Synchronous data-flow is a programming paradigm which has been successfully applied in reactive systems. In this context, it can be characterized as some class of static bounded memory data-flow networks. In particular, these networks are not recursively defined, and obey some kind of "synchronous" constraints (clock calculus). Based on Kahn's relationship between data-flow and stream functions, the synchronous constraints can be related to Wadler's listlessness, and can be seen as sufficient conditions ensuring listless evaluation. As a by-product, those networks enjoy efficient compiling techniques. In this paper, we show that it is possible to extend the class of static synchronous data-flow to higher order and dynamical networks, thus giving sense to a larger class of synchronous data-flow networks.

Lustre is a data-flow programming language for reactive purposes, which has been given a synchronous operational semantic. Static checks called "clock calculus" restrict Lustre programs to those data-flow networks which can be executed synchronously. As a by-product of this restriction, Lustre programs enjoy efficient compiling techniques. Yet, due to its reactive origin, Lustre applies only to static networks. We show here, that both this operational semantic, and clock calculus can be extended toward accounting for general functional features : abstraction, application and recursion. This allows us to give sense to both higher order, and dynamical synchronous data-flow networks, which can thus be expected to share the same efficient compiling techniques. 1. Introduction 1.1. Some milestones in data-flow programming In the seventies, the Lucid language was proposed 2;1 as a way of overcoming the lack of efficency of functional languages by providing them with stream based iteration...