Attribute Computations in the DPoPb Graph Transformation Engine

One of the challenges of attributed graph rewriting systems concerns the implementation of attribute computations. Most of the existing systems adopt the standard algebraic approach where graphs are attributed using sigma-algebras. However, for the sake of efficiency considerations and convenient uses, these systems do not generally implement the whole attribute computations but rely on programs written in a host language. In previous works we introduced the Double Pushout Pullback (DPoPb) framework which integrates attributed graph rewriting and computation on attributes in a unified categorical approach. This paper discusses the DPoPb’s theoretical and practical advantages when using inductive types and lambda-calculus. We also present an implementation of the DPoPb system in the Haskell language which thoroughly covers the semantics of this graph rewriting system

Typed lambda-terms in categorical attributed graph transformation

This paper deals with model transformation based on attributed graph rewriting. Our contribution investigates a single pushout approach for applying the rewrite rules. The computation of graph attributes is obtained through the use of typed lambda-calculus with inductive types. In this paper we present solutions to cope with single pushout construction for the graph structure and the computations functions. As this rewrite system uses inductive types, the expressiveness of attribute computations is facilitated and appears more efficient than the one based on Sigma-algebras. Some examples showing the interest of our computation approach are described in this paper

Towards a Rule-level Verification Framework for Property-Preserving Graph Transformations

International audienceWe report in this paper a method for proving that a graph transformation is property-preserving. Our approach uses a relational representation for graph grammar and a logical representation for graph properties with first-order logic formulas. The presented work consists in identifying the general conditions for a graph grammar to preserve graph properties, in particular structural properties. We aim to implement all the relevant notions of graph grammar in the Isabelle/HOL proof assistant in order to allow a (semi) automatic verification of graph transformation with a reasonable complexity. Given an input graph and a set of graph transformation rules, we can use mathematical induction strategies to verify statically if the transformation preserves a particular property of the initial graph. The main highlight of our approach is that such a verification is done without calculating the resulting graph and thus without using a transformation engine

Trust in MDE Components: the DOMINO Experiment

International audienceA large number of modeling activities can be automatic or computer assisted. This automation ensures a more rapid and robust software development. However, engineers must ensure that the models have the properties required for the application. In order to tend towards this requirement, the DOMINO project (DOMaINs and methodological prOcess) proposes to use the socalled trustworthy Model-Driven Engineering (MDE) components and aims to provide a methodology for the validation and qualification of such components

Inductive representation, proofs and refinement of pointer structures

Cette thèse s'intègre dans le domaine général des méthodes formelles qui donnent une sémantique aux programmes pour vérifier formellement des propriétés sur ceux-ci. Sa motivation originale provient d'un besoin de certification des systèmes industriels souvent développés à l'aide de l'Ingénierie Dirigée par les Modèles (IDM) et de langages orientés objets (OO). Pour transformer efficacement des modèles (ou graphes), il est avantageux de les représenter à l'aide de structures de pointeurs, économisant le temps et la mémoire grâce au partage qu'ils permettent. Cependant la vérification de propriétés sur des programmes manipulant des pointeurs est encore complexe. Pour la simplifier, nous proposons de démarrer le développement par une implémentation haut-niveau sous la forme de programmes fonctionnels sur des types de données inductifs facilement vérifiables dans des assistants à la preuve tels que Isabelle/HOL. La représentation des structures de pointeurs est faite à l'aide d'un arbre couvrant contenant des références additionnelles. Ces programmes fonctionnels sont ensuite raffinés si nécessaire vers des programmes impératifs à l'aide de la bibliothèque Imperative_HOL. Ces programmes sont en dernier lieu extraits vers du code Scala (OO). Cette thèse décrit la méthodologie de représentation et de raffinement et fournit des outils pour la manipulation et la preuve de programmes OO dans Isabelle/HOL. L'approche est éprouvée par de nombreux exemples dont notamment l'algorithme de Schorr-Waite et la construction de Diagrammes de Décision Binaires (BDDs).This thesis stands in the general domain of formal methods that gives semantics to programs to formally prove properties about them. It originally draws its motivation from the need for certification of systems in an industrial context where Model Driven Engineering (MDE) and object-oriented (OO) languages are common. In order to obtain efficient transformations on models (graphs), we can represent them as pointer structures, allowing space and time savings through the sharing of nodes. However verification of properties on programs manipulating pointer structures is still hard. To ease this task, we propose to start the development with a high-level implementation embodied by functional programs manipulating inductive data-structures, that are easily verified in proof assistants such as Isabelle/HOL. Pointer structures are represented by a spanning tree adorned with additional references. These functional programs are then refined - if necessary - to imperative programs thanks to the library Imperative_HOL. These programs are finally extracted to Scala code (OO). This thesis describes this kind of representation and refinement and provides tools to manipulate and prove OO programs in Isabelle/HOL. This approach is put in practice with several examples, and especially with the Schorr-Waite algorithm and the construction of Binary Decision Diagrams (BDDs)

Attribute Computations in the DPoPb Graph Transformation Engine

Abstract: One of the challenges of attributed graph rewriting systems concerns the implementation of attribute computations. Most of the existing systems adopt the standard algebraic approach where graphs are attributed using sigma-algebras. However, for the sake of efficiency considerations and convenient uses, these systems do not generally implement the whole attribute computations but rely on programs written in a host language. In previous works we introduced the Double Pushout Pullback (DPoPb) framework which integrates attributed graph rewriting and computation on attributes in a unified categorical approach. This paper discusses the DPoPb’s theoretical and practical advantages when using inductive types and lambda-calculus. We also present an implementation of the DPoPb system in the Haskell language which thoroughly covers the semantics of this graph rewriting system