Replicated data stores provide highly available, low-latency access to data at the expense of consistency, i.e., observers can perceive differences in the state of a system. Storages adopt different strategies to cope with temporary inconsistencies and resolve conflicts among concurrent updates, such as Replicated data types (RDTs). The selected solution impacts on the properties ensured by a store, i.e., on the kind of inconsistencies or anomalies that are allowed to happened and observed by applications. Such anomalies are characterised in terms of consistency models (such as read-your-write and causal consistency) defined axiomatically by constraining the execution traces of a data store.

In this talk, we review the semantics of replicated data stores, moving from the operational approaches for RDTs to a purely functional description. We comment how this approach enables a categorical presentation. In addition, we propose an alternative characterisation for consistency models, offering an operational model that is general enough for capturing some of the well-known consistency model.