Event a represents a stream of events as they occur in time. Semantically, you can think of Event a as an infinite list of values that are tagged with their corresponding time of occurence,

type Event a = [(Time,a)]

Behavior a represents a value that varies in time. Think of it as

type Behavior a = Time -> a

An event handler is a function that takes an event value and performs some computation.

Create a new event. Also returns a function that triggers an event occurrence.

Register an event Handler for an Event. All registered handlers will be called whenever the event occurs.

When registering an event handler, you will also be given an action that unregisters this handler again.

do unregisterMyHandler <- register event myHandler

FIXME: Unregistering event handlers does not work yet.

Read the current value of a Behavior.

Event that never occurs. Think of it as never = [].

Return all event occurrences that are Just values, discard the rest. Think of it as

filterJust es = [(time,a) | (time,Just a) <- es]

Merge two event streams of the same type. In case of simultaneous occurrences, the event values are combined with the binary function. Think of it as

unionWith f ((timex,x):xs) ((timey,y):ys)
   | timex == timey = (timex,f x y) : unionWith f xs ys
   | timex <  timey = (timex,x)     : unionWith f xs ((timey,y):ys)
   | timex >  timey = (timey,y)     : unionWith f ((timex,x):xs) ys

The accumE function accumulates a stream of events. Example:

accumE "x" [(time1,(++"y")),(time2,(++"z"))]
   = return [(time1,"xy"),(time2,"xyz")]

Note that the output events are simultaneous with the input events, there is no "delay" like in the case of accumB.

Apply a time-varying function to a stream of events. Think of it as

apply bf ex = [(time, bf time x) | (time, x) <- ex]

Construct a time-varying function from an initial value and a stream of new values. Think of it as

stepper x0 ex = return $ \time ->
    last (x0 : [x | (timex,x) <- ex, timex < time])

Note that the smaller-than-sign in the comparison timex < time means that the value of the behavior changes "slightly after" the event occurrences. This allows for recursive definitions.

Infix synonym for apply, similar to <*>.

Variant of apply similar to <*

Return all event occurrences that fulfill the predicate, discard the rest.

Return all event occurrences that fulfill the time-varying predicate, discard the rest. Generalization of filterE.

Return event occurrences only when the behavior is True. Variant of filterApply.

Split event occurrences according to a tag. The Left values go into the left component while the Right values go into the right component of the result.

Collect simultaneous event occurrences in a list.

Apply a list of functions in succession. Useful in conjunction with unions.

concatenate [f,g,h] = f . g . h

The accumB function is similar to a strict left fold, foldl'. It starts with an initial value and combines it with incoming events. For example, think

accumB "x" [(time1,(++"y")),(time2,(++"z"))]
   = stepper "x" [(time1,"xy"),(time2,"xyz")]

Note that the value of the behavior changes "slightly after" the events occur. This allows for recursive definitions.

Efficient combination of accumE and accumB.

Data type representing a behavior (facts) and suggestions to change it (rumors).

Smart constructor. Combine facts and rumors into Tidings.

Register an event Handler for a Behavior. All registered handlers will be called whenever the behavior changes.

However, note that this is only an approximation, as behaviors may change continuously. Consequently, handlers should be idempotent.

Create a series of events with delayed initialization.

For each name, the initialization handler will be called exactly once when the event is first "brought to life", e.g. when an event handler is registered to it.