Ultrametric Semantics of Reactive Programs

We describe a denotational model of higher-order functional reactive programming using ultra metric spaces and non expansive maps, which provide a natural Cartesian closed generalization of causal stream functions and guarded recursive definitions. We define a type theory corresponding to this semantics and show that it satisfies normalization. Finally, we show how to efficiently implement reactive programs written in this language using an imperatively updated data flow graph, and give a separation logic proof that this low-level implementation is correct with respect to the high-level semantics.