Graph Transformation Unitsand Modules

The aim of this chapter is to introduce the notions of transformation units and transformation modules as means of constructing large graph transformation systems from small ones in a structured and systematic way. A transformation unit comprises a set of rules, descriptions of initial and terminal graphs, and a control condition. Moreover, it may use other transformation units for structuring purposes. Its semantics is a binary relation between initial and terminal graphs which is given by interleaving ordinary direct derivation steps with calls of imported transformation units. Putting transformation units together yields transformation modules. A module may have an import interface consisting of formal parameter units and an export interface consisiting of the units that are made available to the environment. The formal parameter units can be instantiated by exported units of other modules. The introduced framework is independent of a particular graph transformation approach and, therefore, it may enhance the usefulness of graph transformations in many contexts. The signiicance of graphs and rules in many areas of computer science is evident: On the one hand, graphs constitute appropriate means for the description of complex relationships between objects. Trees, Petri nets, circuit diagrams, data ow graphs, state charts, and entity-relationship diagrams are some typical examples. On the other hand, rules are used to describe \permit-ted" actions on objects as, for example, in the areas of functional and logic programming, formal languages, algebraic speciication, theorem proving, and rule-based systems. The intention of bringing graphs and rules together|motivated by several application areas|has led to the theory of graph grammars and graph transformation (see volume I of the Handbook and 1{7] for a survey). A wide spectrum of approaches exists within this theory and some of them are implemented (see, With the aim of enhancing the usefulness of graph transformation, we introduce approach-independent structuring methods for building up large systems of graph transformation rules from small pieces. The methods are based on the notion of a transformation unit and its interleaving semantics. A transformation unit is allowed to use other units such that a system of graph transformation rules can be structured and existing transformation units can be re-used.