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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.

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This article presents data-driven scene graphs, a set of models that address the needs of safety-critical user interfaces design. Data-driven scene graphs merge a description of the user interface behavior as a data-flow program with a description of its graphics content as a hierarchical structure of vector and raster elements. We present a formal description of these models, discuss their semantics and equivalence, and demonstrate that they are suitable for a class of rasterization optimizations based on selective pre-rendering.

We introduce a framework for the description of a large class of delay-differential algebraic systems, in which we study three core problems: first we characterize abstractly the well-posedness of the initial-value problem, then we design a practical test for well-posedness based on a graph-theoretic representation of the system; finally, we provide a general stability criterion. We apply each of these results to a structure that commonly arises in the control of delay systems.