{-# LANGUAGE DeriveDataTypeable, TypeSynonymInstances, FlexibleInstances #-}
{-# LANGUAGE DeriveFunctor #-}
{-# OPTIONS_GHC -fno-warn-orphans #-}

module Sound.Tidal.Pattern where

import           Prelude hiding ((<*), (*>))

import           Control.Applicative (liftA2)
--import           Data.Bifunctor (Bifunctor(..))
import           Data.Data (Data) -- toConstr
import           Data.List (delete, findIndex, sort, intercalate)
import qualified Data.Map.Strict as Map
import           Data.Maybe (isJust, fromJust, catMaybes, fromMaybe, mapMaybe)
import           Data.Ratio (numerator, denominator)
import           Data.Typeable (Typeable)
import           Control.DeepSeq (NFData(rnf))
import           Data.Word (Word8)

------------------------------------------------------------------------
-- * Types

-- | Time is rational
type Time = Rational 

-- | The 'sam' (start of cycle) for the given time value
sam :: Time -> Time
sam = fromIntegral . (floor :: Time -> Int)

-- | Turns a number into a (rational) time value. An alias for 'toRational'.
toTime :: Real a => a -> Rational
toTime = toRational

-- | The end point of the current cycle (and starting point of the next cycle)
nextSam :: Time -> Time
nextSam = (1+) . sam

-- | The position of a time value relative to the start of its cycle.
cyclePos :: Time -> Time
cyclePos t = t - sam t

-- | An arc of time, with a start time (or onset) and a stop time (or offset)
data ArcF a = Arc
  { start :: a
  , stop :: a
  } deriving (Eq, Ord, Functor)

type Arc = ArcF Time

instance NFData a => 
  NFData (ArcF a) where 
    rnf (Arc s e) = rnf s `seq` rnf e

instance {-# OVERLAPPING #-} Show Arc where
  show (Arc s e) = prettyRat s ++ ">" ++ prettyRat e

instance Num a => Num (ArcF a) where
  negate      = fmap negate
  (+)         = liftA2 (+)
  (*)         = liftA2 (*)
  fromInteger = pure . fromInteger
  abs         = fmap abs
  signum      = fmap signum

instance (Fractional a) => Fractional (ArcF a) where
  recip        = fmap recip
  fromRational = pure . fromRational

sect :: Arc -> Arc -> Arc
sect (Arc s e) (Arc s' e') = Arc (max s s') (min e e')

-- | convex hull union
hull :: Arc -> Arc -> Arc
hull (Arc s e) (Arc s' e') = Arc (min s s') (max e e')

-- | @subArc i j@ is the timespan that is the intersection of @i@ and @j@.
-- intersection
-- The definition is a bit fiddly as results might be zero-width, but
-- not at the end of an non-zero-width arc - e.g. (0,1) and (1,2) do
-- not intersect, but (1,1) (1,1) does.
subArc :: Arc -> Arc -> Maybe Arc
subArc a@(Arc s e) b@(Arc s' e')
  | and [s'' == e'', s'' == e, s < e] = Nothing
  | and [s'' == e'', s'' == e', s' < e'] = Nothing
  | s'' <= e'' = Just (Arc s'' e'')
  | otherwise = Nothing
  where (Arc s'' e'') = sect a b

subMaybeArc :: Maybe Arc -> Maybe Arc -> Maybe (Maybe Arc)
subMaybeArc (Just a) (Just b) = do sa <- subArc a b
                                   return $ Just sa
subMaybeArc _ _ = Just Nothing

instance Applicative ArcF where
  pure t = Arc t t
  (<*>) (Arc sf ef) (Arc sx ex) = Arc (sf sx) (ef ex)

-- | The arc of the whole cycle that the given time value falls within
timeToCycleArc :: Time -> Arc
timeToCycleArc t = Arc (sam t) (sam t + 1)

-- | Shifts an arc to the equivalent one that starts during cycle zero
cycleArc :: Arc -> Arc
cycleArc (Arc s e) = Arc (cyclePos s) (cyclePos s + (e-s))

-- | A list of cycle numbers which are included in the given arc
cyclesInArc :: Integral a => Arc -> [a]
cyclesInArc (Arc s e)
  | s > e = []
  | s == e = [floor s]
  | otherwise = [floor s .. ceiling e-1]

-- | A list of arcs of the whole cycles which are included in the given arc
cycleArcsInArc :: Arc -> [Arc]
cycleArcsInArc = map (timeToCycleArc . (toTime :: Int -> Time)) . cyclesInArc

-- | Splits the given 'Arc' into a list of 'Arc's, at cycle boundaries.
arcCycles :: Arc -> [Arc]
arcCycles (Arc s e) | s >= e = []
                | sam s == sam e = [Arc s e]
                | otherwise = Arc s (nextSam s) : arcCycles (Arc (nextSam s) e)

-- | Like arcCycles, but returns zero-width arcs
arcCyclesZW :: Arc -> [Arc]
arcCyclesZW (Arc s e) | s == e = [Arc s e]
                  | otherwise = arcCycles (Arc s e)

-- | Similar to 'fmap' but time is relative to the cycle (i.e. the
-- sam of the start of the arc)
mapCycle :: (Time -> Time) -> Arc -> Arc
mapCycle f (Arc s e) = Arc (sam' + f (s - sam')) (sam' + f (e - sam'))
         where sam' = sam s

-- | @isIn a t@ is @True@ if @t@ is inside
-- the arc represented by @a@.
isIn :: Arc -> Time -> Bool
isIn (Arc s e) t = t >= s && t < e

data Context = Context {contextPosition :: [((Int, Int), (Int, Int))]}
  deriving (Eq, Ord)

instance NFData Context where 
    rnf (Context c) = rnf c

instance Show Context where
  show (Context cs) = show cs

combineContexts :: [Context] -> Context
combineContexts = Context . concatMap contextPosition

setContext :: Context -> Pattern a -> Pattern a
setContext c pat = withEvents (map (\e -> e {context = c})) pat

withContext :: (Context -> Context) -> Pattern a -> Pattern a
withContext f pat = withEvents (map (\e -> e {context = f $ context e})) pat

deltaContext :: Int -> Int -> Pattern a -> Pattern a
deltaContext column line pat = withEvents (map (\e -> e {context = f $ context e})) pat
  where f :: Context -> Context
        f (Context xs) = Context $ map (\((bx,by), (ex,ey)) -> ((bx+column,by+line), (ex+column,ey+line))) xs

-- | An event is a value that's active during a timespan. If a whole
-- is present, the part should be equal to or fit inside it.
data EventF a b = Event
  { context :: Context
  , whole :: Maybe a
  , part :: a
  , value :: b
  } deriving (Eq, Ord, Functor)

type Event a = EventF (ArcF Time) a

instance (NFData a, NFData b) => 
  NFData (EventF a b) where 
    rnf (Event c w p v) = rnf c `seq` rnf w `seq` rnf p `seq` rnf v

{-instance Bifunctor EventF where
  bimap f g (Event w p e) = Event (f w) (f p) (g e)
-}

instance {-# OVERLAPPING #-} Show a => Show (Event a) where
  show (Event c (Just (Arc ws we)) a@(Arc ps pe) e) =
    show c ++ h ++ "(" ++ show a ++ ")" ++ t ++ "|" ++ show e
    where h | ws == ps = ""
            | otherwise = prettyRat ws ++ "-"
          t | we == pe = ""
            | otherwise = "-" ++ prettyRat we
  show (Event c Nothing a e) =
    show c ++ "~" ++ show a ++ "~|" ++ show e

isAnalog :: Event a -> Bool
isAnalog (Event {whole = Nothing}) = True
isAnalog _ = False

isDigital :: Event a -> Bool
isDigital = not . isAnalog

-- | `True` if an `Event`'s starts is within given `Arc`
onsetIn :: Arc -> Event a -> Bool
onsetIn a e = isIn a (wholeStart e)

-- | Compares two lists of events, attempting to combine fragmented events in the process
-- for a 'truer' compare
compareDefrag :: (Ord a) => [Event a] -> [Event a] -> Bool
compareDefrag as bs = sort (defragParts as) == sort (defragParts bs)

-- | Returns a list of events, with any adjacent parts of the same whole combined
defragParts :: Eq a => [Event a] -> [Event a]
defragParts [] = []
defragParts [e] = [e]
defragParts (e:es) | isJust i = defraged : defragParts (delete e' es)
                   | otherwise = e : defragParts es
  where i = findIndex (isAdjacent e) es
        e' = es !! fromJust i
        defraged = Event (context e) (whole e) u (value e)
        u = hull (part e) (part e')

-- | Returns 'True' if the two given events are adjacent parts of the same whole
isAdjacent :: Eq a => Event a -> Event a -> Bool
isAdjacent e e' = (whole e == whole e')
                  && (value e == value e')
                  && ((stop (part e) == start (part e'))
                      ||
                      (stop (part e') == start (part e))
                     )

wholeOrPart :: Event a -> Arc
wholeOrPart (Event {whole = Just a}) = a
wholeOrPart e = part e

-- | Get the onset of an event's 'whole'
wholeStart :: Event a -> Time
wholeStart = start . wholeOrPart

-- | Get the offset of an event's 'whole'
wholeStop :: Event a -> Time
wholeStop = stop . wholeOrPart

-- | Get the onset of an event's 'whole'
eventPartStart :: Event a -> Time
eventPartStart = start . part

-- | Get the offset of an event's 'part'
eventPartStop :: Event a -> Time
eventPartStop = stop . part

-- | Get the timespan of an event's 'part'
eventPart :: Event a -> Arc
eventPart = part

eventValue :: Event a -> a
eventValue = value

eventHasOnset :: Event a -> Bool
eventHasOnset e | isAnalog e = False
                | otherwise = start (fromJust $ whole e) == start (part e)

-- TODO - Is this used anywhere? Just tests, it seems
-- TODO - support 'context' field
toEvent :: (((Time, Time), (Time, Time)), a) -> Event a
toEvent (((ws, we), (ps, pe)), v) = Event (Context []) (Just $ Arc ws we) (Arc ps pe) v

-- | an Arc and some named control values
data State = State {arc :: Arc,
                    controls :: StateMap
                   }

-- | A function that represents events taking place over time
type Query a = (State -> [Event a])

-- | A datatype that's basically a query
data Pattern a = Pattern {query :: Query a}

data Value = VS { svalue :: String }
           | VF { fvalue :: Double }
           | VR { rvalue :: Rational }
           | VI { ivalue :: Int }
           | VB { bvalue :: Bool }
           | VX { xvalue :: [Word8] } -- Used for OSC 'blobs'
           deriving (Typeable,Data)

class Valuable a where
  toValue :: a -> Value

instance NFData Value where 
  rnf (VS s) = rnf s 
  rnf (VF f) = rnf f 
  rnf (VR r) = rnf r 
  rnf (VI i) = rnf i 
  rnf (VB b) = rnf b
  rnf (VX xs) = rnf xs

instance Valuable String where
  toValue = VS
instance Valuable Double where
  toValue a = VF a
instance Valuable Rational where
  toValue a = VR a
instance Valuable Int where
  toValue a = VI a
instance Valuable Bool where
  toValue a = VB a
instance Valuable [Word8] where
  toValue a = VX a

instance Eq Value where
  (VS x) == (VS y) = x == y
  (VB x) == (VB y) = x == y
  (VF x) == (VF y) = x == y
  (VI x) == (VI y) = x == y
  (VR x) == (VR y) = x == y
  (VX x) == (VX y) = x == y
  
  (VF x) == (VI y) = x == (fromIntegral y)
  (VI y) == (VF x) = x == (fromIntegral y)

  (VF x) == (VR y) = (toRational x) == y
  (VR y) == (VF x) = (toRational x) == y
  (VI x) == (VR y) = (toRational x) == y
  (VR y) == (VI x) = (toRational x) == y

  _ == _ = False
  
instance Ord Value where
  compare (VS x) (VS y) = compare x y
  compare (VB x) (VB y) = compare x y
  compare (VF x) (VF y) = compare x y
  compare (VI x) (VI y) = compare x y
  compare (VR x) (VR y) = compare x y
  compare (VX x) (VX y) = compare x y
  compare (VS _) _ = LT
  compare _ (VS _) = GT
  compare (VB _) _ = LT
  compare _ (VB _) = GT
  compare (VX _) _ = LT
  compare _ (VX _) = GT
  compare (VF x) (VI y) = compare x (fromIntegral y)
  compare (VI x) (VF y) = compare (fromIntegral x) y

  compare (VR x) (VI y) = compare x (fromIntegral y)
  compare (VI x) (VR y) = compare (fromIntegral x) y

  compare (VF x) (VR y) = compare x (fromRational y)
  compare (VR x) (VF y) = compare (fromRational x) y

type StateMap = Map.Map String (Pattern Value)
type ControlMap = Map.Map String Value
type ControlPattern = Pattern ControlMap

------------------------------------------------------------------------
-- * Instances

instance NFData a => 
  NFData (Pattern a) where 
    rnf (Pattern q) = rnf $ \s -> q s

instance Functor Pattern where
  -- | apply a function to all the values in a pattern
  fmap f p = p {query = fmap (fmap f) . query p}

applyPatToPat :: (Maybe Arc -> Maybe Arc -> Maybe (Maybe Arc)) -> Pattern (a -> b) -> Pattern a -> Pattern b
applyPatToPat combineWholes pf px = Pattern q
    where q st = catMaybes $ concatMap match $ query pf st
            where
              match (ef@(Event (Context c) _ fPart f)) =
                map
                (\ex@(Event (Context c') _ xPart x) ->
                  do whole' <- combineWholes (whole ef) (whole ex)
                     part' <- subArc fPart xPart
                     return (Event (Context $ c ++ c') whole' part' (f x))
                )
                (query px $ st {arc = (wholeOrPart ef)})

instance Applicative Pattern where
  -- | Repeat the given value once per cycle, forever
  pure v = Pattern $ \(State a _) ->
    map (\a' -> Event (Context []) (Just a') (sect a a') v) $ cycleArcsInArc a

  (<*>) = applyPatToPatBoth

applyPatToPatBoth :: Pattern (a -> b) -> Pattern a -> Pattern b
applyPatToPatBoth pf px = Pattern q
    where q st = catMaybes $ (concatMap match $ query pf st) ++ (concatMap matchX $ query (filterAnalog px) st)
            where
              -- match analog events from pf with all events from px
              match ef@(Event _ Nothing fPart _)   = map (withFX ef) (query px $ st {arc = fPart}) -- analog
              -- match digital events from pf with digital events from px
              match ef@(Event _ (Just fWhole) _ _) = map (withFX ef) (query (filterDigital px) $ st {arc = fWhole}) -- digital
              -- match analog events from px (constrained above) with digital events from px
              matchX ex@(Event _ Nothing fPart _)  = map (\ef -> withFX ef ex) (query (filterDigital pf) $ st {arc = fPart}) -- digital
              matchX _ = error "can't happen"
              withFX ef ex = do whole' <- subMaybeArc (whole ef) (whole ex)
                                part' <- subArc (part ef) (part ex)
                                return (Event (combineContexts [context ef, context ex]) whole' part' (value ef $ value ex))

applyPatToPatLeft :: Pattern (a -> b) -> Pattern a -> Pattern b
applyPatToPatLeft pf px = Pattern q
    where q st = catMaybes $ (concatMap match $ query pf st)
            where
              match ef = map (withFX ef) (query px $ st {arc = wholeOrPart ef})
              withFX ef ex = do let whole' = whole ef
                                part' <- subArc (part ef) (part ex)
                                return (Event (combineContexts [context ef, context ex]) whole' part' (value ef $ value ex))

applyPatToPatRight :: Pattern (a -> b) -> Pattern a -> Pattern b
applyPatToPatRight pf px = Pattern q
    where q st = catMaybes $ (concatMap match $ query px st)
            where
              match ex = map (\ef -> withFX ef ex) (query pf $ st {arc = wholeOrPart ex})
              withFX ef ex = do let whole' = whole ex
                                part' <- subArc (part ef) (part ex)
                                return (Event (combineContexts [context ef, context ex]) whole' part' (value ef $ value ex))


-- | Like <*>, but the 'wholes' come from the left
(<*) :: Pattern (a -> b) -> Pattern a -> Pattern b
(<*) = applyPatToPatLeft

-- | Like <*>, but the 'wholes' come from the right
(*>) :: Pattern (a -> b) -> Pattern a -> Pattern b
(*>) = applyPatToPatRight

infixl 4 <*, *>

instance Monad Pattern where
  return = pure
  p >>= f = unwrap (f <$> p)

-- | Turns a pattern of patterns into a single pattern.
-- (this is actually 'join')
--
-- 1/ For query 'arc', get the events from the outer pattern @pp@
-- 2/ Query the inner pattern using the 'part' of the outer
-- 3/ For each inner event, set the whole and part to be the intersection
--    of the outer whole and part, respectively
-- 4/ Concatenate all the events together (discarding wholes/parts that didn't intersect)
--
-- TODO - what if a continuous pattern contains a discrete one, or vice-versa?
unwrap :: Pattern (Pattern a) -> Pattern a
unwrap pp = pp {query = q}
  where q st = concatMap
          (\(Event c w p v) ->
             mapMaybe (munge c w p) $ query v st {arc = p})
          (query pp st)
        munge oc ow op (Event ic iw ip v') =
          do
            w' <- subMaybeArc ow iw
            p' <- subArc op ip
            return (Event (combineContexts [ic, oc]) w' p' v')

-- | Turns a pattern of patterns into a single pattern. Like @unwrap@,
-- but structure only comes from the inner pattern.
innerJoin :: Pattern (Pattern a) -> Pattern a
innerJoin pp = pp {query = q}
  where q st = concatMap
               (\(Event oc _ op v) -> mapMaybe (munge oc) $ query v st {arc = op}
          )
          (query pp st)
          where munge oc (Event ic iw ip v) =
                  do
                    p <- subArc (arc st) ip
                    p' <- subArc p (arc st)
                    return (Event (combineContexts [ic, oc]) iw p' v)

-- | Turns a pattern of patterns into a single pattern. Like @unwrap@,
-- but structure only comes from the outer pattern.
outerJoin :: Pattern (Pattern a) -> Pattern a
outerJoin pp = pp {query = q}
  where q st = concatMap
          (\e ->
             mapMaybe (munge (context e) (whole e) (part e)) $ query (value e) st {arc = pure (start $ wholeOrPart e)}
          )
          (query pp st)
          where munge oc ow op (Event ic _ _ v') =
                  do
                    p' <- subArc (arc st) op
                    return (Event (combineContexts [oc, ic]) ow p' v')

-- | Like @unwrap@, but cycles of the inner patterns are compressed to fit the
-- timespan of the outer whole (or the original query if it's a continuous pattern?)
-- TODO - what if a continuous pattern contains a discrete one, or vice-versa?
squeezeJoin :: Pattern (Pattern a) -> Pattern a
squeezeJoin pp = pp {query = q}
  where q st = concatMap
          (\e@(Event c w p v) ->
             mapMaybe (munge c w p) $ query (compressArc (cycleArc $ wholeOrPart e) v) st {arc = p}
          )
          (query pp st)
        munge oContext oWhole oPart (Event iContext iWhole iPart v) =
          do w' <- subMaybeArc oWhole iWhole
             p' <- subArc oPart iPart
             return (Event (combineContexts [iContext, oContext]) w' p' v)

noOv :: String -> a
noOv meth = error $ meth ++ ": not supported for patterns"

class TolerantEq a where
   (~==) :: a -> a -> Bool

instance TolerantEq Value where
         (VS a) ~== (VS b) = a == b
         (VI a) ~== (VI b) = a == b
         (VR a) ~== (VR b) = a == b
         (VF a) ~== (VF b) = abs (a - b) < 0.000001
         _ ~== _ = False

instance TolerantEq ControlMap where
  a ~== b = Map.differenceWith (\a' b' -> if a' ~== b' then Nothing else Just a') a b == Map.empty

instance TolerantEq (Event ControlMap) where
  (Event _ w p x) ~== (Event _ w' p' x') = w == w' && p == p' && x ~== x'

instance TolerantEq a => TolerantEq [a] where
  as ~== bs = (length as == length bs) && all (uncurry (~==)) (zip as bs)


instance Eq (Pattern a) where
  (==) = noOv "(==)"

instance Ord a => Ord (Pattern a) where
  min = liftA2 min
  max = liftA2 max
  compare = noOv "compare"
  (<=) = noOv "(<=)"

instance Num a => Num (Pattern a) where
  negate      = fmap negate
  (+)         = liftA2 (+)
  (*)         = liftA2 (*)
  fromInteger = pure . fromInteger
  abs         = fmap abs
  signum      = fmap signum

instance Enum a => Enum (Pattern a) where
  succ           = fmap succ
  pred           = fmap pred
  toEnum         = pure . toEnum
  fromEnum       = noOv "fromEnum"
  enumFrom       = noOv "enumFrom"
  enumFromThen   = noOv "enumFromThen"
  enumFromTo     = noOv "enumFromTo"
  enumFromThenTo = noOv "enumFromThenTo"

instance (Num a, Ord a) => Real (Pattern a) where
  toRational = noOv "toRational"

instance (Integral a) => Integral (Pattern a) where
  quot          = liftA2 quot
  rem           = liftA2 rem
  div           = liftA2 div
  mod           = liftA2 mod
  toInteger     = noOv "toInteger"
  x `quotRem` y = (x `quot` y, x `rem` y)
  x `divMod`  y = (x `div`  y, x `mod` y)

instance (Fractional a) => Fractional (Pattern a) where
  recip        = fmap recip
  fromRational = pure . fromRational

instance (Floating a) => Floating (Pattern a) where
  pi    = pure pi
  sqrt  = fmap sqrt
  exp   = fmap exp
  log   = fmap log
  sin   = fmap sin
  cos   = fmap cos
  asin  = fmap asin
  atan  = fmap atan
  acos  = fmap acos
  sinh  = fmap sinh
  cosh  = fmap cosh
  asinh = fmap asinh
  atanh = fmap atanh
  acosh = fmap acosh

instance (RealFrac a) => RealFrac (Pattern a) where
  properFraction = noOv "properFraction"
  truncate       = noOv "truncate"
  round          = noOv "round"
  ceiling        = noOv "ceiling"
  floor          = noOv "floor"

instance (RealFloat a) => RealFloat (Pattern a) where
  floatRadix     = noOv "floatRadix"
  floatDigits    = noOv "floatDigits"
  floatRange     = noOv "floatRange"
  decodeFloat    = noOv "decodeFloat"
  encodeFloat    = ((.).(.)) pure encodeFloat
  exponent       = noOv "exponent"
  significand    = noOv "significand"
  scaleFloat n   = fmap (scaleFloat n)
  isNaN          = noOv "isNaN"
  isInfinite     = noOv "isInfinite"
  isDenormalized = noOv "isDenormalized"
  isNegativeZero = noOv "isNegativeZero"
  isIEEE         = noOv "isIEEE"
  atan2          = liftA2 atan2

instance Num ControlMap where
  negate      = (applyFIS negate negate id <$>)
  (+)         = Map.unionWith (fNum2 (+) (+))
  (*)         = Map.unionWith (fNum2 (*) (*))
  fromInteger i = Map.singleton "n" $ VI $ fromInteger i
  signum      = (applyFIS signum signum id <$>)
  abs         = (applyFIS abs abs id <$>)

instance Fractional ControlMap where
  recip        = fmap (applyFIS recip id id)
  fromRational = Map.singleton "speed" . VF . fromRational

showPattern :: Show a => Arc -> Pattern a -> String
showPattern a p = intercalate "\n" $ map show $ queryArc p a

instance (Show a) => Show (Pattern a) where
  show = showPattern (Arc 0 1)

instance Show Value where
  show (VS s) = ('"':s) ++ "\""
  show (VI i) = show i
  show (VF f) = show f ++ "f"
  show (VR r) = show r ++ "r"
  show (VB b) = show b
  show (VX xs) = show xs

instance {-# OVERLAPPING #-} Show ControlMap where
  show m = intercalate ", " $ map (\(name, v) -> name ++ ": " ++ show v) $ Map.toList m

prettyRat :: Rational -> String
prettyRat r | unit == 0 && frac > 0 = showFrac (numerator frac) (denominator frac)
            | otherwise =  show unit ++ showFrac (numerator frac) (denominator frac)
  where unit = floor r :: Int
        frac = r - toRational unit

showFrac :: Integer -> Integer -> String
showFrac 0 _ = ""
showFrac 1 2 = "½"
showFrac 1 3 = "⅓"
showFrac 2 3 = "⅔"
showFrac 1 4 = "¼"
showFrac 3 4 = "¾"
showFrac 1 5 = "⅕"
showFrac 2 5 = "⅖"
showFrac 3 5 = "⅗"
showFrac 4 5 = "⅘"
showFrac 1 6 = "⅙"
showFrac 5 6 = "⅚"
showFrac 1 7 = "⅐"
showFrac 1 8 = "⅛"
showFrac 3 8 = "⅜"
showFrac 5 8 = "⅝"
showFrac 7 8 = "⅞"
showFrac 1 9 = "⅑"
showFrac 1 10 = "⅒"

showFrac n d = fromMaybe plain $ do n' <- up n
                                    d' <- down d
                                    return $ n' ++ d'
  where plain = " " ++ show n ++ "/" ++ show d
        up 1 = Just "¹"
        up 2 = Just "²"
        up 3 = Just "³"
        up 4 = Just "⁴"
        up 5 = Just "⁵"
        up 6 = Just "⁶"
        up 7 = Just "⁷"
        up 8 = Just "⁸"
        up 9 = Just "⁹"
        up 0 = Just "⁰"
        up _ = Nothing
        down 1 = Just "₁"
        down 2 = Just "₂"
        down 3 = Just "₃"
        down 4 = Just "₄"
        down 5 = Just "₅"
        down 6 = Just "₆"
        down 7 = Just "₇"
        down 8 = Just "₈"
        down 9 = Just "₉"
        down 0 = Just "₀"
        down _ = Nothing

------------------------------------------------------------------------
-- * Internal functions

empty :: Pattern a
empty = Pattern {query = const []}

queryArc :: Pattern a -> Arc -> [Event a]
queryArc p a = query p $ State a Map.empty 

-- | Splits queries that span cycles. For example `query p (0.5, 1.5)` would be
-- turned into two queries, `(0.5,1)` and `(1,1.5)`, and the results
-- combined. Being able to assume queries don't span cycles often
-- makes transformations easier to specify.
splitQueries :: Pattern a -> Pattern a
splitQueries p = p {query = \st -> concatMap (\a -> query p st {arc = a}) $ arcCyclesZW (arc st)}

-- | Apply a function to the arcs/timespans (both whole and parts) of the result
withResultArc :: (Arc -> Arc) -> Pattern a -> Pattern a
withResultArc f pat = pat
  { query = map (\(Event c w p e) -> Event c (f <$> w) (f p) e) . query pat}

-- | Apply a function to the time (both start and end of the timespans
-- of both whole and parts) of the result
withResultTime :: (Time -> Time) -> Pattern a -> Pattern a
withResultTime f = withResultArc (\(Arc s e) -> Arc (f s) (f e))

-- | Apply a function to the timespan of the query
withQueryArc :: (Arc -> Arc) -> Pattern a -> Pattern a
withQueryArc f p = p {query = query p . (\(State a m) -> State (f a) m)}

-- | Apply a function to the time (both start and end) of the query
withQueryTime :: (Time -> Time) -> Pattern a -> Pattern a
withQueryTime f = withQueryArc (\(Arc s e) -> Arc (f s) (f e))

-- | @withEvent f p@ returns a new @Pattern@ with each event mapped over
-- function @f@.
withEvent :: (Event a -> Event b) -> Pattern a -> Pattern b
withEvent f p = p {query = map f . query p}

-- | @withEvent f p@ returns a new @Pattern@ with f applied to the resulting list of events for each query
-- function @f@.
withEvents :: ([Event a] -> [Event b]) -> Pattern a -> Pattern b
withEvents f p = p {query = f . query p}

-- | @withPart f p@ returns a new @Pattern@ with function @f@ applied
-- to the part.
withPart :: (Arc -> Arc) -> Pattern a -> Pattern a
withPart f = withEvent (\(Event c w p v) -> Event c w (f p) v)

-- | Apply one of three functions to a Value, depending on its type
applyFIS :: (Double -> Double) -> (Int -> Int) -> (String -> String) -> Value -> Value
applyFIS f _ _ (VF f') = VF $ f f'
applyFIS _ f _ (VI i ) = VI $ f i
applyFIS _ _ f (VS s ) = VS $ f s
applyFIS _ _ _ v = v

-- | Apply one of two functions to a Value, depending on its type (int
-- or float; strings and rationals are ignored)
fNum2 :: (Int -> Int -> Int) -> (Double -> Double -> Double) -> Value -> Value -> Value
fNum2 fInt _      (VI a) (VI b) = VI $ fInt a b
fNum2 _    fFloat (VF a) (VF b) = VF $ fFloat a b
fNum2 _    fFloat (VI a) (VF b) = VF $ fFloat (fromIntegral a) b
fNum2 _    fFloat (VF a) (VI b) = VF $ fFloat a (fromIntegral b)
fNum2 _    _      x      _      = x

getI :: Value -> Maybe Int
getI (VI i) = Just i
getI (VR x) = Just $ floor x
getI (VF x) = Just $ floor x
getI _  = Nothing

getF :: Value -> Maybe Double
getF (VF f) = Just f
getF (VR x) = Just $ fromRational x
getF (VI x) = Just $ fromIntegral x
getF _  = Nothing

getS :: Value -> Maybe String
getS (VS s) = Just s
getS _  = Nothing

getB :: Value -> Maybe Bool
getB (VB b) = Just b
getB _  = Nothing

getR :: Value -> Maybe Rational
getR (VR r) = Just r
getR (VF x) = Just $ toRational x
getR (VI x) = Just $ toRational x
getR _  = Nothing

getBlob :: Value -> Maybe [Word8]
getBlob (VX xs) = Just xs
getBlob _  = Nothing

compressArc :: Arc -> Pattern a -> Pattern a
compressArc (Arc s e) p | s > e = empty
                        | s > 1 || e > 1 = empty
                        | s < 0 || e < 0 = empty
                        | otherwise = s `rotR` _fastGap (1/(e-s)) p

compressArcTo :: Arc -> Pattern a -> Pattern a
compressArcTo (Arc s e) = compressArc (Arc (cyclePos s) (e - sam s))

_fastGap :: Time -> Pattern a -> Pattern a
_fastGap 0 _ = empty
_fastGap r p = splitQueries $ 
  withResultArc (\(Arc s e) -> Arc (sam s + ((s - sam s)/r'))
                             (sam s + ((e - sam s)/r'))
                 ) $ p {query = f}
  where r' = max r 1
        -- zero width queries of the next sam should return zero in this case..
        f st@(State a _) | start a' == nextSam (start a) = []
                         | otherwise = query p st {arc = a'}
          where mungeQuery t = sam t + min 1 (r' * cyclePos t)
                a' = (\(Arc s e) -> Arc (mungeQuery s) (mungeQuery e)) a

-- | Shifts a pattern back in time by the given amount, expressed in cycles
rotL :: Time -> Pattern a -> Pattern a
rotL t p = withResultTime (subtract t) $ withQueryTime (+ t) p

-- | Shifts a pattern forward in time by the given amount, expressed in cycles
rotR :: Time -> Pattern a -> Pattern a
rotR t = rotL (negate t)

-- ** Event filters

-- | Remove events from patterns that to not meet the given test
filterValues :: (a -> Bool) -> Pattern a -> Pattern a
filterValues f p = p {query = filter (f . value) . query p}

-- | Turns a pattern of 'Maybe' values in to a pattern of values,
-- dropping the events of 'Nothing'.
filterJust :: Pattern (Maybe a) -> Pattern a
filterJust p = fromJust <$> filterValues isJust p

-- formerly known as playWhen
filterWhen :: (Time -> Bool) -> Pattern a -> Pattern a
filterWhen test p = p {query = filter (test . wholeStart) . query p}

filterOnsets :: Pattern a -> Pattern a
filterOnsets p = p {query = filter (\e -> eventPartStart e == wholeStart e) . query (filterDigital p)}

filterEvents :: (Event a -> Bool) -> Pattern a -> Pattern a
filterEvents f p = p {query = filter f . query p}

filterDigital :: Pattern a -> Pattern a
filterDigital = filterEvents isDigital

filterAnalog :: Pattern a -> Pattern a
filterAnalog = filterEvents isAnalog

playFor :: Time -> Time -> Pattern a -> Pattern a
playFor s e = filterWhen (\t -> (t >= s) && (t < e))

-- ** Temporal parameter helpers

tParam :: (t1 -> t2 -> Pattern a) -> Pattern t1 -> t2 -> Pattern a
tParam f tv p = innerJoin $ (`f` p) <$> tv

tParam2 :: (a -> b -> c -> Pattern d) -> Pattern a -> Pattern b -> c -> Pattern d
tParam2 f a b p = innerJoin $ (\x y -> f x y p) <$> a <*> b

tParam3 :: (a -> b -> c -> Pattern d -> Pattern e) -> (Pattern a -> Pattern b -> Pattern c -> Pattern d -> Pattern e)
tParam3 f a b c p = innerJoin $ (\x y z -> f x y z p) <$> a <*> b <*> c

tParamSqueeze :: (a -> Pattern b -> Pattern c) -> (Pattern a -> Pattern b -> Pattern c)
tParamSqueeze f tv p = squeezeJoin $ (`f` p) <$> tv

-- | Mark values in the first pattern which match with at least one
-- value in the second pattern.
matchManyToOne :: (b -> a -> Bool) -> Pattern a -> Pattern b -> Pattern (Bool, b)
matchManyToOne f pa pb = pa {query = q}
  where q st = map match $ query pb st
          where
            match (ex@(Event xContext xWhole xPart x)) =
              Event (combineContexts $ xContext:(map context as')) xWhole xPart (any (f x) (map value $ as'), x)
                where as' = as $ start $ wholeOrPart ex
            as s = query pa $ fQuery s
            fQuery s = st {arc = Arc s s}