Marc Pouzet

A conservative extension of synchronous data-flow with state machines

This paper presents an extension of a synchronous data-flow language such as Lustre with imperative features expressed in terms of powerful state machine à la SyncChart. This extension is fully conservative in the sense that all the programs from the basic language still make sense in the extended language and their semantics is preserved.From a syntactical point of view this extension consists in hierarchical state machines that may carry at each hierarchy level a bunch of equations. This proposition is an alternative to the joint use of Simulink and Stateflow but improves it by allowing a fine grain mix of both styles.The central idea of the paper is to base this extension on the use of clocks, translating imperative constructs into well clocked data-flow programs from the basic language. This clock directed approach is an easy way to define a semantics for the extension, it is light to implement in an existing compiler and experiments show that the generated code compete favorably with ad-hoc techniques. The proposed extension has been implemented in the ReLuC compiler of Scade/Lustre and in the Lucid Synchrone compiler.

ReactiveML: a reactive extension to ML

We present ReactiveML, a programming language dedicated to the implementation of complex reactive systems as found in graphical user interfaces, video games or simulation problems. The language is based on the reactive model introduced by Boussinot. This model combines the so-called synchronous model found in Esterel which provides instantaneous communication and parallel composition with classical features found in asynchronous models like dynamic creation of processes.The language comes as a conservative extension of an existing call-by-value ML language and it provides additional constructs for describing the temporal part of a system. The language receives a behavioral semantics á la Esterel and a transition semantics describing precisely the interaction between ML values and reactive constructs. It is statically typed through a Milner type inference system and programs are compiled into regular ML programs. The language has been used for programming several complex simulation problems (e.g., routing protocols in mobile ad-hoc networks).

N -synchronous Kahn networks: a relaxed model of synchrony for real-time systems

The design of high-performance stream-processing systems is a fast growing domain, driven by markets such like high-end TV, gaming, 3D animation and medical imaging. It is also a surprisingly demanding task, with respect to the algorithmic and conceptual simplicity of streaming applications. It needs the close cooperation between numerical analysts, parallel programming experts, real-time control experts and computer architects, and incurs a very high level of quality insurance and optimization.In search for improved productivity, we propose a programming model and language dedicated to high-performance stream processing. This language builds on the synchronous programming model and on domain knowledge -- the periodic evolution of streams -- to allow correct-by-construction properties to be proven by the compiler. These properties include resource requirements and delays between input and output streams. Automating this task avoids tedious and error-prone engineering, due to the combinatorics of the composition of filters with multiple data rates and formats. Correctness of the implementation is also difficult to assess with traditional (asynchronous, simulation-based) approaches. This language is thus provided with a relaxed notion of synchronous composition, called n-synchrony: two processes are n-synchronous if they can communicate in the ordinary (0-)synchronous model with a FIFO buffer of size n.Technically, we extend a core synchronous data-flow language with a notion of periodic clocks, and design a relaxed clock calculus (a type system for clocks) to allow non strictly synchronous processes to be composed or correlated. This relaxation is associated with two sub-typing rules in the clock calculus. Delay, buffer insertion and control code for these buffers are automatically inferred from the clock types through a systematic transformation into a standard synchronous program. We formally define the semantics of the language and prove the soundness and completeness of its clock calculus and synchronization transformation. Finally, the language is compared with existing formalisms.

Clocks as First Class Abstract Types

Clocks in synchronous data-flow languages are the natural way to define several time scales in reactive systems. They play a fundamental role during the specification of the system and are largely used in the compilation process to generate efficient sequential code. Based on the formulation of clocks as dependent types, the paper presents a simpler clock calculus reminiscent to ML type systems with first order abstract types a la Laufer & Odersky. Not only this system provides clock inference, it shares efficient implementations of ML type systems and appears to be expressive enough for many real applications.

A Co-iterative Characterization of Synchronous Stream Functions

This paper presents an attempt to characterize synchronous stream functions within the framework of co-iteration and to use this characterization in building a compiler for (higher order and recursive) synchronous data-flow programs. First, length-preserving functions are considered and we show that streams equipped with such functions form a Cartesian-closed category. Then this point of view is extended toward non length-preserving ones and we stress the use of “empty” values in handling this case. Finally, the implementation we did of this material in a synchronous stream language built on top of an ML-like language is briefly described.

Towards a higher-order synchronous data-flow language

The paper introduces a higher-order synchronous data-flow language in which communication channels may themselves transport programs. This provides a mean to dynamically reconfigure data-flow processes. The language comes as a natural and strict extension of both lustre and lucy. This extension is conservative, in the sense that a first-order restriction of the language can receive the same semantics.We illustrate the expressivity of the language with some examples, before giving the formal semantics of the underlying calculus. The language is equipped with a polymorphic type system allowing types to be automatically inferred and a clock calculus rejecting programs for which synchronous execution cannot be statically guaranteed. To our knowledge, this is the first higher-order synchronous data-flow language where stream functions are first class citizens.

Clock-directed modular code generation for synchronous data-flow languages

The compilation of synchronous block diagrams into sequential imperative code has been addressed in the early eighties and can now be considered as folklore. However, separate, or modular, code generation, though largely used in existing compilers and particularly in industrial ones, has never been precisely described or entirely formalized. Such a formalization is now fundamental in the long-term goal to develop a mathematically certified compiler for a synchronous language as well as in simplifying existing implementations. This article presents in full detail the modular compilation of synchronous block diagrams into sequential code. We consider a first-order functional language reminiscent of LUSTRE, which it extends with a general n-ary merge operator, a reset construct, and a richer notion of clocks. The clocks are used to express activation of computations in the program and are specifically taken into account during the compilation process to produce efficient imperative code. We introduce a generic machine-based intermediate language to represent transition functions, and we present a concise clock-directed translation from the source to this intermediate language. We address the target code generation phase by describing a translation from the intermediate language to JAVA and C.

Modular static scheduling of synchronous data-flow networks: an efficient symbolic representation

This paper addresses the question of producing modular sequential imperative code from synchronous data-flow networks. Precisely, given a system with several input and output flows, how to decompose it into a minimal number of sub-systems executed atomically and statically scheduled without restricting possible feedback loops between input and output? Though this question has been identified by Raymond in the early years of Lustre, it has almost been left aside until the recent work of Lublinerman, Szegedy and Tripakis. The problem is proven to be intractable, in the sense that it belongs to the family of optimization problems where the corresponding decision problem -- there exists a solution with size c -- is NP-complete. Then, the authors derive an iterative algorithm looking for solutions for c = 1, 2, ... where each step is encoded as a SAT problem. Despite the apparent intractability of the problem, our experience is that real programs do not exhibit such a complexity. Based on earlier work by Raymond, this paper presents a new symbolic encoding of the problem in terms of input/output relations. This encoding simplifies the problem, in the sense that it rejects solutions, while keeping all the optimal ones. It allows, in polynomial time, (1) to identify nodes for which several schedules are feasible and thus are possible sources of combinational explosion; (2) to obtain solutions which in some cases are already optimal; (3) otherwise, to get a non trivial lower bound for c to start an iterative combinational search. The solution applies to a large class of block-diagram formalisms based on atomic computations and a delay operator, ranging from synchronous languages such as Lustre or Scade to modeling tools such as Simulink.

Zélus: a synchronous language with ODEs

Zélus is a new programming language for modeling systems that mix discrete logical time and continuous time behaviors. From a users perspective, its main originality is to extend an existing Lustre-like synchronous language with Ordinary Differential Equations (ODEs). The extension is conservative: any synchronous program expressed as data-flow equations and hierarchical automata can be composed arbitrarily with ODEs in the same source code. A dedicated type system and causality analysis ensure that all discrete changes are aligned with zero-crossing events so that no side effects or discontinuities occur during integration. Programs are statically scheduled and translated into sequential code that, by construction, runs in bounded time and space. Compilation is effected by source-to-source translation into a small synchronous subset which is processed by a standard synchronous compiler architecture. The resultant code is paired with an off-the-shelf numeric solver. We show that it is possible to build a modeler for explicit hybrid systems à la Simulink/Stateflow on top of an existing synchronous language, using it both as a semantic basis and as a target for code generation.

Mixing signals and modes in synchronous data-flow systems

Synchronous data-flow languages such as SCADE LUSTRE manage infinite sequences, or streams, as primitive values making them naturally adapted to the description of dominated systems. Their conservative extension with means to define control-structures or modes has been a long-term research topic through which several solutions have emerged.In this paper, we pursue this effort and generalize existing solutions by providing two constructs: a general form of state machines called parameterized state machines, and valued signals, as can be found in ESTEREL. Parameterized state machines greatly reduce the reliance on error-prone mechanisms such as shared memory in automaton-based programming. Signals provide a new way of programming with multi-rate data in synchronous dataflow languages. Together, they allow for a much more direct and natural programming of systems that combine dataflow and state-machines.The proposed extension is fully implemented in the new LUCID SYNCHRONE compiler.