Confluence of Typed Attributed Graph Transformation Systems

From UML 2 Sequence Diagrams to State Machines by Graph Transformation.

“…In addition to the above, we adopt the theory of typed attributed graphs [HKT02], where graphs are extended by assigning types to nodes and edges, and by assigning a set of named attributes to each node type. A graph morphism must now also preserve the node and edge types, and the attribute values.…”

Analysing Graph Transformation Rules through OCL

“…The term critical pair is used in graph transformation to denote two direct derivations in conflict (applying one disables the other), where the starting model is minimal [8,12]. The set of critical pairs gives all potential conflicts, and if empty, it means that the transformation is confluent (i.e.…”

“…In the former direction, graph transformation has developed a number of analysis techniques [8,12,18], but they usually work with simple type graphs. Our present work redefines some of these analysis properties, but taking into consideration a full-fledged meta-model, as well as OCL constraints in rules.…”

“…Prominent examples of this approach are the double [8] and single [9] pushout (DPO and SPO), which have developed interesting analysis techniques, e.g. to check independence between pairs of derivations [8,18], or to calculate critical pairs (minimal context of pairs of conflicting rules) [12]. However, graph grammar analysis techniques work with simplified meta-models (so called type graphs), with neither inheritance, cardinalities nor textual OCL-like constraints.…”

Translating Java Code to Graph Transformation Systems

“…Rule Equal T of Figure 2 shows that "==" is interpreted as reference identity, and this both for reference types (classes) and for basic data types. The correctness of this rule is ensured by assuming (as in [14]) that all constants of basic data types are present in the start graph, and that they are preserved by all rules. Such an assumption allows to deal with values of all data types uniformly at the graphical level (that is, using non-attributed graphs), at the price of making the size of the graphs practically unmanageable.…”