Section: Software and Platforms

Zélus

Participants : Timothy Bourke, Marc Pouzet [contact] .

Zélus is a new programming language for hybrid system modeling. It is based on a synchronous language but extends it with Ordinary Differential Equations (ODEs) to model continuous-time behabiors. It allows for combining arbitrarily data-flow equations, hierarchical automata and ODEs. The language keeps all the fundamental features of synchronous languages: the compiler statically ensure the absence of deadlocks and critical races; it is able to generate statically scheduled code running in bounded time and space and a type-system is used to distinguish discrete and logical-time signals from continuous-time ones. The ability to combines those features with ODEs made the language usable both for programming discrete controllers and their physical environment.

The Zélus implementation has two main parts: a compiler that transforms Zélus programs into OCaml programs and a runtime library that orchestrates compiled programs and numeric solvers. The runtime can use the Sundials numeric solver, or custom implementations of well-known algorithms for numerically approximating continuous dynamics.

This year we reimplemented several basic numeric solver algorithms after a careful analysis of the Simulink versions together with the binding to SUNDIALS CVODE. This was necessary to enable detailed comparsions between our tool and Simulink (the de facto industrial standard in this domain). We also improved the algorithm for zero-crossing detection, simplified and streamlined the back-end interface.

We developed several new examples to aid in the development, debugging, and dissemination of our work together with various talks and demonstrations. These included a simple backhoe model (which served as a introducing example in the HSCC paper [12] ), an adaptive control example from Astrom and Wittenmark's text, and a model of Zeno behaviour based on a zig-zagging object (presented at Synchron).

Zélus has been released officially in 2013 with several complete documented examples on http://zelus.di.ens.fr . An important software development has been done in the compiler internals during year 2013: a new causality analysis has been designed and implemented and a new back-end to generate efficient sequential code for both the discrete step and the continuous step.