Off the Beaten Track 2: Take FRP to the limit

A second talk I enjoyed at Off the Beaten Track was Kengo Kido's Integrability in Nonstandard Modeling of Hybrid Systems, because it might hold the secret to resolving a conflict that has bugged me for many years.

Elliott and Hudak's original description of Functional Reactive Animation carefully separated behaviours (continuous maps from time to values) from events (a value is supplied at a given time). However, many developments of Functional Reactive Programming (FRP) instead supply a stream of discrete values, casting out continuity and conflating the notions of behaviour and event. For instance, the discrete approach is taken by Causal Commutative Arrows and by Asynchronous Functional Reactive Programming for GUIs (the basis for Elm).

As I commented in a previous post, streams have the advantage of permitting feedback loops, which permit the definition of important functions such as integral, and relate to the categorical notion of trace: can we combine the advantages of feedback with continuity? Kido's paper suggests a way forward: use discrete streams, but let the time interval between them to approach zero in the limit, as in his language WHILEdt. It would be great to see someone work out the details.

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Kido's approach is similar to what I proposed in my thesis (relevant section: http://www.ee.bgu.ac.il/~noamle/_downloads/gaccum.pdf). The idea was to define FRP "behaviors" as discrete time point-wise functions where dt -> 0. Unfortunately I didn't have much of an audience. Would love to see someone continue this approach...
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