Abstract
In this work, we focus on the correctness of Conflict-free Replicated
Data Types (CRDTs), a class of algorithm that provides strong eventual
consistency guarantees for replicated data. We develop a modular and
reusable framework for verifying the correctness of CRDT algorithms.
We avoid correctness issues that have dogged previous mechanised
proofs in this area by including a network model in our formalisation,
and proving that our theorems hold in all possible network behaviours.
Our axiomatic network model is a standard abstraction that accurately
reflects the behaviour of real-world computer networks. Moreover, we
identify an abstract convergence theorem, a property of order
relations, which provides a formal definition of strong eventual
consistency. We then obtain the first machine-checked correctness
theorems for three concrete CRDTs: the Replicated Growable Array, the
Observed-Remove Set, and an Increment-Decrement Counter.