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ELSEVIER Electronic Notes in Theoretical Computer Science 152 (2006) 143-159

www.elsevier.com/locate/entcs

Applying a Model Transformation Taxonomy to Graph Transformation Technology

Tom Mens1

Software Engineering Lab Université de Mons-Hainaut Mons, Belgium

Pieter Van Gorp2

Formal Techniques in Software Engineering Universiteit Antwerpen Antwerpen, Belgium

Daniel Varro3

Department of Measurement and Information Systems Budapest University of Technology and Economics Budapest, Hungary

Gabor Karsai4

Institute for Software-Integrated Systems Vanderbilt University Nashville, Tennessee, USA

Abstract

A taxonomy of model transformations was introduced in [18]. Among others, such a taxonomy can help developers in deciding which language, forma lism, tool or mechanism is best suited to carry out a particular model transformation activity. In this paper we apply the taxonomy to the technique of graph transformation, and we exemplify it by referring to four representative graph transformation tools. As a byproduct of our analysis, we discuss how well each of the considered tools carry out the activity of model transformation.

Keywords: model transformation, taxonomy, graph transformation, MDA, MDD, MDE

1571-0661/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.entcs.2005.10.022

1 Introduction

A taxonomy of model transformation was introduced in [18]. By taxonomy we mean "A system for naming and organizing things [... ] into groups which share similar qualities" (Cambridge Dictionaries Online). Such a taxonomy can be used for a wide variety of purposes. Among others, it can help a software developer choosing a particular model transformation approach that is best suited for his needs, it can help tool builders to assess the strengths and weaknesses of their tools compared to other tools, and it can help scientists to identify limitations across tools or technology that need to be overcome by improving the underlying techniques and formalisms.

In this paper we use the taxonomy to study the technique of graph transformation, in order to find out what are the merits and drawbacks of graph transformation technology with respect to the activity of model transformation. We exemplify this by applying the taxonomy to a representative subset of tools relying on graph transformation technology. As a byproduct of this analysis, we identify how well these tools carry out the activity of model transformation.

As indicated by [27], the presence of taxonomies and benchmarks, when embraced by a community, have a strong positive effect on the scientific maturity of a discipline. While this paper will focus on the application of a model transformation taxonomy to graph transformation tools, a related paper proposed a benchmark for graph transformation [32].

Because graph transformation consists of a large set of different theories, languages, techniques and tools, we need to restrict ourselves to a representative subset somehow. Therefore, we tried to classify existing tools relying on graph transformation technology according to their principal domain of application, and we came up with four important categories:

General-purpose graph transformation tools include AGG 5 [29] and PROGRES [26];

Reengineering tools based on graph transformation include Fujaba 6 (From UML to Java And Back Again) [2] that supports round-trip engineering between UML and Java, and VARLET 7 that performs information system

1 Email: tom.mens@umh.ac.be

2 Email:pieter.vangorp@ua.ac.be

3 Email:varro@mit.bme.hu

4 Email:gabor. karsai@vanderbilt. edu

5 http://tfs.cs.tu-berlin.de/agg/

6 http://wwwcs.uni-paderborn.de/cs/fujaba/

7 http://wwwcs.uni-paderborn.de/cs/varlet/

reengineering based on triple graph grammars;

Model transformation tools that make use of graph transformation include GReAT 8 [28] and MOLA [12];

Model checking and verification tools that rely on graph transformation include VIATRA (Visual Automated model TRAnsformations) [4], GROOVE 9 [21] and CheckVML [22].

We have selected the following tools from each category, because we had easy access to them: AGG, Fujaba, GReAT and VIATRA. In the remainder we will use these four tools to illustrate the use of the taxonomy of [18]. However, we believe that the taxonomy is general and applicable to the other tools as well.

The structure of the paper follows the main structure of the taxonomy, which is summarised below:

What needs to be transformed into what? This dimension comprises the following criteria:

• Number of source and target models

• Technical space of the transformation (e.g., MDA, XML)

• Endogenous versus exogenous transformations (i.e., within the same language or between languages)

• Horizontal versus vertical transformations (i.e., on the same level of abstraction or across levels of abstractions)

• Syntactical versus semantical transformations (i.e., simple syntactical rewriting or complex transformations that take semantics into account)

Important characteristics of a transformation :

• Level of automation provided by the tool

• Complexity of the transformation

• Preservation of properties by the transformation

Success criteria for a transformation tool :

• Suggesting when to apply transformations

• Customising or reusing transformations

• Verifying and guaranteeing correctness of transformations

• Testing and validating transformations

• Dealing with incomplete or inconsistent models

• Grouping, composing, and decomposing transformations

• Genericity of transformations

• Bidirectionality of transformations

8 http://repo.isis.vanderbilt.edu/tools/

9 http://groove.sourceforge.net

• Supporting traceability and change propagation Quality requirements for a transformation tool :

• Usability and usefulness

• Verbosity versus conciseness

• Performance and scalability

• Extensibility

• Interoperability

• Acceptability by user community

• Standardization

2 What needs to be transformed into what?

Graphs seem to be a natural representation of models since many models are intrinsically graph-based in nature (e.g., statecharts, activity diagrams, collaboration diagrams, class diagrams, Petri nets), in contrast to source code where a tree structure is likely to be more appropriate (e.g., parse trees, abstract syntax trees). As a consequence, graph transformations seem to a natural means to specify and execute model transformations.

Number of source and target models.

Graph transformation theory allows us to express one-to-one model transformations directly as a graph production (also known as graph transformation rule) with a left-hand side (LHS) representing the source model, and a right-hand side (RHS) representing the target model. One-to-many transformations (e.g., branching and splitting of models), many-to-one transformations (e.g., merging of models) and many-to-many transformations can also be defined formally as graph transformations, but this requires a more complex solution.

Triple graph grammars [24], for example, allow the specification of many-to-many model transformations that transform pairs of related models simultaneously while maintaining their consistency. Using this idea, multi graph rewriting rules can be defined that transform any number of (related) source models in a consistent way [15].

Technical space.

All of the considered graph transformation tools allow us to deal with models in the XML or MDA technical space directly, or using some translators. The AGG tool uses GXL 10, a standard graph exchange format as meta-

10 http://www.gupro.de/GXL/

metamodel. However, since GXL is based on XML, it is relatively easy to provide a mapping to the XML technical space. AGG also supports export into GTXL 11, a standard exchange format for graph transformations.

The VIATRA model transformation tool uses an XMI input/output format that conforms to the MOF model. It primarily supports the MDA technical space, but business process models and XSD models are also targeted.

The Fujaba CASE tool suite supports UML development and automatic generation of Java code. The underlying technology to represent UML diagrams is based on graph transformations. Fujaba uses a vendor-specific version of UML, so it can be considered as part of the MDA technical space.

The GReAT model transformation tool uses UML and OCL notation to specify metamodels and transformations. As such, it belongs to the MDA technical space.

Endogenous versus exogenous transformations.

In graph transformation, the structure of a metamodel is described by means of a type graph [3]. In an endogenous graph transformation, the source and target graphs are instances of the same type graph. This is the case in the AGG tool, in which only a single type graph can be specified for a given graph transformation system. However, one can easily specify two different metamodels and their interrelationships within the same type graph, as shown in [5].

Exogenous transformations, where the source and target are expressed in a different domain (i.e., have a different metamodel) can be expressed using graph transformations, provided that a different type graph can be specified for source and target model. Note that (temporary) edges (so called "cross-links") between nodes belonging to different type graphs might also be required. This is supported by GReAT and VIATRA, where multiple type graphs (as well as a cross-links) are supported.

Horizontal versus vertical transformations.

Graph transformation technology can be, and has been, used for specifying horizontal as well as vertical model transformations.

As an example of vertical exogenous model transformation, Karsai et al. show how to transform a platform-independent model (PIM) into a more platform-specific model (PSM) using GReAT [13]. As another example, Baresi

11 http://tfs.cs.tu-berlin.de/projekte/gxl-gtxl.html

et al. illustrate the use of graph transformation for refinement of software architectures [1].

As an example of horizontal endogenous model transformation, graph transformations have been used to specify program refactorings [19,30], and model refactorings in AGG and Fujaba [17]. A typical example is a statechart flattening, where all composite (nested) states are recursively expanded until one obtains a statechart only containing simple states [8].

As an example of horizontal exogenous transformation, graph transformations have been used for migration from one domain-specific language to another using GReAT [28].

Finally, GroBe-Rhode et al. [20] illustrate vertical endogenous transformations by specifying formal refinements as typed graph transformations.

Syntactical versus semantical transformations.

Graphs and graph transformations can be used to specify and modify the syntactic structure of a model, but also to specify the dynamic behaviour of a model. Even syntactic transformations can take semantic information into account, by specifying graph constraints (invariants) that need to be preserved by the transformation. This is especially needed in the case of model refactoring, where the structure of a model is improved while preserving its behaviour [19,17].

3 Important characteristics of a transformation

Level of automation.

Graph transformation theory offers two flavours of automating the application of a series of graph transformations: graph grammars and programmed graph transformation.

The graph grammar approach is supported by AGG. Starting from an initial graph, all possible applicable graph productions are applied repeatedly, and in parallel. This iterative process is repeated as long as possible. The set of result graphs obtained by this process is called the language generated by the graph grammar.

Programmed graph transformation is supported by Fujaba, VIATRA, and GReAT. In this approach, rules are specified to control the order of graph transformations. Fujaba uses so-called story-driven modelling, where an activity diagram is used to specify in which order graph transformations should be applied. In VIATRA, the graph transformations are driven by abstract state machines as the specification formalism. GReAT uses explicitly sequenced

transformation rules with input and output parameters that specify the initial bindings for selected pattern variables, as well as allow passing selected graph nodes to subsequent rules. The connectivity between the parameters of rules determines the flow of execution.

Complexity of the transformation.

Complex transformations require more complex control mechanisms to govern the execution order of rules. Graph transformation languages may vary significantly in the strength of these control structures or the way they are specified.

AGG supports layered graph grammars to impose a certain order on the graph production rules to be applied. If only the internal graph transformation of AGG is used, however, one can write arbitrarily complex Java programs to control the order of execution of graph transformations.

Fujaba uses story diagrams (a kind of activity diagrams) to control the application of graph transformations.

In GReAT, the control structure is based on hierarchical dataflow-like diagrams (that represent control-flow as well), but an explicit loop control structure is missing. Loops can be expressed as transitions to previous rules in the flow.

VIATRA uses another formal specification language, namely, abstract state machines as control language with constructs for as long as possible, parallel or recursive rule applications.

Even with these advanced control mechanisms it remains to be seen whether graph transformation alone suffices to express complex transformations. For practical purposes, a hybrid approach combining the virtues of a graph transformation language and a textual constraint language may be more opportune. Given that many of the graph transformation tools rely on UML notation in one way or another, OCL seems to be a viable alternative to specify textual constraints of graph transformations. For instance, GReAT uses OCL constraints to impose restrictions on the result of the matching process. An OCL evaluator is available to check whether the result of the transformation complies with the constraints.

Preservation of properties.

Graph transformation theory seems promising to formally specify model refactorings and to show that these refactorings preserve behavioural properties. An initial feasibility study has shown, however, that current graph transformation formalisms lack expressiveness in order to accomplish this goal [19].

Therefore, Van Eetvelde and Janssens [30,11] proposed a number of extensions to graph transformations in order to enhance their expressive power. Incorporating these extensions in graph transformation tools remains to be done.

4 Success criteria for a graph transformation tool

Suggesting when to apply transformations.

Most graph transformation languages and tools provide a mechanism and language to express constraints on the graphs that need to be transformed. Graph constraints consist of path expressions that state that particular links and / or node values should be present or not.

In AGG, one can use the graphical user interface to define constraints as negative application conditions, but one can also specify general graph constraints that can be translated into postconditions of graph transformation rules. In VIATRA, graph patterns (used as constraints) may contain negative application conditions embedded into each other at arbitrary depth. In Fu-jaba, control constructs can be used to combine graph constraints and graph transformations in arbitrary ways. In GReAT, constraints can be used to restrict the results of the graph matching, and zero cardinality on association ends is used to implement a restricted form of negative application conditions.

Customising or reusing transformations.

A simple yet crucial way to customise graph transformations is by means of parameterisation. A parameterised graph production represents an infinite set of possible graph productions, each one obtained by providing concrete values for the parameters. A parameterisation mechanism is available in all considered graph transformation tools.

Some graph transformation tools are integrated into an object-oriented development environment, thus allowing to exploit well-known object-oriented mechanisms such as inheritance to enable reuse. For example, in Fujaba, graph productions are used as specifications of methods, and inheritance can be used to reuse these methods in subclasses. Similarly, GReAT supports reusability via features provided by the visual modeling environment (GME) it is implemented in: transformation rules (or higher-level transformation sequences called blocks) can be reused through the type/instance machinery supported by the environment.

In VIATRA, a graph transformation can be built up from predefined patterns, that are reusable across transformations. Another important way to

enhance the reusability of transformations is by making use of generic and meta transformations [31].

Verifying and guaranteeing correctness of the transformations.

A model is syntactically correct if it conforms to its metamodel structure and well-formedness rules. In graph transformation, structure conformance is enforced by means of type graphs. Type graphs may include cardinality constraints, and may also support inheritance (as in the UML metamodel). The type graph mechanism is supported in all four considered tools.

Another way to enforce syntactical correctness is by defining a dedicated graph grammar that contains rules to be used for syntax-directed editing.

AGG can check termination and consistency of a graph grammar based on graph constraints. More specifically, it is the only available tool that implements the mechanism of critical pair analysis to check termination and confluence of graph grammars [10]. Two graph productions may form a critical pair if they are in conflict, in the sense that they do not preserve the confluence property. This property is needed to guarantee that a rewriting system has a functional behaviour.

VIATRA aims at providing verification of transformations by an ongoing integration with the CheckVML tool [22]. CheckVML projects graph transformation rules into transition systems verified by the SPIN model checker.

Testing and validating transformations.

While systematic testing approaches such as unit testing are commonplace in traditional (object-oriented) software development, this is much less the case for graph transformations. Ideally, each graph production specification should come with a suite of tests that verify that the graph production has the desired behaviour. Geiger et al. investigate graph-transformation based testing and debugging in the Fujaba environment [9,7].

To a certain extent, AGG's critical pair analysis can also be considered as validation of transformations since it allows the developer to test whether a give set of graph transformations (i.e., a graph grammar) is consistent.

Dealing with incomplete or inconsistent models.

In all the graph transformation tools we studied, the models (i.e., graphs) under consideration have to be well-formed. In other words, none of the approaches allow for inconsistent models. Incompleteness poses less of a problem, as long as the well-formedness constraints are guaranteed.

Grouping, composing and decomposing transformations.

Composition of graph transformations can be achieved by using controlled or programmed graph transformation, i.e., a set of control mechanisms to govern the execution order of rules [25]. Typical control mechanisms are sequencing, branching and looping. They are supported in Fujaba by means of so-called story diagrams, and in VIATRA by means of abstract state machines that drive the transformations. Additionally, in Fujaba, transformations are implemented as method bodies, so composition of transformations can be achieved by performing method calls. In VIATRA, graph transformations can be composed out of more primitive patterns, though recursive patterns are not supported yet.

Another mechanism that has been proposed to group and compose graph transformation is the structuring mechanism of graph transformation units [16,14]. In the graph grammar variant of graph transformation (e.g., AGG), one can use layered graph grammars as a primitive kind of structuring mechanism. The layers fix the order in which rules are applied. Rules of layer 0 are applied as long as possible, followed by rules of layer 1, and so on.

In GReAT, one can form blocks from sequenced transformation rules. Blocks encapsulate rules, are hierarchical, and can participate in recursive calls. Rules of a special form, called tests are available to implement control flow within a block that is dependent on the input models.

Genericity of transformations.

The only graph transformation tool that supports higher-order transformations is VIATRA [31]. Higher-order transformations enable a very compact description of certain transformation problems in MDA. A possible disadvantage is a degradation in performance. But this problem is addressed by automatically deriving efficient first-order transformations from generic higher-order ones. To this extent, meta transformations are used, i.e., transformations whose source and target models are transformations themselves.

Bidirectionality of transformations.

By definition, a graph transformation rule is unidirectional. This does not mean, however, that it is impossible to support bidirectionality in a graph transformation tool. One obvious way would be to define two graph grammars, one for each direction. Another possibility is to rely on a transaction an rollback mechanism to undo (i.e., reverse) earlier transformations.

Supporting traceability and change propagation.

Most of the considered graph transformation tools have no or poor support for traceability and change propagation and do not provide an incremental update mechanism. Meta transformations can be very helpful here in order to maintain or upgrade existing model transformations.

5 Quality requirements for a graph transformation tool

Usability and usefulness.

That graph transformation technology is useful for the purpose of model transformation has been amply illustrated by experiments performed with transformation tools such as GReAT and VIATRA. Even general-purpose graph transformation tools like AGG and Fujaba have been shown to support model transformation.

That graph transformations are also usable is more difficult to assess, as this depends on several factors, such as the intended target audience. For research purposes, all of the studied tools are already quite usable. To become usable in an industrial setting, most tools still need to mature to make them more performant and user-friendly, but this is just a matter of time. Some ways to make the GReAT language more usable are proposed in [34].

Verbosity versus conciseness.

Compared to XML-based transformation technology, graph transformation seems to give rise to more concise and better readable code. Whether this code is also easier to produce and maintain is not clear and should be investigated further.

Within the realm of graph transformation tools, a distinction should be made between general purpose tools and dedicated model transformation tools. Due to their dedicated nature, the latter tend to produce more concise code. This goes at the expense of verbosity, since it requires the introduction of extra syntactic constructs that are specifically tuned to model transformation.

Performance and scalability.

Graph transformations are sometimes accused of generating inefficient programs or having inefficient algorithms. However, this poor performance is not an inherent limitation of the technique per se. For example, Varro et al. show how to transform higher-order model transformations automatically in

efficient first-order transformations [31]. They also suggest to use database technology as an underlying engine of graph transformation in order to increase its efficiency. As another example, Vizhanyo et al. have illustrated significant performance gains by optimising traditional graph matching algorithms on the one hand and bypassing the generic transformation engine of GReAT by native transformation code on the other hand [33].

In important characteristic of the graph transformation tool influencing the performance is the ability to compile the graph transformations into native code or into bytecode. This is indeed possible for Fujaba which can generate Java bytecode from graph transformations, as well as for GReAT, which is able to compile "production" code from the transformation models. AGG and VIATRA, on the other hand, use an interpreted approach, which makes them inherently less performant.

Extensibility.

The AGG tool is extensible in the sense that its internal graph transformation engine, which is implemented in Java, can be extended freely to cover a wide variety of different applications. The tools Fujaba and VIATRA, offer a powerful plug-in mechanism for extending the tool with new functionality. In the case of VIATRA this plug-in mechanism can be used to write importers and exporters for models from other technical spaces than MOF/UML. For example, there are already importers for business process models and XSD. In GReAT extensibility is achieved by using a procedural language for implementing the code for attribute mapping that gets executed after all the graph operations done in a transformation rule. While this makes the formal analysis of transformation programs (at least) very difficult, it was found to be very practical. This procedural source code is compiled into executable code that is dynamically linked into the execution engine (or statically linked with the compiled transformation code).

Acceptability by user community.

In order to get accepted by an existing user community, a language should not diverge too much from what people are accustomed to. For example, for people trained in procedural programming, a procedural style is probably more readable than the declarative grammar approach of AGG. For people accustomed to UML notation, Fujaba story diagrams provide a very natural notation to express graph transformations without the user even being aware of it. GReAT is based on the meta-programmable Generic Modeling Environment (GME), and is tailored for constructing software that performs

transformation on models (typically, but not exclusively constructed in GME). It is equipped with an interpretive engine, a debugger, and a compiler. It relies on standard C++ development tools.

Standardization.

Another way to make graph transformation technology accepted is by supporting existing standards such as UML and XML. This is already the case for the considered graph transformation tools. They either support UML or XML directly, or provide some translators (e.g., XMI export facilities) to bridge between technical spaces. For example, VIATRA provides a very flexible import/export mechanism for models from other technical spaces. On the other hand, the metamodelling notation used by VIATRA is different from the MOF standard.

Graph transformation tools can also be applied using MDA standards like UML, MOF and XMI. Type graphs can be defined as class diagrams in UML editors with proper XMI export facilities. The resulting model can be transformed into a MOF metamodel. Existing MDA frameworks can be used to monitor the OCL well-formedness rules of this metamodel on models residing in a MOF repository. Model transformations can be developed as graph transformations expressed in UML statechart and class diagram editors that export the transformation models to XMI. The transformation models can be transformed into executable MOF transformation code that can transform any model that is an instance of the original type graph [23,6].

For graph transformation languages in particular, two standards are available. GXL is an exchange format for graphs, while GTXL is an exchange format for graph transformations. Both standards are supported by AGG.

6 Discussion

In this paper, we used a taxonomy of model transformation to evaluate the technique of graph transformation as a way to support the activity of model transformation. The proposed taxonomy assisted in identifying and evaluating the appropriateness of a representative subset of four tools based on graph transformation technology. A summary of our initial analysis is presented in Table 6. Not all criteria of the model transformation taxonomy appear in this table, since we only displayed those criteria where a difference could be discerned. In the future, we intend to carry out a more detailed analysis, and we will consider other tools based on graph transformation as well.

Nevertheless, based on the analysis we performed, we can already conclude that graph transformation is a promising approach to deal with model

transformation. First of all, for many types of models, that are intrinsically graph-based in nature, graph transformations offer a natural and direct way to specify model transformations. Secondly, the graph transformation approach is formally founded: one can resort to many theorems to prove certain properties of a transformation system. Finally, graph transformation technology offers mechanisms to reuse transformations, and to compose smaller transformations into more complex ones.

A disadvantage is that the various graph transformation approaches are not always compatible. With respect to standardization, there is a tendency to combine graph transformation technology with XML and UML notation. This tendency favours acceptability by the user community because of their familiarity with these languages. Compared to AGG and Fujaba, the VIA-TRA tool is more tuned to the activity of model transformation since it was specifically built for this purpose. Concerning expressiveness, VIATRA seems to be one of the most advanced tools since it offers such unique features as higher-order and meta-transformations. On the other hand, GReAT and Fu-jaba provide a full environment for developing transformation programs: a (visual) modeling tool, interpreter with debugger, and a code generator.

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Table 1

criterion AGG Fujaba VIATRA GReAT

number of source and target models one-to-one many-to-many many-to-many many-to-many

kind of transformation endogenous endogenous endogenous + exogenous endogenous + exogenous

technical space XML, GXL, GTXL MDA, UML, Java MDA, XSD, business process models MDA, UML

level of automation graph grammars story-driven modelling transformations driven by abstract state machines explicitly sequenced transformation steps with context parameters

complexity layered grammars controlled graph transformations higher-order and meta transformations controlled graph transformations

customisability / reusability parameterised transformations parameterised transformations / inheritance of transformations reuse of predefined patterns reuse of transformation rules and blocks

verification / validation termination and consistency checking, critical pair analysis debugger; graph-transformation-based J Unit tests full-fledged verification/validation by CheckVML debugger; well-formedness of transformation results

composition layered graph grammar method calls in story driven modelling non-recursive composition of patterns into rules hierarchical blocks of sequences, recursion

performance / scalability interpreted interpreted + compiled interpreted interpreted + compiled

extensibility by extending AGG's internal engine plug-in mechanism plug-in mechanism for writing importers and exporters procedural code

acceptability for research purposes for software development for model transformation for model transformation

standardisation GXL, GTXL UML, Java, XMI, MOF UML, XMI, MOF UML, XMI