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1 Abstract

Reactive is a simple foundation for programming reactive systems functionally. Like Fran/FRP, it has a notions of (reactive) behaviors and events. Like DataDriven, Reactive has an efficient, data-driven implementation. The main difference between Reactive and DataDriven are

  • Reactive provides and builds on "functional futures", which in turn build on Concurrent Haskell threads, while DataDriven builds on continuation-based computations; and
  • The algebras of events and reactive values (called events and sources in DataDriven) are purely functional. I couldn't figure out how to accomplish that in DataDriven.
  • Reactive manages (I hope) to get the efficiency of data-driven computation with a (sort-of) demand-driven architecture. For that reason, Reactive is garbage-collector-friendly, while DataDriven depends on weak references (because GC favors demand-driven computation.)
  • Reactive elegantly and efficiently caches values.
  • Reactive uses the term "reactive values" (
    Reactive
    ), where DataDriven uses "sources" (
    Source
    ).
The inspiration for Reactive was Mike Sperber's [Lula] implementation of FRP. Mike used blocking threads, which I had never considered for FRP before a conversation with him at ICFP 2007. While playing with the idea, I realized that I could give a very elegant and efficient solution to caching, which DataDriven doesn't do. (For an application
f <*> a
of a varying function to a varying argument, caching remembers the latest function to apply to a new argument and the latest argument to which to apply a new function.) As with DataDriven, Reactive provides instances for
Monoid
,
Functor
,
Applicative
, and
Monad
.

Besides this wiki page, here are more ways to find out about Reactive:

Please leave comments at the Talk page.

2 Modules

2.1 Data.Future

A future is a value that will become knowable only later. Primitive futures can be things like "the value of the next key you press", or "the value of LambdaPix stock at noon next Monday".

Composition is via standard type classes:
Functor
,
Applicative
,
Monad
, and
Monoid
.
  • Monoid
    :
    mempty
    is a future that never becomes knowable.
    a `mappend` b
    is whichever of
    a
    and
    b
    is knowable first.
  • Functor
    : apply a function to a future. The result is knowable when the given future is knowable.
  • Applicative
    :
    pure
    gives value knowable since the beginning of time.
    (<*>)
    applies a future function to a future argument. Result available when both are available, i.e., it becomes knowable when the later of the two futures becomes knowable.
  • Monad:
    return
    is the same as
    pure
    (as always).
    (>>=)
    cascades futures.
    join
    resolves a future future value into a future value.
The current implementation is nondeterministic in
mappend
for futures that become knowable at the same time or nearly the same time. I want to make a deterministic implementation.

2.1.1 Garbage collection of futures

Baker & Hewitt's 1977 paper The Incremental Garbage Collection of Processes discusses using garbage collection to prevent the useless threads from consuming resources. In particular, consider
Future
's
mappend
(sometimes called "parallel or"). Once one thread completes, the other threads are then useless, and some might consume resources forever. My current implementation kill the losing threads. Baker & Hewitt suggest instead using garbage collection. I'm stumped about how to GC non-winning threads in a race between futures ("parallel or"). The winner-kills-loser approach seems to work fine, though is potentially dangerous w.r.t locked resources. Still, the elegance of a GC-based solution appeals to me.

2.1.2 Concurrent Haskell vs STM

Futures are implemented using Concurrent Haskell's
MVar
s. I first tried using STM and
TVar
s, simply using
orElse
to implement
mappend
for futures. However, I didn't see how to avoid nesting
atomically
, which yielded a run-time error.

2.2 Data.SFuture

A target denotational semantics for Data.Future -- simple, precise, and deterministic, in terms of time/value pairs.

2.3 Data.Reactive

This module defines events and reactive values. An event is stream of future values in order of availability. A reactive value is a discretly time-varying value. These two types are closely linked: a reactive value is defined by an initial value and an event that yields future values; while an event is simply a future reactive value.

newtype Event a = Event (Future (Reactive a))
data Reactive a = a `Stepper` Event a
This
Reactive
representation can be thought of a reactive weak head normal form, to which arbitrary reactive expressions may be rewritten. The rewrite rules and their justification in terms of simple denotational semantics will be described in an upcoming paper.

Many of the operations on events and reactive values are packaged as instances of standard classes, as described below. See the module documentation for the other operations.

2.3.1 Instances for Event

  • Monoid
    :
    mempty
    is the event that never occurs, and
    e `mappend` e'
    is the event that combines occurrences from
    e
    and
    e'
    . (Fran's
    neverE
    and
    (.|.)
    .)
  • Functor
    :
    fmap f e
    is the event that occurs whenever
    e
    occurs, and whose occurrence values come from applying
    f
    to the values from
    e
    . (Fran's
    (==>)
    .)
  • Applicative
    :
    pure a
    is an event with a single occurrence, available from the beginning of time.
    ef <*> ex
    is an event whose occurrences are made from the product of the occurrences of
    ef
    and
    ex
    . For every occurrence
    f
    at time
    tf
    of
    ef
    and occurrence
    x
    at time
    tx
    of
    ex
    ,
    ef <*> ex
    has an occurrence
    f x
    at time
    max tf tx
    .
  • Monad
    :
    return a
    is the same as
    pure a
    (as always). In
    e >>= f
    , each occurrence of
    e
    leads, through
    f
    , to a new event. Similarly for
    join ee
    , which is somehow simpler for me to think about. The occurrences of
    e >>= f
    (or
    join ee
    ) correspond to the union of the occurrences of all such events. For example, suppose we're playing Asteroids and tracking collisions. Each collision can break an asteroid into more of them, each of which has to be tracked for more collisions. Another example: A chat room has an "enter" event, whose occurrences contain new events like "speak".

2.3.2 Instances for Reactive

The instances for
Reactive
can be understood in terms of (a) a simple semantics of reactive values as functions of time, and (b) the corresponding instances for functions. The semantics is given by the function
at :: Reactive a -> (Time -> a)
.
  • Monoid
    : a typical lifted monoid. If
    o
    is a monoid, then
    Reactive o
    is a monoid, with
    mempty = pure mempty
    , and
    mappend = liftA2 mappend
    . In other words,
    mempty `at` t == mempty
    , and
    (r `mappend` s) `at` t == (r `at` t) `mappend` (s `at` t).
  • Functor
    :
    fmap f r `at` t == f (r `at` t)
    .
  • Applicative
    :
    pure a `at` t == a
    , and
    (s <*> r) `at` t == (s `at` t) (r `at` t)
    .
  • Monad
    :
    return a `at` t == a
    , and
    join rr `at` t == (rr `at` t) `at` t
    . As always,
    (r >>= f) == join (fmap f r)
    .

2.3.3 Continuous reactive behaviors

Although the basic
Reactive
type describes discretely-changing values, continuously-changing are defined simply by composing
Reactive
and a simple type functions of time (see below).
type Time = Double
type ReactiveB = Reactive :. Fun Time
Because the combination of
Reactive
and
Fun Time
is wrapped in a type composition, we get
Functor
and
Applicative
instances for free. The exact packaging of discrete vs continuous will probably change with more experience. Perhaps I'll fold
Fun Time a
into the
Reactive
type, making a dynamic rather than static distinction.

2.4 Data.Fun

This module defines a type of functions optimized for the constant case, together with instances of
Functor
,
Applicative
,
Monad
, and
Arrow
.