Optimisation of dynamic, hybrid signal function networks

Functional Reactive Programming (FRP) is an approach to reactive programming where systems are structured as networks of functions operating on signals. FRP is based on the synchronous data-flow paradigm and supports both continuous-time and discrete-time signals (hybrid systems). What sets FRP apart from most other languages for similar applications is its support for systems with dynamic structure and for higher-order data-flow constructs. This raises a range of implementation challenges. This paper contributes towards advancing the state of the art of FRP implementation by studying the notion of signal change and change propagation in a setting of hybrid signal function networks with dynamic structure. To sidestep some problems of certain previous FRP implementations that are structured using arrows, we suggest working with a notion of composable, multi-input and multi-output signal functions. A clear conceptual distinction is also made between continuous-time and discrete-time signals. We then show how establishing change-related properties of the signal functions in a network allows such networks to be simplified (static optimisation) and can help reducing the amount of computation needed for executing the networks (dynamic optimisation). Interestingly, distinguishing between continuous-time and discrete-time signals allows us to characterise the change-related properties of signal functions more precisely than what we otherwise would have been able to, which is helpful for optimisation.