Abstract
Replicated Data Types (rdts) have been introduced as an abstraction for dealing with weakly consistent data stores, which may (temporarily) expose multiple, inconsistent views of their state. In the literature, rdts are usually presented in set-theoretical terms: Only recently different specification flavours have been proposed, among them a denotational formalism that inter alia captures specification refinement. So far, however, no abstract model has been proposed for the implementations and their correctness with respect to specifications. This paper fills the gap: We first give categorical constructions for distilling an operational model from a specification, as well as its implementations, and then we define a notion of implementation correctness via simulation.
Research partially supported by the MIUR PRIN 2017FTXR7S “IT-MaTTerS”, by the EU H2020 RISE programme under the Marie Skłodowska-Curie grant agreement 778233, by the UBACyT projects 20020170100544BA and 20020170100086BA, by the PIP project 11220130100148CO and by the EPSRC Standard Grant EP/S028641/1.
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Notes
- 1.
Note that this is more general than the lattice of states proposed in [14]. First of all, we consider a pre-order instead of a partial order, and furthermore we do not require \(\otimes \) to be induced by \(\le \). This weakening results in an algebraic structure that allows for modelling a large family of rdts.
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Gadducci, F., Melgratti, H., Roldán, C., Sammartino, M. (2020). Implementation Correctness for Replicated Data Types, Categorically. In: Pun, V.K.I., Stolz, V., Simao, A. (eds) Theoretical Aspects of Computing – ICTAC 2020. ICTAC 2020. Lecture Notes in Computer Science(), vol 12545. Springer, Cham. https://doi.org/10.1007/978-3-030-64276-1_15
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