Type Annotation for Adaptive Systems

Typing systems define the admissible structures and behaviours of models formed by their instances, possibly defining relations among types in terms of inheritance and composition. Such a general notion is at the basis both of object-oriented analysis and design, and of metamodeling techniques, for both of which the relations with the field of graph transformations have been explored [10, 9]. When using an approach based on graph transformation theory, admissible structures are defined by graph constraints, either explicitly presented as such or included in the graph type, while behaviours are defined by collections of rules, possibly regulated by some control mechanism. This supports a view of an application domain as defined by a type graph and a policy for model generation (i.e. a collection of constraints) and evolution (i.e. a collection of rules). However, the development of concrete applications often requires bringing together concerns that are expressed with respect to different domains, or are cross-domains. In such cases, two possibilities are typically offered: either to merge different domains in a comprehensive one, which might become inflexible in view of possible evolutions of the application, or to maintain the domains separated, but to build explicit connections among them through specific constructs. In particular, triple graphs are a way to construct explicit relations between types in two different domains, allowing the definition of traces of model transformations [15]. In a series of recent papers we have proposed annotations to add context-specific information in a flexible way to elements of a graph, while preserving the separation of the original domains [4, 3]. In this paper, we bring the notion of annotation to bear on the context of model adaptation, by proposing to replace the notion of typing as traditionally expressed via a typing morphism from an instance graph to a type graph with the notion of annotation of model elements with type information, thus embedding the type information in the model itself. This achieves three important objectives: