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

Stability | stable |

Maintainer | haskell@henning-thielemann.de |

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

- data T time body
- 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, [time0]) -> T time1 body -> T time2 body
- 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)
- getTimes :: T time body -> [time]
- getBodies :: T time body -> [body]
- duration :: Num time => T time body -> time
- 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
- pad :: C time => time -> T time body -> T time body
- moveForward :: C time => T time (time, body) -> T time body
- moveForwardRestricted :: (Ord body, C time) => time -> T time (time, body) -> T time body
- moveBackward :: C time => T time (time, body) -> T time body
- arrange :: (Ord body, C time) => T time (T time body) -> T time body
- arrangeBy :: C time => (body -> body -> Bool) -> T time (T time body) -> T time body
- moveForwardRestrictedBy :: C time => (body -> body -> Bool) -> time -> T time (time, body) -> T time body
- moveForwardRestrictedByQueue :: C time => (body -> body -> Bool) -> time -> T time (time, body) -> T time body
- moveForwardRestrictedByStrict :: C time => (body -> body -> Bool) -> time -> T time (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)
- partitionMaybe :: Num time => (body0 -> Maybe body1) -> T time body0 -> (T time body1, T time body0)
- partitionMaybeR :: Num time => (body0 -> Maybe body1) -> T time body0 -> (T time body1, T time body0)
- slice :: (Eq a, Num time) => (body -> a) -> T time body -> [(a, T time body)]
- foldr :: (time -> a -> b) -> (body -> b -> a) -> a -> T time body -> b
- foldl :: (a -> time -> b) -> (b -> body -> a) -> a -> T time body -> b
- pause :: time -> T time body
- isPause :: T time body -> Bool
- cons :: time -> body -> T time body -> T time body
- snoc :: T time body -> body -> time -> T time body
- viewL :: T time body -> (time, Maybe (body, T time body))
- viewR :: T time body -> (Maybe (T time body, body), time)
- switchL :: (time -> a) -> ((time, body) -> T time body -> a) -> T time body -> a
- switchR :: (time -> a) -> (T time body -> body -> time -> 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
- catMaybesR :: Num time => T time (Maybe body) -> T time body
- append :: C time => T time body -> T time body -> T time body
- concat :: C time => [T time body] -> T time body
- concatNaive :: C time => [T time body] -> T time body
- cycle :: C time => T time body -> T time body
- cycleNaive :: C time => T time body -> T time body
- reverse :: T time body -> T time body
- splitAtTime :: C time => time -> T time body -> (T time body, T time body)
- takeTime :: C time => time -> T time body -> T time body
- dropTime :: C time => time -> 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
- collectCoincident :: C time => T time body -> T time [body]
- flatten :: Num time => T time [body] -> T time body
- mapCoincident :: C time => ([a] -> [b]) -> T time a -> T time b
- normalize :: (Ord body, C time) => T time body -> T time body
- isNormalized :: (C time, Ord body) => T time body -> Bool
- toAbsoluteEventList :: Num time => time -> T time body -> T time body
- fromAbsoluteEventList :: Num time => T time body -> T time body

# Documentation

zipWithBody :: (body0 -> body1 -> body2) -> [body0] -> T time body1 -> T time body2Source

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

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

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

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

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

insert :: (C time, Ord body) => 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.

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

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.

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

Like `moveForward`

but restricts the look-ahead time.
For `moveForwardRestricted maxTimeDiff xs`

all time differences (aka the moveForward offsets) in `xs`

must be at most `maxTimeDiff`

.
With this restriction the function is lazy enough
for handling infinite event lists.
However the larger `maxTimeDiff`

the more memory and time is consumed.

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

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

Merge several event lists respecting the start time of the outer event list.

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

currently only for testing

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

currently only for testing

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

currently only for testing

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

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

Analogously to the `concat`

/ `concatNaive`

pair
we have to versions of `filter`

,
where the clever implementation sums up pauses
from the beginning to the end.

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

partitionMaybeR :: Num time => (body0 -> Maybe body1) -> T time body0 -> (T time body1, T time body0)Source

Cf. `catMaybesR`

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.

catMaybes :: Num time => T time (Maybe body) -> T time bodySource

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

catMaybesR :: Num time => T time (Maybe body) -> T time bodySource

Adds times in a right-associative fashion. Use this if the time is a data type like lazy Peano numbers or Numeric.NonNegative.Chunky.

concatNaive :: C time => [T time body] -> T time bodySource

`concat`

and `concatNaive`

are essentially the same.
`concat`

must use `foldr`

in order to work on infinite lists,
however if there are many empty lists,
summing of their durations will be done from right to left,
which is inefficient.
Thus we detect subsequent empty lists and merge them from left to right.

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

splitAtTime :: C time => time -> T time body -> (T time body, T time body)Source

If there is an event at the cutting time,
this event is returned in the suffix part.
That is
`splitAtTime t0 (t0 .`

* x *. t1 ./ empty) ==
(pause t0, 0 .* x *. t1 ./ empty)

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

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

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

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