Synchronous languages have been designed to ease the development of reactive systems, by providing a methodological framework for assisting system designers from the early stages of requirement specifications to the final stages of code generation or circuit production. Synchronous languages enable a very high-level specification and an extremely modular design of complex reactive systems by structural decomposition of them into elementary processes. We define an order-theoretical model that gives a unified mathematical formalisation of all the above aspects of the synchronous methodology and characterises the essentials of the synchronous paradigm.

This article presents a causality analysis for a synchronous stream language with higher-order functions. This analysis takes the shape of a type system with rows. Rows were originally designed to add extensible records to the ML type system (Didier Remy, Mitchell Wand). We also restate briey the coiterative semantics for synchronous streams (Paul Caspi, Marc Pouzet), and prove the correctness of our analysis with respect to this semantics.

Functional Reactive Programming (FRP) is an approach to reactive programming where systems are structured as networks of functions operating on time-varying values (signals). FRP is based on the synchronous data-flow paradigm and supports both continuous-time and discretetime signals (hybrid systems). What sets FRP apart from most other reactive languages is its support for systems with highly dynamic structure (dynamism) and higher-order reactive constructs (higher-order data-flow). However, the price paid for these features has been the loss of the safety and performance guarantees provided by other, less expressive, reactive languages. Statically guaranteeing safety properties of programs is an attractive proposition. This is true in particular for typical application domains for reactive programming such as embedded systems. To that end, many existing reactive languages have type systems or other static checksthatguaranteedomain-specificconstraints, suchasfeedbackbeingwell-formed(causality analysis). However, comparedwithFRP,theyarelimitedintheircapacitytosupportdynamism andhigher-orderdata-flow. Ontheotherhand, asestablishedstatictechniquesdonotsufficefor highly structurally dynamic systems, FRP generally enforces few domain-specific constraints, leaving the FRP programmer to manually check that the constraints are respected. Thus, there

This article presents the very first effective design of higherorder modules in the synchronous programming language Esterel. Higher-order modules, together with the robust separate compilation scheme that implements it, allow us to address a yet unexplored application spectrum ranging from rapid prototyping of embedded functionality to hot reconfiguration of embedded software within the formal modeling framework of the “synchronous hypothesis”. While extensions of data-flow synchronous languages had already been proposed for Lustre [11] and Signal [25], the adaptation of similar programming concepts to imperative synchronous frameworks like Esterel has long posed major technical challenges, due to the specificity of its model of computation. We present a framework including a formal semantics, a type system, and a modular code generator, that tackle this challenge. We consider a specific stack-based module call convention and a simple event pooling protocol; in consequence signals can refer to modules and modules can be transmitted and instantiated by referencing a signal. We define a type system that computes the potential emissions of a module and prove it sound. Our type system seamlessly fits an extension of Esterel’s constructive semantics with higher-order modules. 1.