{- |
Copyright   :  (c) Henning Thielemann 2007

Maintainer  :  haskell@henning-thielemann.de
Stability   :  stable
Portability :  Haskell 98

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.

module Data.EventList.Relative.TimeBody
    empty, singleton, null,
    viewL, viewR, cons, snoc,
    fromPairList, toPairList,
    getTimes, getBodies, duration,
    mapBody, mapTime,
    mapM, mapM_, mapBodyM, mapTimeM,
    foldr, foldrPair,
    merge, mergeBy, insert, insertBy,
    decreaseStart, delay, filter, partition, slice, span,
    mapMaybe, catMaybes,
    normalize, isNormalized,
    collectCoincident, flatten, mapCoincident,
    append, concat, cycle,
    discretize, resample,
    toAbsoluteEventList, fromAbsoluteEventList,
   ) where

import Data.EventList.Relative.TimeBodyPrivate
import qualified Data.EventList.Relative.BodyBodyPrivate as BodyBodyPriv

import qualified Data.EventList.Absolute.TimeBodyPrivate as AbsoluteEventPriv
import qualified Data.EventList.Absolute.TimeBody as AbsoluteEventList

import qualified Data.AlternatingList.List.Disparate as Disp
import qualified Data.AlternatingList.List.Uniform as Uniform
import qualified Data.AlternatingList.List.Mixed as Mixed

import qualified Data.List as List
import qualified Data.EventList.Utility as Utility

import qualified Numeric.NonNegative.Class as NonNeg
import Data.EventList.Utility (floorDiff, mapFst, mapSnd, toMaybe, isMonotonic, beforeBy)
import Control.Monad.State (evalState, modify, get, put)

import Prelude hiding (mapM, mapM_, null, foldr, filter, concat, cycle, span)

empty :: T time body
empty = Cons Disp.empty

null :: T time body -> Bool
null = Disp.null . decons

singleton :: time -> body -> T time body
singleton time body = Cons $ Disp.singleton time body

cons :: time -> body -> T time body -> T time body
cons time body = lift (Disp.cons time body)

snoc :: T time body -> time -> body -> T time body
snoc xs time body = Cons $ (Disp.snoc $~* xs) time body

viewL :: T time body -> Maybe ((time, body), T time body)
viewL = fmap (mapSnd Cons) . Disp.viewL . decons

viewR :: T time body -> Maybe (T time body, (time, body))
viewR = fmap (mapFst Cons) . Disp.viewR . decons

fromPairList :: [(a,b)] -> T a b
fromPairList = Cons . Disp.fromPairList

toPairList :: T a b -> [(a,b)]
toPairList = Disp.toPairList . decons

getBodies :: T time body -> [body]
getBodies = Disp.getSeconds . decons

getTimes :: T time body -> [time]
getTimes = Disp.getFirsts . decons

duration :: Num time => T time body -> time
duration = sum . getTimes

mapBody :: (body0 -> body1) -> T time body0 -> T time body1
mapBody f = lift (Disp.mapSecond f)

mapTime :: (time0 -> time1) -> T time0 body -> T time1 body
mapTime f = lift (Disp.mapFirst f)

mapM :: Monad m =>
   (time0 -> m time1) -> (body0 -> m body1) ->
   T time0 body0 -> m (T time1 body1)
mapM f g = liftM (Disp.mapM f g)

mapM_ :: Monad m =>
   (time -> m ()) -> (body -> m ()) ->
   T time body -> m ()
mapM_ f g = Disp.mapM_ f g . decons

mapBodyM :: Monad m =>
   (body0 -> m body1) -> T time body0 -> m (T time body1)
mapBodyM f = liftM (Disp.mapSecondM f)

mapTimeM :: Monad m =>
   (time0 -> m time1) -> T time0 body -> m (T time1 body)
mapTimeM f = liftM (Disp.mapFirstM f)

foldr :: (time -> a -> b) -> (body -> b -> a) -> b -> T time body -> b
foldr f g x = Disp.foldr f g x . decons

foldrPair :: (time -> body -> a -> a) -> a -> T time body -> a
foldrPair f x = Disp.foldrPair f x . decons

{- |

The function 'partition' is somehow the inverse to 'merge'.
It is similar to 'List.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.


filter :: (Num time) =>
   (body -> Bool) -> T time body -> T time body
filter p = mapMaybe (\b -> toMaybe (p b) b)
-- filter p = fst . partition p

mapMaybe :: (Num time) =>
   (body0 -> Maybe body1) ->
   T time body0 -> T time body1
mapMaybe f = catMaybes . mapBody f

catMaybes :: (Num time) =>
   T time (Maybe body) -> T time body
catMaybes =
   Cons .
   fst . Mixed.viewSecondR .
   Uniform.mapSecond sum .
   Uniform.catMaybesFirst .
   flip Mixed.snocSecond (error "catMaybes: no trailing time") .

Could be implemented more easily in terms of Uniform.partition
partition :: (Num time) =>
   (body -> Bool) -> T time body -> (T time body, T time body)
partition p = partitionRec p 0 0

partitionRec :: (Num time) =>
   (body -> Bool) -> time -> time ->
       T time body -> (T time body, T time body)
partitionRec p =
   let recurse t0 t1 =
             (empty, empty)
             (\ ((t, b), es) ->
                let t0' = t0 + t
                    t1' = t1 + t
                in  if p b
                      then mapFst (cons t0' b) (recurse 0 t1' es)
                      else mapSnd (cons t1' b) (recurse t0' 0 es)) .
   in  recurse

{- |
Since we need it later for MIDI generation,
we will also define a slicing into equivalence classes of events.
slice :: (Eq a, Num time) =>
   (body -> a) -> T time body -> [(a, T time body)]
slice = Utility.slice (fmap (snd . fst) . viewL) partition

span :: (body -> Bool) -> T time body -> (T time body, T time body)
span p = Utility.mapPair (Cons, Cons) . Disp.spanSecond p . decons

{- |
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.
collectCoincident :: (NonNeg.C time) => T time body -> T time [body]
collectCoincident =
   mapTimeTail $ BodyBodyPriv.lift $ Uniform.filterFirst (0<)

flatten :: (NonNeg.C time) => T time [body] -> T time body
flatten =
   Cons .
      (uncurry $ \time ->
         unlift (delay time) .
         fst . Mixed.viewSecondR .
            (Mixed.appendUniformUniform . Uniform.fromSecondList 0)
            Mixed.consSecond Disp.empty .
         Uniform.mapSecond sum .
         Uniform.filterSecond (not . List.null)) .
   Mixed.viewFirstL .

{- |
Apply a function to the lists of coincident events.

mapCoincident :: (NonNeg.C time) =>
   ([a] -> [b]) -> T time a -> T time b
mapCoincident f = flatten . mapBody f . collectCoincident

{- |

'List.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.

normalize :: (NonNeg.C time, Ord body) => T time body -> T time body
normalize = mapCoincident List.sort

isNormalized :: (NonNeg.C time, Ord body) =>
   T time body -> Bool
isNormalized =
   all isMonotonic . getBodies . collectCoincident

{- |
The first important function is 'merge'
which merges the events of two lists into a new time order list.

merge :: (NonNeg.C time, Ord body) =>
   T time body -> T time body -> T time body
merge = mergeBy (<)

{- |
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.

Could be implemented using as 'splitAt' and 'insert'.
mergeBy :: (NonNeg.C time) =>
   (body -> body -> Bool) ->
   T time body -> T time body -> T time body
mergeBy before xs0 ys0 =
   case (viewL xs0, viewL ys0) of
      (Nothing, _) -> ys0
      (_, Nothing) -> xs0
      (Just (x@(xt,xb),xs), Just (y@(yt,yb),ys)) ->
         if beforeBy before x y
           then uncurry cons x $ mergeBy before xs $ cons (yt-xt) yb ys
           else uncurry cons y $ mergeBy before ys $ cons (xt-yt) xb xs

{- |
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.

insert :: (NonNeg.C time, Ord body) =>
   time -> body -> T time body -> T time body
insert t0 me0 =
      (singleton t0 me0)
      (\(mev1@(t1, me1), mevs) ->
          let mev0 = (t0, me0)
          in  if mev0 < mev1
                then uncurry cons mev0 $ cons   (t1-t0) me1 mevs
                else uncurry cons mev1 $ insert (t0-t1) me0 mevs)
    . viewL

insertBy :: (NonNeg.C time, Ord body) =>
   (body -> body -> Bool) ->
   time -> body -> T time body -> T time body
insertBy before t0 me0 =
      (singleton t0 me0)
      (\(mev1@(t1, me1), mevs) ->
          if beforeBy before (t0, me0) mev1
            then cons t0 me0 $ cons   (t1-t0) me1 mevs
            else cons t1 me1 $ insert (t0-t1) me0 mevs)
    . viewL

append :: T time body -> T time body -> T time body
append xs = lift (Disp.append $~* xs)

concat :: [T time body] -> T time body
concat = Cons . Disp.concat . map decons

cycle :: T time body -> T time body
cycle = lift Disp.cycle

decreaseStart :: (NonNeg.C time) =>
   time -> T time body -> T time body
decreaseStart dif =
   mapTimeHead (subtract dif)

delay :: (NonNeg.C time) =>
   time -> T time body -> T time body
delay dif =
   mapTimeHead (dif+)

{- |
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 'Utility.roundDiff'
in order to compute exclusively with non-negative numbers.

discretize :: (NonNeg.C time, RealFrac time, NonNeg.C i, Integral i) =>
   T time body -> T i body
discretize =
   flip evalState 0.5 . mapTimeM floorDiff

resample :: (NonNeg.C time, RealFrac time, NonNeg.C i, Integral i) =>
   time -> T time body -> T i body
resample rate =
   discretize . mapTime (rate*)

{- |
We tried hard to compute everything with respect to relative times.
However sometimes we need absolute time values.
toAbsoluteEventList :: (Num time) =>
   time -> T time body -> AbsoluteEventList.T time body
toAbsoluteEventList start =
   AbsoluteEventPriv.Cons . decons .
   flip evalState start .
   mapTimeM (\dur -> modify (dur+) >> get)

fromAbsoluteEventList :: (Num time) =>
   AbsoluteEventList.T time body -> T time body
fromAbsoluteEventList =
   flip evalState 0 .
      (\time -> do lastTime <- get; put time; return (time-lastTime)) .
   Cons . AbsoluteEventPriv.decons