The class RandomGen provides a common interface to random number generators.

With a source of random number supply in hand, the Random class allows the programmer to extract random values of a variety of types.

Minimal complete definition: randomR and random.

Time is used both for time intervals (duration), and time w.r.t. some agreed reference point in time.

DTime is the time type for lengths of sample intervals. Conceptually, DTime = R+ = { x in R | x > 0 }. Don't assume Time and DTime have the same representation.

Signal function that transforms a signal carrying values of some type a into a signal carrying values of some type b. You can think of it as (Signal a -> Signal b). A signal is, conceptually, a function from Time to value.

A single possible event occurrence, that is, a value that may or may not occur. Events are used to represent values that are not produced continuously, such as mouse clicks (only produced when the mouse is clicked, as opposed to mouse positions, which are always defined).

Lifts a pure function into a signal function (applied pointwise).

Lifts a pure function into a signal function applied to events (applied pointwise).

Identity: identity = arr id

Using identity is preferred over lifting id, since the arrow combinators know how to optimise certain networks based on the transformations being applied.

Identity: constant b = arr (const b)

Using constant is preferred over lifting const, since the arrow combinators know how to optimise certain networks based on the transformations being applied.

Outputs the time passed since the signal function instance was started.

Alternative name for localTime.

Initialization operator (cf. Lustre/Lucid Synchrone).

The output at time zero is the first argument, and from that point on it behaves like the signal function passed as second argument.

Output pre-insert operator.

Insert a sample in the output, and from that point on, behave like the given sf.

Input initialization operator.

The input at time zero is the first argument, and from that point on it behaves like the signal function passed as second argument.

Transform initial output value.

Applies a transformation f only to the first output value at time zero.

Transform initial input value.

Applies a transformation f only to the first input value at time zero.

Override initial value of input signal.

Applies a function point-wise, using the last output as next input. This creates a well-formed loop based on a pure, auxiliary function.

Generic version of sscan, in which the auxiliary function produces an internal accumulator and an "held" output.

Applies a function point-wise, using the last known Just output to form the output, and next input accumulator. If the output is Nothing, the last known accumulators are used. This creates a well-formed loop based on a pure, auxiliary function.

Event source that never occurs.

Event source with a single occurrence at time 0. The value of the event is given by the function argument.

Event source with a single occurrence at or as soon after (local) time q as possible.

Event source with repeated occurrences with interval q. Note: If the interval is too short w.r.t. the sampling intervals, the result will be that events occur at every sample. However, no more than one event results from any sampling interval, thus avoiding an "event backlog" should sampling become more frequent at some later point in time.

Event source with consecutive occurrences at the given intervals. Should more than one event be scheduled to occur in any sampling interval, only the first will in fact occur to avoid an event backlog.

Event source with consecutive occurrences at the given intervals. Should more than one event be scheduled to occur in any sampling interval, the output list will contain all events produced during that interval.

Delay for events. (Consider it a triggered after, hence basic.)

Delay an event by a given delta and catenate events that occur so closely so as to be inseparable.

A rising edge detector. Useful for things like detecting key presses. It is initialised as up, meaning that events occuring at time 0 will not be detected.

A rising edge detector that can be initialized as up (True, meaning that events occurring at time 0 will not be detected) or down (False, meaning that events ocurring at time 0 will be detected).

Like edge, but parameterized on the tag value.

Edge detector particularized for detecting transtitions on a Maybe signal from Nothing to Just.

Edge detector parameterized on the edge detection function and initial state, i.e., the previous input sample. The first argument to the edge detection function is the previous sample, the second the current one.

Convert a maybe value into a event (Event is isomorphic to Maybe).

Suppression of initial (at local time 0) event.

Suppress all but the first event.

Suppress all but the first n events.

Suppress first n events.

Make the NoEvent constructor available. Useful e.g. for initialization, ((-->) & friends), and it's easily available anyway (e.g. mergeEvents []).

Suppress any event in the first component of a pair.

Suppress any event in the second component of a pair.

An event-based version of the maybe function.

Extract the value from an event. Fails if there is no event.

Tests whether the input represents an actual event.

Negation of isEvent.

Tags an (occurring) event with a value ("replacing" the old value).

Applicative-based definition: tag = ($>)

Tags an (occurring) event with a value ("replacing" the old value). Same as tag with the arguments swapped.

Applicative-based definition: tagWith = (<$)

Attaches an extra value to the value of an occurring event.

Left-biased event merge (always prefer left event, if present).

Right-biased event merge (always prefer right event, if present).

Unbiased event merge: simultaneous occurrence is an error.

Event merge parameterized by a conflict resolution function.

Applicative-based definition: mergeBy f le re = (f $ le * re) | le | re

A generic event merge-map utility that maps event occurrences, merging the results. The first three arguments are mapping functions, the third of which will only be used when both events are present. Therefore, mergeBy = mapMerge id id

Applicative-based definition: mapMerge lf rf lrf le re = (f $ le * re) | (lf $ le) | (rf $ re)

Merge a list of events; foremost event has priority.

Foldable-based definition: mergeEvents :: Foldable t => t (Event a) -> Event a mergeEvents = asum

Collect simultaneous event occurrences; no event if none.

Traverable-based definition: catEvents :: Foldable t => t (Event a) -> Event (t a) carEvents e = if (null e) then NoEvent else (sequenceA e)

Join (conjunction) of two events. Only produces an event if both events exist.

Applicative-based definition: joinE = liftA2 (,)

Split event carrying pairs into two events.

Filter out events that don't satisfy some predicate.

Combined event mapping and filtering. Note: since Event is a Functor, see fmap for a simpler version of this function with no filtering.

Enable/disable event occurences based on an external condition.

Basic switch.

By default, the first signal function is applied. Whenever the second value in the pair actually is an event, the value carried by the event is used to obtain a new signal function to be applied *at that time and at future times*. Until that happens, the first value in the pair is produced in the output signal.

Important note: at the time of switching, the second signal function is applied immediately. If that second SF can also switch at time zero, then a double (nested) switch might take place. If the second SF refers to the first one, the switch might take place infinitely many times and never be resolved.

Remember: The continuation is evaluated strictly at the time of switching!

Switch with delayed observation.

By default, the first signal function is applied.

Whenever the second value in the pair actually is an event, the value carried by the event is used to obtain a new signal function to be applied *at future times*.

Until that happens, the first value in the pair is produced in the output signal.

Important note: at the time of switching, the second signal function is used immediately, but the current input is fed by it (even though the actual output signal value at time 0 is discarded).

If that second SF can also switch at time zero, then a double (nested) -- switch might take place. If the second SF refers to the first one, the switch might take place infinitely many times and never be resolved.

Remember: The continuation is evaluated strictly at the time of switching!

Recurring switch.

Uses the given SF until an event comes in the input, in which case the SF in the event is turned on, until the next event comes in the input, and so on.

See https://wiki.haskell.org/Yampa#Switches for more information on how this switch works.

Recurring switch with delayed observation.

Uses the given SF until an event comes in the input, in which case the SF in the event is turned on, until the next event comes in the input, and so on.

Uses decoupled switch (dSwitch).

See https://wiki.haskell.org/Yampa#Switches for more information on how this switch works.

Call-with-current-continuation switch.

Applies the first SF until the input signal and the output signal, when passed to the second SF, produce an event, in which case the original SF and the event are used to build an new SF to switch into.

See https://wiki.haskell.org/Yampa#Switches for more information on how this switch works.

kSwitch with delayed observation.

Applies the first SF until the input signal and the output signal, when passed to the second SF, produce an event, in which case the original SF and the event are used to build an new SF to switch into.

The switch is decoupled (dSwitch).

See https://wiki.haskell.org/Yampa#Switches for more information on how this switch works.

Spatial parallel composition of a signal function collection. Given a collection of signal functions, it returns a signal function that broadcasts its input signal to every element of the collection, to return a signal carrying a collection of outputs. See par.

For more information on how parallel composition works, check http://haskell.cs.yale.edu/wp-content/uploads/2011/01/yampa-arcade.pdf

Parallel switch (dynamic collection of signal functions spatially composed in parallel) with broadcasting. See pSwitch.

For more information on how parallel composition works, check http://haskell.cs.yale.edu/wp-content/uploads/2011/01/yampa-arcade.pdf

Decoupled parallel switch with broadcasting (dynamic collection of signal functions spatially composed in parallel). See dpSwitch.

For more information on how parallel composition works, check http://haskell.cs.yale.edu/wp-content/uploads/2011/01/yampa-arcade.pdf

Recurring parallel switch with broadcasting.

Uses the given collection of SFs, until an event comes in the input, in which case the function in the Event is used to transform the collections of SF to be used with rpSwitch again, until the next event comes in the input, and so on.

Broadcasting is used to decide which subpart of the input goes to each SF in the collection.

See rpSwitch.

For more information on how parallel composition works, check http://haskell.cs.yale.edu/wp-content/uploads/2011/01/yampa-arcade.pdf

Decoupled recurring parallel switch with broadcasting.

Uses the given collection of SFs, until an event comes in the input, in which case the function in the Event is used to transform the collections of SF to be used with rpSwitch again, until the next event comes in the input, and so on.

Broadcasting is used to decide which subpart of the input goes to each SF in the collection.

This is the decoupled version of rpSwitchB.

For more information on how parallel composition works, check http://haskell.cs.yale.edu/wp-content/uploads/2011/01/yampa-arcade.pdf

Spatial parallel composition of a signal function collection parameterized on the routing function.

Parallel switch parameterized on the routing function. This is the most general switch from which all other (non-delayed) switches in principle can be derived. The signal function collection is spatially composed in parallel and run until the event signal function has an occurrence. Once the switching event occurs, all signal function are "frozen" and their continuations are passed to the continuation function, along with the event value.

Parallel switch with delayed observation parameterized on the routing function.

The collection argument to the function invoked on the switching event is of particular interest: it captures the continuations of the signal functions running in the collection maintained by dpSwitch at the time of the switching event, thus making it possible to preserve their state across a switch. Since the continuations are plain, ordinary signal functions, they can be resumed, discarded, stored, or combined with other signal functions.

Recurring parallel switch parameterized on the routing function.

Uses the given collection of SFs, until an event comes in the input, in which case the function in the Event is used to transform the collections of SF to be used with rpSwitch again, until the next event comes in the input, and so on.

The routing function is used to decide which subpart of the input goes to each SF in the collection.

This is the parallel version of rSwitch.

Recurring parallel switch with delayed observation parameterized on the routing function.

Uses the given collection of SFs, until an event comes in the input, in which case the function in the Event is used to transform the collections of SF to be used with rpSwitch again, until the next event comes in the input, and so on.

The routing function is used to decide which subpart of the input goes to each SF in the collection.

This is the parallel version of drSwitch.

Zero-order hold.

Converts a discrete-time signal into a continuous-time signal, by holding the last value until it changes in the input signal. The given parameter may be used for time zero, and until the first event occurs in the input signal, so hold is always well-initialized.

>>> embed (hold 1) (deltaEncode 0.1 [NoEvent, NoEvent, Event 2, NoEvent, Event 3, NoEvent])
[1,1,2,2,3,3]

Zero-order hold with a delay.

Converts a discrete-time signal into a continuous-time signal, by holding the last value until it changes in the input signal. The given parameter is used for time zero (until the first event occurs in the input signal), so dHold shifts the discrete input by an infinitesimal delay.

>>> embed (dHold 1) (deltaEncode 0.1 [NoEvent, NoEvent, Event 2, NoEvent, Event 3, NoEvent])
[1,1,1,2,2,3]

Tracks input signal when available, holding the last value when the input is Nothing.

This behaves similarly to hold, but there is a conceptual difference, as it takes a signal of input Maybe a (for some a) and not Event.

>>> embed (trackAndHold 1) (deltaEncode 0.1 [Nothing, Nothing, Just 2, Nothing, Just 3, Nothing])
[1,1,2,2,3,3]

Given an initial value in an accumulator, it returns a signal function that processes an event carrying transformation functions. Every time an Event is received, the function inside it is applied to the accumulator, whose new value is outputted in an Event.

Zero-order hold accumulator (always produces the last outputted value until an event arrives).

Zero-order hold accumulator with delayed initialization (always produces the last outputted value until an event arrives, but the very initial output is always the given accumulator).

Accumulator parameterized by the accumulation function.

Zero-order hold accumulator parameterized by the accumulation function.

Zero-order hold accumulator parameterized by the accumulation function with delayed initialization (initial output sample is always the given accumulator).

Accumulator parameterized by the accumulator function with filtering, possibly discarding some of the input events based on whether the second component of the result of applying the accumulation function is Nothing or Just x for some x.

Uninitialized delay operator.

The output has an infinitesimal delay (1 sample), and the value at time zero is undefined.

Initialized delay operator.

Creates an SF that delays the input signal, introducing an infinitesimal delay (one sample), using the given argument to fill in the initial output at time zero.

Delay a signal by a fixed time t, using the second parameter to fill in the initial t seconds.

Given a value in an accumulator (b), a predicate signal function (sfC), and a second signal function (sf), pause will produce the accumulator b if sfC input is True, and will transform the signal using sf otherwise. It acts as a pause with an accumulator for the moments when the transformation is paused.

Loop with an initial value for the signal being fed back.

Loop by integrating the second value in the pair and feeding the result back. Because the integral at time 0 is zero, this is always well defined.

Integration using the rectangle rule.

"Immediate" integration (using the function's value at the current time)

Integrate the first input signal and add the discrete accumulation (sum) of the second, discrete, input signal.

Count the occurrences of input events.

>>> embed count (deltaEncode 1 [Event 'a', NoEvent, Event 'b'])
[Event 1,NoEvent,Event 2]

A very crude version of a derivative. It simply divides the value difference by the time difference. Use at your own risk.

Integrate using an auxiliary function that takes the current and the last input, the time between those samples, and the last output, and returns a new output.

Noise (random signal) with default range for type in question; based on "randoms".

Noise (random signal) with specified range; based on "randomRs".

Stochastic event source with events occurring on average once every t_avg seconds. However, no more than one event results from any one sampling interval in the case of relatively sparse sampling, thus avoiding an "event backlog" should sampling become more frequent at some later point in time.

Convenience function to run a signal function indefinitely, using a IO actions to obtain new input and process the output.

This function first runs the initialization action, which provides the initial input for the signal transformer at time 0.

Afterwards, an input sensing action is used to obtain new input (if any) and the time since the last iteration. The argument to the input sensing function indicates if it can block. If no new input is received, it is assumed to be the same as in the last iteration.

After applying the signal function to the input, the actuation IO action is executed. The first argument indicates if the output has changed, the second gives the actual output). Actuation functions may choose to ignore the first argument altogether. This action should return True if the reactimation must stop, and False if it should continue.

Note that this becomes the program's main loop, which makes using this function incompatible with GLUT, Gtk and other graphics libraries. It may also impose a sizeable constraint in larger projects in which different subparts run at different time steps. If you need to control the main loop yourself for these or other reasons, use reactInit and react.

A reference to reactimate's state, maintained across samples.

Initialize a top-level reaction handle.

Process a single input sample.

Given a signal function and a pair with an initial input sample for the input signal, and a list of sampling times, possibly with new input samples at those times, it produces a list of output samples.

This is a simplified, purely-functional version of reactimate.

Synchronous embedding. The embedded signal function is run on the supplied input and time stream at a given (but variable) ratio >= 0 to the outer time flow. When the ratio is 0, the embedded signal function is paused.

Spaces a list of samples by a fixed time delta, avoiding unnecessary samples when the input has not changed since the last sample.

deltaEncode parameterized by the equality test.

Reverse function composition

Duplicate an input.