a total order over events. Second, it does not cover the consistency models in which each event is required to be aware of the return values of some events that are visible to it when justifying its return value. These limitations make the $(vis, ar)$ framework not generic enough to specify and reason about important weak consistency models such as Causal Memory and PRAM. In this article, we extend this framework to a more generic one called $(vis, ar, V)$ for weakly consistent replicated data types. To specify non-convergent consistency models as well, we relax the arbitration relation $ar$ to be a partial order. To overcome the second limitation, we allow to specify for each event $e$, a subset $V(e)$ of its visible set whose return values cannot be ignored when justifying the return value of $e$. To make it practically feasible, we provide candidates for the visibility and arbitration relations and the $V$ function. By combining candidates for these three components, we are able to specify not only existing consistency models but also new ones that are reasonable and promising for practical usefulness. We then show how to specify consistency models in our framework, and provide three case studies.