Data.EventList.Relative.TimeBody

Event lists starting with a time difference and ending with a body.

The time is stored in differences between the events. Thus there is no increase of time information for long, or even infinite, streams of events. Further on, the time difference is stored in the latter of two neighbouring events. This is necessary for real-time computing where it is not known whether and when the next event happens.

Documentation

data T time body

Instances

Functor (T time)

Foldable (T time)

Traversable (T time)

(Eq time, Eq body) => Eq (T time body)

(Ord time, Ord body) => Ord (T time body)

(Show time, Show body) => Show (T time body)

(Arbitrary time, Arbitrary body) => Arbitrary (T time body)

Monoid (T time body)

empty :: T time body

singleton :: time -> body -> T time body

null :: T time body -> Bool

viewL :: T time body -> Maybe ((time, body), T time body)

viewR :: T time body -> Maybe (T time body, (time, body))

switchL :: c -> ((time, body) -> T time body -> c) -> T time body -> c

switchR :: c -> (T time body -> (time, body) -> c) -> T time body -> c

cons :: time -> body -> T time body -> T time body

snoc :: T time body -> time -> body -> T time body

fromPairList :: [(a, b)] -> T a b

toPairList :: T a b -> [(a, b)]

getTimes :: T time body -> [time]

getBodies :: T time body -> [body]

duration :: C time => T time body -> time

mapBody :: (body0 -> body1) -> T time body0 -> T time body1

mapTime :: (time0 -> time1) -> T time0 body -> T time1 body

zipWithBody :: (body0 -> body1 -> body2) -> [body0] -> T time body1 -> T time body2

zipWithTime :: (time0 -> time1 -> time2) -> [time0] -> T time1 body -> T time2 body

unzip :: T time (body0, body1) -> (T time body0, T time body1)

concatMapMonoid :: Monoid m => (time -> m) -> (body -> m) -> T time body -> m

traverse :: Applicative m => (time0 -> m time1) -> (body0 -> m body1) -> T time0 body0 -> m (T time1 body1)

traverse_ :: Applicative m => (time -> m ()) -> (body -> m ()) -> T time body -> m ()

traverseBody :: Applicative m => (body0 -> m body1) -> T time body0 -> m (T time body1)

traverseTime :: Applicative m => (time0 -> m time1) -> T time0 body -> m (T time1 body)

mapM :: Monad m => (time0 -> m time1) -> (body0 -> m body1) -> T time0 body0 -> m (T time1 body1)

mapM_ :: Monad m => (time -> m ()) -> (body -> m ()) -> T time body -> m ()

mapBodyM :: Monad m => (body0 -> m body1) -> T time body0 -> m (T time body1)

mapTimeM :: Monad m => (time0 -> m time1) -> T time0 body -> m (T time1 body)

foldr :: (time -> a -> b) -> (body -> b -> a) -> b -> T time body -> b

foldrPair :: (time -> body -> a -> a) -> a -> T time body -> a

merge :: (C time, Ord body) => T time body -> T time body -> T time body

This function merges the events of two lists into a new event list. Note that merge compares entire events rather than just start times. This is to ensure that it is commutative, one of the properties we test for.

mergeBy :: C time => (body -> body -> Bool) -> T time body -> T time body -> T time body

mergeBy is like merge but does not simply use the methods of the Ord class but allows a custom comparison function. If in event lists xs and ys there are coinciding elements x and y, and cmp x y is True, then x comes before y in mergeBy cmp xs ys.

EventList> EventList.mergeBy (\_ _ -> True) (0 /. 'a' ./ empty) (0 /. 'b' ./ empty)
0 /. 'a' ./ 0 /. 'b' ./ empty

EventList> EventList.mergeBy (\_ _ -> False) (0 /. 'a' ./ empty) (0 /. 'b' ./ empty)
0 /. 'b' ./ 0 /. 'a' ./ empty

insert :: (C time, Ord body) => time -> body -> T time body -> T time body

insert inserts an event into an event list at the given time.

insertBy :: C time => (body -> body -> Bool) -> time -> body -> T time body -> T time body

moveForward :: (Ord time, Num time) => T time (time, body) -> T time body

Move events towards the front of the event list. You must make sure, that no event is moved before time zero. This works only for finite lists.

decreaseStart :: C time => time -> T time body -> T time body

delay :: C time => time -> T time body -> T time body

filter :: C time => (body -> Bool) -> T time body -> T time body

Keep only events that match a predicate while preserving absolute times.

partition :: C time => (body -> Bool) -> T time body -> (T time body, T time body)

partitionMaybe :: C time => (body0 -> Maybe body1) -> T time body0 -> (T time body1, T time body0)

slice :: (Eq a, C time) => (body -> a) -> T time body -> [(a, T time body)]

Using a classification function we splice the event list into lists, each containing the same class. Absolute time stamps are preserved.

span :: (body -> Bool) -> T time body -> (T time body, T time body)

mapMaybe :: C time => (body0 -> Maybe body1) -> T time body0 -> T time body1

catMaybes :: C time => T time (Maybe body) -> T time body

Adds times in a left-associative fashion. Use this if the time is a strict data type.

normalize :: (C time, Ord body) => T time body -> T time body

sort sorts a list of coinciding events, that is all events but the first one have time difference 0. normalize sorts all coinciding events in a list thus yielding a canonical representation of a time ordered list.

isNormalized :: (C time, Ord body) => T time body -> Bool

collectCoincident :: C time => T time body -> T time [body]

Group events that have equal start times (that is zero time differences).

flatten :: C time => T time [body] -> T time body

Reverse to collectCoincident: Turn each body into a separate event.

  xs  ==  flatten (collectCoincident xs)

mapCoincident :: C time => ([a] -> [b]) -> T time a -> T time b

Apply a function to the lists of coincident events.

append :: T time body -> T time body -> T time body

concat :: [T time body] -> T time body

cycle :: T time body -> T time body

discretize :: (C time, RealFrac time, C i, Integral i) => T time body -> T i body

We provide discretize and resample for discretizing the time information. When converting the precise relative event times to the integer relative event times we have to prevent accumulation of rounding errors. We avoid this problem with a stateful conversion which remembers each rounding error we make. This rounding error is used to correct the next rounding. Given the relative time and duration of an event the function floorDiff creates a State which computes the rounded relative time. It is corrected by previous rounding errors.

The resulting event list may have differing time differences which were equal before discretization, but the overall timing is uniformly close to the original.

We use floorDiff rather than roundDiff in order to compute exclusively with non-negative numbers.

resample :: (C time, RealFrac time, C i, Integral i) => time -> T time body -> T i body

toAbsoluteEventList :: Num time => time -> T time body -> T time body

We tried hard to compute everything with respect to relative times. However sometimes we need absolute time values.

fromAbsoluteEventList :: Num time => T time body -> T time body

toAbsoluteEventListGen :: (absTime -> relTime -> absTime) -> absTime -> T relTime body -> T absTime body

Convert from relative time stamps to absolute time stamps using a custom accumulator function (like (+)).

fromAbsoluteEventListGen :: (absTime -> absTime -> relTime) -> absTime -> T absTime body -> T relTime body

Convert from absolute time stamps to relative time stamps using custom subtraction (like (-)) and zero.