Compositionality in Graph Transformation

Graph transformation works under a whole-world assumption. In modelling realistic systems, this typically makes for large graphs and sometimes also large, hard to understand rules. From process algebra, on the other hand, we know the principle of reactivity, meaning that the system being modelled is embedded in an environment with which it continually interacts. This has the advantage of allowing modular system specifications and correspondingly smaller descriptions of individual components. Reactivity can alternatively be understood as enabling compositionality: the specification of components and subsystems are composed to obtain the complete model. In this work we show a way to ingest graph transformation with compositionality, reaping the same benefits from modularity as enjoyed by process algebra. In particular, using the existing concept of graph interface, we show under what circumstances rules can be decomposed into smaller subrules, each working on a subgraph of the complete, whole-world graph, in such a way that the effect of the original rule is precisely captured by the synchronisation of subrules.