Generalised compositionality in graph transformation

We present a notion of composition applying both to graphs and to rules, based on graph and rule interfaces along which they are glued. The current paper generalises a previous result in two different ways. Firstly, rules do not have to form pullbacks with their interfaces; this enables graph passing between components, meaning that components may “learn” and “forget” subgraphs through communication with other components. Secondly, composition is no longer binary; instead, it can be repeated for an arbitrary number of components