Correctness of Incremental Model Synchronization with Triple Graph Grammars

In model-driven software development, we may have several models describing the same system or artifact, by providing different views on it. In this case, we say that these models are consistently integrated.

Triple Graph Grammars (TGGs), defined by Schürr, are a general and powerful tool to describe (bidirectional) model transformations. In this context, model synchronization is the operation that, given two consistent models and an update or modification of one of them, finds the corresponding update on the other model, so that consistency is restored. There are different approaches to describe this operation in terms of TGGs, but most of them have a computational cost that depends on the size of the given models. In general this may be very costly since these models may be quite large. To avoid this problem, Giese and Wagner have advocated for the need of

incremental

synchronization procedures, meaning that their cost should depend only on the size of the given update. In particular they proposed one such procedure. Unfortunately, the correctness of their approach is not studied and, anyhow, it could only be ensured under severe restrictions on the kind of TGGs considered.

In the work presented, we study the problem from a different point of view. First, we discuss what it means for a procedure to be incremental, defining a correctness notion that we call

incremental consistency

. Moreover, we present a general incremental synchronization procedure and we show its correctness, completeness and incrementality.