Ultrametric Semantics of Reactive Programs

In this talk, I describe a denotational model of higher-order functional reactive programming using ultrametric spaces and nonexpansive maps, which provides a natural Cartesian closed generalization of causal stream functions and guarded recursive defnitions. To write programs, I also show how to define a normalizing type theory corresponding to this semantics.

Finally, I show how reactive programs written in this language can be implemented efficiently using an imperatively updated dataflow graph (with correctness proof, but not in this talk!), and demonstrate how GUI (graphical user interface) programs look when written in this style.

Joint work with Nick Benton.