Ulrike Golas

Efficient analysis and execution of correct and complete model transformations based on triple graph grammars

Triple Graph Grammars are a well-established, formal and intuitive concept for the specification and analysis of bidirectional model transformations. In previous work we have formalized and analyzed already termination, correctness, completeness, local confluence and functional behaviour. In this paper, we show how to improve the efficiency of the execution and analysis of model transformations in practical applications by using triple rules with negative application conditions (NACs). In addition to specification NACs, which improve the specification of model transformations, the generation of filter NACs improves the efficiency of the execution and the analysis of functional behaviour supported by critical pair analysis of the tool AGG. We illustrate the results for the well-known model transformation from class diagrams to relational database models.

Formal analysis of functional behaviour for model transformations based on triple graph grammars

Triple Graph Grammars (TGGs) are a well-established concept for the specification of model transformations. In previous work we have formalized and analyzed already crucial properties of model transformations like termination, correctness and completeness, but functional behaviour is missing up to now. In order to close this gap we generate forward translation rules, which extend standard forward rules by translation attributes keeping track of the elements which have been translated already. In the first main result we show the equivalence of model transformations based on forward resp. forward translation rules. This way, an additional control structure for the forward transformation is not needed. This allows to apply critical pair analysis and corresponding tool support by the tool AGG. However, we do not need general local confluence, because confluence for source graphs not belonging to the source language is not relevant for the functional behaviour of a model transformation. For this reason we only have to analyze a weaker property, called translation confluence. This leads to our second main result, the functional behaviour of model transformations, which is applied to our running example, the model transformation from class diagrams to database models.

M-Adhesive Transformation Systems with Nested Application Conditions. Part 2: Embedding, Critical Pairs and Local Confluence

Graph transformation systems have been studied extensively and applied to several areas of computer science like formal language theory, the modeling of databases, concurrent or distributed systems, and visual, logical, and functional programming. In most kinds of applications it is necessary to have the possibility of restricting the applicability of rules. This is usually done by means of application conditions. In this paper, we continue the work of extending the fundamental theory of graph transformation to the case where rules may use arbitrary (nested) application conditions. More precisely, we generalize the Embedding theorem, and we study how local confluence can be checked in this context. In particular, we define a new notion of critical pair which allows us to formulate and prove a Local Confluence Theorem for the general case of rules with nested application conditions. All our results are presented, not for a specific class of graphs, but for any arbitrary M-adhesive category, which means that our results apply to most kinds of graphical structures. We demonstrate our theory on the modeling of an elevator control by a typed graph transformation system with positive and negative application conditions.

M-adhesive transformation systems with nested application conditions. Part 1: parallelism, concurrency and amalgamation

Nested application conditions generalise the well-known negative application conditions and are important for several application domains. In this paper, we present Local Church-Rosser, Parallelism, Concurrency and Amalgamation Theorems for rules with nested application conditions in the framework of M-adhesive categories, where M-adhesive categories are slightly more general than weak adhesive high-level replacement categories. Most of the proofs are based on the corresponding statements for rules without application conditions and two shift lemmas stating that nested application conditions can be shifted over morphisms and rules.

Attributed graph transformation with inheritance: Efficient conflict detection and local confluence analysis using abstract critical pairs

Inheritance is an important and widely spread concept enabling the elegant expression of hierarchy in object-oriented software programs or models. It has been defined for graphs and graph transformations enhancing the applicability of this formal technique. Up to now, for the analysis of transformations with inheritance a flattening construction has been used, which yields all the well-known results for graph transformation but results in a large number of graphs and rules that have to be analyzed. In this paper, we introduce a new category of typed attributed graphs with inheritance. For the detection of conflicts between graph transformations on these graphs, the notion of abstract critical pairs is defined. This allows us to perform the analysis on polymorphic rules and transformations without the need for flattening, which significantly increases the efficiency of the analysis and eases the interpretation of the analysis results. The new main result is the Local Confluence Theorem for typed attributed graph transformation with inheritance using abstract critical pairs. All constructions and results are demonstrated on an example for the analysis of refactorings.

Multi-amalgamation in adhesive categories

Amalgamation is a well-known concept for graph transformations in order to model synchronized parallelism of rules with shared subrules and corresponding transformations. This concept is especially important for an adequate formalization of the operational semantics of statecharts and other visual modeling languages, where typed attributed graphs are used for multiple rules with general application conditions. However, the theory of amalgamation for the double pushout approach has been developed up to now only on a set-theoretical basis for pairs of standard graph rules without any application conditions. For this reason, we present the theory of amalgamation in this paper in the framework of adhesive categories for a bundle of rules with (nested) application conditions. In fact, it is also valid for weak adhesive HLR categories. The main result is the Multi-Amalgamation Theorem, which generalizes the well-known Parallelism and Amalgamation Theorems to the case of multiple synchronized parallelism. The constructions are illustrated by a small running example. A more complex case study for the operational semantics of statecharts based on multi-amalgamation is presented in a separate paper.

Parallel independence of amalgamated graph transformations applied to model transformation

The theory of algebraic graph transformation has proven to be a suitable underlying formal framework to reason about the behavior of model transformations. In order to model an arbitrary number of actions at different places in the same model, the concept of amalgamated graph transformation has been proposed. Rule applications of certain regularity are described by a rule scheme which contains multirules modeling elementary actions and a common kernel rule for their synchronization (amalgamation). The amalgamation theorem by Bohm et al. ensures that for two multi-rules, the application of the amalgamated rule yields the same result as two iterative rule applications, respecting their common kernel rule application. In this paper, we propose an extension of the amalgamation theorem to an arbitrary finite number of synchronous rule applications. The theorem is used to show parallel independence of amalgamated graph transformations by analyzing the underlying multi-rules. As example, we specify an excerpt of a model transformation from Business Process Models (BPM) to the Business Process Execution Language (BPEL).

Local confluence for rules with nested application conditions

Local confluence is an important property in many rewriting and transformation systems. The notion of critical pairs is central for being able to verify local confluence of rewriting systems in a static way. Critical pairs are defined already in the framework of graphs and adhesive rewriting systems. These systems may hold rules with or without negative application conditions. In this paper however, we consider rules with more general application conditions -- also called nested application conditions -- which in the graph case are equivalent to finite first-order graph conditions. The classical critical pair notion denotes conflicting transformations in a minimal context satisfying the application conditions. This is no longer true for combinations of positive and negative application conditions -- an important special case of nested ones -- where we have to allow that critical pairs do not satisfy all the application conditions. This leads to a new notion of critical pairs which allows to formulate and prove a Local Confluence Theorem for the general case of rules with nested application conditions. We demonstrate this new theory on the modeling of an elevator control by a typed graph transformation system with positive and negative application conditions.

A general attribution concept for models in M-adhesive transformation systems

Attributes are an important concept for modeling data in practical applications. Up to now there is no adequate way to define attributes for different kinds of models used in

A Visual Interpreter Semantics for Statecharts Based on Amalgamated Graph Transformation

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