Effects, Asynchrony, and Choice in Arrowized Functional Reactive Programming

Functional reactive programming facilitates programming with time-varying data that can be perceived as streams flowing through time. Thus, one can think of FRP as an inversion of flow control from the structure of the program to the structure of the data itself. In a typical (say, imperative) program, the structure of the program governs how the program will behave over time; as time moves forward, the program sequentially executes its statements, and at any line of code, one can make a clear distinction between code that has already been run (the past) and code that has yet to be run (the future). However, in FRP, the program acts as a signal function, and, as such, we are allowed to assume that the program executes continuously on its time-varying inputs—essentially, it behaves as if it is running infinitely fast and infinitely often. We consider this to be the core principle of the design and call it the fundamental abstraction of FRP. Design and Performance This work is specifically rooted in Arrowized FRP, where these signal functions remain static as they process the dynamic signals they act upon. However, in practice, it is often valuable to be able to dynamically alter the way that a signal function behaves over time. Typically, this is achieved with “switching” or other monadic features, but this significantly reduces the usefulness of the arrows. We develop an extension to arrows to allow “predictably dynamic” behavior along with a notion of settability, which together recover the desired dynamic power. We further demonstrate that optimizations designed specifically for arrowized FRP and which do not apply to monadic FRP, such as those for Causal Commutative Arrows, are applicable to the system. Thus, it can be powerfully optimized.