Domain Completeness of Model Transformations and Synchronisations

The intrinsic question of most activities in information science, in practice or science, is “Does a given system satisfy the requirements regarding its application?” Commonly, requirements are expressed and accessible by means of models, mostly in a diagrammatic representation by visual models. The requirements may change over time and are often defined from different perspectives and within different domains. This implies that models may be transformed either within the same domain-specific visual modelling language or into models in another language. Furthermore, model updates may be synchronised between different models. Most types of visual models can be represented by graphs where model transformations and synchronisations are performed by graph transformations. The theory of graph transformations emerged from its origins in the late 1960s and early 1970s as a generalisation of term and tree rewriting systems to an important field in (theoretical) computer science with applications particularly in visual modelling techniques, model transformations, synchronisations and behavioural specifications of models. Its formal foundations but likewise visual notation enable both precise definitions and proofs of important properties of model transformations and synchronisations from a theoretical point of view and an intuitive approach for specifying transformations and model updates from an engineer’s point of view. The recent results were presented in the EATCS monographs “Fundamentals of Algebraic Graph Transformation” (FAGT) in 2006 and its sequel “Graph and Model Transformation: General Framework and Applications” (GraMoT) in 2015. This thesis concentrates on one important property of model transformations and synchronisations, i.e., syntactical completeness. Syntactical completeness of model transformations means that given a specification for transforming models from a source modelling language into models in a target language, then all source models can be completely transformed into corresponding target models. In the same given context, syntactical completeness of model synchronisations means that all source model updates can be completely synchronised, resulting in corresponding target model updates. This work is essentially based on the GraMoT book and mainly extends its results for model transformations and synchronisations based on triple graph grammars by a new more general notion of syntactical completeness, namely domain completeness, together with corresponding verification techniques. Furthermore, the results are instantiated to the verification of the syntactical completeness of software transformations and synchronisations. The well-known transformation of UML class diagrams into relational database models and the transformation of programs of a small object-oriented programming language into class diagrams serve as running examples. The existing AGG tool is used to support the verification of the given examples in practice.