Algebraic Laws for Weak Consistency

Modern distributed systems often rely on so called weakly consistent databases, which achieve scalability by weakening consistency guarantees of distributed transaction processing. The semantics of such databases have been formalised in two different styles, one based on abstract executions and the other based on dependency graphs. The choice between these styles has been made according to intended applications. The former has been used for specifying and verifying the implementation of the databases, while the latter for proving properties of client programs of the databases. In this paper, we present a set of novel algebraic laws (inequalities) that connect these two styles of specifications. The laws relate binary relations used in a specification based on abstract executions to those used in a specification based on dependency graphs. We then show that this algebraic connection gives rise to so called robustness criteria: conditions which ensure that a client program of a weakly consistent database does not exhibit anomalous behaviours due to weak consistency. These criteria make it easy to reason about these client programs, and may become a basis for dynamic or static program analyses. For a certain class of consistency models specifications, we prove a full abstraction result that connects the two styles of specifications