Section: New Results

Zélus: Synchronous Languages + Ordinary Differential Equations

Participants : Timothy Bourke, Marc Pouzet.

Zélus is a synchronous language extended with Ordinary Differential Equations (ODEs) to model systems with complex interactions between discrete-time and continuous-time dynamics. It shares the basic principles of Lustre with features from Lucid Synchrone (type inference, hierarchical automata, and signals). The compiler is written in OCaml and is structured as a series of source-to-source and traceable transformations that ultimately yield statically scheduled sequential code. Continuous components are simulated using off-the-shelf numerical solvers (here Sundials CVODE) and, for the moment, two built-in solvers (ode23 and ode45).

Zélus is used to experiment with new techniques for building hybrid modelers like Simulink/Stateflow and Modelica on top of a synchronous language. The language exploits novel techniques for defining the semantics of hybrid modelers, it provides dedicated type systems to ensure the absence of discontinuities during integration and the generation of sequential code. In particular, all discrete computations must be aligned to zero-crossing events; programs with causality loops and uninitialized values are statically rejected.

This year we added arrays with iterators and statically expanded higher-order functions to the language. Both extensions required adapting the existing type and causality systems, and extending the compilation algorithms. These extensions allowed us to show that a fairly large set of blocks from the Simulink standard library can be programmed in a precise, purely functional language using stream equations, hierarchical automata, Ordinary Differential Equations (ODEs), and deterministic synchronous parallel composition. Although some blocks cannot be expressed as they mix discrete-time and continuous-time signals in unprincipled ways; they are statically rejected by the type checker. This work was presented at EMSOFT in October [9]

Our work on analyzing causality loops in hybrid systems modelers was published in the NAHS journal [2].

In collaboration with B. Caillaud and A. Benveniste (Inria Rennes); and F. Carcenac, B. Pagano, and C. Pasteur (ANSYS/Esterel Technologies).