A higher-order extension for imperative synchronous languages

This article presents the very first effective design of higher-order 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.