# Difference between revisions of "Netwire"

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==== Calculus ==== |
==== Calculus ==== |
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− | 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: |
+ | 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: |

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

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− | 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 at first, while gradually becoming slower, until it reverses its direction and moves towards negative infinity. |
+ | 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: |
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+ | |||

+ | <haskell> |
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+ | integral :: |
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+ | (NFData v, VectorSpace v, Scalar v ~ Double) => |
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+ | v -> Wire v v |
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+ | </haskell> |
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+ | |||

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

+ | <haskell> |
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+ | particle2D :: Wire a (Double, Double) |
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+ | particle2D = |
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+ | proc _ -> do |
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+ | v <- integral (1, -0.5) -< (-0.1, 0.4) |
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+ | integral (0, 0) -< v |
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+ | </haskell> |
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+ | |||

+ | Differentiation works similarly, although there are two variants: |
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+ | |||

+ | <haskell> |
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+ | derivative :: Wire Double Double |
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+ | derivativeFrom :: Double -> Wire Double Double |
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+ | </haskell> |
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+ | |||

+ | 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. |
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+ | |||

+ | 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. |

## Revision as of 01:28, 7 August 2011

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 its input and output types:

```
data Wire 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 metioned earlier in general a wire is a function, which can mutate itself over time. The session value captures the current state of the wire.

```
initWire :: Wire a b -> (Session a b -> IO c) -> IO c
stepWire :: a -> Session a b -> IO (Maybe 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 :: Double -> a -> Session a b -> IO (Maybe b)
stepWireTime :: UTCTime -> a -> Session a b -> IO (Maybe 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 *Maybe b*. If the wire inhibits, then the result is *Nothing*, otherwise it will be *Just* the output. Here is a complete example:

```
{-# LANGUAGE Arrows #-}
module Main where
import Control.Monad
import FRP.NetWire
import Text.Printf
myWire :: Wire () 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 () String -> IO ()
loop session =
forever $ do
mResult <- stepWire () session
case mResult of
Nothing -> putStr "Signal inhibted."
Just x -> putStr x
putChar '\r'
```

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.

### 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.

#### 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 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 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 a Double
```

As the type suggests, time is measured in seconds and represented as a *Double*. 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 :: Double -> Wire a Double
```

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

You can integrate over time in any real vectorspace. Some examples of vectorspaces 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 :: Wire 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 Double Double
derivativeFrom :: Double -> Wire 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.