[Haskell-cafe] Arrow laws of Netwire

[Ertugrul Söylemez]

Hi Ivan,

>> The easiest way to see the difference is by looking at some of the
>> combinators.  Notice that things like 'hold', 'scan'/'accum', and
>> 'tag' are real functions.  In a first-class FRP system these would
>> have types like the following:
>>
>>     hold :: a -> Event a -> Moment (Behaviour a)
>>     scan :: a -> Event (a -> a) -> Moment (Event a)
>>     tag  :: Behaviour (a -> b) -> Event a -> Event b
>>
>> The Moment monad is not inherent to the way the underlying state
>> machine is constructed, but acts merely as a provider for the notion
>> of "now".  Since 'tag' doesn't need that notion, it's a completely
>> pure function.
>
> Well, in a way. Yes, it can be a pure function, and an event can
> somehow be a delayed computation of how/when it is actually produced,
> computed/consumed the moment you want to actually evaluate the
> network.
>
> Saying that they are pure would be just fine if Behaviours did not
> depend on the outside world (that is, if they were "calculated" from
> pure haskell functions). But I don't think they are. Not always. Not
> if you want to depend on any external user input.

Behaviours are actually pure values.  They don't really depend on time
or any effects.  Their values may very well be generated from effects,
for example the "current cursor position", but conceptually the
behaviour that represents the whole timeline of values is indeed a pure
value.

There is a caveat of course:  We like to think of behaviours as
functions of time, but that's not the whole truth, because our
capability to observe the value of a behaviour is very limited, in most
implementations to an abstract notion of "now".  The same is true for
events: we can only ever ask whether an event is happening "now".

That's how effects and a pure API can be compatible.  We can think of
behaviours as pure timelines (or functions of time), but the API cannot
possibly give us full access to it.


> In Reflex (and I'm not trying to discuss the particularities of this
> implementation), yes, Behaviour and Event are types in a family, but
> the actual definitions in Spider I can seee are records of IORefs with
> bangs.  Far from pure.

Yes, of course.  The implementation is shockingly impure and hacky,
which is why there is such a massive test suite. =)

There are much less hacky ways to implement it, but unfortunately some
impurity is inevitable.  The reason for Spider's hacikness is
efficiency: Reflex is incredibly fast, and a lot of effort went into
only ever computing things that matter, and never computing them twice.
In my benchmarks it comes very close to wires, which is quite
impressive, if you consider what thin an abstraction layer Wire (or MSF)
is.


>> You can have that function in AFRP as well:
>>
>>     fmap :: (a -> b) -> Event a -> Event b
>>
>> However, unlike 'fmap', 'tag' makes sense in a pure context.  You can
>> pass an Event and a Behaviour to a different thread via an MVar,
>> combine them there, then send the result back, and it will still work
>> in the context of the greater application (no isolated state
>> machines).
>
> I don't see how you cannot do that with wires. For instance, you can
> send a Wire m () (Event b), and a Wire m () (a -> b), and compose them
> in a pure context. Then you can bring that back and use it.

Right.  The difference is that you need to be very careful about
context.  If you have a "main wire", you must make sure to communicate
that result back into it *or* run two wires concurrently.  This caution
is not necessary with first-class FRP, because it does not have that
context-sensitivity.


>> You can hold an event in any concurrent thread, etc.
>
> Can you use it without doing IO and executing the computation
> associated to calculating/polling the behaviour? If so, it must be
> because the FRP evaluation method has some inherent thread-safety (I
> you need IO + more for that). Wouldn't you be able to put that thread
> safety in your monad, and then use it with MSFs/Wires?

Thread safety is a different matter, and yes, the implementation must be
thread-safe for that to work.  This is the reason why I was
investigating an FRP implementation based on STM to see how fine-grained
regions would pan out, but it was so slow that i abandoned that
approach.  Reflex does global locking, which sucks, but I can't think of
a better way.

To answer your question: it depends on the controller API of the
framework.  For example in Reflex the frame boundary is created by
'fireEventsAndRead'.  This is the only action that can "advance time".
You can use it from multiple threads, and it will have a timeline-global
effect (you can have multiple timelines in Reflex, but if that doesn't
make sense to you, just think of "timeline-global" as "global").

In reactive-banana the frame boundery is created by registered
callbacks.  R-b registers callbacks for events that matter (that's where
'fromAddHandler' and 'reactimate' meet), and whenever one of them is
invoked, a new frame begins.

In both cases the clock ticks as events fire.


>> Another example is that if the underlying monad is nontrivial (say
>> IO) you can't easily split behaviours in a pure context in AFRP.
>
> You can, but you need a monad such that: (,) <$> ma <*> ma == (\x ->
> (x,x)) <$> ma.
>
> Is this called idempotent?
>
> But to implement any form of Classic FRP or Reactive Programming on
> top of MSFs, you want that kind of monad.

Not sure if idempotency is the right term, but in any case you have that
monad in fist-class FRP.  It's called Behavio(u)r. =)

Note: The Monad instance for Behavior is not implemented yet in Reflex
0.4.0, but you can easily achieve the same by using 'pull' and 'sample':

    pull (liftA2 (,) (sample b1) (sample b2))

The instance is implemented in the git version.


>> This restriction does not exist in first-class FRP:
>
> Well, it is not exposed to the user, but someone must have thought
> about it and solved it. Duplication of effects is inherent to having
> monadic computations associated to obtaining the values of
> behaviours. If you don't cache for a given timestamp, you duplicate
> effects.

This is only really inherent to the mealy-machine approach (i.e. "what
AFRP does").  The monads involved in first-class FRP really only serve
to tie reactive combinators to "now".  Their implementations only
control when exactly (in which frame) you hold an event, which is
usually a simple matter of effect sequencing, i.e. "having a monad".  In
other words: moment monads are generally just IO in disguise.


> I cannot say I like arrow notation, or inputs based on tuples. We need
> more work on this.
>
> However, I decided to embrace the A and I am finding a lot of
> extensions and guarantees that are possible, or easier, thanks to
> that.

Cale Gibbard has done some work on desugaring arrow notation in smarter
ways than the tuple-based approach we have now, but ultimately the whole
arrow approach was abandoned (and eventually Reflex was born).

My original approach with Netwire was to provide higher-level
composition capabilities to reduce the amount of "side channels"
necessary, which lead to an interesting Alternative instance for
Netwire's version of Wire.  One of the defining features of Netwire is
the ability to "inhibit", which facilitates a form of switching that
eliminates most use cases of Yampa's event-based switches.  The
following is a string-valued wire that displays "---", but every five
seconds it switches to "Ding!" temporarily for one second:

    ("Ding!" . holdFor 1 <|> "---") . periodic 5

However, nowadays I think first-class FRP is the superior approach.


Greets
ertes
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