The type of discrete signals.

A discrete signal is a sequence of values assigned to discrete times. A pair of a time and a corresponding value is called an occurrence. You can think of DSignal era val as being equivalent to Map (Time era) val where Time era is the type of all times of the given era. However, an occurence at the starting time of the era is not possible. In contrast to Map, a discrete signal may cover infinitely many values.

Discrete signals can describe sequences of events. For example, the sequence of all key presses could be described by a discrete signal of characters. Discrete signals are also used in conjunction with sampling.

The discrete signal instances of Functor and Monoid provide the following method definitions:

       fmap    = map
       mempty  = empty
       mappend = union
       mconcat = unions
       

A signal with no occurrences.

Constructs the left-biased union of two discrete signals.

union is equivalent to unionWith const.

Constructs the union of two discrete signals, combining simultaneously occuring values via a combining function.

unionWith is equivalent to transUnion id id.

Union with conversion and combination.

At each time, a signal dSignal1 or a signal dSignal2 has an occurence, the signal

       transUnion conv1 conv2 comb dSignal1 dSignal2
       

has an occurence, too. The value of this occurence is formed as follows:

conv1 val1

if dSignal1 has an occurence of value val1 and dSignal2 has no occurence

conv2 val2

if dSignal2 has an occurence of value val2 and dSignal1 has no occurence

comb val1 val2

if dSignal1 has an occurence of value val1 and dSignal2 has an occurence of value val2

Repeated left-biased union.

unions is equivalent to foldl union empty and unionsWith const.

Repeated union with a combining function.

unionsWith comb is equivalent to foldl (unionWith comb) empty.

Constructs the difference of two discrete signals.

difference is equivalent to differenceWith (\_ _ -> Nothing).

Constructs a kind of difference of two discrete signals where occurences may be modified instead of being dropped.

At each time, a signal dSignal1 has an occurence of a value val1, the signal differenceWith comb dSignal1 dSignal has

an occurence of val1

if dSignal2 has no occurence

an occurence of val'

if dSignal2 has an occurence of a value val2 and comb val1 val2 = Just val'

no occurence

if dSignal2 has an occurence of a value val2 and comb val1 val2 = Nothing

Constructs the left-biased intersection of two discrete signals.

intersection is equivalent to intersectionWith const.

Constructs the intersection of two discrete signals, combining values via a combining function.

Converts each value occuring in a discrete signal by applying a function to it.

Drops all occurence of a discrete signal whose values do not fulfill a given predicate.

Converts all occurences with values of the form Just val into occurences with value val and drops all occurences with value Nothing.

The combination of map and catMaybes.

mapMaybe fun is equivalent to catMaybes . map fun.

Accumulates the values of a discrete signal, starting with a given initial value.

Applying scan init fun to a discrete signal replaces its occurence values val_1, val_2 and so on by the values init `fun` val_1, (init `fun` val_1) `fun` val_2 and so on.

Accumulates the values of a discrete signal, starting with the first occuring value.

Applying scan1 init fun to a discrete signal replaces its occurence values val_1, val_2, val_3 and so on by the values val_1, val_1 `fun` val_2, (val_1 `fun` val_2) `fun` val_3 and so on.

Constructs a discrete signal by repeatedly applying state transformers.

Applying stateful init to a discrete signal replaces its occurence values trans_1, trans_2, trans_3 and so on by the values fst . trans_1 $ init, fst . trans_2 $ snd . trans_1 $ init, fst . trans_3 $ snd . trans_2 $ snd . trans_1 $ init and so on.

Converts an event handler into a discrete signal consumer.

If a discrete signal is consumed with such a consumer, the handler is called at each occurence with the occuring value as its argument.

Converts an event handler registration into a discrete signal producer.

Applying the argument of producer to an event handler has to yield a setup which makes the handler be called with a certain value everytime the produced signal shall have an occurence of this value.