Structured reactive programming with polymorphic temporal tiles

In functional reactive programming (FRP), system inputs and outputs are generally modeled as functions over continuous time (behaviors) whose future values are governed by sudden changes (events). In this approach, discrete events are embedded into piece-wise continuous behaviors. In the field of reactive music system programming, we develop an orthogonal approach that seems to better fit our need. Much like piano keys can be played and combined both in sequence and in parallel, we model system inputs and outputs as spatio temporal combinations of what we call temporal values: continuous functions over time whose domain lays between two events: a start and a stop event. Various high level data types and program constructs can then be derived from such a model. They are shown to satisfy robust algebraic and category theoretic properties. Altogether, this eventually provides a simple, robust and elegant programming front-end, temporal tile programming, for reading, memorizing, stretching, combining and transforming flows of inputs into flows of outputs. Although at its infancy, the resulting approach has been experimentally validated for reactive and real-time music system programming.