Section: New Results

Discrete control and reactive language support

Participants : Gwenaël Delaval, Eric Rutten, Stéphane Mocanu.

Concerning language support, we have designed and implemented BZR, a mixed imperative/declarative programming language: declarative contracts are enforced upon imperatively described behaviors (see 5.1 ). The semantics of the language uses the notion of Discrete Controller Synthesis (DCS) [5] . We target the application domain of adaptive and reconfigurable systems: our language can serve programming closed-loop adaptation controllers, enabling flexible execution of functionalities w.r.t. changing resource and environment conditions. DCS is integrated into a programming language compiler, which facilitates its use by users and programmers, performing executable code generation. The tool is concretely built upon the basis of a reactive programming language compiler, where the nodes describe behaviors that can be modeled in terms of transition systems. Our compiler integrates this with a DCS tool [3] . This work is done in close cooperation with the Inria team Sumo at Inria Rennes (H. Marchand). Ongoing work concerns aspects of compilation and debugging and logico-numeric extension of BZR based on the ReaX tool developed at Inria Rennes in the framework of the ANR Ctrl-Green project (see 8.2.1 ).

We are also currently working on on combining maximally permissive discrete control with runtime mechanisms for choosing between valid control values, involving e.g. a classical controller or stochastic aspects ; and on exploring the notion of adaptive discrete control, which is yet an open question in discrete control in contrast to the well-known adaptive continuous control.

Another activity related to discrete control is or work with Leiden University and CWI (N. Khakpour, now at Linnaeus U., and F. Arbab) on enforcing correctness of the behavior of an adaptive software system during dynamic adaptation is an important challenge along the way to realize correct adaptive systems. In this research, we model adaptation as a supervisory control problem and synthesize a controller that guides the behavior of a software system during adaptation. The system during adaptation is modeled using a graph transition system and properties to be enforced are specified using an automaton. To ensure correctness, we then synthesize a controller that imposes constraints on the system during adaptation [14] .