A formal framework for heterogeneous systems semantics

Cyber physical systems are usually complex systems which are often critical, meaning their failure can have significant negative impacts on human lives. A key point in their development is the verification and validation (V & V) activities which are used to assess their correctness towards user requirements and the associated specifications. This process aims at avoiding failure cases, thus preventing any incident or accident. In order to conduct these V & V steps on such complex systems, separations of concerns of various nature are used. In that purpose, the system is modeled using heterogeneous models that have to be combined together. The nature of these separations of concerns can be as follows: horizontal, which corresponds to a structural decomposition of the system; vertical, which corresponds to the different steps leading from the abstract specification to the concrete implementation; and transversal, which consists in gathering together the parts that are thematically identical (function, performance, security, safety...). These parts are usually expressed using domain specific modeling languages, while the V & V activities are historically conducted using testing and proofreading, and more and more often, using formal methods, which is advocated in our approach. In all these cases, the V & V activities must take into account these separations in order to provide confidence in the global system from the confidence of its sub-parts bound to the separation in question. In other words, to ensure the correctness of the system, a behavioral semantics is needed which has to rely on the ad-hoc semantics of the subsystems. In order to define it, these semantics must be successfully combined in a single formalism. This thesis stems from the GEMOC project a workbench that allows the definition of various languages along with their coordination properties, and target the formal modeling of the GEMOC core through the association of trace semantics to each preoccupation and the expression of constraints between them to encode the correct behavior of the system. This thesis follows several other works conducted under the TOPCASED, OPEES, QuarteFt, P and GEMOC projects, and provides four contributions in that global context: the first one proposes a methodology to give an operational semantics to executable models illustrated through two case studies: Petri nets and models of processes. The second one proposes a formal context on which refinement can be expressed to tackle vertical separation. The third one gives a denotational semantics to CCSL which is the language that is currently used in the GEMOC projects to express behavioural properties between events from one or several models, possibly heterogeneous. Finally, the fourth one proposes an investigation on how to extend CCSL with the notion of refinement we proposed. All these contribution are mechanized in the Agda proof assistant, and thus have been modeled and proven in a formal manner