\begin{code}
module Music.Analysis.MusicXML.Level3Num (
    module Music.Analysis.MusicXML.Level3Num,
    )where
import Music.Analysis.Base 
import Music.Analysis.PF
import qualified Music.Analysis.MusicXML.Level1Num as Layer1Num
import qualified Music.Analysis.MusicXML.Level2Num as Layer2Num
import Data.Maybe 
import qualified Text.XML.MusicXML as MusicXML
\end{code}

\begin{code}
-- |
type Score_Partwise = 
    (MusicXML.Document_Attributes, (MusicXML.Score_Header, [Part]))
-- |
type Part = [Measure]
-- | 
type Measure = [Music_Data]
-- |
data Music_Data =   
      Music_Data_1 Note 
    | Music_Data_2 MusicXML.Backup 
    | Music_Data_3 MusicXML.Forward 
---    | Music_Data_4 MusicXML.Direction 
    | Music_Data_5 Attributes 
---    | Music_Data_6 MusicXML.Harmony
---    | Music_Data_7 MusicXML.Figured_Bass
---    | Music_Data_8 MusicXML.Print
---    | Music_Data_9 MusicXML.Sound
    | Music_Data_10 Barline
---    | Music_Data_11 MusicXML.Grouping
---    | Music_Data_12 MusicXML.Link
---    | Music_Data_13 MusicXML.Bookmark
      deriving (Eq, Show)
-- |
type Barline = MusicXML.Barline
-- |
type Note = 
    (Note_, Maybe Instrument, Editorial_Voice,
        Maybe Type, [Dot], Maybe Accidental, 
        Maybe Staff)
-- |
data Note_ = 
---          Note_1 (Grace, Full_Note, Maybe (Tie, Maybe Tie))
---        | Note_2 (Cue, Full_Note, Duration)
          Note_3 (Full_Note, Duration) -- , Maybe (Tie, Maybe Tie))
          deriving (Eq, Show)
-- | 
type Full_Note = (Maybe MusicXML.Chord, Full_Note_)
-- |
data Full_Note_ = Full_Note_1 Layer2Num.Pitch
---                | Full_Note_2 Unpitched
                | Full_Note_3 Rest
                  deriving (Eq, Show)
-- | 
type Rest = () -- MusicXML.Rest
-- |
type Duration = IntegerNumber
-- |
type Editorial_Voice = MusicXML.Editorial_Voice
-- |
type Instrument = MusicXML.Instrument
-- |
type Type = Layer1Num.Type_
-- |
type Dot = MusicXML.Dot
-- |
type Accidental = Layer1Num.Accidental_
-- | positive number
type Staff = IntegerNumber
-- |
type Attributes = (Maybe Divisions, [Key], [Time],
    Maybe Staves, Maybe Instruments,
    [Clef], Maybe Transpose)
-- | 
type Editorial = MusicXML.Editorial
-- |
type Divisions = IntegerNumber
-- |
type Key = (Key_, [IntegerNumber])
-- |
data Key_ = Key_1 (Maybe MusicXML.Cancel, Layer2Num.Fifths, Maybe Layer2Num.Mode)
          | Key_2 [(IntegerNumber, Number)]
            deriving (Eq, Show)
-- |
type Time = Time_B
-- |
data Time_B = Time_5 [(Beats, Beat_Type)]
            | Time_6 MusicXML.Senza_Misura
              deriving (Eq, Show)
-- | MusicXML Schema specify "xs:string"
type Beats = (IntegerNumber, Maybe IntegerNumber)
-- | MusicXML Schema specify "xs:string"
type Beat_Type = IntegerNumber
-- |
type Staves = MusicXML.Staves
-- |
type Part_Symbol = MusicXML.Part_Symbol
-- |
type Instruments = MusicXML.Instruments
-- |
type Clef = Layer2Num.Clef
    --(Sign, Maybe Line, Clef_Octave_Change)
-- |
type Staff_Details = MusicXML.Staff_Details
-- |
type Transpose = MusicXML.Transpose
-- |
type Directive = MusicXML.Directive
-- |
type Measure_Style = MusicXML.Measure_Style
\end{code}


\begin{code}
-- |
abst_Score_Partwise :: Score_Partwise -> Layer2Num.Score_Partwise
abst_Score_Partwise = 
    (either (const []) (fmap abst_Measure . head) . grd null) . 
    p2 . p2
--(id -|- fmap abst_Measure . head) . grd null . p2 . p2
-- |
abst_Measure :: Measure -> Layer2Num.Measure
abst_Measure = catMaybes . fmap abst_Music_Data
-- |
abst_Music_Data :: Music_Data -> Maybe Layer2Num.Music_Data
abst_Music_Data (Music_Data_1 x) = Just (Layer2Num.Music_Data_1 (abst_Note x))
--    x' <- abst_Note x
--    return (Layer2Num.Music_Data_1 x')
--    Layer2Num.Music_Data_1 ((catMaybes . (fmap abst_Note)) x)
abst_Music_Data (Music_Data_2 _) = Nothing
abst_Music_Data (Music_Data_3 _) = Nothing
--abst_Music_Data (Music_Data_4 _) = Nothing
abst_Music_Data (Music_Data_5 x) = 
    Just (Layer2Num.Music_Data_5 (abst_Attributes x))
--abst_Music_Data (Music_Data_6 _) = Nothing
--abst_Music_Data (Music_Data_7 _) = Nothing
--abst_Music_Data (Music_Data_8 _) = Nothing
--abst_Music_Data (Music_Data_9 _) = Nothing
abst_Music_Data (Music_Data_10 _) = Nothing
--abst_Music_Data (Music_Data_11 _) = Nothing
--abst_Music_Data (Music_Data_12 _) = Nothing
--abst_Music_Data (Music_Data_13 _) = Nothing
-- |
abst_Note :: Note -> Layer2Num.Note
abst_Note = 
    (\(x1,_,_,x4,x5,x6,_) -> 
        (abst_Note_ x1, fmap abst_Type x4, 
         fmap abst_Dot x5, fmap abst_Accidental x6)) 
-- |
abst_Note_ :: Note_ -> Layer2Num.Note_
--abst_Note_ (Note_1 _) = Nothing
--    Layer2Num.Note_1 (abst_Grace x1, abst_Full_Note x2, 
--      fmap (abst_Tie >< fmap abst_Tie) x3)
--abst_Note_ (Note_2 _) = Nothing
--    Layer2Num.Note_2 (abst_Cue x1, abst_Full_Note x2, abst_Duration x3)
abst_Note_ (Note_3 (x1,x2)) = 
    Layer2Num.Note_3 (abst_Full_Note x1, abst_Duration x2)
--    x1' <- abst_Full_Note x1
--    return (Layer2Num.Note_3 (x1', abst_Duration x2))
-- |
abst_Full_Note :: Full_Note -> Layer2Num.Full_Note
abst_Full_Note = abst_Full_Note_ . p2
--    b' <- abst_Full_Note_ b
--    return (fmap id a, b')
--abst_Full_Note :: Full_Note -> (Maybe Layer2Num.Chord, Maybe Layer2Num.Full_Note_)
--abst_Full_Note = (fmap id >< abst_Full_Note_)
--abst_Full_Note (x,y) = do 
--    y' <- abst_Full_Note_ y
--    return (fmap id x >< fmap id y'))
-- (fmap id >< (\x -> do 
--    y <- abst_Full_Note_ x
--    ))
-- |
abst_Full_Note_ :: Full_Note_ -> Layer2Num.Full_Note_
abst_Full_Note_ (Full_Note_1 x) = (Layer2Num.Full_Note_1 x)
--abst_Full_Note_ (Full_Note_2 _) = Nothing 
abst_Full_Note_ (Full_Note_3 _) = (Layer2Num.Full_Note_3 ())
-- |
abst_Duration :: Duration -> Layer2Num.Duration
abst_Duration = id
-- |
abst_Type :: Type -> Layer2Num.Type
abst_Type = id
-- |
abst_Dot :: Dot -> Layer2Num.Dot
abst_Dot = const ()
-- |
abst_Accidental :: Accidental -> Layer2Num.Accidental
abst_Accidental = id
-- |
abst_Divisions :: Divisions -> Layer2Num.Divisions
abst_Divisions = id
-- |
abst_Attributes :: Attributes -> Layer2Num.Attributes
abst_Attributes (x2,x3,x4,_,_,x8,_) = 
    (fmap abst_Divisions x2, fmap abst_Key x3,
     fmap abst_Time x4, fmap abst_Clef x8)
-- |
abst_Key :: Key -> Layer2Num.Key
abst_Key = (abst_Key_ >< fmap id) 
-- |
abst_Key_ :: Key_ -> Layer2Num.Key_
abst_Key_ (Key_1 x) = (Layer2Num.Key_1 . p2 . unflatr) x
abst_Key_ (Key_2 x) = Layer2Num.Key_2 x
-- |
abst_Time :: Time -> Layer2Num.Time
abst_Time (Time_5 l) = Layer2Num.Time_5 l
abst_Time (Time_6 _) = Layer2Num.Time_5 []
-- |
abst_Clef :: Clef -> Layer2Num.Clef
abst_Clef = id

\end{code}

\begin{code}
-- |
map_Score_Partwise :: (Music_Data -> Music_Data) -> 
    Score_Partwise -> Score_Partwise 
map_Score_Partwise f = (id >< (id >< fmap (map_Part f)))
-- |
map_Part :: (Music_Data -> Music_Data) -> Part -> Part
map_Part f = fmap (map_Measure f)
-- |
map_Measure :: (Music_Data -> Music_Data) -> Measure -> Measure
map_Measure f = fmap (map_Music_Data f)
-- |
map_Music_Data :: (Music_Data -> Music_Data) -> Music_Data -> Music_Data
map_Music_Data f = f
--map_Music_Data :: Music_Data -> Music_Data
--map_Music_Data f (Music_Data_1 x) =  f (Music_Data_1 x)
--map_Music_Data f (Music_Data_2 x) =  f (Music_Data_2 x)
--map_Music_Data f (Music_Data_3 x) =  f (Music_Data_3 x)
--map_Music_Data (Music_Data_4 x) =  Music_Data_4 x
--map_Music_Data f (Music_Data_5 x) =  f (Music_Data_5 x)
--map_Music_Data (Music_Data_6 x) =  Music_Data_6 x
--map_Music_Data (Music_Data_7 x) =  Music_Data_7 x
--map_Music_Data (Music_Data_8 x) =  Music_Data_8 x
--map_Music_Data (Music_Data_9 x) =  Music_Data_9 x
--map_Music_Data f (Music_Data_10 x) = f (Music_Data_10 x)
--map_Music_Data (Music_Data_11 x) = Music_Data_11 x
--map_Music_Data (Music_Data_12 x) = Music_Data_12 x
--map_Music_Data (Music_Data_13 x) = Music_Data_13 x
\end{code}

\begin{nocode}
-- |
type Music = [Part]
-- |
type Part = (PartName, [Measure])
-- |
type PartName = Text
-- |
type Measure = [Either Attributes Note]

-- |
type Attributes = (Maybe Divisions, [Key], [Time], [Clef])

-- |
type Note = ((Maybe Chord, Maybe Instrument, Maybe Staff, Maybe Voice), 
    ((Either Pitch Rest, Accidental), ((Duration, Maybe Type), Dots)))
-- |
type Chord = ()
-- |
type Instrument = Text
-- |
type Staff = Text
-- | 
type Voice = Text
\end{nocode}


\begin{nocode}
rep :: Layer2Num.Music -> Music
rep = (:[]) . 
    split (const "noPartName") 
          ((map . map) (rep_Settings -||- rep_Note)) where 
    rep_Settings :: Layer2Num.Settings -> Settings
    rep_Settings = flatl . 
                   (( e2m . (id -|- (rep_ClefSign >< id)) . m2e >< 
                      e2m . (id -|- (id >< rep_KeyMode)) . m2e) >< id) . 
                   unflatl
    rep_Note :: Layer2Num.Note -> Note
    rep_Note = split (const (Nothing, Nothing, Nothing)) 
                     ((rep_Pitch -|- id) >< (rep_Type >< id))
    rep_Pitch :: Layer2Num.Pitch -> Pitch
    rep_Pitch = flatl . 
                ((rep_Step >< e2m . (id -|- rep_Accidental) . m2e) >< id) . 
                unflatl
rep_Step :: Layer2Num.Step -> Step
rep_Step Layer2Num.A = A
rep_Step Layer2Num.B = B
rep_Step Layer2Num.C = C
rep_Step Layer2Num.D = D
rep_Step Layer2Num.E = E
rep_Step Layer2Num.F = F
rep_Step Layer2Num.G = G
rep_Type :: Layer2Num.Type -> Type
rep_Type Layer2Num.Whole   = Whole
rep_Type Layer2Num.Half    = Half
rep_Type Layer2Num.Quarter = Quarter
rep_Type Layer2Num.Eighth  = Eighth
rep_Type Layer2Num.Th16    = Th16
rep_Type Layer2Num.Th32    = Th32
rep_Type Layer2Num.Th64    = Th64
-- ||
rep_Accidental :: Layer2Num.Accidental -> Accidental
rep_Accidental Layer2Num.DoubleFlat  = DoubleFlat
rep_Accidental Layer2Num.Flat        = Flat
rep_Accidental Layer2Num.Natural     = Natural
rep_Accidental Layer2Num.Sharp       = Sharp
rep_Accidental Layer2Num.DoubleSharp = DoubleSharp
-- ||
rep_ClefSign :: Layer2Num.ClefSign -> ClefSign 
rep_ClefSign Layer2Num.SignC = SignC
rep_ClefSign Layer2Num.SignF = SignF
rep_ClefSign Layer2Num.SignG = SignG
-- ||
rep_KeyMode :: Layer2Num.KeyMode -> KeyMode
rep_KeyMode Layer2Num.Major = Major
rep_KeyMode Layer2Num.Minor = Minor
\end{nocode}


\begin{nocode}
abst :: Music -> Layer2Num.Music
abst = cond null (const []) 
        ((map . map) (abst_Settings -|- abst_Note) . p2 . head) where
    abst_Settings :: Settings -> Layer2Num.Settings
    abst_Settings = flatl . 
                   (( e2m . (id -|- (abst_ClefSign >< id)) . m2e >< 
                      e2m . (id -|- (id >< abst_KeyMode)) . m2e) >< id) . 
                   unflatl
    abst_Note :: Note -> Layer2Num.Note
    abst_Note = ((abst_Pitch -|- id) >< (abst_Type >< id)) . p2
    abst_Pitch :: Pitch -> Layer2Num.Pitch 
    abst_Pitch = (flatl . 
                 ((abst_Step >< e2m . (id -||- abst_Accidental) . m2e) >< id) . 
                 unflatl)
abst_Step :: Step -> Layer2Num.Step 
abst_Step A = Layer2Num.A
abst_Step B = Layer2Num.B
abst_Step C = Layer2Num.C
abst_Step D = Layer2Num.D
abst_Step E = Layer2Num.E
abst_Step F = Layer2Num.F
abst_Step G = Layer2Num.G
abst_Type :: Type -> Layer2Num.Type 
abst_Type Whole   = Layer2Num.Whole
abst_Type Half    = Layer2Num.Half
abst_Type Quarter = Layer2Num.Quarter
abst_Type Eighth  = Layer2Num.Eighth
abst_Type Th16    = Layer2Num.Th16
abst_Type Th32    = Layer2Num.Th32
abst_Type Th64    = Layer2Num.Th64
abst_Accidental :: Accidental -> Layer2Num.Accidental
abst_Accidental DoubleFlat  = Layer2Num.DoubleFlat
abst_Accidental Flat        = Layer2Num.Flat
abst_Accidental Natural     = Layer2Num.Natural
abst_Accidental Sharp       = Layer2Num.Sharp
abst_Accidental DoubleSharp = Layer2Num.DoubleSharp
abst_ClefSign :: ClefSign -> Layer2Num.ClefSign 
abst_ClefSign SignC = Layer2Num.SignC
abst_ClefSign SignF = Layer2Num.SignF
abst_ClefSign SignG = Layer2Num.SignG
abst_KeyMode :: KeyMode -> Layer2Num.KeyMode
abst_KeyMode Major = Layer2Num.Major
abst_KeyMode Minor = Layer2Num.Minor
\end{nocode}


\begin{nocode}
--mapLayer2Num :: (Layer2Num.Music -> Layer2Num.Music) -> Music -> Music
--    [(Text, [[Either Settings (Either Pitch Rest)]])]
--mapLayer2Num :: (Layer2Num.Music -> Layer2Num.Music) -> Music -> 
--    [(PartName, ([[Either Settings (Maybe Instrument, Maybe Staff, Maybe Voice)]],
--        [[Either Settings (Either Pitch Rest, (Type, Dots))]]))]
mapLayer2Num :: ([[Either Settings (a,(Either Pitch Rest,(Type, Dots)))]] -> 
    [[Either Settings (a,(Either Pitch Rest,(Type, Dots)))]]) -> Music -> Music
mapLayer2Num f = 
    map (id >< (map.map) aux1) .
    map (id >< map (uncurry zip) . uncurry zip ) . map (unflatr . flatl) .
    map (id >< post2 . f . pre2) . map (unflatl . flatr) .
    map (id >< 
        split ((map.map) ((id -|- p1))) ((map.map) (id -|- p2))) 
    where
    aux1 :: (Either b a, Either b c) -> Either b (a,c)
    aux1 (Right a, Right c) = Right (a,c)
    aux1 (Left b, _) = Left b
    aux1 (_, Left b) = Left b
    pre2 :: [[Either Settings (Either Pitch Rest, (Type, Dots))]] -> 
        [[Either Settings (Either Pitch Rest, (Type, Dots))]]
    pre2 = (map . map) (id -|- id) -- where
--        abst_Settings :: Settings -> Layer2Num.Settings
--        abst_Settings = flatl . 
--                       (( e2m . (id -|- (abst_ClefSign >< id)) . m2e >< 
--                          e2m . (id -|- (id >< abst_KeyMode)) . m2e) >< id) . 
--                       unflatl
--        abst_Note :: (Either Pitch Rest, (Type, Dots)) -> Layer2Num.Note
--        abst_Note = ((abst_Pitch -|- id) >< (abst_Type >< id)) 
--        abst_Pitch :: Pitch -> Layer2Num.Pitch 
--        abst_Pitch = (flatl . 
--                     ((abst_Step >< e2m .(id -|- abst_Accidental). m2e) >< id) . 
--                     unflatl)
    post2 :: [[Either Settings (Either Pitch Rest, (Type, Dots))]] -> 
        [[Either Settings (Either Pitch Rest, (Type, Dots))]]
    post2 = ((map . map) (id -|- id)) -- where 
--        rep_Settings :: Layer2Num.Settings -> Settings
--        rep_Settings = flatl . 
--                       (( e2m . (id -|- (rep_ClefSign >< id)) . m2e >< 
--                          e2m . (id -|- (id >< rep_KeyMode)) . m2e) >< id) . 
--                       unflatl
--        rep_Note :: Layer2Num.Note -> (Either Pitch Rest, (Type, Dots))
--        rep_Note = ((rep_Pitch -|- id) >< (rep_Type >< id))
--        rep_Pitch :: Layer2Num.Pitch -> Pitch
--        rep_Pitch = flatl . 
--                    ((rep_Step >< e2m . (id -|- rep_Accidental) . m2e) >< id) . 
--                    unflatl
\end{nocode}

\begin{nocode}
mapLayer2' :: (Either Attributes Note -> Either Attributes Note) -> 
    Music -> Music
mapLayer2' f = 
--    map (id >< (map . map) (id -|- swap)) .
    map (id >< (map . map) (post2 . f . pre2))
--    map (id >< (map . map) )
    where
        pre2 :: Either a Note -> Either a Note
        pre2 = (id -|- (id >< id)) -- where
--        abst_Settings :: Settings -> Layer2Num.Settings
--        abst_Settings = flatl . 
--                       (( e2m . (id -|- (abst_ClefSign >< id)) . m2e >< 
--                          e2m . (id -|- (id >< abst_KeyMode)) . m2e) >< id) . 
--                       unflatl
--        abst_Note :: (Either Pitch Rest, (Type, Dots)) -> Layer2Num.Note
--        abst_Note = ((abst_Pitch -|- id) >< (abst_Type >< id)) 
--        abst_Pitch :: Pitch -> Layer2Num.Pitch 
--        abst_Pitch = (flatl . 
--                     ((abst_Step >< e2m .(id -|- abst_Accidental). m2e) >< id) . 
--                     unflatl)
        post2 :: Either a Note -> Either a Note
        post2 = (id -|- (id >< id)) -- where 
--        rep_Settings :: Layer2Num.Settings -> Settings
--        rep_Settings = flatl . 
--                       (( e2m . (id -|- (rep_ClefSign >< id)) . m2e >< 
--                          e2m . (id -|- (id >< rep_KeyMode)) . m2e) >< id) . 
--                       unflatl
--        rep_Note :: Layer2Num.Note -> (Either Pitch Rest, (Type, Dots))
--        rep_Note = ((rep_Pitch -|- id) >< (rep_Type >< id))
--        rep_Pitch :: Layer2Num.Pitch -> Pitch
--        rep_Pitch = flatl . 
--                    ((rep_Step >< e2m . (id -|- rep_Accidental) . m2e) >< id) . 
--                    unflatl
--    map (id >< (map . map) (id -|- swap)) 
\end{nocode}