A Typed Attributed Graph Grammar with Inheritance for the Abstract Syntax of UML Class and Sequence Diagrams

According to the UML Standard 2.0 class and sequence diagrams are defined in a descriptive way by a MOF meta-model and semi-formal constraints. This paper presents a formal and constructive definition of the abstract syntax of UML class and sequence diagrams based on the well-defined theory of typed attributed graph transformation with inheritance and application conditions. The generated language covers all important features of these parts of UML diagrams and is shown to satisfy all of the corresponding constraints by construction. An explicit model transformation demonstrates the close correspondence between the graph grammar and the MOF definition of UML class and sequence diagrams. The graph grammar is validated by well-established benchmarks showing that all important features of the MOF definition of UML are covered. This formal constructive syntax definition of UML class and sequence diagrams is the basis for syntax directed editing, formal analysis, formal operational and denotational semantics and correctness of model transformations.