OpSets: Sequential Specifications for Replicated Datatypes (Extended Version)

We introduce OpSets, an executable framework for specifying and reasoning about the semantics of replicated datatypes that provide eventual consistency in a distributed system, and for mechanically verifying algorithms that implement these datatypes. Our approach is simple but expressive, allowing us to succinctly specify a variety of abstract datatypes, including maps, sets, lists, text, graphs, trees, and registers. Our datatypes are also composable, enabling the construction of complex data structures. To demonstrate the utility of OpSets for analysing replication algorithms, we highlight an important correctness property for collaborative text editing that has traditionally been overlooked; algorithms that do not satisfy this property can exhibit awkward interleaving of text. We use OpSets to specify this correctness property and prove that although one existing replication algorithm satisfies this property, several other published algorithms do not. We also show how OpSets can be used to develop new replicated datatypes: we provide a simple specification of an atomic move operation for trees, an operation that had previously been thought to be impossible to implement without locking. We use the Isabelle/HOL proof assistant to formalise the OpSets approach and produce mechanised proofs of correctness of the main claims in this paper, thereby eliminating the ambiguity of previous informal approaches, and ruling out reasoning errors that could occur in handwritten proofs.