A Denotational View of Replicated Data Types

Abstract

Weak consistency" refers to a family of properties concerning the state of a distributed system. One of the key issues in their description is the way in which systems are specified. In this regard, a major advance is represented by the introduction of Replicated Data Types (rdts), in which the meaning of operators is given in terms of two relations, namely, visibility and arbitration. Concretely, a data type operation is defined as a function that maps visibility and arbitration into a return value. In this paper we recast such standard approaches into a denotational framework in which a data type is seen as a function that maps visibility into admissible arbitrations. This characterisation provides a more abstract view of RDTs that (i) highlights some of the implicit assumptions shared in operational approaches to specification; (ii) accommodates underspecification and refinement; (iii) enables a categorical presentation of RDT and the development of composition operators for specifications.

Higher-Order Patterns in Replicated Data Types

“…We are not the first to suggest that more complex CRDTs can be composed out of simpler ones [3], nor are we the first to formalize the behavior of CRDTs [3,6,7]. The work on composite data types by Gotsman and Yang [3] formalized the use of CRDT-valued key-value stores with causal transaction support to build new CRDTs.…”

“…Gaducci et al [6] also take a denotational look at CRDT semantics, basing their analysis on causal graphs of events, similarly to how our events form a causal graph through the "knows of" property. Interestingly, the authors take a view of CRDTs in which definitions for abstract data types such as the set and register are refined using a conflict resolution policy to obtain concrete data types.…”