Abstract Labeled graphs are particularly well adapted to represent objects in the context of topology-based geometric modeling. Thus, graph transformation theory is used to implement modeling operations and check their consistency. This article defines a class of graph transformation rules dedicated to embedding computations. Objects are here defined as a particular subclass of labeled graphs in which arc labels encode their topological structure (i.e., cell subdivision: vertex, edge, face) and node labels encode their embedding (i.e., relevant data: vertex positions, face colors, volume density). Object consistency is defined by labeling constraints which must be preserved by modeling operations that modify topology and/or embedding. Dedicated graph transformation variables allow us to access the existing embedding from the underlying topological structure (e.g., collecting all the points of a face) in order to compute the new embedding using user-provided functions (e.g., compute the barycenter of several points). To ensure the safety of the defined operations, we provide syntactic conditions on rules that preserve the object consistency constraints.

Summary In the context of testing from algebraic specifications, test cases are ground formulas chosen amongst the ground semantic consequences of the specification, according to some possible additional observability conditions. A test set is said to be exhaustive if every programmePpassing all the tests is correct and if for every incorrect programmeP, there exists a test case on whichPfails. Because correctness can be proved by testing on such a test set, it is an appropriate basis for the selection of a test set of practical size. The largest candidate test set is the set of observable consequences of the specification. However, depending on the nature of specifications and programmes, this set is not necessarily exhaustive. In this paper, we study conditions to ensure the exhaustiveness property of this set for several algebraic formalisms (equational, conditional positive, quantifier free and with quantifiers) and several test hypotheses. Copyright © 2016 John Wiley & Sons, Ltd.

In this article, we present a rule-based language dedicated to topological operations and based on graph transformations. Generalized maps are described as a particular class of graphs determined by consistency constraints. Hence, topological operations over generalized maps can be specified using graph transformations. The rules we define are provided with syntactic criteria which ensure that graphs computed by applying rules on generalized maps are also generalized maps. We have developed a static analyzer of transformation rules which checks the syntactic criteria in order to ensure the preservation of generalized map consistency constraints. Based on this static analyzer, we have designed a rule-based prototype of a kernel of a topology-based modeler that is generic in dimension. Since adding a new topological operation can be reduced to write a graph transformation rule, we directly obtain an extensible prototype where handled topological objects satisfy built-in consistency. Moreover, first benchmarks show that our prototype is reasonably efficient compared to a reference implementation of 3D generalized maps which use a classical implementation style.

In this paper, we present a code generator transforming a class of CASL specifications into O'Caml programs. This code generator is dedicated to rapid prototyping of CASL specifications especially in the area of geometric modeling where algebraic formalisms have been used since the last decade. A large class of constructive equational specifications is handled by this generator while insuring the correctness of generated O'Caml programs. In particular, CASL specifications with many interpretation models (i.e. incomplete) are automatically supplemented in order to produce a program that implements one of them. Underlying properties, such as termination, completeness and confluence hold when equations satisfy some syntactic criteria given in the paper.

We describe a test sequence generation method from LUSTRE descriptions and its companion tool, GATEL. The LUSTRE language is declarative and describes synchronous data-flow computations. It is used for reactive control/command systems, mainly for electrical power production applications. Such critical applications require a high level of reliability. While this language benefits from powerful verification tools, there is still a demand for adequate testing techniques. The method and the tool described can be applied during unit and integration testing, according to a structural (glass box) or functional (black box) test selection strategy. The test generation tool uses some interpretation of the language constructs as boolean and integer interval constraints. Test sequence generation is automated using constraint logic programming techniques. The method and the tool are illustrated on an example extracted from an industrial case study.