Satisfaction, Restriction and Amalgamation of Constraints in the Framework of M-Adhesive Categories

Application conditions for rules and constraints for graphs are well-known in the theory of graph transformation and have been extended already to M-adhesive transformation systems. According to the literature we distinguish between two kinds of satisfaction for constraints, called general and initial satisfaction of constraints, where initial satisfaction is defined for constraints over an initial object of the base category. Unfortunately, the standard definition of general satisfaction is not compatible with negation in contrast to initial satisfaction. Based on the well-known restriction of objects along type morphisms, we study in this paper restriction and amalgamation of application conditions and constraints together with their solutions. In our main result, we show compatibility of initial satisfaction for positive constraints with restriction and amalgamation, while general satisfaction fails in general. Our main result is based on the compatibility of composition via pushouts with restriction, which is ensured by the horizontal van Kampen property in addition to the vertical one that is generally satisfied in M-adhesive categories.Comment: In Proceedings ACCAT 2012, arXiv:1208.430

Coupled Transformations of Graph Structures applied to Model Migration

Model-Driven Engineering (MDE) is a relatively new paradigm in software engineering that pursues the goal to master the increased complexity of modern software products. While software applications have been developed for a specific platform in the past, today they are targeting various platforms and devices from classical desktop PCs to smart phones. In addition, they interact with other applications. To easier cope with these new requirements, software applications are specified in MDE at a high abstraction level in so called models prior to their implementation. Afterward, model transformations are used to automate recurring development tasks as well as to generate software artifacts for different runtime environments. Thereby, software artifacts are not necessarily files containing program code, they can also cover configuration files as well as machine readable input for model checking tools. However, MDE does not only address software engineering problems, it also raises new challenges. One of these new challenges is connected to the specification of modeling languages, which are used to create models. The creation of a modeling language is a creative process that requires several iterations similar to the creation of models. New requirements as well as a better understanding of the application domain result in an evolution of modeling languages over time. Models developed in an earlier version of a modeling language often needs to be co-adopted (migrated) to language changes. This migration should be automated, as migrating models manually is time consuming and error-prone. While application modelers use ad-hoc solutions to migrate their models, there is still a lack of theory to ensure well-defined migration results. This work contributes to a formalization of modeling language evolution with corresponding model migration on the basis of algebraic graph transformations that have successfully been used earlier as theoretical foundations of model transformation. The goal of this research is to develop a theory that considers the problem of modeling language evolution with corresponding model migration on a conceptual level, independent of a specific modeling framework

Formal Foundations for Information-Preserving Model Synchronization Processes Based on Triple Graph Grammars

Zwischen verschiedenen Artefakten, die Informationen teilen, wieder Konsistenz herzustellen, nachdem eines von ihnen geändert wurde, ist ein wichtiges Problem, das in verschiedenen Bereichen der Informatik auftaucht. Mit dieser Dissertation legen wir eine Lösung für das grundlegende Modellsynchronisationsproblem vor. Bei diesem Problem ist ein Paar solcher Artefakte (Modelle) gegeben, von denen eines geändert wurde; Aufgabe ist die Wiederherstellung der Konsistenz. Tripelgraphgrammatiken (TGGs) sind ein etablierter und geeigneter Formalismus, um dieses und verwandte Probleme anzugehen. Da sie auf der algebraischen Theorie der Graphtransformation und dem (Double-)Pushout Zugang zu Ersetzungssystemen basieren, sind sie besonders geeignet, um Lösungen zu entwickeln, deren Eigenschaften formal bewiesen werden können. Doch obwohl TGG-basierte Ansätze etabliert sind, leiden viele von ihnen unter dem Problem des Informationsverlustes. Wenn ein Modell geändert wurde, können während eines Synchronisationsprozesses Informationen verloren gehen, die nur im zweiten Modell vorliegen. Das liegt daran, dass solche Synchronisationsprozesse darauf zurückfallen Konsistenz dadurch wiederherzustellen, dass sie das geänderte Modell (bzw. große Teile von ihm) neu übersetzen. Wir schlagen einen TGG-basierten Ansatz vor, der fortgeschrittene Features von TGGs unterstützt (Attribute und negative Constraints), durchgängig formalisiert ist, implementiert und inkrementell in dem Sinne ist, dass er den Informationsverlust im Vergleich mit vorherigen Ansätzen drastisch reduziert. Bisher gibt es keinen TGG-basierten Ansatz mit vergleichbaren Eigenschaften. Zentraler Beitrag dieser Dissertation ist es, diesen Ansatz formal auszuarbeiten und seine wesentlichen Eigenschaften, nämlich Korrektheit, Vollständigkeit und Termination, zu beweisen. Die entscheidende neue Idee unseres Ansatzes ist es, Reparaturregeln anzuwenden. Dies sind spezielle Regeln, die es erlauben, Änderungen an einem Modell direkt zu propagieren anstatt auf Neuübersetzung zurückzugreifen. Um diese Reparaturregeln erstellen und anwenden zu können, entwickeln wir grundlegende Beiträge zur Theorie der algebraischen Graphtransformation. Zunächst entwickeln wir eine neue Art der sequentiellen Komposition von Regeln. Im Gegensatz zur gewöhnlichen Komposition, die zu Regeln führt, die Elemente löschen und dann wieder neu erzeugen, können wir Regeln herleiten, die solche Elemente stattdessen bewahren. Technisch gesehen findet der Synchronisationsprozess, den wir entwickeln, außerdem in der Kategorie der partiellen Tripelgraphen statt und nicht in der der normalen Tripelgraphen. Daher müssen wir sicherstellen, dass die für Double-Pushout-Ersetzungssysteme ausgearbeitete Theorie immer noch gültig ist. Dazu entwickeln wir eine (kategorientheoretische) Konstruktion neuer Kategorien aus gegebenen und zeigen, dass (i) diese Konstruktion die Axiome erhält, die nötig sind, um die Theorie für Double-Pushout-Ersetzungssysteme zu entwickeln, und (ii) partielle Tripelgraphen als eine solche Kategorie konstruiert werden können. Zusammen ermöglichen diese beiden grundsätzlichen Beiträge es uns, unsere Lösung für das grundlegende Modellsynchronisationsproblem vollständig formal auszuarbeiten und ihre zentralen Eigenschaften zu beweisen.Restoring consistency between different information-sharing artifacts after one of them has been changed is an important problem that arises in several areas of computer science. In this thesis, we provide a solution to the basic model synchronization problem. There, a pair of such artifacts (models), one of which has been changed, is given and consistency shall be restored. Triple graph grammars (TGGs) are an established and suitable formalism to address this and related problems. Being based on the algebraic theory of graph transformation and (double-)pushout rewriting, they are especially suited to develop solutions whose properties can be formally proven. Despite being established, many TGG-based solutions do not satisfactorily deal with the problem of information loss. When one model is changed, in the process of restoring consistency such solutions may lose information that is only present in the second model because the synchronization process resorts to restoring consistency by re-translating (large parts of) the updated model. We introduce a TGG-based approach that supports advanced features of TGGs (attributes and negative constraints), is comprehensively formalized, implemented, and is incremental in the sense that it drastically reduces the amount of information loss compared to former approaches. Up to now, a TGG-based approach with these characteristics is not available. The central contribution of this thesis is to formally develop that approach and to prove its essential properties, namely correctness, completeness, and termination. The crucial new idea in our approach is the use of repair rules, which are special rules that allow one to directly propagate changes from one model to the other instead of resorting to re-translation. To be able to construct and apply these repair rules, we contribute more fundamentally to the theory of algebraic graph transformation. First, we develop a new kind of sequential rule composition. Whereas the conventional composition of rules leads to rules that delete and re-create elements, we can compute rules that preserve such elements instead. Furthermore, technically the setting in which the synchronization process we develop takes place is the category of partial triple graphs and not the one of ordinary triple graphs. Hence, we have to ensure that the elaborate theory of double-pushout rewriting still applies. Therefore, we develop a (category-theoretic) construction of new categories from given ones and show that (i) this construction preserves the axioms that are necessary to develop the theory of double-pushout rewriting and (ii) partial triple graphs can be constructed as such a category. Together, those two more fundamental contributions enable us to develop our solution to the basic model synchronization problem in a fully formal manner and to prove its central properties

Graph Modelling and Transformation: Theory meets Practice

In this paper, we focus on the role of graphs and graph transformation for four practical application areas from software system development. We present the typical problems in these areas and investigate how the respective systems are modelled by graphs and graph transformation. In particular, we are interested in the usefulness of theoretical graph transformation results and graph transformation tools in order to solve these problems. Finally, we characterize concepts and tool features which are still missing in practice to solve the presented and related problems even better. Keywords: graph modelling, graph transformation, graph transformation tool

Matrix Graph Grammars

This book objective is to develop an algebraization of graph grammars. Equivalently, we study graph dynamics. From the point of view of a computer scientist, graph grammars are a natural generalization of Chomsky grammars for which a purely algebraic approach does not exist up to now. A Chomsky (or string) grammar is, roughly speaking, a precise description of a formal language (which in essence is a set of strings). On a more discrete mathematical style, it can be said that graph grammars -- Matrix Graph Grammars in particular -- study dynamics of graphs. Ideally, this algebraization would enforce our understanding of grammars in general, providing new analysis techniques and generalizations of concepts, problems and results known so far.Comment: 321 pages, 75 figures. This book has is publisehd by VDM verlag, ISBN 978-363921255

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