FRP.Elerea.Internal

This is the core module of Elerea, which contains the signal implementation and the primitive constructors.

The basic idea is to create a dataflow network whose structure closely resembles the user's definitions by turning each combinator into a mutable variable (an IORef). In other words, each signal is represented by a variable. Such a variable contains information about the operation to perform and (depending on the operation) references to other signals. For instance, a pointwise function application created by the <*> operator contains an SNA node, which holds two references: one to the function signal and another to the argument signal.

In order to have a pure(-looking) applicative interface, the library relies on unsafePerformIO to create the references on demand. In contrast, the execution of the network is explicitly marked as an IO operation. The core library exposes a single function to animate the network called superstep, which takes a signal and a time interval, and mutates all the variables the signal depends on. It is supposed to be called repeatedly in a loop that also takes care of user input.

To ensure consistency, a superstep has three phases: sampling, aging and finalisation. Each signal reachable from the top-level signal passed to superstep is sampled at the current point of time (sample), and the sample is stored along with the old signal in its reference. If the value of a signal is requested multiple times, the sample is simply reused. After successfully sampling the top-level signal, the network is traversed again to advance by the desired time (advance), and when that's completed, the finalisation process throws away the intermediate samples and marks the aged signals as the current ones, ready to be sampled again. If there is a dependency loop, the system tries to use the sampleDelayed function instead of sample to get a useful value at the problematic spot instead of entering an infinite loop. Evaluation is initiated by the signalValue function (which is used in both the sampling and the aging phase to calculate samples and retrieve the cached values if they are requested again), aging is performed by age, while finalisation is done by commit. Since these functions are invoked recursively on a data structure with existential types, their types also need to be explicity quantified.

As a bonus, applicative nodes are automatically collapsed into lifted functions of up to five arguments. This optimisation significantly reduces the number of nodes in the network.

Implementation

Some type synonyms

type Time = Double

Time is continuous. Nothing fancy.

type DTime = Double

type Sink a = a -> IO ()

Sinks are used when feeding input into peripheral-bound signals.

The data structures behind signals

newtype Signal a

A signal is represented as a transactional structural node.

Constructors

S (IORef (SignalTrans a))

Instances

Functor Signal

Applicative Signal

The Applicative instance with run-time optimisation. The <*> operator tries to move all the pure parts to its left side in order to flatten the structure, hence cutting down on book-keeping costs. Since applicatives are used with pure functions and lifted values most of the time, one can gain a lot by merging these nodes.

Eq (Signal a)

The equality test checks whether two signals are physically the same.

Floating t => Floating (Signal t)

Fractional t => Fractional (Signal t)

Num t => Num (Signal t)

Show (Signal a)

The Show instance is only defined for the sake of Num...

data SignalTrans a

A node can have four states that distinguish various stages of sampling and aging.

Constructors

Ready (SignalNode a)

Ready s is simply the signal s that was not sampled yet

Sampling (SignalNode a)

Sampling s is still s after its current value was requested, but still not delivered

Sampled a (SignalNode a)

Sampled x s is signal s paired with its current value x

Aged a (SignalNode a)

Aged x s is the aged version of signal s paired with its current value x

data SignalNode a

The possible structures of a node are defined by the SignalNode type. Note that the SNLx nodes are only needed to optimise applicatives, they can all be expressed in terms of SNK and SNA.

Constructors

SNK a

SNK x: constantly x

SNS a (DTime -> a -> a)

SNS x t: stateful generator, where x is current state and t is the update function

forall t . SNT (Signal t) a (DTime -> t -> a -> a)

SNT s x t: stateful transfer function, which also depends on an input signal s

forall t . SNA (Signal (t -> a)) (Signal t)

SNA sf sx: pointwise function application

SNE (Signal a) (Signal Bool) (Signal (Signal a))

SNE s e ss: latcher that starts out as s and becomes the current value of ss at every moment when e is true

SNR (IORef a)

SNR r: opaque reference to connect peripherals

SND a (Signal a)

SND s: the s signal delayed by one superstep

forall t . SNKA (Signal a) (Signal t)

SNKA s l: equivalent to s while aging signal l

forall t . SNL1 (t -> a) (Signal t)

SNL1 f: fmap f

forall t1 t2 . SNL2 (t1 -> t2 -> a) (Signal t1) (Signal t2)

SNL2 f: liftA2 f

forall t1 t2 t3 . SNL3 (t1 -> t2 -> t3 -> a) (Signal t1) (Signal t2) (Signal t3)

SNL3 f: liftA3 f

forall t1 t2 t3 t4 . SNL4 (t1 -> t2 -> t3 -> t4 -> a) (Signal t1) (Signal t2) (Signal t3) (Signal t4)

SNL4 f: liftA4 f

forall t1 t2 t3 t4 t5 . SNL5 (t1 -> t2 -> t3 -> t4 -> t5 -> a) (Signal t1) (Signal t2) (Signal t3) (Signal t4) (Signal t5)

SNL5 f: liftA5 f

debugLog :: String -> IO a -> IO a

You can uncomment the verbose version of this function to see the applicative optimisations in action.

Internal functions to run the network

createSignal :: SignalNode a -> Signal a

This function is really just a shorthand to create a reference to a given node.

signalValue :: forall a. Signal a -> DTime -> IO a

Sampling the signal and all of its dependencies, at the same time. We don't need the aged signal in the current superstep, only the current value, so we sample before propagating the changes, which might require the fresh sample because of recursive definitions.

age :: forall a. Signal a -> DTime -> IO ()

Aging the network of signals the given signal depends on.

commit :: forall a. Signal a -> IO ()

Finalising aged signals for the next round.

advance :: SignalNode a -> a -> DTime -> IO (SignalNode a)

Aging the signal. Stateful signals have their state forced to prevent building up big thunks, and the latcher also does its job here. The other nodes are structurally static.

sample :: SignalNode a -> DTime -> IO a

Sampling the signal at the current moment. This is where static nodes propagate changes to those they depend on. Transfer functions (SNT) and latchers (SNE) work without delay, i.e. the effects of their input signals can be observed in the same superstep.

sampleDelayed :: SignalNode a -> DTime -> IO a

Sampling the signal with some kind of delay in order to resolve dependency loops. Transfer functions simply return their previous output, while latchers postpone the change and pass through the current value of their current signal even if the latch control signal is true at the moment. Other types of signals are always handled by the sample function, so it is not possible to create a stateful loop composed of solely stateless combinators.

Userland primitives

superstep

Arguments

:: Signal a

the top-level signal

-> DTime

the amount of time to advance

-> IO a

the current value of the signal

Advancing the whole network that the given signal depends on by the amount of time given in the second argument.

stateful

Arguments

:: a

initial state

-> (DTime -> a -> a)

state transformation

-> Signal a

A pure stateful signal. The initial state is the first output.

transfer

Arguments

:: a

initial internal state

-> (DTime -> t -> a -> a)

state updater function

-> Signal t

input signal

-> Signal a

A stateful transfer function. The current input affects the current output, i.e. the initial state given in the first argument is considered to appear before the first output, and can only be directly observed by the sampleDelayed function.

latcher

Arguments

:: Signal a

s: initial behaviour

-> Signal Bool

e: latch control signal

-> Signal (Signal a)

ss: signal of potential future behaviours

-> Signal a

Reactive signal that starts out as s and can change its behaviour to the one supplied in ss whenever e is true. The change can be observed immediately, unless the signal is sampled by sampleDelayed, which puts a delay on the latch control (but not on the latched signal!).

external

Arguments

:: a

initial value

-> IO (Signal a, Sink a)

the signal and an IO function to feed it

A signal that can be directly fed through the sink function returned. This can be used to attach the network to the outer world.

delay

Arguments

:: a

initial output

-> Signal a

the signal to delay

-> Signal a

The delay transfer function emits the value of a signal from the previous superstep, starting with the filler value given in the first argument. It has to be a primitive, otherwise it could not be used to prevent automatic delays.

keepAlive

Arguments

:: Signal a

the actual output

-> Signal t

a signal guaranteed to age when this one is sampled

-> Signal a

Dependency injection to allow aging signals whose output is not necessarily needed to produce the current sample of the first argument. It is more or less equivalent to liftA2 const, the difference being that it evaluates its second argument first.