High-level replacement units and their termination properties

Visual rewriting techniques, in particular graph transformations, are increasingly used to model transformations of systems specified through diagrammatic sentences. Several rewriting models have been proposed, differing in the expressivity of the types of rules and in the complexity of the rewriting mechanism; yet, for many of them, basic results concerning the formal properties of these models are still missing. In this paper, we give a contribution towards solving the termination problem for rewriting systems with external control mechanisms. In particular, we obtain results of more general validity by extending the concept of transformation unit to high-level replacement systems, a generalization of graph transformation systems. For high-level replacement units, we state and prove several abstract properties based on termination criteria. Then, we instantiate the high-level replacement systems by attributed graph transformation systems and present concrete termination criteria. We explore some types of rules and replacement units for which the criterion can be established. These are used to show the termination of some replacement units needed to express model transformations formalizing refactoring.     

Definition and validation of model transformations

With model transformations becoming more widely used, there is an increasing need for approaches focussing on a systematic development of model transformations. Although a number of approaches for specifying model transformations exist, none of them focusses on systematically validating model transformations with respect to termination and confluence. Termination and confluence ensure that a model transformation always produces a unique result. Also called functionality, these properties are important requirements for practical applications of model transformations. In this paper, we introduce our approach to model transformation. Using and extending results from the theory of graph transformation, we investigate termination and confluence properties of model transformations specified in our approach. We establish a set of criteria for termination and confluence to be checked at design time by static analysis of the transformation rules and the underlying metamodels. Moreover, the criteria are formulated in such a way that they require less experience with the theory of graph transformation. Our concepts are illustrated by a running example of a model tranformation from statecharts to the process algebra Communicating Sequential Processes.     

Termination Criteria for DPO Transformations with Injective Matches

Reasoning about graph and model transformation systems is an important means to underpin model-driven software engineering, such as Model-Driven Architecture (MDA) and Model Integrated Computing (MIC). Termination criteria for graph and model transformation systems have become a focused area recently. This paper provides termination criteria for graph and model transformation systems with injective matches and finite input structure. It proposes a treatment for infinite sequences of rule applications, and takes attribute conditions, negative application conditions, and type constraints into account. The results are illustrated on case studies excerpted from real-world transformations, which show the termination properties of the frequently used "transitive closure" and "leaf collector" transformation idioms. An intuitive comparison with other approaches is also given.     

A Component Framework Based on High-Level Replacement Systems

This paper is based on two general concepts. The first one is a generic component framework for system modeling presented at FASE 2002, which is especially useful for graph- and net-based modeling techniques. The second one is the concept of high-level replacement systems, which has been studied within the last decade as an abstraction of the DPO-approach for graph transformation systems in a categorical framework, with instantiations to a large class of different modeling techniques. In this contribution both concepts are combined in the sense that the generic transformation concept - essentially used in the component framework - is instantiated by high-level replacement systems. As the main result we show how the properties for transformations required in the component framework can be shown in the case of high-level replacement systems. Moreover, some interesting extensions concerning multiple interfaces, union, and operational semantics of components are proposed.     

Modeling and Verifying Graph Transformations in Proof Assistants

This paper takes first steps towards a formalization of graph transformations in a general setting of interactive theorem provers, which will form the basis for proofs of correctness of graph transformation systems. Whereas graph rewriting is usually performed by mapping a pattern graph into a source graph by means of a graph morphism and then carrying out operations on the image node and edge set, this article generalises the notion of pattern graph to path expressions, which are formulae in a fragment of first-order logic. We examine the correspondence with traditional graph rewriting and show that this interpretation is beneficial when formally reasoning about model transformations with the aid of proof assistants.     

Scope in model transformations

A notion of hierarchical scope is commonplace in many programmatic systems. In the context of model, and in particular graph transformation, the use of scope can present two advantages: first, more natural expression of transformation application locality, and second, reduction in the number of match candidates, promising performance improvements. Previous work on scope, however, has focused on applying it to rule hierarchies, which reduces the number of matches performed, but not necessarily the cost of finding a single match. In this paper we define and explore a hierarchical scope formalism applied to the input graph, with associated modifications to the transformation rule definition. We then experimentally evaluate the benefits and challenges of our scoped model transformations in the state-of-the-art graph rewriting tool GrGen and our research-oriented, meta-modeling and rule-based model transformation tool AToMPM. We use a non-trivial “fire spreading” simulation transformation taken from distributed simulation community and a mutual exclusion transformation benchmark to demonstrate that integration of scope results in an elegant, intuitive, and efficient way of solving model transformation problems.     

A component framework for system modeling based on high-level replacement systems

The aim of this paper is to present a generic component framework for system modeling that satisfies main requirements for component-based development in software engineering. In this sense, we have defined a framework that can be used, by providing an adequate instantiation, in connection with a large class of semi-formal and formal modeling techniques. Moreover, the framework is also flexible with respect to the connection of components, providing a compositional semantics of components. This means more precisely that the semantics of a system can be inferred from the semantics of its components. In contrast to other component concepts for data type specification techniques, our component framework is based on a generic notion of transformations. In particular, refinements and transformations are used to express intradependencies, between the export interface and the body of a component, and interdependencies, between the import and the export interfaces of different components. The generic component framework generalizes module concepts for different kinds of Petri nets and graph transformation systems proposed in the literature, and seems to be also suitable for visual modeling techniques, including parts of the UML, if these techniques provide a suitable refinement or transformation concept. In this paper the generic approach is instantiated in two steps. First to high-level replacement systems generalizing the transformation concept of graph transformations. In a second step it is further instantiated to low-level and high-level Petri nets. To show applicability we present sample components from a case study in the domain of production automation as proposed in a priority program of the German Research Council (DFG).     

Preface: UNIGRA''03 - Uniform Approaches to Graphical Process Specification Techniques

This volume contains selected papers of the proceedings of the workshop on Uniform Approaches to Graphical Process Specification Techniques (UNIGRA'03). The workshop was held in Warsaw, Poland, on April 5 and 6, 2003, as a satellite event of the sixth European Joint Conference on Theory and Practice of Software (ETAPS 2003). The workshop continues the UNIGRA workshop in 2001 which has been a successful satellite event of ETAPS 2001.Workshop ObjectivesDue to the increasing amount of divergent formalisms, the main idea of the UNIGRA workshops is to bring together people working especially in the following three areas:

• Low Level and High-Level Petri Nets

• Graph Transformation and High-Level Replacement Systems

• Visual Modeling Techniques including UML

In each of these areas there is a large variety of different approaches, however, first attempts for uniform approaches have been made already. According to the main idea and in order to further stimulate the research in this important area, this volume presents some uniform approaches and further introduce unifying and comparative studies across the borders of the three and related areas.Workshop ProgramIn the first part, unifying approaches for low-level and high-level Petri nets are proposed:The contribution by Ehrig shows how the notions occurrence net and process can be generalized from low-level to high-level Petri nets, and studies the behavior and instantiations of this new view of processes for high-level nets.In his overview on new developments in the area of Petri net transformations for Software Engineering, Urbášek presents recent work on net model transformations and net class transformations. Both kinds of transformations are studied with regard to the preservation of system properties such as safety properties or liveness. The formalization of Petri net transformations is originally based on the theory of graph transformation.Padberg considers a case study (the call center of a phone company)which is modeled using Petri net modules for structuring the operational behavior of the system. The notion of Petri net modules was achieved by a transfer from the concepts of algebraic module specifications to the modeling of component-based systems by Petri nets.Desel, Juhás and Lorenz deal with the semantics of place/transition nets. The authors relate the process semantics based on partial orders (individual token semantics) to the collective token semantics by defining partial orders associated to process terms of place/transition nets.In the second part concerning graph transformation and high-level replacement systems, new aspects of component modeling and application of graph transformation techniques are discussed:In their contribution on components for algebra transformation systems, Ehrig and Orejas define a component transformation semantics in terms of the semantics of the specifications included in the components. The underlying formal basis of the instantiation of their generic component framework are algebra transformation systems and high-level replacement rules.An application of the formal unifying framework of distributed transformation units is presented by Kuske and Knirsch. The authors illustrate how different features of agent systems can be modeled by distributed graph transformation systems in a uniform way.Another application for graph rewriting, presented by Van Eetvelde and Janssens, is the modeling of refactoring operations for programs. The authors propose a hierarchical graph representation for programs to facilitate the study of refactoring operation effects at class level.The third part contains contributions focusing on unifying concepts for visual modeling techniques including UML:Minas describes a graphical specification tool for DIAGEN, a diagram editor generator based on hypergraph transformation. The specification tool simplifies the specification and generation of diagram editors. It uses an XML-based specification language and comes with a generic XML editor.In his contribution on dynamic aspects of visual modeling languages, Bottoni proposes an approach to the definition of the syntax and semantics of visual languages based on a notion of transition of production/consumption of resources. Abstract meta-models for this notion of transition are presented.An approach to the model-based verification and validation of properties of UML models is presented by Engels, Kïster, Heckel and Lohmann. The authors use graph transformation techniques as a meta-language for the translation and analysis of models.In model-driven architectures, the problem arises to deal with multiple models. Kent and Smith focus in their contribution on bidirectional mappings between models for software requirements and models for software design as basis for tools checking model traceability and consistency.Program CommitteeThe following program committee of UNIGRA'03 has given valuable scientific support:

• Hartmut Ehrig (TU Berlin, Germany) [chair]

• Roswitha Bardohl (TU Berlin, Germany) [co-chair]

• Luciano Baresi (University of Milano, Italy)

• Paolo Bottoni (University of Pisa, Italy)

• Claudia Ermel (TU Berlin, Germany)

• Reiko Heckel (University of Paderborn, Germany)

• Dirk Janssens (University of Antwerp, Belgium)

• Stuart Kent (University of Kent, Great Britain)

• Hans-Jörg Kreowski (University of Bremen, Germany)

• Fernando Orejas (University of Catalunya, Espania)

• Julia Padberg (University of Bremen, Germany)

• Grzegorz Rozenberg (University of Leiden, The Netherlands)

AcknowledgementThis workshop is supported by the European research training network SegraVis, and by the steering committee of the International Conference on Graph Transformation (ICGT).June 2003, Roswitha Bardohl and Hartmut Ehrig     

Change-driven model transformations

In this paper, we investigate change-driven model transformations, a novel class of transformations, which are directly triggered by complex model changes carried out by arbitrary transactions on the model (e.g. editing operation, transformation, etc). After a classification of relevant change scenarios, we identify challenges for change-driven transformations. As the main technical contribution of the current paper, we define an expressive, high-level language for specifying change-driven transformations as an extension of graph patterns and graph transformation rules. This language generalizes previous results on live model transformations by offering trigger events for arbitrarily complex model changes, and dedicated reactions for specific kinds of changes, making this way the concept of change to be a first-class citizen of the transformation language. We discuss how the underlying transformation engine needs to be adapted in order to use the same language uniformly for different change scenarios. The technicalities of our approach will be discussed on a (1) model synchronization case study with non-materialized target models and (2) a case study on detecting the violation of evolutionary (temporal) constraints in the security requirements engineering domain.     

A survey of strategies in rule-based program transformation systems

Program transformation is the mechanical manipulation of a program in order to improve it relative to some cost function and is understood broadly as the domain of computation where programs are the data. The natural basic building blocks of the domain of program transformation are transformation rules expressing a ‘one-step’ transformation on a fragment of a program. The ultimate perspective of research in this area is a high-level, language parametric, rule-based program transformation system, which supports a wide range of transformations, admitting efficient implementations that scale to large programs. This situation has not yet been reached, as trade-offs between different goals need to be made. This survey gives an overview of issues in rule-based program transformation systems, focusing on the expressivity of rule-based program transformation systems and in particular on transformation strategies available in various approaches. The survey covers term rewriting, extensions of basic term rewriting, tree parsing strategies, systems with programmable strategies, traversal strategies, and context-sensitive rules.     

Termination of term rewriting: interpretation and type elimination

We investigate proving termination of term rewriting systems by interpretation of terms in a well-founded monotone algebra. The well-known polynomial interpretations can be considered as a particular case in this framework. A classification of types of termination, including simple termination, is proposed based on properties in the semantic level. A transformation on term rewriting systems eliminating distributive rules is introduced. Using this distribution elimination a new termination proof of the system SUBST of Hardin and Laville (1986) is given. This system describes explicit substitution in λ-calculus.Another tool for proving termination is based on introduction and removal of type restrictions. A property of many-sorted term rewriting systems is called persistent if it is not affected by removing the corresponding typing restriction. Persistence turns out to be a generalization of direct sum modularity, but is more powerful for both proving confluence and termination. Termination is proved to be persistent for the class of term rewriting systems for which not both duplicating rules and collapsing rules occur, generalizing a similar result of Rusinowitch for modularity. This result has nice applications, in particular in undecidability proofs.     

Transformation for Refining Unraveled Conditional Term Rewriting Systems

Unravelings, transformations from conditional term rewriting systems (CTRSs, for short) into unconditional term rewriting systems, are valuable for analyzing properties of CTRSs. In order to completely simulate rewrite sequences of CTRSs, the restriction by a particular context-sensitive and membership condition that is determined by extra function symbols introduced due to the unravelings, must be imposed on the rewrite relations of the unraveled CTRSs. In this paper, in order to weaken the context-sensitive and membership condition, we propose a transformation applied to the unraveled CTRSs, that reduces the number of the extra symbols. In the transformation, updating the context-sensitive condition properly, we remove the extra symbols that satisfy a certain condition. If the transformation succeeds in removing all of the extra symbols, we obtain the TRSs that are computationally equivalent with the original CTRSs.     

Proving termination of context-sensitive rewriting by transformation

Context-sensitive rewriting (CSR) is a restriction of rewriting that forbids reductions on selected arguments of functions. With CSR, we can achieve a terminating behavior with non-terminating term rewriting systems, by pruning (all) infinite rewrite sequences. Proving termination of CSR has been recently recognized as an interesting problem with several applications in the fields of term rewriting and programming languages. Several methods have been developed for proving termination of CSR. Specifically, a number of transformations that permit treating this problem as a standard termination problem have been described. The main goal of this paper is to contribute to a better comprehension and practical use of transformations for proving termination of CSR. We provide new completeness results regarding the use of the transformations in two restricted (but relevant) settings: (a) proofs of termination of canonical CSR and (b) proofs of termination of CSR by using transformations together with simplification orderings. We have also made an experimental evaluation of the transformations, which complements the theoretical analysis from a practical point of view. This leads to new hierarchies of the transformations which are useful to guide their practical use when implementing tools for proving termination of CSR.     

Graph rewriting systems for the entity-relationship approach

Sequential graph rewriting systems are proposed as a meta-level formalism providing the concise and sound definition of different ER diagram languages. These rewriting systems can be used to define ER-based approaches for various DB modelling subtasks like schema design, evolution and integration. In addition, they are a natural choice for syntax directed ER CASE workbenches. In particular, by using specialized ER graph rewriting systems as meta input for CASE tools, the resulting tool behavior can be guided and controlled. Moreover, grammar driven modelling tools can be easily adapted for the needs of a particular enterprise or software factory without superimposing a particular ER dialect on the end users. Additional benefits result from the use of ER graph rewriting systems as a comparison framework for the continuously enlarging set of ER dialects.

The presentation includes material on the ER graph rewriting formalism, i.e., the actual tool, as well as an introduction to some formal graph rewriting prerequisites. An exemplary application, in particular ER graph generation, is used to clarify the underlying formal concepts.     

A sound and complete theory of graph transformations for service programming with sessions and pipelines

Graph transformation techniques, the Double-Pushout (DPO) approach in particular, have been successfully applied in the modeling of concurrent systems. In this area, a research thread has addressed the definition of concurrent semantics for process calculi. In this paper, we propose a theory of graph transformations for service programming with sophisticated features such as sessions and pipelines. Through graph representation of CaSPiS, a recently proposed process calculus, we show how graph transformations can cope with advanced features of service-oriented computing, such as several logical notions of scoping together with the interplay between linking and containment. We first exploit a graph algebra and set up a graph model that supports graph transformations in the DPO approach. Then, we show how to represent CaSPiS processes as hierarchical graphs in the graph model and their behaviors as graph transformation rules. Finally, we provide the soundness and completeness results of these rules with respect to the reduction semantics of CaSPiS.     

Fujaba-Based Tool Development for eHome Systems

One of the main reasons preventing a wide application of eHome systems in practice is the effort needed to combine all appliances, necessary controller and infrastructure components to benefit from derived value-added services. The properties, dependencies, locations, and installation conditions have to be properly specified for this composition and its deployment. Due to the great variance in services and eHome configurations there is a need for tool support for eHome systems. In this paper we address the software development issues of such tools. In our approach we base the software development on graph rewriting language techniques. Based on our experience, we consider this approach as a possibility to improve the productivity of the eHome system tool development. With the aid of Fujaba, we created a model capable of specifying functions, devices, environments, and value-added services. Furthermore, we used Fujaba to create the activities as graph rewriting rules for model modifications. To apply the model and to carry out the actual specification for a particular eHome and particular appliances we generated the eHomeSpecificator tool from the model and its activities. This tool can serve as a base for a wider range of tools supporting eHome systems.     

Formal foundation of consistent EMF model transformations by algebraic graph transformation

Model transformation is one of the key activities in model-driven software development. An increasingly popular technology to define modeling languages is provided by the Eclipse Modeling Framework (EMF). Several EMF model transformation approaches have been developed, focusing on different transformation aspects. To validate model transformations with respect to functional behavior and correctness, a formal foundation is needed. In this paper, we define consistent EMF model transformations as a restricted class of typed graph transformations using node type inheritance. Containment constraints of EMF model transformations are translated to a special kind of graph transformation rules such that their application leads to consistent transformation results only. Thus, consistent EMF model transformations behave like algebraic graph transformations and the rich theory of algebraic graph transformation can be applied to these EMF model transformations to show functional behavior and correctness. Furthermore, we propose parallel graph transformation as a suitable framework for modeling EMF model transformations with multi-object structures. Rules extended by multi-object structures can specify a flexible number of recurring structures. The actual number of recurring structures is dependent on the application context of such a rule. We illustrate our approach by selected refactorings of simplified statechart models. Finally, we discuss the implementation of our concepts in a tool environment for EMF model transformations.     

Comparative Evaluation of Model Transformation Specification Approaches

Model transformations have become a key element of model-driven software development, being used to transform platform-independent models to platform-specific models, to improve model quality, to introduce design patterns and refactorings, and to map models from one language to another. A large number of model transformation notations and tools exist. However, there are no guidelines on how to select appropriate notations for particular model transformation tasks, and no comprehensive comparisons of the relative merits of particular approaches. In this paper we provide a unified semantic treatment of model transformations, and show how correctness properties of model transformations can be defined using this semantics. We evaluate several approaches which have been developed for model transformation specification, with respect to their expressivity, complexity and support for verification, and make recommendations for resolving the outstanding problems concerning model transformation specification.     

Towards language-to-language transformation

This paper proposes a simplicity-oriented approach and framework for language-to-language transformation of, in particular, graphical languages. Key to simplicity is the decomposition of the transformation specification into sub-rule systems that separately specify purpose-specific aspects. We illustrate this approach by employing a variation of Plotkin’s Structural Operational Semantics (SOS) for pattern-based transformations of typed graphs in order to address the aspect ‘computation’ in a graph rewriting fashion. Key to our approach are two generalizations of Plotkin’s structural rules: the use of graph patterns as the matching concept in the rules, and the introduction of node and edge types. Types do not only allow one to easily distinguish between different kinds of dependencies, like control, data, and priority, but may also be used to define a hierarchical layering structure. The resulting Type-based Structural Operational Semantics (TSOS) supports a well-structured and intuitive specification and realization of semantically involved language-to-language transformations adequate for the generation of purpose-specific views or input formats for certain tools, like, e.g., model checkers. A comparison with the general-purpose transformation frameworks ATL and Groove, illustrates along the educational setting of our graphical WebStory language that TSOS provides quite a flexible format for the definition of a family of purpose-specific transformation languages that are easy to use and come with clear guarantees.

     

An Efficient Solution for Model Checking Graph Transformation Systems

This paper presents an efficient solution for modeling checking graph transformation systems. The approach transforms AGG specifications into Bogor models and supports both attributed typed graphs and layered transformations. Resulting models are amenable to check interesting properties expressed as combinations of LTL (Linear Temporal Logic) and graph transformation rules. The first experimental results are encouraging and show that in most cases our proposal improves existing approaches, both in terms of performance and expressiveness.