[reactive] More on delayed switching
Patai Gergely
I opened a thread some time ago where I asked whether it's enough to
have only immediate switching. But it dawned on me that Reactive
switches are actually all delayed, since even though the delay is
infinitesimal in principle, we still have to wait for the next point of
observation until we can see its effect. This is a huge problem in
practice, because this way every stateful signal imposes a delay equal
to the length of the period between observations. Here's a simple test
case for illustration:
> import Control.Applicative
> import FRP.Reactive
>
> tick :: Event ()
> tick = atTimes [0..]
>
> behs :: [Behavior Double]
> behs = pure 1 : map (integral tick) behs
>
> eventList :: Event a -> [a]
> eventList e = x : eventList e'
> where (x,e') = firstRestE e
>
> testBeh :: Behavior a -> [a]
> testBeh b = take 10 $ eventList (snapshot_ b tick)
>
> test :: IO ()
> test = mapM_ (print . testBeh) (take 5 behs)
Running test prints the following:
[1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0]
[0.0,0.0,1.0,2.0,3.0,4.0,5.0,6.0,7.0,8.0]
[0.0,0.0,0.0,1.0,3.0,6.0,10.0,15.0,21.0,28.0]
[0.0,0.0,0.0,0.0,1.0,4.0,10.0,20.0,35.0,56.0]
[0.0,0.0,0.0,0.0,0.0,1.0,5.0,15.0,35.0,70.0]
I ran into the very same problem when working on the first version of
Elerea. Transfer functions in version 0.1.0 behave exactly the same way,
and I switched to immediate transfer functions from 0.2.0. The
difference is obvious if you look at the breakout example in action: in
0.1.0, the ball takes long to react to collisions, since the dependency
cycle consists of three items (bricks, velocity, position), so any
change takes just as many frames to propagate. From 0.2.0 onwards,
collisions are much more accurate without any change in the example
code.
Sure, it is possible to work around the delay by combining the switching
value with the one that caused its switch, but this adds a lot of
complexity to the code on the user end. You can make life easier by
introducing immediate versions as helper functions, but then you just
reintroduced this distinction. Of course this is not surprising, since
neither delayed nor immediate switching is sufficient on its own. But
this means that Reactive should support both out of the box and not
encourage ad hoc workarounds that are likely to break in unexpected
ways. Also, immediate switching seems the more sensible default, because
it's more straightforward to derive the delayed version from it than the
other way around, and it is what we need most of the time.
Are there any plans to address this problem? Or a completely new angle
to look at it from?
Gergely
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Conal Elliott
1. Infinitesimal delay semantics of switch
2. Euler integration
3. Exact synchronization of numerical integration time samples with display samples
Of these three factors, I see the first one as benign and semantically ideal. The imposed delay is the theoretical minimum (infinitesimal) while still allowing meaningful specification of self-reactive and mutually-reactive systems. And it's consistent with differentially specified continuous behavior. On the other hand, the second and third factors are implementation artifacts rather than desirable semantics. Moreover, they're artifacts that cause the implementation to stray from the semantic ideal.
My inclination is to embrace 1 and somehow fix 2 & 3. I'm guessing 3 is easy and 2 is hard.
For 3, I know of no benefit to having integration sample times correspond to display times, or even to match the frequency. I implemented it that way just for simplicity, and now I see it was a terrible idea. My intention is to use a variable-step-size method that adapts to both the nature of the behavior being integrated and to the available compute cycles.
As for 2, I've used much better integration methods in the past. What's tricky here is getting an integration method that works for self- or mutully-recursive integration (i.e. ODE systems) *without* the ability to see the cycles. Euler is easy but is terribly inaccurate or inefficient&instable.
- Conal
Patai Gergely
> see as ideal semantics. The imposed delay is the theoretical minimum
> (infinitesimal) while still allowing meaningful specification of
> self-reactive and mutually-reactive systems.
combinators to be able to exploit this potential.
> For 3, I know of no benefit to having integration sample times correspond
> to display times, or even to match the frequency.
The fact that the test uses integral is really beside the point. We can
talk about any arbitrary behaviour and its changes.
The heart of the problem is that according to the current Reactive
approach there's no way to derive an event solely from behaviours, since
we inevitably need sampling events to get to the values. In order to
avoid unnecessary delays in the presence of mandatory infinitesimal
delays, we'd have to make sure that if A depends on B, then A is
switched only after some non-zero time elapsed since the switch of B,
otherwise we'll observe the propagation of delays as in the example. It
is big enough of a problem to generate appropriate sampling events all
around the system that take the dynamically changing dependencies into
consideration (in fact, this is a huge burden on the programmer!), but
there's obviously no way to do so in the presence of a dependency cycle.
And again, we arrive at the need of breaking cycles somehow. You even
have to be explicit about the place of this break if you want a
deterministic system.
Because of all this, I believe that Fran's predicate events make much
more sense at least in the semantic basis. You're among the most
knowledgeable about all the issues concerning them, and I'm sure you had
a fleet of good reasons to give up on this approach, but the Reactive
way doesn't seem to be the right answer either.
> to use a variable-step-size method that adapts to both the nature of the
> behavior being integrated and to the available compute cycles.
I'm afraid there's no way that would fit every application, so any kind
of advanced sampling can only be an option. After all, even a single
application can have wildly different stability properties if you start
tweaking some parameters. And you have to be able to tell apart desired
behaviour from unwanted artifacts. If you look at a real-time physics
engine, you'll see trade-offs everywhere. For instance, allowing some
interpenetration between supposedly solid objects improves stability
when there are lots of collisions around without resorting to extreme
supersampling. It is up to you how much (both in time and space)
inconsistency you can live with for the sake of real-time reactivity.
In short, I don't think adaptive time step is the real solution here.
You'll have to be able to express trade-offs in general in order to get
a practical system, and playing around with the sampling rate is just
one special case. Committing to it means not letting the programmer
decide whether they prefer smooth or accurate animation, or more
precisely put, where on that scale their preference lies.
> As for 2, I've used much better integration methods in the past.
As I said, this is not really about integration, which only served as an
example. It's about reactivity in general.
Gergely
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