Distributed Consistency Beyond Queries

Programming asynchronous distributed systems is a challenging task in which consistency is often achieved by use of expensive coordination protocols like Paxos and 2PC. The CALM theorem, first conjectured by Hellerstein, is one of the first results to challenge this practice by stating that a problem can have a consistent, coordination-free distributed implementation if (and only if) the problem is monotonic. This result was proven for queries and shown to extend beyond monotonic (yet monotonic-like) queries for data systems having specific knowledge about the partitioning of data over the network. In this article, we extend the latter results in several ways. We consider problems that can be modeled as mappings from distributed instances to distributed instances, enabling insights into a much broader range of problems than queries. Furthermore, our model can express arbitrary system configurations, allowing us to reason about the expressiveness of any particular distributed system and thereby revealing a nuanced gradient of problems with increasing coordination-needs. Finally, we apply our model to a recent question about the expressiveness of coordination-free queries, raised by Hellerstein and Alvaro.