# Netwire

Netwire is a library for functional reactive programming, which uses the concept of arrows for modelling an embedded domain-specific language. This language lets you express reactive systems, which means systems that change over time. It shares the basic concept with Yampa and its fork Animas, but it is itself not a fork.

## Features

Here is a list of some of the features of *netwire*:

- arrowized interface,
- applicative interface,
- signal inhibition (
*ArrowZero*/*Alternative*), - choice and combination (
*ArrowPlus*/*Alternative*), - self-adjusting wires (
*ArrowChoice*), - rich set of event wires,
- signal analysis wires (average, peak, etc.),
- impure wires.

## Quickstart

This is a quickstart introduction to Netwire for Haskell programmers familiar with arrowized functional reactive programming (AFRP), for example Yampa or Animas. It should quickly give you an idea of how the library works and how it differs from the two mentioned.

### The wire

Netwire calls its signal transformation functions *wires*. You can think of a wire as a device with an input line and an output line. The difference between a function and a wire is that a wire can change itself throughout its lifetime. This is the basic idea of arrowized FRP. It gives you time-dependent values.

A wire is parameterized over an underlying monad and its input and output types:

```
data Wire m a b
```

### Differences from Yampa

If you are not familiar with Yampa or Animas, you can safely skip this section.

The main difference between Yampa and Netwire is that the underlying arrow is impure. While you can choose not to use the impure wires inside of the **FRP.NetWire.IO** module, it is a design choice for this library to explicitly allow impure computations. One theoretical implication is that you need to differentiate between pure stateless, pure stateful and impure signal transformations.

A concept not found in Yampa is signal inhibition. A wire can choose not to return anything. This way you can temporarily block entire subnetworks. This is most useful with the combination operator *<+>*. Example:

```
w = w1 <+> w2
```

The *w* wire runs its signal through the wire *w1*, and if it inhibits, it passes the signal to *w2*.

Another concept not found in Yampa is choice. Through the *ArrowChoice* instance wires allow you to choose one of a set of subwires for its signal without needing a switch. Essentially you can write *if* and *case* constructs inside of arrow notation.

Because of their impurity wires do not have an *ArrowLoop* instance. It is possible to write one, but it will diverge most of the time, rendering it useless.

### Using a wire

To run a wire you will need to use the *withWire* and *stepWire* functions. The *withWire* initializes a wire and gives you a *Session* value. As mentioned earlier in general a wire is a function, which can mutate itself over time. The session value captures the current state of the wire.

```
withWire :: (MonadIO m, MonadIO sm) => Wire m a b -> (Session m a b -> sm c) -> sm c
stepWire :: MonadIO m => a -> Session m a b -> m (Output b)
```

The *stepWire* function passes the given input value through the wire. If you use *stepWire*, then the wire will mutate in real time. If you need a different rate of time, you can use *stepWireDelta* or *stepWireTime* instead. The *stepWireDelta* function takes a time delta, and the *stepWireTime* function takes the current time (which doesn't need to be the real time):

```
stepWireDelta :: MonadIO m => NominalDiffTime -> a -> Session m a b -> m (Output b)
stepWireTime :: MonadIO m => UTCTime -> a -> Session m a b -> m (Output b)
```

Note that it is allowed to give zero or negative deltas and times, which are earlier than the last time. This lets you run the system backwards in time. If you do that, your wire should be prepared to handle it properly.

The stepping functions return a *Output b*, which is just an alias for *Either SomeException b*:

```
type Output = Either SomeException
```

If the wire inhibits (which is analogous to raising an exception), then the result is *Left SomeException*, otherwise it will be *Right b*, with *b* being the output. Here is a complete example:

```
{-# LANGUAGE Arrows #-}
module Main where
import Control.Monad
import FRP.NetWire
import Text.Printf
myWire :: Wire IO () String
myWire =
proc _ -> do
t <- time -< ()
fps <- avgFps 1000 -< ()
fpsPeak <- highPeak -< fps
if t < 4
then identity -< "Waiting four seconds."
else identity -<
printf "Got them! (%8.0f FPS, peak: %8.0f)"
fps fpsPeak
main :: IO ()
main = withWire myWire loop
where
loop :: Session IO () String -> IO ()
loop session =
forever $ do
output <- stepWire () session
case output of
Left e -> print e
Right x -> putStrLn x
```

This program should display the string "Waiting four seconds." for four seconds and then switch to a string, which displays the current average frames per second and peak frames per second.

Note: Sessions are thread-safe. You are allowed to use the stepping functions for the same session from multiple threads. This makes it easy to implement conditional stepping based on system events.

Note: The type signatures of all Wires have an implicit *Monad* constraint on its first parameter. This constraint has been omit for the sake of brevity.

## Signal inhibition

A wire may choose not to return anything, at which point it is said to be inhibiting. If the whole wire network inhibits, then the stepping functions will return *Left e*, where *e :: SomeException*. Otherwise, a *Right* value is returned. If a wire in a sequence of wires inhibits, the later wires are not run.

## Writing a wire

I will assume that you are familiar with arrow notation, and I will use it instead of the raw arrow combinators most of the time. If you haven't used arrow notation before, see the GHC arrow notation manual.

### Time

To use this library you need to understand the concept of time very well. Netwire has a continuous time model, which means that when you write your applications you disregard the discrete steps, in which your wire is executed.

Technically at each execution instant (i.e. each time you run *stepWire* or one of the other stepping functions) the wire is fed with the input as well as a time delta, which is the time passed since the last instant. Hence wires do not by themselves keep track of what time it is, since most applications don't need that anyway. If you need a clock, you can use the predefined *time* wire, which will be explained later.

Wires have a local time, which can be different from the global time. This can happen, when a wire is not actually run, because an earlier wire inhibited the signal. It also happens, when you use choice. For example you can easily write a gateway, which repeatedly runs one wire the one second and another wire the other second. While one wire is run, the other wire is suspended, including its local time.

Local time is a switching effect, which is especially visible, when you use the switching combinators from **FRP.NetWire.Switch**. Local time starts when switching in.

Time is measured in *Double* in Netwire. To improve type signatures there is a type aliases defined for you:

```
type Time = Double
```

*Time* is used to refer to local time and time deltas, i.e. time differences. It is represented in seconds.

### Pure stateless wires

Pure stateless wires are easy to explain, so let's start with them. A pure stateless wire is essentially just a function of input. The simplest wire is the *identity* wire. It just returns its input verbatim:

```
identity :: Wire m a a
```

If you run such a wire (see the previous section), then you will just get your input back all the time. Another simple wire is the *constant* wire, which also disregards time:

```
constant :: b -> Wire m a b
```

If you run the wire `constant 15`

, you will get as output the number 15 all the time, regardless of the current time and the input.

**Note**: You can express*identity*as*arr id*, but you should prefer*identity*, because it's faster. Likewise you can express*constant x*as*arr (const x)*, but again you should prefer*constant*.

### Pure stateful wires

Let's see a slightly more interesting wire. The *time* wire will return the current local time. What *local* means in this context was explained earlier.

```
time :: Wire m a Time
```

As the type suggests, time is measured in seconds and represented as a *Time*. The local time starts from 0 at the point, where the wire starts to run. There is also a wire, which counts time from a different origin:

```
timeFrom :: Time -> Wire a Time
```

The difference between these stateful and the stateless wires from the previous section is that stateful wires mutate themselves over time. The *timeFrom x* wire calculates the current time as *x* plus the current time delta. Let's say that sum is *y*. It then mutates into the wire *timeFrom y*. As you can see there is no internal clock. It is really this self-mutation, which gives you a clock.

### Calculus

One of the compelling features of FRP is integration and differentiation over time. It is a very cheap operation to integrate over time. In fact the *time* wire you have seen in the last section is really just the integral of the constant 1. Here is the type of the *integral* wire, which integrates over time:

```
integral :: Double -> Wire m Double Double
```

The argument is the integration constant or starting value. The input is the subject of integration. Let's write a clock, which runs at half the speed of the real clock:

```
slowClock :: Wire m a Double
slowClock = proc _ -> integral 0 -< 0.5
```

Since the integration constant is 0, the time will start at zero. Integration becomes more interesting, as soon as you integrate non-constants:

```
particle :: Monad m => Wire m a Double
particle =
proc _ -> do
v <- integral 1 -< -0.1
integral 15 -< v
```

This wire models a one-dimensional particle, which starts at position 15 and velocity +1. A constant acceleration of -0.1 per second per second is applied to the velocity, hence the particle moves right towards positive infinity at first, while gradually becoming slower, until it reverses its direction and moves left towards negative infinity.

The above type signature is actually a special case, which I provided for the sake of simplicity. The real type signature is a bit more interesting:

```
integral ::
(Monad m, NFData v, VectorSpace v, Scalar v ~ Double) =>
v -> Wire m v v
```

You can integrate over time in any real vector space. Some examples of vector spaces include tuples, complex numbers and any type, for which you define *NFData* and *VectorSpace* instances. Let's see the particle example in two dimensions:

```
particle2D :: Monad m => Wire m a (Double, Double)
particle2D =
proc _ -> do
v <- integral (1, -0.5) -< (-0.1, 0.4)
integral (0, 0) -< v
```

Differentiation works similarly, although there are two variants:

```
derivative :: Wire m Double Double
derivativeFrom :: Double -> Wire m Double Double
```

The difference between the two variants is that *derivative* will inhibit at the first instant (inhibition is explained later), because it needs at least two samples to compute the rate of change over time. The *derivativeFrom* variant does not have that shortcoming, but you need to provide the first sample as an argument.

Again I have simplified the types to help understanding. Just like with integration you can differentiate over any vectorspace, as long as your type has an *NFData* instance.

### Events

Events are a useful tool to add discrete values to the system. As the name states an event usually denotes some condition or external event, which can be present at some instants and absent at others. A common use case for events is user input. Events are wires that run if the event that it models has occurred and inhibit if otherwise.

There is a large number of event wires in the **FRP.NetWire.Event** module. I will give you examples for some of the common ones here. It is worthwhile to have a look at the aforementioned module.

#### after

```
after :: Time -> Wire m a a
```

The *after* wire causes an event after a certain number of seconds. This means that the wire inhibits until the specified time has passed, at which point it runs for a single instant. After that the event never happens again, i.e. it always inhibits.

#### once

```
once :: Wire m a a
```

This wire produces an event at the first instant and never again.

#### repeatedly

```
repeatedly :: Wire m (Time, a) a
```

This wire takes two input signals. It produces events repeatedly after the time delta given by the left signal. This delta can change over time, making the event happen more or less frequently. The right signal is the desired event value.

#### hold

```
hold :: Wire m a b -> Wire m a b
```

This wire turns events into continuous signals. It inhibits until the first signal from the argument wire. Each time the input event occurs, the output switches to its value and keeps it until the next event occurs.

### Random numbers

Netwire provides a few wires for random noise generation. Probably the most important one is the *noise* wire:

```
noise :: Wire m a Double
```

This wire outputs a random number between 0 (inclusive) and 1 (exclusive). The underlying random number generator is a fast implementation of the Mersenne Twister algorithm provided by Don Stewart's mersenne-random package.

### Signal analysis

Netwire provides some wires to perform signal analysis. One useful wire is *diff*:

```
diff :: Eq a => Wire m a (a, Time)
```

This wire emits an event, whenever the input signal changes. The event contains the last value as well as the time elapsed since then. One possible use case is file monitoring. Pass the file's modification time or even its contents as the input signal. This wire inhibits on no change.

Another useful wire is *avg*, which computes the average value of the input signal over the specified number of most recent samples:

```
avg :: Int -> Wire m Double Double
```

Since the *noise* wire returns random numbers between 0 and 1, if you pass the output of *noise* through *avg x* you should get a value close to 0.5, if the argument *x* is suitably large:

```
avgOfNoise :: Wire m a Double
avgOfNoise = avg 1000 <<< noise
```

An interesting special case of *avg* is the *avgFps* wire, which is very useful for performance analysis. It returns the average frames per second:

```
avgFps :: Int -> Wire m a Double
```

Both *avg* and *avgFps* calculate the average over a certain number of most recent samples. While they have a constant time complexity O(1) they have a linear space complexity of O(n), where *n* is the number of samples. In some cases it can be fine to consider calculating the average over all samples forever. The *avgAll* wire does exactly that:

```
avgAll :: Wire Double Double
```

Unlike *avg* and *avgFps* this variant uses not only constant time, but also constant space.

There are also wires for finding peaks. The *highPeak* and *lowPeak* wires output the high and low peaks respectively for their input:

```
highPeak :: (NFData a, Ord a) => Wire m a a
lowPeak :: (NFData a, Ord a) => Wire m a a
```

Again the type signatures are only special cases. See the library documentation for the real types. In short, you can get averages of any fractional input value.

### Unique request numbers

Sometimes you might want to generate numbers, which are unique throughout the wire session. For example you might want to manage game objects, open file handles or something similar. The *identifier* wire generates such unique numbers:

```
identifier :: MonadIO m => Wire m a Int
```

At the first instance it chooses a unique number and then returns that number forever.

### Impure wires

As noted earlier wires are allowed to perform impure operations:

```
execute :: MonadIO m => Wire m (m a) a
```

The *execute* wire is the simplest wire for impure operations. It takes an *IO* action as its input signal and outputs its result. If the action throws an exception, then this wire inhibits.

You may want to combine this wire with the *diff* wire to develop a wire, which reacts to changes, or with the *sample* wire, which periodically samples a wire given a time delta, or with the *swallow* wire, which transmits the first signal from an input wire forever.

```
liftWire :: Monad m => Wire m (m a) a
```

The *liftWire* wire lifts the given monadic computation to a wire. The action is run at every instant. This wire never inhibits.

## Choice

Wires can branch into multiple subwires, sending a signal to a subset of them. The easiest method to do that is using the *ArrowChoice* instance, which effectively enables you to use *if* and *case* inside of arrow notation:

```
myWire :: Monad m => Wire m Double Double
myWire =
proc x -> do
t <- time -< ()
if t < 4
then identity -< x
else integral 0 -< 0.2
```

This wire acts like the identity wire for four seconds and then switches into a clock, which starts at 0 and runs at 1/5 of the speed of time. The clock indeed starts at 0, because choice is exclusive. The wires, which have not been chosen are suspended. This effectively freezes their local time.

Another method to perform choice is to use one of the parallel switches, which are explained in a later section.

### Inhibiting

There are many ways to inhibit, the simplest being unconditional inhibition, which can be done with the *inhibit_* wire:

```
inhibit_ :: Wire m a b
```

This wire disregards its input and doesn't return. Note that *inhibit* is just a better name for the *zeroArrow* wire from the *ArrowZero* type class. You can use that one, if you prefer.

In general you would prefer inhibition based on a predicate, for which there exist multiple ways. One simple way is to use *inhibit_* together with choice:

```
waitOneSecond :: Monad m => Wire m a a
waitOneSecond =
proc x -> do
t <- time -< ()
if t < 1 then inhibit_ -< ()
else identity -< x
```

This wire inhibits for one second and after that acts like the identity wire. Note that there is another way to write this wire using some of the predefined wires:

```
waitOneSecond :: Monad m => Wire m a a
waitOneSecond =
proc x -> do
ev <- after 1 -< ()
swallow wait -< ev
identity -< x
```

The *after* wire was explained earlier. It will emit an event after one second. The *wait* wire extracts the event's value and returns it, unless no event happened, at which point it simply inhibits. However, the event occurs only once, so this would normally act like the identity wire for an instant and then return to inhibition. This is where *swallow* comes into play.

```
swallow :: Wire m a b -> Wire m a b
```

The *swallow* wire encapsulates the wire given as its argument and modifies its behaviour in the following way: As long as the inner wire inhibits, the *swallow* wire also inhibits, but as soon as the inner wire produces a result, *swallow* switches into the constant wire with that result. In other words, it waits for the first signal from the inner wire and then keeps that result forever.

In this case *wait* would only produce a result once, but because it is wrapped by *swallow* this result is kept forever and the inner *wait* wire is dropped from the network.

The *swallow* function is actually our first wire transformer. It takes a wire and encapsulates it modifying its behaviour.

### Combining

You can combine two wires using the *<+>* combinator. This combinator comes from the *ArrowPlus* class and takes two wires as its argument. It passes the signal through the left wire. If that wire inhibits, it passes the signal to the right wire. The result of the first non-inhibiting wire is returned. If both wires inhibit, their combination inhibits.

Note that if the first wire results, the second one is not run at all, thus *<+>* is left-biased. The following identities hold:

```
w1 <+> inhibit = w1
inhibit <+> w2 = w2
```

### Exhibition

Sometimes you may want to observe inhibition. You can use the *exhibit* wire transformer for that purpose:

```
exhibit :: Wire m a b -> Wire m a (Output b)
-- Recall that Output ~ Left SomeExpection
```

It takes its argument wire and runs the input signal through it. If the inner wire inhibits, then *exhibit* returns a *Left* value. It never inhibits. Thus the following identity holds:

```
exhibit w1 <+> w2 = exhibit w1
```

Note that this suggests correctly that signal inhibition can be interpreted as arrow exceptions, and *exhibit* acts like the *try* combinator.