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This <hask>Reactive</hask> 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. | This <hask>Reactive</hask> 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. | ||
+ | |||
+ | ==== Instances for Event ==== | ||
+ | |||
+ | * '''<hask>Monoid</hask>''': <hask>mempty</hask> is the event that never occurs, and <hask>e `mappend` e'</hask> is the event that combines occurrences from <hask>e</hask> and <hask>e'</hask>. (Fran's <hask>neverE</hask> and <hask>(.|.)</hask>.) | ||
+ | * '''<hask>Functor</hask>''': <hask>fmap f e</hask> is the event that occurs whenever <hask>e</hask> occurs, and whose occurrence values come from applying <hask>f</hask> to the values from <hask>e</hask>. (Fran's <hask>(==>)</hask>.) | ||
+ | * '''<hask>Applicative</hask>''': <hask>pure a</hask> is an event with a single occurrence, available from the beginning of time. <hask>ef <*> ex</hask> is an event whose occurrences are made from the ''product'' of the occurrences of <hask>ef</hask> and <hask>ex</hask>. For every occurrence <hask>f</hask> at time <hask>tf</hask> of <hask>ef</hask> and occurrence <hask>x</hask> at time <hask>tx</hask> of <hask>ex</hask>, <hask>ef <*> ex</hask> has an occurrence <hask>f x</hask> at time <hask>max tf tx</hask>. | ||
+ | * '''<hask>Monad</hask>''': <hask>return a</hask> is the same as <hask>pure a</hask> (as always). In <hask>e >>= f</hask>, each occurrence of <hask>e</hask> leads, through <hask>f</hask>, to a new event. Similarly for <hask>join ee</hask>, which is somehow simpler for me to think about. The occurrences of <hask>e >>= f</hask> (or <hask>join ee</hask>) 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". | ||
+ | |||
+ | ==== Instances for Reactive ==== | ||
+ | |||
+ | The instances for <hask>Reactive</hask> 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 <hask>at :: Reactive a -> (Time -> a)</hask>. | ||
+ | * '''<hask>Monoid</hask>''': a typical lifted monoid. If <hask>o</hask> is a monoid, then <hask>Reactive o</hask> is a monoid, with <hask>mempty = pure mempty</hask>, and <hask>mappend = liftA2 mappend</hask>. In other words, <hask>mempty `at` t == mempty</hask>, and <hask>(r `mappend` s) `at` t == (r `at` t) `mappend` (s `at` t).</hask> | ||
+ | * '''<hask>Functor</hask>''': <hask>fmap f r `at` t == f (r `at` t)</hask>. | ||
+ | * '''<hask>Applicative</hask>''': <hask>pure a `at` t == a</hask>, and <hask>(s <*> r) `at` t == (s `at` t) (r `at` t)</hask>. | ||
+ | * '''<hask>Monad</hask>''': <hask>return a `at` t == a</hask>, and <hask>join rr `at` t == (rr `at` t) `at` t</hask>. As always, <hask>(r >>= f) == join (fmap f r)</hask>. | ||
+ | |||
+ | ==== Continuous reactive behaviors ==== | ||
Although the basic <hask>Reactive</hask> type describes ''discretely''-changing values, ''continuously''-changing are defined simply by composing <hask>Reactive</hask> and a simple type functions of time (see below). | Although the basic <hask>Reactive</hask> type describes ''discretely''-changing values, ''continuously''-changing are defined simply by composing <hask>Reactive</hask> and a simple type functions of time (see below). |
Revision as of 04:44, 20 December 2007
Contents |
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" (), where DataDriven uses "sources" (Reactive).Source
Besides this wiki page, here are more ways to find out about Reactive:
- Read the Haddock docs.
- Get the code repository: darcs get http://darcs.haskell.org/packages/reactive.
- Install from Hackage.
- See the version history.
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:- :Monoidis a future that never becomes knowable.memptyis whichever ofa `mappend` bandais knowable first.b
- : apply a function to a future. The result is knowable when the given future is knowable.Functor
- :Applicativegives value knowable since the beginning of time.pureapplies 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: is the same asreturn(as always).purecascades futures.(>>=)resolves a future future value into a future value.join
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
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
- :Monoidis the event that never occurs, andmemptyis the event that combines occurrences frome `mappend` e'ande. (Fran'se'andneverE.)(.|.)
- :Functoris the event that occurs wheneverfmap f eoccurs, and whose occurrence values come from applyingeto the values fromf. (Fran'se.)(==>)
- :Applicativeis an event with a single occurrence, available from the beginning of time.pure ais an event whose occurrences are made from the product of the occurrences ofef <*> exandef. For every occurrenceexat timefoftfand occurrenceefat timexoftx,exhas an occurrenceef <*> exat timef x.max tf tx
- :Monadis the same asreturn a(as always). Inpure a, each occurrence ofe >>= fleads, throughe, to a new event. Similarly forf, which is somehow simpler for me to think about. The occurrences ofjoin ee(ore >>= f) 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".join ee
2.3.2 Instances for Reactive
The instances for- : a typical lifted monoid. IfMonoidis a monoid, thenois a monoid, withReactive o, andmempty = pure mempty. In other words,mappend = liftA2 mappend, andmempty `at` t == mempty(r `mappend` s) `at` t == (r `at` t) `mappend` (s `at` t).
- :Functor.fmap f r `at` t == f (r `at` t)
- :Applicative, andpure a `at` t == a.(s <*> r) `at` t == (s `at` t) (r `at` t)
- :Monad, andreturn a `at` t == a. As always,join rr `at` t == (rr `at` t) `at` t.(r >>= f) == join (fmap f r)
2.3.3 Continuous reactive behaviors
Although the basictype Time = Double type ReactiveB = Reactive :. Fun Time