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

Stability | stable |

Maintainer | haskell@henning-thielemann.de |

- 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)
- merge :: (Ord time, Ord body) => T time body -> T time body -> T time body
- mergeBy :: Ord time => (body -> body -> Bool) -> T time body -> T time body -> T time body
- insert :: (Ord time, Ord body) => time -> body -> T time body -> T time body
- insertBy :: Ord time => (body -> body -> Bool) -> time -> body -> T time body -> T time body
- decreaseStart :: (Ord time, Num time) => time -> T time body -> T time body
- delay :: (Ord time, Num time) => time -> T time body -> T time body
- filter :: Num time => (body -> Bool) -> T time body -> T time body
- partition :: (body -> Bool) -> T time body -> (T time body, T time body)
- slice :: Eq a => (body -> a) -> T time body -> [(a, T time body)]
- foldr :: (time -> a -> b) -> (body -> b -> a) -> b -> T time body -> b
- foldrPair :: (time -> body -> a -> a) -> a -> T time body -> a
- mapMaybe :: Num time => (body0 -> Maybe body1) -> T time body0 -> T time body1
- catMaybes :: Num time => T time (Maybe body) -> T time body
- normalize :: (Ord time, Num time, Ord body) => T time body -> T time body
- isNormalized :: (Ord time, Num time, Ord body) => T time body -> Bool
- collectCoincident :: Eq time => T time body -> T time [body]
- flatten :: (Ord time, Num time) => T time [body] -> T time body
- mapCoincident :: (Ord time, Num time) => ([a] -> [b]) -> T time a -> T time b
- append :: (Ord time, Num time) => T time body -> T time body -> T time body
- concat :: (Ord time, Num time) => [T time body] -> T time body
- cycle :: (Ord time, Num time) => T time body -> T time body
- discretize :: (RealFrac time, Integral i) => T time body -> T i body
- resample :: (RealFrac time, Integral i) => time -> T time body -> T i body
- checkTimes :: Ord time => T time body -> T time body
- collectCoincidentFoldr :: Eq time => T time body -> T time [body]
- collectCoincidentNonLazy :: Eq time => T time body -> T time [body]

# Documentation

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

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

duration :: Num time => T time body -> timeSource

Duration of an empty event list is considered zero. However, I'm not sure if this is sound.

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

merge :: (Ord 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 :: Ord 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 :: (Ord 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.

slice :: Eq a => (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 :: Eq 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 :: (Ord time, Num time) => ([a] -> [b]) -> T time a -> T time bSource

Apply a function to the lists of coincident events.

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

Here are some functions 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 a note
the function `discretizeEventM`

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.

checkTimes :: Ord time => T time body -> T time bodySource

collectCoincidentFoldr :: Eq time => T time body -> T time [body]Source

collectCoincidentNonLazy :: Eq time => T time body -> T time [body]Source

Will fail on infinite lists.