Certified mergeable replicated data types

Replicated data types (RDTs) are data structures that permit concurrent modification of multiple, potentially geo-distributed, replicas without coordination between them. RDTs are designed in such a way that conflicting operations are eventually deterministically reconciled ensuring convergence. Constructing correct RDTs remains a difficult endeavour due to the complexity of reasoning about independently evolving states of the replicas. With the focus on the correctness of RDTs (and rightly so), existing approaches to RDTs are less efficient compared to their sequential counterparts in terms of the time and space complexity of local operations. This is unfortunate since RDTs are often used in a local-first setting where the local operations far outweigh remote communication. This paper presents PEEPUL, a pragmatic approach to building and verifying efficient RDTs. To make reasoning about correctness easier, we cast RDTs in the mould of the distributed version control system, and equip it with a three-way merge function for reconciling conflicting versions. Further, we go beyond just verifying convergence, and provide a methodology to verify arbitrarily complex specifications. We develop a replication-aware simulation relation to relate RDT specifications to their efficient purely functional implementations. We implement PEEPUL as an F* library that discharges proof obligations to an SMT solver. The verified efficient RDTs are extracted as OCaml code and used in Irmin, a distributed database built on the principles of Git.