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 two phases: evaluation and
finalisation. During evaluation, each signal affected is sampled at
the current point of time (sample
), advanced by the desired time
(advance
), and both of these pieces of data are stored in its
reference. If the value of a signal is requested multiple times, the
sample is simply reused, and no further aging is performed. After
successfully sampling the top-level signal, 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 done by the signalValue
function, 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.
- type Time = Double
- type DTime = Double
- type Sink a = a -> IO ()
- newtype Signal a = S (IORef (SignalTrans a))
- data SignalTrans a
- = Ready (SignalNode a)
- | Sampling (SignalNode a)
- | Sample a
- | Aged a (SignalNode a)
- data SignalNode a
- = SNK a
- | SNS a (DTime -> a -> a)
- | forall t . SNT (Signal t) a (DTime -> t -> a -> a)
- | forall t . SNA (Signal (t -> a)) (Signal t)
- | SNE (Signal a) (Signal Bool) (Signal (Signal a))
- | SNR (IORef a)
- | forall t . SNL1 (t -> a) (Signal t)
- | forall t1 t2 . SNL2 (t1 -> t2 -> a) (Signal t1) (Signal t2)
- | forall t1 t2 t3 . SNL3 (t1 -> t2 -> t3 -> a) (Signal t1) (Signal t2) (Signal t3)
- | forall t1 t2 t3 t4 . SNL4 (t1 -> t2 -> t3 -> t4 -> a) (Signal t1) (Signal t2) (Signal t3) (Signal t4)
- | forall t1 t2 t3 t4 t5 . SNL5 (t1 -> t2 -> t3 -> t4 -> t5 -> a) (Signal t1) (Signal t2) (Signal t3) (Signal t4) (Signal t5)
- debugLog :: String -> IO a -> IO a
- createSignal :: SignalNode a -> Signal a
- signalValue :: forall a. Signal a -> DTime -> IO a
- commit :: forall a. Signal a -> IO ()
- advance :: SignalNode a -> a -> DTime -> IO (SignalNode a)
- sample :: SignalNode a -> DTime -> IO a
- sampleDelayed :: SignalNode a -> DTime -> IO a
- superstep :: Signal a -> DTime -> IO a
- stateful :: a -> (DTime -> a -> a) -> Signal a
- transfer :: a -> (DTime -> t -> a -> a) -> Signal t -> Signal a
- latcher :: Signal a -> Signal Bool -> Signal (Signal a) -> Signal a
- external :: a -> IO (Signal a, Sink a)
Implementation
Some type synonyms
The data structures behind signals
A signal is represented as a transactional structural node.
S (IORef (SignalTrans a)) |
Functor Signal | |
Applicative Signal | The |
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 |
data SignalTrans a Source
A node can have four states that distinguish various stages of sampling and aging.
Ready (SignalNode a) |
|
Sampling (SignalNode a) |
|
Sample a |
|
Aged a (SignalNode a) |
|
data SignalNode a Source
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
.
SNK a |
|
SNS a (DTime -> a -> a) |
|
forall t . SNT (Signal t) a (DTime -> t -> a -> a) |
|
forall t . SNA (Signal (t -> a)) (Signal t) |
|
SNE (Signal a) (Signal Bool) (Signal (Signal a)) |
|
SNR (IORef a) |
|
forall t . SNL1 (t -> a) (Signal t) |
|
forall t1 t2 . SNL2 (t1 -> t2 -> a) (Signal t1) (Signal t2) |
|
forall t1 t2 t3 . SNL3 (t1 -> t2 -> t3 -> a) (Signal t1) (Signal t2) (Signal t3) |
|
forall t1 t2 t3 t4 . SNL4 (t1 -> t2 -> t3 -> t4 -> a) (Signal t1) (Signal t2) (Signal t3) (Signal t4) |
|
forall t1 t2 t3 t4 t5 . SNL5 (t1 -> t2 -> t3 -> t4 -> t5 -> a) (Signal t1) (Signal t2) (Signal t3) (Signal t4) (Signal t5) |
|
debugLog :: String -> IO a -> IO aSource
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 aSource
This function is really just a shorthand to create a reference to a given node.
signalValue :: forall a. Signal a -> DTime -> IO aSource
Sampling and aging 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.
advance :: SignalNode a -> a -> DTime -> IO (SignalNode a)Source
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 aSource
sampleDelayed :: SignalNode a -> DTime -> IO aSource
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
:: 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.
A pure stateful signal. The initial state is the first output.
:: 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.
:: Signal a |
|
-> Signal Bool |
|
-> Signal (Signal a) |
|
-> 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!).