Keeping calm in the face of change - Towards optimisation of FRP by reasoning about change

Functional Reactive Programming (FRP) is an approach to reactive programming where systems are structured as networks of functions operating on signals (time-varying values). FRP is based on the synchronous data-flow paradigm and supports both (an approximation to) 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 reactive constructs. 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 structurally dynamic networks of n-ary signal functions operating on mixed continuous-time and discretetime signals. We first define an ideal denotational semantics (time is truly continuous) for this kind of FRP, along with temporal properties, expressed in temporal logic, of signals and signal functions pertaining to change and change propagation. Using this framework, we then show how to reason about change; specifically, we identify and justify a number of possible optimisations, such as avoiding recomputation of unchanging values. Note that due to structural dynamism, and the fact that the output of a signal function may change because time is passing even if the input is unchanging, the problem is significantly more complex than standard change propagation in networks with static structure.