elerea-2.1.0: A minimalistic FRP library



This version differs from the simple one in adding associated freeze control signals ('clocks') to stateful entities to be able to pause entire subnetworks without having to write all the low-level logic explicitly. The clocks are fixed to signals upon their creation, and the withClock function can be used to specify the common clock for the signals created in a given generator.

A clock signal affects delay elements the following way: if the clock signal is true, the delay works as usual, otherwise it remembers its current output and throws away its current input. If we consider signals to be functions of time (natural numbers), the behaviour of delay can be described by the following function:

 delay x0 s (t_start,clk) t_sample
   | t_start == t_sample = x0
   | t_start < t_sample  = if clk t_sample
                             then s (t_sample-1)
                             else delay x0 s (t_start (t_sample-1)
   | otherwise           = error "stream doesn't exist yet"

A simple example to create counters operating at different rates using the same generator:

 divisibleBy n x = x `mod` n == 0
 counter = stateful 0 (+1)
 drift = do
   time <- counter
   c1 <- withClock (divisibleBy 2 <$> time) counter
   c2 <- withClock (divisibleBy 3 <$> time) counter
   return ((,) <$> c1 <*> c2)

Note that if you want to slow down the drift system defined above, the naive approach might lead to surprising results:

 slowDrift = do
   time <- counter
   withClock (divisibleBy 2 <$> time) drift

The problem is that the clocks are also slowed down, and their spikes double in length. This may or may not be what you want. To overcome this problem, we can define a clock oblivious edge detector to be used within the definition of drift:

 edge = withClock (pure True) . transfer False (\b b' -> b && not b')
 drift = do
   time <- counter
   t2 <- edge (divisibleBy 2 <$> time)
   t3 <- edge (divisibleBy 3 <$> time)
   c1 <- withClock t2 counter
   c2 <- withClock t3 counter
   return ((,) <$> c1 <*> c2)

This works because the withClock function overrides any clock imposed on the generator from outside.



data Signal a Source

A signal can be thought of as a function of type Nat -> a, where the argument is the sampling time, and the Monad instance agrees with the intuition (bind corresponds to extracting the current sample).


data SignalGen a Source

A signal generator is the only source of stateful signals. It can be thought of as a function of type Nat -> a, where the result is an arbitrary data structure that can potentially contain new signals, and the argument is the creation time of these new signals. It exposes the MonadFix interface, which makes it possible to define signals in terms of each other.



:: SignalGen (Signal a)

the generator of the top-level signal

-> IO (IO a)

the computation to sample the signal

Embedding a signal into an IO environment. Repeated calls to the computation returned cause the whole network to be updated, and the current sample of the top-level signal is produced as a result. This is the only way to extract a signal generator outside the network, and it is equivalent to passing zero to the function representing the generator.



:: a

initial value

-> IO (Signal a, a -> IO ())

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.



:: IO (SignalGen (Signal [a]), a -> IO ())

a generator for the event signal and the associated sink

An event-like signal that can be fed through the sink function returned. The signal carries a list of values fed in since the last sampling, i.e. it is constantly [] if the sink is never invoked. The order of elements is reversed, so the last value passed to the sink is the head of the list. Note that unlike external this function only returns a generator to be used within the expression constructing the top-level stream, and this generator can only be used once.



:: a

initial output at creation time

-> Signal a

the signal to delay

-> SignalGen (Signal a)

the delayed signal

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 can be thought of as the following function (which should also make it clear why the return value is SignalGen):

  delay x0 s t_start t_sample
    | t_start == t_sample = x0
    | t_start < t_sample  = s (t_sample-1)
    | otherwise           = error "Premature sample!"

The way signal generators are extracted ensures that the error can never happen.



:: Signal (SignalGen a)

the signal of generators to run

-> SignalGen (Signal a)

the signal of generated structures

A reactive signal that takes the value to output from a signal generator carried by its input with the sampling time provided as the time of generation. It is possible to create new signals in the monad. It can be thought of as the following function:

  generator g t_start t_sample = g t_sample t_sample

It has to live in the SignalGen monad, because it needs to maintain an internal state to be able to cache the current sample for efficiency reasons. However, this state is not carried between samples, therefore starting time doesn't matter and can be ignored.



:: Signal a

the signal to cache

-> SignalGen (Signal a)

a signal observationally equivalent to the argument

Memoising combinator. It can be used to cache results of applicative combinators in case they are used in several places. It is observationally equivalent to return in the SignalGen monad.



:: Signal Bool

the boolean input signal

-> SignalGen (Signal Bool)

a one-shot signal true only the first time the input is true

A signal that is true exactly once: the first time the input signal is true. Afterwards, it is constantly false, and it holds no reference to the input signal. Note that until always follows the master clock, i.e. the fastest one, therefore it never creates a long spike of True.

withClock :: Signal Bool -> SignalGen a -> SignalGen aSource

Override the clock used in a generator. Note that clocks don't interact unless one is used in the definition of the other, i.e. it is possible to provide a fast clock within a generator with a slow associated clock.



:: a

initial state

-> (a -> a)

state transformation

-> SignalGen (Signal a) 

A pure stateful signal. The initial state is the first output, and every subsequent state is derived from the preceding one by applying a pure transformation. It is equivalent to the following expression:

  stateful x0 f = mfix $ sig -> delay x0 (f <$> sig)



:: a

initial internal state

-> (t -> a -> a)

state updater function

-> Signal t

input signal

-> SignalGen (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 never be observed, and subsequent states are determined by combining the preceding state with the current output of the input signal using the function supplied. It is equivalent to the following expression:

  transfer x0 f s = mfix $ sig -> liftA2 f s <$> delay x0 sig

noise :: MTRandom a => SignalGen (Signal a)Source

A random signal.

getRandom :: MTRandom a => SignalGen aSource

A random source within the SignalGen monad.

debug :: String -> SignalGen ()Source

A printing action within the SignalGen monad.