[Haskell-cafe] A question about causality in FRP

[David Barbour]

On Fri, Oct 14, 2011 at 7:27 AM, Alan Jeffrey <ajeffrey at bell-labs.com>wrote:

> On 10/13/2011 10:43 PM, David Barbour wrote:
>
>> On Thu, Oct 13, 2011 at 7:54 AM, Alan Jeffrey <ajeffrey at bell-labs.com
>> <mailto:ajeffrey at 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
>  [snip]
>
> Making worlds explicit like this I think helps clarify why one person's
> "weird" is another person's "perfectly reasonable function" :-)
>
>
Well, I think you have the concept right. But `weird` is always causal. The
burden of violating causality has been shifted to the user of weird.

Regards,

Dave
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