Functional Reactive Progamming, or FRP, is an approach to programming hybrid systems in a declarative style using two particular abstractions: a continuous (functional) model of arbitrary behaviors, and a discrete (reactive) calculus for user and process interaction. FRP is a generalization of the fundamental ideas underlying two domain-specific languages that we have previously worked on: Fran, a language for functional reactive graphics and animation, and Frob, a language for functional robotics. We believe that FRP can provide a unified framework for rapidly and reliably creating hybrid software systems ranging from simple behavioral loops to large systems involving complex control strategies and multiple interacting modules. The objectives of this research are to further develop the ideas in FRP, study the principles underlying FRP, and explore ways to analyze, transform, and ultimately implement, domain-specific languages based on FRP. The research will emphasize the use of techniques common in the programming language semantics community. Amongst the issues to be investigated are: denotational as well as operational semantics for a small reactive language with continuous behaviors, an implementation synthesized from first principles (i.e. correct with respect to a specification), and practical ramifications of using numerical methods to simulate continuous behaviors.
