Formal analysis of model transformations based on triple graph grammars

Abstract

Triple graph grammars (TGGs) are a well-established concept for the specification and execution of bidirectional model transformations within model driven software engineering. Their main advantage is an automatic generation of operational rules for forward and backward model transformations, which simplifies specification and enhances usability as well as consistency. In this paper we present several important results for analysing model transformations based on the formal categorical foundation of TGGs within the framework of attributed graph transformation systems.Our first main result shows that the crucial properties of correctness and completeness are ensured for model transformations. In order to analyse functional behaviour, we generate a new kind of operational rule, called a forward translation rule. We apply existing results for the analysis of local confluence for attributed graph transformation systems. As additional main results, we provide sufficient criteria for the verification of functional behaviour as well as a necessary and sufficient condition for strong functional behaviour. In fact, these conditions imply polynomial complexity for the execution of the model transformation. We also analyse information and complete information preservation of model transformations, that is, whether a source model can be reconstructed (uniquely) from the target model ¶ The participation of Fernando Orejas was supported by the MEC project FORMALISM (ref. TIN2007-66923).

Correctness of Incremental Model Synchronization with Triple Graph Grammars

“…, p n are forward rules associated to G. Finding source consistent derivations or checking if a derivation with forward rules is source consistent is, in general, quite costly. For this reason, [6] introduces a new technique based on the use of Boolean-valued translation attributes. These attributes are associated to all elements in the graph (i.e.…”

“…We can say that these new rules reuse the elements in G. A similar idea was informally introduced in [5]. For example, forward translation rules [6] follow this idea to solve the model transformation problem. The part that is reused is the given source graph G S , and the extension that we are looking for consists of the target and correspondence parts of the result.…”

“…That triple graph could have been generated by a derivation d 1 consisting of, first, applying twice the rule Class2Table, to create classes C 1 ,C 2 and tables T 1 , T 2 ; then, applying the rule Subclass2Table, to create C 3 , and applying three times the rule Attribute2Column to create attributes A 1 , A 2 , A 3 and columns c 1 , c 2 , c 3 ; finally applying the rule FooCreation to create the foo node associated to column c 3 . But it could have also been created by other derivations that are permutation equivalent to d 1 [2], like derivation d 2 , consisting of applying twice the rules Class2Table and Attribute2Column, to create classes C 1 ,C 2 , ta- Finally, in the rest of the paper, we will use green colour 6 to depict the elements affected by an update, in contrast to the black coloured elements that are not affected by the update.…”

“…On the other hand, in [4], Giese and Wagner advocate that synchronization should be incremental, meaning that its computational cost should depend mainly on the size 6 For readers of black and white prints, green elements appear as lighter grey.…”

“…As we will discuss, this second step is only needed in some cases when the update does not allow incremental consistency with respect to the largest consistent submodel not affected by the update, but with respect to a smaller one. In the third step, following the same idea presented informally in [5], we build a model that is already consistent, by applying a variation of forward translation rules [8,6] allowing us to reuse most relevant information from the target model. For this reason, we call these rules forward translation rules with reuse.…”