netwire-4.0.7: Flexible wire arrows for FRP

MaintainerErtugrul Soeylemez <>
Safe HaskellNone




Netwire is a library for functional reactive programming, that is for time-varying values. It allows you to express various reactive systems elegantly and concisely by using an embedded domain-specific language. Examples of such systems include

  • games,
  • network applications with time-varying components,
  • simulations,
  • stateful web applications,
  • widget-based user interfaces.

This library is based on an extension of the automaton arrow. The usage is explained in the following tutorial.


Quickstart tutorial

This section is a quickstart tutorial for the experienced, impatient Haskell programmer.

The main concept used in Netwire is a family of wire categories:

 data Wire e m a b

A value of type Wire e m a b represents a function that takes as arguments

  • a time delta of type Time (which is just Double) that will be explained below,
  • an input value of type a.

From these inputs it

  • either produces an output value of type b or inhibits with a value of type e,
  • produces a new wire of type Wire e m a b.

So you can think of Wire as:

 newtype Wire e m a b =
     Wire {
       stepWire :: Time -> a -> m (Either e b, Wire e m a b)

To summarize a wire of type Wire e m a b takes a value of type a and supposedly produces a value of type b. It can be invoked multiple times, where each invocation is called an instant and the wire can behave differently at every instant. Additionally it can choose not to produce anything, but instead inhibit with an inhibition exception of type e. This is Netwire's notion of a time-varying value.

Running wires

To actually invoke a wire you can use the stepWire function (simplified type):

 stepWire ::
     (Monad m) =>
     Wire e m a b ->
     Time ->
     a ->
     m (Either e b, Wire e m a b)

The idea is simple: You have an application loop that invokes a given wire with a time delta, which is just the number of seconds passed since the last instant and an application-specific input value. It then does something with the output value (or inhibition value) and restarts the loop with the new wire produced by the current wire. Such an application loop based on stepWire could look like this:

 loop w' = do
     dt <- timeDeltaToLastInstant
     (mx, w) <- stepWire w' dt ()
     case mx of
       Left ex -> printf "Inhibited: %s\n" (show ex)
       Right x -> printf "Produced: %s\n" (show x)
     loop w

Usually the time deltas are based on actual clock time. To simplify invocation for this common case there is a set of convenience functions like stepSession for stepping that calculate the time deltas for you:

 stepSession ::
     (Monad m) =>
     Wire e m a b ->
     Session m ->
     a ->
     m (Either e b, Wire e m a b, Session m)

To construct the initial session value you can use clockSession or one of the other predefined intial session values:

 clockSession :: (MonadIO m) => Session m

This simplifies the application loop, because you don't have to calculate the time deltas yourself:

 loop w' session' = do
     (mx, w, session) <- stepSession w' session' ()
     case mx of
       Left ex -> printf "Inhibited: %s\n" (show ex)
       Right x -> printf "Produced: %s\n" (show x)
     loop w session

For the common case where the wire's underlying monad is Identity, but the application monad is something else, there are convenience functions like stepWireP, stepSessionP and other *P variants.

We haven't covered constructing wires yet. This is explained in the next section. But we now have everything necessary to write our first small application:

 module Main where

 import Control.Monad.Identity (Identity)
 import Control.Wire
 import Prelude hiding ((.), id)
 import Text.Printf

 testApp :: Wire () Identity a Time
 testApp = timeFrom 10

 main :: IO ()
 main = loop testApp clockSession
     loop w' session' = do
         (mx, w, session) <- stepSessionP w' session' ()
         case mx of
           Left ex -> putStrLn ("Inhibited: " ++ show ex)
           Right x -> putStrLn ("Produced: " ++ show x)
         loop w session

When you run this program, it will continuously display a number of seconds starting with 10. That's the timeFrom 10 wire. Notice that the Prelude module is imported with hidden . and id. Don't worry, the Control.Wire module reexports the Control.Category module, which includes generalized version of both.

Constructing wires

A number of convenience types are defined in the Control.Wire.Types module, in particular the WireP type:

 type WireP = Wire LastException Identity

Wires can be composed categorically, applicatively or by using wire combinators. To feed the output of one wire w1 into another wire w2 you just use categorical composition:

 w2 . w1

For example the noise wire generates random noise based on the given random number generator. If its output type is Double, it generates noise 0 <= x t < 1. The avg wire calculates the average value of its input over the last given number of samples:

 let myNoise = noise (mkStdGen 0) :: WireP a Double
     myAvg   = avg 1000
 in myAvg . myNoise

That wire should produce values near 0.5, the average noise value over the last 1000 samples of random noise between 0 and 1. There is a bit of cruft here to tell the type system that noise's output type is Double. To make this easier you can simply use outAs or inAs:

 avg 1000 . outAs pDouble (noise (mkStdGen 0))

The Wire type gives rise to a family of applicative functors. Using applicative style you can apply a function to the output of a wire or zip together the outputs of two wires (the Control.Applicative module is reexported by this module):

 timeString = fmap (printf "%8.2f") time

 noisyTime = liftA2 (+) time (noise (mkStdGen 0))

Constant wires can be produced using pure. The following wire starts at 0 and increases with a constant speed of 3:

 integral_ 0 . pure 3

There are lots of convenience instances for wires. For example there are instances for Num, Fractional and IsString, so you can actually just use regular arithmetical operators and numeric literals. If you have enabled the OverloadedStrings extension you can also write string literals:

 let n = noise (mkStdGen 0)
 in time + 3*n

 integral_ 0 . 3

There is a large library of predefined wires below the Control.Wire.Prefab tree.

Signal inhibition and events

As noted a few times wires can choose not to produce a value. In those cases the wire inhibits the signal. This is where the e type comes into play. That type is called the inhibition monoid.

Signal inhibition is what makes Netwire different. The Wire type is an Alternative functor, where the empty wire always inhibits and wires can be combined with the following semantics:

 w1 <|> w2

If w1 inhibits, then the combination w1 <|> w2 acts like w2. In other words, the combination chooses the first wire that produces. If both inhibit, then the combination inhibits.

Events are modelled around this. An event wire is usually a wire that acts like the identity wire, but it may inhibit depending on whether an event has occurred or not. One simple event wire is the for wire:

 for 3

This wire acts like the identity wire for three seconds and then stops producing forever. You can use it to construct a wire that produces yes for three seconds and then switches to no:

 "yes" . for 3 <|> "no"

Another useful event wire is the wackelkontakt wire (a Netwire running gag; it's the German word for slack joint):

 wackelkontakt 0.9

This wire acts like the identity wire most of the time (90%), but occasionally inhibits (10%). Using it you can produce a broken clock, which occasionally refuses to display the current time:

 brokenClock =
     printf "%8.2f" <$> wackelkontakt 0.9 . time <|>
     "sorry, slack joint"

The periodically wire produces once every given number of seconds. The following wire produces once every two seconds:

 periodically 2

There are various combinators for event wires in the Control.Wire.Trans.Event module, most notably hold and holdFor. Given an inhibiting wire the hold combinator holds the last produced value, so it turns instantaneous events into continuous ones:

 secondClock = printf "%8.2f" <$> hold (periodically 1 . time)

This one displays the time in seconds and is only updated every second. The holdFor combinator allows you to limit the time the last output is held for:

 jumpyClock =
     printf "%8.2f" <$> holdFor 0.5 (periodically 1 . time) <|>
     "wait 500ms for the next second"

You find a library of predefined event wires in the Control.Wire.Prefab.Event module.

Custom wires

From time to time you will want to write your own wire on a lower level. In this case there are a number of options. The simplest option is mkPure:

 mkPure ::
     (Time -> a -> (Either e b, Wire e m a b)) ->
     Wire e m a b

The type quite literally tells what this function does. It takes a function and turns it into a wire quite straightforwardly. Another option is to use mkState, which is equivalent to mkPure, but allows you to express the wire as a local state transformer:

 mkState ::
     s ->
     (Time -> (a, s) -> (Either e b, s)) ->
     Wire e m a b

The first argument is a starting state, the second is the state transformation function.

Netwire reexports

Other reexports

module Data.Proxy

class Profunctor h where


lmap :: (a -> b) -> h b c -> h a c

rmap :: (b -> c) -> h a b -> h a c

class (Typeable e, Show e) => Exception e where

Any type that you wish to throw or catch as an exception must be an instance of the Exception class. The simplest case is a new exception type directly below the root:

 data MyException = ThisException | ThatException
     deriving (Show, Typeable)

 instance Exception MyException

The default method definitions in the Exception class do what we need in this case. You can now throw and catch ThisException and ThatException as exceptions:

*Main> throw ThisException `catch` \e -> putStrLn ("Caught " ++ show (e :: MyException))
Caught ThisException

In more complicated examples, you may wish to define a whole hierarchy of exceptions:

 -- Make the root exception type for all the exceptions in a compiler

 data SomeCompilerException = forall e . Exception e => SomeCompilerException e
     deriving Typeable

 instance Show SomeCompilerException where
     show (SomeCompilerException e) = show e

 instance Exception SomeCompilerException

 compilerExceptionToException :: Exception e => e -> SomeException
 compilerExceptionToException = toException . SomeCompilerException

 compilerExceptionFromException :: Exception e => SomeException -> Maybe e
 compilerExceptionFromException x = do
     SomeCompilerException a <- fromException x
     cast a

 -- Make a subhierarchy for exceptions in the frontend of the compiler

 data SomeFrontendException = forall e . Exception e => SomeFrontendException e
     deriving Typeable

 instance Show SomeFrontendException where
     show (SomeFrontendException e) = show e

 instance Exception SomeFrontendException where
     toException = compilerExceptionToException
     fromException = compilerExceptionFromException

 frontendExceptionToException :: Exception e => e -> SomeException
 frontendExceptionToException = toException . SomeFrontendException

 frontendExceptionFromException :: Exception e => SomeException -> Maybe e
 frontendExceptionFromException x = do
     SomeFrontendException a <- fromException x
     cast a

 -- Make an exception type for a particular frontend compiler exception

 data MismatchedParentheses = MismatchedParentheses
     deriving (Typeable, Show)

 instance Exception MismatchedParentheses where
     toException   = frontendExceptionToException
     fromException = frontendExceptionFromException

We can now catch a MismatchedParentheses exception as MismatchedParentheses, SomeFrontendException or SomeCompilerException, but not other types, e.g. IOException:

*Main> throw MismatchedParentheses catch e -> putStrLn ("Caught " ++ show (e :: MismatchedParentheses))
Caught MismatchedParentheses
*Main> throw MismatchedParentheses catch e -> putStrLn ("Caught " ++ show (e :: SomeFrontendException))
Caught MismatchedParentheses
*Main> throw MismatchedParentheses catch e -> putStrLn ("Caught " ++ show (e :: SomeCompilerException))
Caught MismatchedParentheses
*Main> throw MismatchedParentheses catch e -> putStrLn ("Caught " ++ show (e :: IOException))
*** Exception: MismatchedParentheses

data SomeException where

The SomeException type is the root of the exception type hierarchy. When an exception of type e is thrown, behind the scenes it is encapsulated in a SomeException.


SomeException :: Exception e => e -> SomeException