Re: [Haskell-cafe] A question about causality in FRP

On 10/13/2011 10:43 PM, David Barbour wrote:

On Thu, Oct 13, 2011 at 7:54 AM, Alan Jeffrey mailto:ajeffrey@bell-labs.com> wrote: The `problem` such as it exists: you will be unable to causally construct the argument toith the `weird` function, except by modeling a nested/simulated world (i.e. modeling one FRP system within another). This is not an unrealistic endeavor, e.g. one might model the future position of a thrown baseball in order to predict it. In this sense, `weird` is not weird.

Ah, I think this is a very good summary. It seems that there's an implicit shift of worlds when you nest FRP behaviours. The top level world (the one that reactimate is executing) uses wall-clock time, but nested behaviours are in a different world, where time is simulated. Making these worlds explicit (I never met a problem that couldn't use some more phantom types :-) we have a type Beh W A for a behaviour in world W of type A, and a definition of causality that's indexed by worlds. Writing RW for the top-level real world, and SW for a simulated world, we have: weird : Beh RW (Beh RW A) -> Beh RW A weird b t = b t (t + 1) -- not causal weird : Beh RW (Beh SW A) -> Beh RW A weird b t = b t (t + 1) -- causal and: double : Beh RW A -> Beh RW (Beh RW A) double b t u = b u -- causal double : Beh RW A -> Beh RW (Beh SW A) double b t u = b u -- not causal [Caveat: details not worked out.] Making worlds explicit like this I think helps clarify why one person's "weird" is another person's "perfectly reasonable function" :-) Does something like this help clarify matters? A.