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.

Formal foundation of consistent EMF model transformations by algebraic graph transformation

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.

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

The integrated development environment AGG supports the specification of algebraic graph transformation systems based on attributed, typed graphs with node type inheritance, graph rules with application conditions, and graph constraints It offers several analysis techniques for graph transformation systems including graph parsing, consistency checking of graphs as well as conflict and dependency detection in transformations by critical pair analysis of graph rules, an important instrument to support the confluence check of graph transformation systems AGG 20 includes various new features added over the past two years It supports the specification of complex control structures for rule application comprising the definition of control and object flow for rule sequences and nested application conditions Furthermore, new possibilities for constructing rules from existing ones (eg, inverse, minimal, amalgamated, and concurrent rules) and for more flexible usability of critical pair analyses have been realized

AGG 2.0 --- new features for specifying and analyzing algebraic graph transformations

We formulate a unified display calculus proof theory for the four principal varieties of bunched logic by combining display calculi for their component logics. Our calculi satisfy cut-elimination, and are sound and complete with respect to their standard presentations. We show how to constrain applications of display-equivalence in our calculi in such a way that an exhaustive proof search need be only finitely branching, and establish a full deduction theorem for the bunched logics with classical additives, BBI and CBI. We also show that the standard sequent calculus for BI can be seen as a reformulation of its display calculus, and argue that analogous sequent calculi for the other varieties of bunched logic are very unlikely to exist.

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Bunched Logics Displayed

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).

Parallel independence of amalgamated graph transformations applied to model transformation

Have you ever seen the Citation Indexes (CIs) for the year 1600? At that time, a very active community was working on the reconstruction of planetary movements by means of epicycles. In principle, any ellipse around the Sun may be approximated by sufficiently many epicycles around the Earth. This is a non-trivial geometrical task, especially given the lack of analytical tools (sums of series). And the books and papers of many talented geometers quoted one another. Scientific knowledge, however, was already taking other directions. Science has a certain ‘inertia’, it is prudent (at times, it has been exceedingly so, mostly for political or metaphysical reasons), but even under the best of conditions, we all know how difficult it is to accept new ideas, to let them blossom in time, away from short-term pressures.

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T. Ehrhard

Papers

Editors' note: bibliometrics and the curators of orthodoxy