{-# LANGUAGE ConstraintKinds            #-}
{-# LANGUAGE DeriveDataTypeable         #-}
{-# LANGUAGE DeriveFunctor              #-}
{-# LANGUAGE DeriveFoldable             #-}
{-# LANGUAGE DeriveTraversable          #-}
{-# LANGUAGE GeneralizedNewtypeDeriving #-}
{-# LANGUAGE MultiParamTypeClasses      #-}
{-# LANGUAGE RankNTypes                 #-}
{-# LANGUAGE StandaloneDeriving         #-}
{-# LANGUAGE TupleSections              #-}
{-# LANGUAGE TypeFamilies               #-}
{-# LANGUAGE ViewPatterns               #-}

-------------------------------------------------------------------------------------
-- |
-- Copyright   : (c) Hans Hoglund 2012-2014
--
-- License     : BSD-style
--
-- Maintainer  : hans@hanshoglund.se
-- Stability   : experimental
-- Portability : non-portable (TF,GNTD)
--
-------------------------------------------------------------------------------------

module Music.Time.Voice (

        -- * Voice type
        Voice,

        -- * Construction
        voice,
        notes,
        pairs,
        durationsVoice,

        -- * Traversal
        -- ** Separating rhythms and values
        valuesV,
        durationsV,
        -- withValues,
        -- withDurations,
        -- rotateValues,
        -- rotateDurations,
        -- reverseValues,
        -- reverseDurations,

        -- ** Zips
        unzipVoice,
        zipVoice,
        zipVoice3,
        zipVoice4,
        zipVoiceNoScale,
        -- FIXME compose with (lens assoc unassoc) for the 3 and 4 versions
        zipVoiceNoScale3,
        zipVoiceNoScale4,
        zipVoiceWith,
        zipVoiceWith',
        zipVoiceWithNoScale,

        -- * Fusion
        fuse,
        fuseBy,

        -- ** Fuse rests
        fuseRests,
        coverRests,
        
        -- * Homophonic/Polyphonic texture
        sameDurations,
        mergeIfSameDuration,
        mergeIfSameDurationWith,
        homoToPolyphonic,

        -- * Points in a voice
        onsetsRelative,
        offsetsRelative,
        midpointsRelative,
        erasRelative,
        
        -- * Context
        -- TODO clean
        withContext,
        -- voiceLens,

        -- * Unsafe versions
        unsafeNotes,
        unsafePairs,

  ) where

import           Data.AffineSpace
import           Data.AffineSpace.Point
import           Data.Functor.Adjunction  (unzipR)
import           Data.Functor.Context
import           Data.Map                 (Map)
import qualified Data.Map                 as Map
import           Data.Maybe
import           Data.Ratio
import           Data.Semigroup
import           Data.Set                 (Set)
import qualified Data.Set                 as Set
import           Data.Sequence            (Seq)
import qualified Data.Sequence            as Seq
import           Data.String
import           Data.VectorSpace

import           Music.Time.Reverse
import           Music.Time.Split
import           Music.Time.Note

import           Control.Applicative
import           Control.Lens             hiding (Indexable, Level, above,
                                           below, index, inside, parts,
                                           reversed, transform, (<|), (|>))
import           Control.Monad
import           Control.Monad.Compose
import           Control.Monad.Plus
import           Data.Foldable            (Foldable)
import qualified Data.Foldable            as Foldable
import qualified Data.List
import           Data.List.NonEmpty       (NonEmpty)
import           Data.Traversable         (Traversable)
import qualified Data.Traversable         as T
import           Data.Typeable
import           Music.Dynamics.Literal
import           Music.Pitch.Literal
import           Music.Time.Internal.Util

-- |
-- A 'Voice' is a sequential composition of non-overlapping note values.
--
-- Both 'Voice' and 'Note' have duration but no position. The difference
-- is that 'Note' sustains a single value throughout its duration, while
-- a voice may contain multiple values. It is called voice because it is
-- generalizes the notation of a voice in choral or multi-part instrumental music.
--
-- It may be useful to think about 'Voice' and 'Note' as vectors in time space
-- (i.e. 'Duration'), that also happens to carry around other values, such as pitches.
--
newtype Voice a = Voice { getVoice :: [Note a] }
  deriving (
    Eq,
    Ord,
    Typeable,
    Foldable, 
    Traversable, 

    Functor, 
    Semigroup, 
    Monoid 
    )

instance (Show a, Transformable a) => Show (Voice a) where
  show x = show (x^.notes) ++ "^.voice"

-- A voice is a list of events with explicit duration. Events can not overlap.
--
-- Voice is a 'Monoid' under sequential composition. 'mempty' is the empty part and 'mappend'
-- appends parts.

--
-- Voice is a 'Monad'. 'return' creates a part containing a single value of duration
-- one, and '>>=' transforms the values of a part, allowing the addition and
-- removal of values under relative duration. Perhaps more intuitively, 'join' scales
-- each inner part to the duration of the outer part, then removes the
-- intermediate structure.

instance Applicative Voice where
  pure  = return
  (<*>) = ap

instance Alternative Voice where
  (<|>) = (<>)
  empty = mempty

instance Monad Voice where
  return = view _Unwrapped . return . return
  xs >>= f = view _Unwrapped $ (view _Wrapped . f) `mbind` view _Wrapped xs

instance MonadPlus Voice where
  mzero = mempty
  mplus = mappend
  
instance Wrapped (Voice a) where
  type Unwrapped (Voice a) = [Note a]
  _Wrapped' = iso getVoice Voice

instance Rewrapped (Voice a) (Voice b)

instance Cons (Voice a) (Voice b) (Note a) (Note b) where
  _Cons = prism (\(s,v) -> (view voice.return $ s) <> v) $ \v -> case view notes v of
    []      -> Left  mempty
    (x:xs)  -> Right (x, view voice xs)

instance Snoc (Voice a) (Voice b) (Note a) (Note b) where
  _Snoc = prism (\(v,s) -> v <> (view voice.return $ s)) $ \v -> case unsnoc (view notes v) of
    Nothing      -> Left  mempty
    Just (xs, x) -> Right (view voice xs, x)

instance Transformable (Voice a) where
  transform s = over notes (transform s)

instance HasDuration (Voice a) where
  _duration = sumOf (notes . each . duration)

instance Reversible a => Reversible (Voice a) where
  rev = over notes reverse . fmap rev

-- instance Splittable a => Splittable (Voice a) where
--   split t x
--     | t <= 0           = (mempty, x)
--     | t >= _duration x = (x,      mempty)
--     | otherwise        = let (a,b) = split' t {-split-} (x^._Wrapped) in (a^._Unwrapped, b^._Unwrapped)
--     where
--       split' = error "TODO"

instance IsString a => IsString (Voice a) where
  fromString = pure . fromString

instance IsPitch a => IsPitch (Voice a) where
  fromPitch = pure . fromPitch

instance IsInterval a => IsInterval (Voice a) where
  fromInterval = pure . fromInterval

instance IsDynamics a => IsDynamics (Voice a) where
  fromDynamics = pure . fromDynamics

-- Bogus instance, so we can use [c..g] expressions
instance Enum a => Enum (Voice a) where
  toEnum = return . toEnum
  fromEnum = list 0 (fromEnum . head) . Foldable.toList

-- Bogus instance, so we can use numeric literals
instance Num a => Num (Voice a) where
  fromInteger = return . fromInteger
  abs    = fmap abs
  signum = fmap signum
  (+)    = (<>)
  (-)    = error "Not implemented"
  (*)    = error "Not implemented"

instance AdditiveGroup (Voice a) where
  zeroV   = mempty
  (^+^)   = (<>)
  negateV = error "Not implemented" -- TODO negate durations

instance VectorSpace (Voice a) where
  type Scalar (Voice a) = Duration
  d *^ s = d `stretch` s


-- | Create a 'Voice' from a list of 'Note's.
voice :: Getter [Note a] (Voice a)
voice = from unsafeNotes
{-# INLINE voice #-}

-- | View a 'Voice' as a list of 'Note' values.
notes :: Lens (Voice a) (Voice b) [Note a] [Note b]
notes = unsafeNotes

--
-- @
-- 'view' 'notes'                        :: 'Voice' a -> ['Note' a]
-- 'set'  'notes'                        :: ['Note' a] -> 'Voice' a -> 'Voice' a
-- 'over' 'notes'                        :: (['Note' a] -> ['Note' b]) -> 'Voice' a -> 'Voice' b
-- @
--
-- @
-- 'preview'  ('notes' . 'each')           :: 'Voice' a -> 'Maybe' ('Note' a)
-- 'preview'  ('notes' . 'element' 1)      :: 'Voice' a -> 'Maybe' ('Note' a)
-- 'preview'  ('notes' . 'elements' odd)   :: 'Voice' a -> 'Maybe' ('Note' a)
-- @
--
-- @
-- 'set'      ('notes' . 'each')           :: 'Note' a -> 'Voice' a -> 'Voice' a
-- 'set'      ('notes' . 'element' 1)      :: 'Note' a -> 'Voice' a -> 'Voice' a
-- 'set'      ('notes' . 'elements' odd)   :: 'Note' a -> 'Voice' a -> 'Voice' a
-- @
--
-- @
-- 'over'     ('notes' . 'each')           :: ('Note' a -> 'Note' b) -> 'Voice' a -> 'Voice' b
-- 'over'     ('notes' . 'element' 1)      :: ('Note' a -> 'Note' a) -> 'Voice' a -> 'Voice' a
-- 'over'     ('notes' . 'elements' odd)   :: ('Note' a -> 'Note' a) -> 'Voice' a -> 'Voice' a
-- @
--
-- @
-- 'toListOf' ('notes' . 'each')                :: 'Voice' a -> ['Note' a]
-- 'toListOf' ('notes' . 'elements' odd)        :: 'Voice' a -> ['Note' a]
-- 'toListOf' ('notes' . 'each' . 'filtered'
--              (\\x -> '_duration' x \< 2))  :: 'Voice' a -> ['Note' a]
-- @

-- | View a score as a list of duration-value pairs. Analogous to 'triples'.
pairs :: Lens (Voice a) (Voice b) [(Duration, a)] [(Duration, b)]
pairs = unsafePairs

-- | A voice is a list of notes up to meta-data. To preserve meta-data, use the more
-- restricted 'voice' and 'notes'.
unsafeNotes :: Iso (Voice a) (Voice b) [Note a] [Note b]
unsafeNotes = _Wrapped

-- | A score is a list of (duration-value pairs) up to meta-data.
-- To preserve meta-data, use the more restricted 'pairs'.
unsafePairs :: Iso (Voice a) (Voice b) [(Duration, a)] [(Duration, b)]
unsafePairs = iso (map (^.from note) . (^.notes)) ((^.voice) . map (^.note))

durationsVoice :: Iso' [Duration] (Voice ())
durationsVoice = iso (mconcat . fmap (\d -> stretch d $ pure ())) (^. durationsV)

-- |
-- Unzip the given voice. This is specialization of 'unzipR'.
--
unzipVoice :: Voice (a, b) -> (Voice a, Voice b)
unzipVoice = unzipR

-- |
-- Join the given voices by multiplying durations and pairing values.
--
zipVoice :: Voice a -> Voice b -> Voice (a, b)
zipVoice = zipVoiceWith (,)

-- |
-- Join the given voices by multiplying durations and pairing values.
--
zipVoice3 :: Voice a -> Voice b -> Voice c -> Voice (a, (b, c))
zipVoice3 a b c = zipVoice a (zipVoice b c)

-- |
-- Join the given voices by multiplying durations and pairing values.
--
zipVoice4 :: Voice a -> Voice b -> Voice c -> Voice d -> Voice (a, (b, (c, d)))
zipVoice4 a b c d = zipVoice a (zipVoice b (zipVoice c d))

-- |
-- Join the given voices by multiplying durations and pairing values.
--
zipVoice5 :: Voice a -> Voice b -> Voice c -> Voice d -> Voice e -> Voice (a, (b, (c, (d, e))))
zipVoice5 a b c d e = zipVoice a (zipVoice b (zipVoice c (zipVoice d e)))

-- |
-- Join the given voices by pairing values and selecting the first duration.
--
zipVoiceNoScale :: Voice a -> Voice b -> Voice (a, b)
zipVoiceNoScale = zipVoiceWithNoScale (,)

-- |
-- Join the given voices by pairing values and selecting the first duration.
--
zipVoiceNoScale3 :: Voice a -> Voice b -> Voice c -> Voice (a, (b, c))
zipVoiceNoScale3 a b c = zipVoiceNoScale a (zipVoiceNoScale b c)

-- |
-- Join the given voices by pairing values and selecting the first duration.
--
zipVoiceNoScale4 :: Voice a -> Voice b -> Voice c -> Voice d -> Voice (a, (b, (c, d)))
zipVoiceNoScale4 a b c d = zipVoiceNoScale a (zipVoiceNoScale b (zipVoiceNoScale c d))

-- |
-- Join the given voices by pairing values and selecting the first duration.
--
zipVoiceNoScale5 :: Voice a -> Voice b -> Voice c -> Voice d -> Voice e -> Voice (a, (b, (c, (d, e))))
zipVoiceNoScale5 a b c d e = zipVoiceNoScale a (zipVoiceNoScale b (zipVoiceNoScale c (zipVoiceNoScale d e)))


-- |
-- Join the given voices by multiplying durations and combining values using the given function.
--
zipVoiceWith :: (a -> b -> c) -> Voice a -> Voice b -> Voice c
zipVoiceWith = zipVoiceWith' (*)

-- |
-- Join the given voices without combining durations.
--
zipVoiceWithNoScale :: (a -> b -> c) -> Voice a -> Voice b -> Voice c
zipVoiceWithNoScale = zipVoiceWith' const

-- |
-- Join the given voices by combining durations and values using the given function.
--
zipVoiceWith' :: (Duration -> Duration -> Duration) -> (a -> b -> c) -> Voice a -> Voice b -> Voice c
zipVoiceWith' f g
  ((unzip.view pairs) -> (ad, as))
  ((unzip.view pairs) -> (bd, bs))
  = let cd = zipWith f ad bd
        cs = zipWith g as bs
     in view (from unsafePairs) (zip cd cs)


-- TODO generalize these to use a Monoidal interface, rather than ([a] -> a)
-- The use of head (see below) if of course the First monoid

-- |
-- Merge consecutive equal notes.
--
fuse :: Eq a => Voice a -> Voice a
fuse = fuseBy (==)

-- |
-- Merge consecutive notes deemed equal by the given predicate.
--
fuseBy :: (a -> a -> Bool) -> Voice a -> Voice a
fuseBy p = fuseBy' p head

-- |
-- Merge consecutive equal notes using the given equality predicate and merge function.
--
fuseBy' :: (a -> a -> Bool) -> ([a] -> a) -> Voice a -> Voice a
fuseBy' p g = over unsafePairs $ fmap foldNotes . Data.List.groupBy (inspectingBy snd p)
  where
    -- Add up durations and use a custom function to combine notes
    --
    -- Typically, the combination function us just 'head', as we know that group returns
    -- non-empty lists of equal elements.
    foldNotes (unzip -> (ds, as)) = (sum ds, g as)

-- | 
-- Fuse all rests in the given voice. The resulting voice will have no consecutive rests.
--
fuseRests :: Voice (Maybe a) -> Voice (Maybe a)
fuseRests = fuseBy (\x y -> isNothing x && isNothing y)

-- | 
-- Remove all rests in the given voice by prolonging the previous note. Returns 'Nothing'
-- if and only if the given voice contains rests only.
--
coverRests :: Voice (Maybe a) -> Maybe (Voice a)
coverRests x = if hasOnlyRests then Nothing else Just (fmap fromJust $ fuseBy merge x)
  where
    norm = fuseRests x
    merge Nothing  Nothing  = error "Voice normalized, so consecutive rests are impossible"
    merge (Just x) Nothing  = True
    merge Nothing  (Just x) = True
    merge (Just x) (Just y) = False
    hasOnlyRests = all isNothing $ toListOf traverse x -- norm

-- | Decorate all notes in a voice with their context, i.e. previous and following value
-- if present.
withContext :: Voice a -> Voice (Ctxt a)
withContext = over valuesV addCtxt

-- TODO more elegant definition?

-- | A lens to the durations in a voice.
durationsV :: Lens' (Voice a) [Duration]
durationsV = lens getDurs (flip setDurs)
  where
    getDurs :: Voice a -> [Duration]
    getDurs = map fst . view pairs

    setDurs :: [Duration] -> Voice a -> Voice a
    setDurs ds as = zipVoiceWith' (\a b -> a) (\a b -> b) (mconcat $ map durToVoice ds) as

    durToVoice d = stretch d $ pure ()

-- | A lens to the values in a voice.
valuesV :: Lens (Voice a) (Voice b) [a] [b]
valuesV = lens getValues (flip setValues)
  where
    -- getValues :: Voice a -> [a]
    getValues = map snd . view pairs

    -- setValues :: [a] -> Voice b -> Voice a
    setValues as bs = zipVoiceWith' (\a b -> b) (\a b -> a) (listToVoice as) bs

    listToVoice = mconcat . map pure

-- Lens "filtered" through a voice
voiceLens :: (s -> a) -> (b -> s -> t) -> Lens (Voice s) (Voice t) (Voice a) (Voice b)
voiceLens getter setter = lens (fmap getter) (flip $ zipVoiceWithNoScale setter)
-- TODO could also use (zipVoiceWith' max) or (zipVoiceWith' min)

-- | Whether two notes have exactly the same duration pattern.
-- Two empty voices are considered to have the same duration pattern.
-- Voices with an non-equal number of notes differ by default.
sameDurations :: Voice a -> Voice b -> Bool
sameDurations a b = view durationsV a == view durationsV b

-- | Pair the values of two voices if and only if they have the same duration
-- pattern (as per 'sameDurations').
mergeIfSameDuration :: Voice a -> Voice b -> Maybe (Voice (a, b))
mergeIfSameDuration = mergeIfSameDurationWith (,)

-- | Combine the values of two voices using the given function if and only if they
-- have the same duration pattern (as per 'sameDurations').
mergeIfSameDurationWith :: (a -> b -> c) -> Voice a -> Voice b -> Maybe (Voice c)
mergeIfSameDurationWith f a b
  | sameDurations a b = Just $ zipVoiceWithNoScale f a b
  | otherwise         = Nothing
-- TODO could also use (zipVoiceWith' max) or (zipVoiceWith' min)

-- |
-- Split all notes of the latter voice at the onset/offset of the former.
--
-- >>> ["a",(2,"b")^.note,"c"]^.voice
-- [(1,"a")^.note,(2,"b")^.note,(1,"c")^.note]^.voice
--
splitLatterToAssureSameDuration :: Voice b -> Voice b -> Voice b
splitLatterToAssureSameDuration = splitLatterToAssureSameDurationWith dup
  where
    dup x = (x,x)

splitLatterToAssureSameDurationWith :: (b -> (b, b)) -> Voice b -> Voice b -> Voice b
splitLatterToAssureSameDurationWith = undefined

polyToHomophonic      :: [Voice a] -> Maybe (Voice [a])
polyToHomophonic = undefined

polyToHomophonicForce :: [Voice a] -> Voice [a]
polyToHomophonicForce = undefined

-- | Split a homophonic texture into a polyphonic one. The returned voice list will not
-- have as many elements as the chord with the fewest number of notes.
homoToPolyphonic      :: Voice [a] -> [Voice a]
homoToPolyphonic xs = case nvoices xs of
  Nothing -> []
  Just n  -> fmap (\n -> fmap (!! n) xs) [0..n-1]
  where                  
    nvoices :: Voice [a] -> Maybe Int
    nvoices = maybeMinimum . fmap length . (^.valuesV)

changeCrossing   :: Ord a => Voice a -> Voice a -> (Voice a, Voice a)
changeCrossing = undefined

changeCrossingBy :: Ord b => (a -> b) -> Voice a -> Voice a -> (Voice a, Voice a)
changeCrossingBy = undefined

processExactOverlaps :: (a -> a -> (a, a)) -> Voice a -> Voice a -> (Voice a, Voice a)
processExactOverlaps = undefined

processExactOverlaps' :: (a -> b -> Either (a,b) (b,a)) -> Voice a -> Voice b -> (Voice (Either b a), Voice (Either a b))
processExactOverlaps' = undefined

-- | Returns the onsets of all notes in a voice given the onset of the first note.
onsetsRelative    :: Time -> Voice a -> [Time]
onsetsRelative o v = case offsetsRelative o v of
  [] -> []
  xs -> o : init xs

-- | Returns the offsets of all notes in a voice given the onset of the first note.
offsetsRelative   :: Time -> Voice a -> [Time]
offsetsRelative o = fmap (\t -> o .+^ (t .-. 0)) . toAbsoluteTime . (^. durationsV)

-- | Returns the midpoints of all notes in a voice given the onset of the first note.
midpointsRelative :: Time -> Voice a -> [Time]
midpointsRelative o v = zipWith between (onsetsRelative o v) (offsetsRelative o v)
  where
    between p q = alerp p q 0.5

-- | Returns the eras of all notes in a voice given the onset of the first note.
erasRelative :: Time -> Voice a -> [Span]
erasRelative o v = zipWith (<->) (onsetsRelative o v) (offsetsRelative o v)

onsetMap  :: Time -> Voice a -> Map Time a
onsetMap = undefined

offsetMap :: Time -> Voice a -> Map Time a
offsetMap = undefined

midpointMap :: Time -> Voice a -> Map Time a
midpointMap = undefined

eraMap :: Time -> Voice a -> Map Span a
eraMap = undefined

durations :: Voice a -> [Duration]
durations = undefined

-- values :: Voice a -> [a] -- Same as Foldable.toList
-- values = undefined



{-

sameDurations           :: Voice a -> Voice b -> Bool
mergeIfSameDuration     :: Voice a -> Voice b -> Maybe (Voice (a, b))
mergeIfSameDurationWith :: (a -> b -> c) -> Voice a -> Voice b -> Maybe (Voice c)
splitAt :: [Duration] -> Voice a -> [Voice a]
-- splitTiesAt :: Tiable a => [Duration] -> Voice a -> [Voice a]
splitLatterToAssureSameDuration :: Voice b -> Voice b -> Voice b
splitLatterToAssureSameDurationWith :: (b -> (b, b)) -> Voice b -> Voice b -> Voice b
polyToHomophonic      :: [Voice a] -> Maybe (Voice [a])
polyToHomophonicForce :: [Voice a] -> Voice [a]
homoToPolyphonic      :: Voice [a] -> [Voice a]
joinVoice             :: Voice (Voice a) -> a
changeCrossing   :: Ord a => Voice a -> Voice a -> (Voice a, Voice a)
changeCrossingBy :: Ord b => (a -> b) -> Voice a -> Voice a -> (Voice a, Voice a)
processExactOverlaps :: (a -> a -> (a, a)) -> Voice a -> Voice a -> (Voice a, Voice a)
processExactOverlaps' :: (a -> b -> Either (a,b) (b,a)) -> Voice a -> Voice b -> (Voice (Either b a), Voice (Either a b))
onsetsRelative    :: Time -> Voice a -> [Time]
offsetsRelative   :: Time -> Voice a -> [Time]
midpointsRelative :: Time -> Voice a -> [Time]
erasRelative      :: Time -> Voice a -> [Span]
onsetMap  :: Time -> Voice a -> Map Time a
offsetMap :: Time -> Voice a -> Map Time a
midpointMap :: Time -> Voice a -> Map Time a
eraMap :: Time -> Voice a -> Map Span a
durations :: Voice a -> [Duration]
values    :: Voice a -> [a] -- Same as Foldable.toList
isPossiblyInfinite :: Voice a -> Bool
hasMelodicDissonanceWith :: (a -> a -> Bool) -> Voice a -> Bool
hasIntervalWith :: AffineSpace a => (Diff a -> Bool) -> Voice a -> Bool
hasDurationWith :: (Duration -> Bool) -> Voice a -> Bool
reifyVoice :: Voice a -> Voice (Duration, a)
mapWithIndex :: (Int -> a -> b) -> Voice a -> Voice b
mapWithDuration :: (Duration -> a -> b) -> Voice a -> Voice b
mapWithIndexAndDuration :: (Int -> Duration -> a -> b) -> Voice a -> Voice b
_ :: Iso (Voice ()) [Duration]
asingleton' :: Prism (Voice a) (Duration, a)
asingleton :: Prism (Voice a) a
separateVoicesWith :: (a -> k) -> Voice a -> Map k (Voice a)
freeVoiceR :: (forall a. -> [a] -> a)          -> Voice a -> (a, Duration)
freeVoiceRNoDur :: ([a] -> a)          -> Voice a -> a
freeVoice  :: (forall a. -> [a] -> [a])        -> Voice a -> Voice a
freeVoice2 :: (forall a. -> [a] -> [a] -> [a]) -> Voice a -> Voice a -> Voice a
empty :: Voice a
singleton :: a -> Voice a
cons :: a -> Voice a -> Voice a
snoc :: Voice a -> a -> Voice a
append :: Voice a -> Voice a -> Voice a
ap :: Voice (a -> b) -> Voice a -> Voice b
apDur :: Voice (Duration -> Duration -> a -> b) -> Voice a -> Voice b
intersperse :: Duration -> a -> Voice a -> Voice a
-- intercalate :: Voice a -> Voice (Voice a) -> Voice a
subsequences :: Voice a -> [Voice a]
permutations :: Voice a -> [Voice a]
iterate :: (a -> a) -> a -> Voice a
repeat :: a -> Voice a
replicate :: Int -> a -> Voice a
unfoldr :: (b -> Maybe (a, b)) -> b -> Voice a
Differences between Voice and Chord (except the obviously different composition styles):
  - Voice is a Monoid, Chord just a Semigroup (??)
  - TODO represent spanners using (Voice a, Map (Int,Int) s)
  Arguably this should be part of Voice
  TODO the MVoice/TVoice stuff
newtype MVoice = Voice (Maybe a)
newtype PVoice = [Either Duration (Voice a)]
expandRepeats :: [Voice (Variant a)] -> Voice a

-}

maybeMinimum xs = if null xs then Nothing else Just (minimum xs)
maybeMaximum xs = if null xs then Nothing else Just (maximum xs)