Portability | Haskell 98 |
---|---|

Stability | stable |

Maintainer | haskell@henning-thielemann.de |

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.

- data 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))
- 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 :: Num time => T time body -> time
- mapBody :: (body0 -> body1) -> T time body0 -> T time body1
- mapTime :: (time0 -> time1) -> T time0 body -> 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
- mergeBy :: C time => (body -> body -> Bool) -> T time body -> T time body -> T time body
- insert :: (C time, Ord body) => time -> body -> T time body -> T time body
- insertBy :: (C time, Ord body) => (body -> body -> Bool) -> time -> body -> T time body -> T time body
- decreaseStart :: C time => time -> T time body -> T time body
- delay :: C time => time -> T time body -> T time body
- filter :: Num time => (body -> Bool) -> T time body -> T time body
- partition :: Num time => (body -> Bool) -> T time body -> (T time body, T time body)
- slice :: (Eq a, Num time) => (body -> a) -> T time body -> [(a, T time body)]
- span :: (body -> Bool) -> T time body -> (T time body, T time body)
- mapMaybe :: Num time => (body0 -> Maybe body1) -> T time body0 -> T time body1
- catMaybes :: Num time => T time (Maybe body) -> T time body
- normalize :: (C time, Ord body) => T time body -> T time body
- isNormalized :: (C time, Ord body) => T time body -> Bool
- collectCoincident :: C time => T time body -> T time [body]
- flatten :: C time => T time [body] -> T time body
- mapCoincident :: C time => ([a] -> [b]) -> T time a -> T time b
- 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
- 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
- fromAbsoluteEventList :: Num time => T time body -> T time body

# Documentation

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

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

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

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

The first important function is `merge`

which merges the events of two lists into a new time order list.

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

Note that `merge`

compares entire events rather than just start
times. This is to ensure that it is commutative, a desirable
condition for some of the proofs used in secref{equivalence}.
It is also necessary to assert a unique representation
of the performance independent of the structure of the 'Music.T note'.
The same function for inserting into a time ordered list with a trailing pause.
The strictness annotation is necessary for working with infinite lists.

Here are two other functions that are already known for non-padded time lists.

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

The final critical function is `insert`

,
which inserts an event
into an already time-ordered sequence of events.
For instance it is used in MidiFiles to insert a `NoteOff`

event
into a list of `NoteOn`

and `NoteOff`

events.

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

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

filter :: Num time => (body -> Bool) -> T time body -> T time bodySource

The function `partition`

is somehow the inverse to `merge`

.
It is similar to `partition`

.
We could use the List function if the event times would be absolute,
because then the events need not to be altered on splits.
But absolute time points can't be used for infinite music
thus we take the burden of adapting the time differences
when an event is removed from the performance list and
put to the list of events of a particular instrument.
`t0`

is the time gone since the last event in the first partition,
`t1`

is the time gone since the last event in the second partition.

Note, that using `Data.EventList.Utility.mapPair`

we circumvent the following problem:
Since the recursive call to `partition`

may end up with Bottom,
pattern matching with, say expression{(es0,es1)},
will halt the bounding of the variables
until the most inner call to `partition`

is finished.
This never happens.
If the pair constructor is made strict,
that is we write expression{~(es0,es1)},
then everything works.
Also avoiding pattern matching and
using `fst`

and `snd`

would help.

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

Since we need it later for MIDI generation, we will also define a slicing into equivalence classes of events.

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

We will also sometimes need a function which groups events by equal start times. This implementation is not so obvious since we work with time differences. The criterion is: Two neighbouring events start at the same time if the second one has zero time difference.

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

Apply a function to the lists of coincident events.

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

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 `Control.Monad.State.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.

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

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 bodySource