Multiple Model Synchronization with Multiary Delta Lenses

Abstract

Multiple (more than 2) model synchronization is ubiquitous and important for MDE, but its theoretical underpinning gained much less attention than the binary case. Specifically, the latter was extensively studied by the bx community in the framework of algebraic models for update propagation called lenses. Now we make a step to restore the balance and propose a notion of multiary delta lens. Besides multiarity, our lenses feature reflective updates, when consistency restoration requires some amendment of the update that violated consistency. We emphasize the importance of various ways of lens composition for practical applications of the framework, and prove several composition results.

Multiple model synchronization with multiary delta lenses with amendment andK-Putput

“…The paper is an essential extension of our FASE'18 paper [7]. The main additions are i) a new section motivating our design choices, ii) a constrained Putput law (KPutput) and its thorough discussion, including a corresponding extension of the running example, iii) a counterexample showing that invertibility is not preserved by star composition, iv) two types of parallel composition of multiary lenses, v) Related Work and Future Work sections are essentially extended, particularly, an important subsection about multimodel updates including correspondence updates (categorification) is added.…”

Incremental Concurrent Model Synchronization using Triple Graph Grammars

“…when synchronizing more than two models. This case has specific complications, see, for instance [32,4]. It has already been approached in [34,35], but just as a straightforward generalization of [14], which means that it shares its limitations.…”

“…Then, a TGG G consists of a start triple graph 4 ⇒ is the reflexive and transitive closure of the one step transformation relation ⇒ defined as follows: G 1 ⇒ G 2 if there is a production rule r : L → R in G and a matching monomorphism m : L → G 1 such that G 2 can be obtained by replacing (the image of) L in G 1 by (a corresponding image of) R. Formally, this means that the diagram above on the right is a pushout in the category of triple graphs. In this case, we write G 1 r,m ⇒ G 2 , or just G 1 ⇒G 2 if r and m are implicit.…”

“…In the context of this paper, it does not make too much sense to speak about source and target models. Nevertheless, we have kept this terminology to simplify the notation for referring to each of the two models involved 4. As said above, without loss of generality, we consider that SG is always the empty triple graph 5.…”

Towards Multiple Model Synchronization with Comprehensive Systems

“…One way to address multiary synchronization is to consider it as a network of well-understood binary synchronization problems. However, not every multiary consistency rule can be factored into binary ones [9]; e.g. the class diagrams A 1 , A 2 and A 3 in fig.…”