{-# LANGUAGE CPP, MultiParamTypeClasses, FlexibleInstances, Safe, DeriveGeneric, RecordWildCards #-}
module Game.Hanabi(
              -- * Functions for Dealing Games
              main, selfplay, start, createGame, startFromCards, createGameFromCards, run, createDeck,
              prettyEndGame, isMoveValid, checkEndGame, help,
              -- * Datatypes
              -- ** The Class of Strategies
              Strategies, Strategy(..), StrategyDict(..), mkSD, DynamicStrategy, mkDS, mkDS', Verbose(..), STDIO, stdio, Blind, ViaHandles(..), Verbosity(..), verbose, quiet, Replay(..),
              -- ** Audience
              Peeker, peek,
              -- ** The Game Specification
              GameSpec(..), defaultGS, Rule(..), defaultRule, isRuleValid, makeRuleValid, colors, handSize, setHandSize,
              -- ** The Game State and Interaction History
              Move(..), Index, State(..), PrivateView(..), PublicInfo(..), Result(..), EndGame(..),
              -- ** The Cards and Annotations
              Card(..), Color(..), Number(..), Marks, Possibilities, Annotation(..), cardToInt, intToCard, readsColorChar, readsNumberChar, colorToBitPos, numberToBitPos,
              -- * Utilities
              -- ** Hints
              isCritical, isUseless, bestPossibleRank, achievedRank, isPlayable, isHinted, currentScore, seeminglyAchievableScore, moreStrictlyAchievableScore, achievableScore,
              definitely, obviously,
              isMoreObviouslyUseless, isObviouslyUseless, isDefinitelyUseless, isDefinitelyUncritical, isDefinitelyCritical, isMoreObviouslyPlayable, isObviouslyPlayable, isDefinitelyPlayable, isObviouslyUnplayable, isDefinitelyUnplayable, obviousChopss, definiteChopss, isDoubleDrop, possibleCards, endGameMove, EndGameStrategy(..), EndGameMirrorStrategy(..), egms, EndGameLite(..), egl, EndGameMirrorLite(..), egml,
              tryMove, (|||), ifA,
              -- ** Legacy functions
              givenHints, possibilities_until_Ver0720,
              -- ** Minor ones
              what'sUp, what'sUp1, ithPlayer, recentEvents, prettyPI, prettySt, ithPlayerFromTheLast, view, replaceNth, shuffle, showPossibilities, showColorPossibilities, showNumberPossibilities, showTrial, showDeck) where
-- module Hanabi where
import qualified Data.IntMap as IM
import qualified Data.Map as M
import System.Random
import Control.Applicative((<*>))
import Control.Monad(when)
import Control.Monad.IO.Class(MonadIO, liftIO)
import Data.Char(isSpace, isAlpha, isAlphaNum, toLower, toUpper)
import Data.Maybe(fromJust)
import Data.List(isPrefixOf, group, maximumBy, delete, sort)
import Data.Function(on)
import System.IO
import Data.Dynamic
import Data.Bits hiding (rotate)

import GHC.Generics hiding (K1)

data Number  = Empty | K1 | K2 | K3 | K4 | K5 deriving (Eq, Ord, Show, Read, Enum, Bounded, Generic)
data Color = White | Yellow | Red | Green | Blue | Multicolor
  deriving (Eq, Ord, Show, Read, Enum, Bounded, Generic)
readsColorChar :: ReadS Color
readsColorChar (c:str)
  | isSpace c = readsColorChar str
  | otherwise = case lookup (toUpper c) [(head $ show i, i) | i <- [White .. Multicolor]] of
                           Nothing -> []
                           Just i  -> [(i, str)]
readsColorChar [] = []
readsNumberChar :: ReadS Number
readsNumberChar xs = [ (toEnum d, rest) | (d, rest) <- reads xs, d<=5 ]

data Card = C {color :: Color, number :: Number} deriving (Eq, Ord, Generic)
instance Show Card where
  showsPrec _ (C color number) = (head (show color) :) . (show (fromEnum number) ++)
  showList = foldr (.) id . map shows
instance Read Card where
  readsPrec _ str = [(C i k, rest) | (i, xs) <- readsColorChar str, (k, rest) <- readsNumberChar xs]
  readList xs = case reads xs of []       -> [([],xs)]
                                 [(c,ys)] -> [ (c:cs, zs) | (cs,zs) <- readList ys ]
cardToInt :: Card -> Int
cardToInt c = fromEnum (color c) * (succ $ fromEnum (maxBound::Number)) + fromEnum (number c)
intToCard :: Int -> Card
intToCard i = case i `divMod` (succ $ fromEnum (maxBound::Number)) of (c,k) -> C (toEnum c) (toEnum k)
type Index = Int -- starts from 0

data Move = Drop {index::Index}            -- ^ drop the card (0-origin)
          | Play {index::Index}            -- ^ play the card (0-origin)
          | Hint Int (Either Color Number) -- ^ give hint to the ith next player
            deriving (Eq, Ord, Generic)
instance Show Move where
    showsPrec _ (Drop i) = ("Drop"++) . shows i
    showsPrec _ (Play i) = ("Play"++) . shows i
    showsPrec _ (Hint i eith) = ("Hint"++) . shows i . (either (\c -> (take 1 (show c) ++)) (\k -> tail . shows k) eith)
instance Read Move where
    readsPrec _ str
      = let (cmd,other) = span (not.isSpace) str'
            str' = dropWhile isSpace str
        in case span (not . (`elem` "dDpP")) cmd of
          (tk, d:dr) | all (not.isAlphaNum) tkdr && null (drop 1 $ group tkdr) -> [((if toLower d == 'd' then Drop else Play) $ length tk, other)]
                    where tkdr = tk++dr
          _ -> case span isAlpha str' of
                        (kw, xs)  | kwl `isPrefixOf` "hint" -> parseHint xs  -- Since kwl can be "", "11" parses as "Hint11".
                                  | kwl `isPrefixOf` "drop" -> [(Drop i, rest) | (i, rest) <- reads xs]
                                  | kwl `isPrefixOf` "play" -> [(Play i, rest) | (i, rest) <- reads xs]
                                  where kwl = map toLower kw
                        _         -> []
                 where parseHint xs = [(Hint i eith, rest) | let (istr, ys) = splitAt 1 $ dropWhile isSpace xs -- These two lines is similar to @(i, ys) <- reads xs@,
                                                           , (i, _) <- reads istr                              -- but additionally accepts something like "hint12".
                                                           , let ys' = dropWhile isSpace ys
                                                           , (eith, rest) <- [ (Left c, zs) | (c,zs) <- readsColorChar ys' ] ++ [ (Right c, zs) | (c,zs) <- readsNumberChar ys' ] ]

-- | The help text.
help :: String
help = "`Play0',  `play0',   `P0', `p0', etc.        ... play the 0th card from the left (0-origin).\n"
     ++"`Drop1',  `drop1',   `D1', `d1', etc.        ... drop the 1st card from the left (0-origin).\n"
     ++"`Hint2W', `hint2w', `h2w', `H2W', `2w', etc. ... tell the White card(s) of the 2nd next player.\n"
     ++"`Hint14',           `h14', `H14', `14', etc. ... tell the Rank-4 card(s) of the next player.\n"
     ++"`---P-',  `@@@p@', `___P', `...p', etc.      ... play the 3rd card from the left (0-origin). Letters other than p or P must not be alphanumeric. Also note that just `p' or `P' means playing the 0th card.\n"
     ++"`D////',  `d~~~~', `D',    `d',    etc.      ... drop the 0th card from the left (0-origin). Letters other than d or D must not be alphanumeric.\n"

-- | 'Rule' is the datatype representing the game variants.
--
--   [Minor remark] When adopting Variant 4, that is, the rule of continuing even after a round after the pile is exhausted, there can be a situation where a player cannot choose any valid move, because she has no card and there is no hint token.
--   This can happen, after one player (who has no critical card) repeats discarding, and other players repeat hinting each other, consuming hint tokens.
--   Seemingly, the rule book does not state what happens in such a case, but I (Susumu) believe the game should end as failure, then, because
--
--   * This situation can easily be made, and easily be avoided;
--
--   * If deadline is set up, this should cause time out;
--
--   * When Variant 4 is adopted, the game must end with either the perfect game or failure.
--
--   See also the definition of 'checkEndGame'.
data Rule = R { numBlackTokens :: Int    -- ^ E.g., if this is 3, the third failure ends the game with failure.
              , funPlayerHand  :: [Int]  -- ^ memoized function taking the number of players; the default is [5,5,4,4,4,4,4,4,4,4]
              , numColors      :: Int    -- ^ number of colors. 5 for the normal rule, and 6 for Variant 1-3 of the rule book.
              , prolong        :: Bool   -- ^ continue even after a round after the pile is exhausted. @True@ for Variant 4 of the rule book.
              , earlyQuit      :: Bool   -- ^ quit the game when the best possible score is achieved. 
              , numMulticolors :: [Int]  -- ^ number of each of multicolor cards. @[3,2,2,2,1]@ for Variant 1 (and Variant 3?), and @[1,1,1,1,1]@ for Variant 2.

--          x , multicolor     :: Bool   -- ^ multicolor play, or Variant 3
              } deriving (Show, Read, Eq, Generic)
isRuleValid :: Rule -> Bool
isRuleValid rl@R{..} = numBlackTokens > 0 && and [ h>0 && h<=mh | (h,mh) <- zip funPlayerHand $ maxPlayerHand rl ] && numColors>0 && numColors <=6 && (numColors < 6 || all (>0) numMulticolors)
makeRuleValid :: Rule -> Rule
makeRuleValid rl@R{..} = rl{numBlackTokens = max 1 numBlackTokens,
                            numColors = max 1 (min 6 numColors),
                            numMulticolors = if numColors<6 then numMulticolors else take 5 (map (max 1) numMulticolors ++ [1,1,1,1,1]),
                            funPlayerHand  = [ max 1 h | h <- zipWith min funPlayerHand $ maxPlayerHand rl ]}
maxPlayerHand rl = [ succ (numberOfCards rl) `div` numP | numP <- [2..]]
        -- This makes sure that there is at least one card on the deck.

-- | @defaultRule@ is the normal rule from the rule book of the original card game Hanabi.
defaultRule :: Rule
defaultRule = R { numBlackTokens = 3
                , funPlayerHand  = [5,5]++take 8 (repeat 4)
                , numColors      = 5
                , prolong        = False
                , earlyQuit      = False
                , numMulticolors = replicate 5 0
--          x , multicolor     = False
              }
defaultGS :: GameSpec
defaultGS = GS{numPlayers=2, rule=defaultRule}
numberOfCards :: Rule -> Int
numberOfCards rl = sum (take (numColors rl) $  [10,10,10,10,10]++[sum (numMulticolors rl)])
initialPileNum :: GameSpec -> Int
initialPileNum gs = numberOfCards (rule gs)
                    - handSize gs * numPlayers gs
handSize :: GameSpec -> Int
handSize GS{..} = (funPlayerHand rule ++ repeat 1) !! (numPlayers - 2)
setHandSize :: GameSpec -> Int -> Rule
setHandSize GS{..} n = rule{funPlayerHand = snd $ replaceNth (numPlayers - 2) n $ funPlayerHand rule}
data GameSpec = GS {numPlayers :: Int, rule :: Rule} deriving (Read, Show, Eq, Generic)

-- | State consists of all the information of the current game state, including public info, private info, and the hidden deck.
data State = St { publicState :: PublicInfo
                , pile :: [(Card,Annotation)]    -- ^ invisible card pile or deck.
                , hands :: [[Card]] -- ^ partly invisible list of each player's hand.
                                    --   In the current implementation (arguably), this represents [current player's hand, next player's hand, second next player's hand, ...]
                                    --   and this is rotated every turn.
                } deriving (Read, Show, Eq, Generic)

-- | PublicInfo is the info that is available to all players.
data PublicInfo = PI { gameSpec  :: GameSpec
                     , pileNum   :: Int               -- ^ The number of cards at the pile.
                     , played    :: IM.IntMap Number  -- ^ @'Color' -> 'Number'@. The maximum number of successfully played cards of etch number.

                                                      -- Just a list with length 5 or 6 could do the job.
                     , discarded :: IM.IntMap Int     -- ^ @'Card' -> Int@. The multiset of discarded cards.

                     , nonPublic :: IM.IntMap Int     -- ^ @'Card' -> Int@. The multiset of Cards that have not been revealed to the public.
                                                      --   This does not include cards whose Color and Number are both revealed.
                                                      --
                                                      --   This is redundant information that can be computed from 'played' and 'discarded'.
                     , turn      :: Int               -- ^ How many turns have been completed since the game started. This can be computed from 'pileNum', 'deadline', and @map length 'annotations'@.
                     , lives      :: Int              -- ^ The number of black tokens. decreases at each failure
                     , hintTokens :: Int              -- ^ The number of remaining hint tokens.

--                 , numHandCards :: [Int]  -- the number of cards each player has. This was used by isMoveValid, but now abolished because @numHandCards == map length . annotations@.
                     , deadline   :: Maybe Int        -- ^ The number of turns until the endgame, after the pile exhausted. @Nothing@ when @pileNum > 0@.
                     , annotations :: [[Annotation]]  -- ^ Known information for each card in each player's hand.
                     , result :: Result               -- ^ The result of the last move. This info may be separated from 'PublicInfo' in future.
                     } deriving (Read, Show, Eq, Generic)

givenHints :: PublicInfo -> [[Marks]]
givenHints = map (map marks) . annotations
possibilities_until_Ver0720 :: PublicInfo -> [[Possibilities]]
possibilities_until_Ver0720 = map (map possibilities) . annotations

-- | 'Marks' is the type synonym representing the hint trace of a card.
type Marks = (Maybe Color, Maybe Number)

-- | A 'Possibilities' is a pair of data that are instances of Bits. The first represents which colors are possible, and the second is for numbers.
type Possibilities = (Int, Int)

colorToBitPos  :: Color -> Int
colorToBitPos  i = 5 - fromEnum i
numberToBitPos :: Number -> Int
numberToBitPos k = 5 - fromEnum k

data Annotation = Ann {ixDeck :: Int                   -- ^ Index in the initial deck
                      , marks :: Marks                 -- ^ The Number and Color hints given to the card.
                      , possibilities :: Possibilities}
  deriving (Eq, Generic)
instance Show Annotation where
  showsPrec p (Ann i ms ps) = showsPrec p (i,ms,ps)
instance Read Annotation where
  readsPrec p str = [ (Ann i ms ps, rest) | ((i,ms,ps), rest) <- readsPrec p str ]

-- | the best achievable rank for each color.
bestPossibleRank :: PublicInfo -> Color -> Number
bestPossibleRank pub iro = toEnum $ length $ takeWhile (/=0) $ zipWith subtract (numEachCard (gameSpec pub) iro)
                                                                                (map ((discarded pub IM.!) . cardToInt . C iro) [K1 .. K5])
numEachCard :: GameSpec -> Color -> [Int]
numEachCard gs iro = if iro==Multicolor then numMulticolors $ rule gs else [3,2,2,2,1]
-- | isUseless pi card means either the card is already played or it is above the bestPossibleRank.
isUseless :: PublicInfo -> Card -> Bool
isUseless pub card =  number card <= achievedRank pub (color card) -- the card is already played
                   || number card > bestPossibleRank pub (color card)
-- | A critical card is a useful card and the last card that has not been dropped.
--
--   Unmarked critical card on the chop should be marked.
isCritical :: PublicInfo -> Card -> Bool
isCritical pub card = not (isUseless pub card)
                      && succ (discarded pub IM.! cardToInt card) == (numEachCard (gameSpec pub) (color card) !! (pred $ fromEnum $ number card))

isPlayable :: PublicInfo -> Card -> Bool
isPlayable pub card = pred (number card) == achievedRank pub (color card)

isHinted :: Marks -> Bool
isHinted = not . (==(Nothing, Nothing))

-- | 'isMostObviouslyPlayable' only looks at the current hint marks (and the played piles) and decides if the card is surely playable.
--   This is useful only for predicting the behaviors of beginner players.
isMostObviouslyPlayable :: PublicInfo -> Marks -> Bool
isMostObviouslyPlayable pub (Just c, Just n) = isPlayable pub $ C c n
isMostObviouslyPlayable _   _                = False

-- | 'isMoreObviouslyPlayable' looks at the publicly available current info and decides if the card is surely playable.
isMoreObviouslyPlayable :: PublicInfo -> Marks -> Bool
isMoreObviouslyPlayable pub = iOP (nonPublic pub) pub

obviously :: (PublicInfo -> Card -> Bool) -> PublicInfo -> Possibilities -> Bool
obviously predicate pub (pc,pn) = all (\card -> (nonPublic pub IM.! cardToInt card) == 0 || predicate pub card)
                                      [ C color number | color <- colorPossibilities pc, number <- numberPossibilities pn ]

-- | In addition to 'isMoreObviouslyPlayable', 'isObviouslyPlayable' also looks into the color/number possibilities of the card and decides if the card is surely playable.
isObviouslyPlayable :: PublicInfo -> Possibilities -> Bool
isObviouslyPlayable = obviously isPlayable

isObviouslyUnplayable :: PublicInfo -> Possibilities -> Bool
isObviouslyUnplayable = obviously (\pub -> not . isPlayable pub)

definitely :: (PrivateView -> Card -> Bool) -> PrivateView -> Annotation -> Bool
definitely predicate pv ann = all (predicate pv) $ possibleCards pv ann

-- | In addition to 'isObviouslyPlayable', 'isDefinitelyPlayable' also looks at other players' hand and decides if the card is surely playable.
{- This is a weaker version not looking into the possibilities.
isDefinitelyPlayable :: PrivateView -> Marks -> Bool
isDefinitelyPlayable pv = iOP (invisibleBag pv) (publicView pv)
-}
isDefinitelyPlayable :: PrivateView -> Annotation -> Bool
isDefinitelyPlayable = definitely (isPlayable . publicView)

isDefinitelyUnplayable :: PrivateView -> Annotation -> Bool
isDefinitelyUnplayable = definitely (\pv -> not . isPlayable (publicView pv))

-- | Unlike 'isDefinitelyUseless', 'isDefinitelyUnciritical' does not care whether the card is the last one or not. 'isDefinitelyUncritical' is, in other words, safe to drop.
isDefinitelyUncritical :: PrivateView -> Annotation -> Bool
isDefinitelyUncritical = definitely (\pv -> not . isCritical (publicView pv))

-- | If all of your cards are marked and not safe to drop, and you do not have enough hint token, one option is to drop a card that can be uncritical. (You can then assign them a priority order.)
--   [NB: Maybe this is not a good idea. E.g. when the other player draws the last W2 to fully-marked [R5,G5,B5,Y5], we usually mark 2 to give up a 5, but if the player does not guess the intention and resort the above option, W2 is dropped.]
isDefinitelyCritical :: PrivateView -> Annotation -> Bool
isDefinitelyCritical = definitely (\pv -> isCritical $ publicView pv)

possibleCards :: PrivateView -> Annotation -> [Card]
possibleCards pv Ann{marks = (Just c, Just n)} = [C c n] -- The condition is indispensable, because now invisibleBag considers fully-marked cards visible.
possibleCards pv Ann{possibilities = (pc,pn)}  = [ card | color <- colorPossibilities pc, number <- numberPossibilities pn, let card = C color number, (invisibleBag pv IM.! cardToInt card) /= 0 ]
                            where pub = publicView pv

iOP :: IM.IntMap Int -> PublicInfo -> (Maybe Color, Maybe Number) -> Bool
iOP _   pub (Just c, Just n) = isPlayable pub $ C c n
iOP bag pub (Nothing,Just n) = all (\card -> (bag IM.! cardToInt card) == 0 || isPlayable pub card) [ C color n | color <- colors pub ]
iOP _   _   _                = False

-- | 'isMoreObviouslyUseless' looks at the publicly available current info and decides if the card is surely useless.
isMoreObviouslyUseless :: PublicInfo -> Marks -> Bool
isMoreObviouslyUseless pub (Just c,  Just n)  = isUseless pub $ C c n
isMoreObviouslyUseless pub (Just c,  Nothing) = bestPossibleRank pub c == achievedRank pub c
isMoreObviouslyUseless pub (Nothing, Just n)  = all (\c -> n <= achievedRank pub c || bestPossibleRank pub c < n) $ colors pub
isMoreObviouslyUseless _   (Nothing, Nothing) = False

isObviouslyUseless :: PublicInfo -> Possibilities -> Bool
isObviouslyUseless = obviously (\pub (C c n) -> n <= achievedRank pub c || bestPossibleRank pub c < n)

isDefinitelyUseless :: PrivateView -> Annotation -> Bool
isDefinitelyUseless = definitely (\pv -> isUseless (publicView pv))

{- This is a weaker version not looking into the possibilities.
isDefinitelyUseless :: PrivateView -> Marks -> Bool
isDefinitelyUseless pv (Just c,  Just n)  = isUseless (publicView pv) $ C c n
isDefinitelyUseless pv (Just c,  Nothing) = all ((==0) . (invisibleBag pv IM.!) . cardToInt . C c . toEnum) [ succ $ fromEnum $ achievedRank (publicView pv) c .. fromEnum $ bestPossibleRank (publicView pv) c ] 
isDefinitelyUseless pv (Nothing, Just n)  = all (\c -> n <= achievedRank (publicView pv) c || bestPossibleRank (publicView pv) c < n || (invisibleBag pv IM.! cardToInt (C c n)) == 0 ) $ colors $ publicView pv
isDefinitelyUseless pv (Nothing, Nothing) = all (\c -> all ((==0) . (invisibleBag pv IM.!) . cardToInt . C c . toEnum) [ succ $ fromEnum $ achievedRank (publicView pv) c .. fromEnum $ bestPossibleRank (publicView pv) c ]) $ colors $ publicView pv
-}
-- In fact, invisibleBag should be included in PrivateView for efficiency of isDefinitelyUseless, etc., but should not be sent via WebSocket. This is the matter of Read and Show (or ToJSON and FromJSON).


-- | @'choppiri' marks@ = [unmarked last, unmarked second last, ...]. This is "beginner players' idea of chops". 
choppiri :: [Marks] -> [(Index, Marks)]
choppiri = reverse . filter (not . isHinted . snd) . zip [0..]

-- | In addition to 'choppiri', 'definiteChopss' and 'obviousChopss' consider 'isDefinitelyUseless' and 'isObviouslyUseless' respectively. Since "from which card to drop among obviously-useless cards" depends on conventions, cards with the same uselessness are wrapped in a list within the ordered list.
definiteChopss :: PrivateView -> [Annotation] -> [[Index]]
definiteChopss pv anns = (if null useless then id else (useless :)) $ map (:[]) $ filter (`notElem` useless) $ map fst (choppiri $ map marks anns)
   where useless = map fst $ filter (isDefinitelyUseless pv . snd) (zip [0..] anns)
obviousChopss :: PublicInfo -> [Annotation] -> [[Index]]
obviousChopss pub anns = (if null useless then id else (useless :)) $ map (:[]) $ filter (`notElem` useless) $ map fst (choppiri $ map marks anns)
   where useless = map fst $ filter (isObviouslyUseless pub . snd) (zip [0..] $ map possibilities anns)
-- | 'chops' is the flattened version of 'obviousChopss'
chops :: PublicInfo -> [Annotation] -> [Index]
chops pub anns = concat $ map reverse $ obviousChopss pub anns

isDoubleDrop :: PrivateView -> Result -> [Index] -> Annotation -> Bool
isDoubleDrop pv@PV{publicView=pub} (Discard c@C{..}) [_i] Ann{possibilities=(pc,pn)} = not (any ((==(Just color, Just number)).marks) myAnns) &&  -- This pattern captures: the last player discards B1; I have a card which is hinted as B and 1; I don't know where the third B1 is.
                                                                                                                        -- This can be improved to check whether any card other than the chop is obviously the just-dropped card or not, by looking at the Possibilities.
                                                                    isCritical pub c &&
                                                                    color  `elem` colorPossibilities pc &&
                                                                    number `elem` numberPossibilities pn &&
                                                                    (invisibleBag pv IM.! cardToInt c) > 0
                                         where myAnns = head $ annotations pub
isDoubleDrop _pv _lastresult _chopset _anns = False

colors :: PublicInfo -> [Color]
colors pub = take (numColors $ rule $ gameSpec pub) [minBound .. maxBound]

achievedRank :: PublicInfo -> Color -> Number
achievedRank pub k = case IM.lookup (fromEnum k) (played pub) of
                            Just n  -> n
#ifdef DEBUG
                            Nothing | numColors (rule $ gameSpec pub) <= k -> error "requesting invalid color."
                                    | otherwise                            -> error "PublicInfo is not initialized."
#else
                            Nothing -> Empty
#endif
currentScore :: PublicInfo -> Int
currentScore pub = sum [ fromEnum $ achievedRank pub k | k <- colors pub ]

-- | achievable score based on the info of extinct cards.
seeminglyAchievableScore :: PublicInfo -> Int
seeminglyAchievableScore pub = sum [ fromEnum $ bestPossibleRank pub k | k <- colors pub ]

-- | alias to 'seeminglyAchievableScore'. This function name may point to the function with stricter check in future.
achievableScore :: PublicInfo -> Int
achievableScore = seeminglyAchievableScore

-- | In addition to 'seeminglyAchievableScore', 'moreStrictlyAchievableScore' checks the number of cards at the deck, unless 'prolong' is @True@.
moreStrictlyAchievableScore :: PublicInfo -> Int
moreStrictlyAchievableScore pub = if prolong $ rule $ gameSpec pub then seeminglyAchievableScore pub else seeminglyAchievableScore pub `min` (currentScore pub + pileNum pub + numPlayers (gameSpec pub))

tryMove :: PrivateView -> Move -> Move -> Move
tryMove pv m alt | isMoveValid pv m = m
                 | otherwise        = alt
(|||) :: (PrivateView -> Move) -> (PrivateView -> Move) -> PrivateView -> Move
a ||| b = tryMove <*> a <*> b
ifA :: (PrivateView -> Bool) -> (PrivateView -> Move) -> (PrivateView -> Move) -> PrivateView -> Move
ifA pred at af = (\pv t f -> if pred pv then t else f) <*> at <*> af

-- | 'Result' is the result of the last move.
data Result = None -- ^ Hinted or at the beginning of the game
            | Discard {revealed::Card} | Success {revealed::Card} | Fail {revealed::Card} deriving (Read, Show, Eq, Generic)

-- The view history [PrivateView] records the memory of what has been visible `as is'. That is, the info of the cards in the history is not updated by revealing them.
-- I guess, sometimes, ignorance of other players might also be an important knowledge.
-- Algorithms that want updated info could implement the functionality for themselves.


-- | PrivateView is the info that is available to the player that has @head 'hands'@.
data PrivateView = PV { publicView :: PublicInfo
                      , handsPV :: [[Card]]           -- ^ Other players' hands. [next player's hand, second next player's hand, ...]
                                                      --   This is based on the viewer's viewpoint (unlike 'hands' which is based on the current player's viewpoint),
                                                      --   and the view history @[PrivateView]@ must be from the same player's viewpoint (as the matter of course).
                      , invisibleBag :: IM.IntMap Int -- ^ @'Card' -> Int@. 'invisibleBag' is the bag of unknown cards (which are either in the pile or in the player's hand and not fully hinted).
                      } deriving (Generic) -- ToDo: Instance for Generic should also be specialized for efficiency.
instance Show PrivateView where
  showsPrec p (PV pub h _) = showsPrec p (pub,h)
instance Read PrivateView where
  readsPrec p str = [ (mkPV pub hs, rest) | ((pub,hs), rest) <- readsPrec p str ]
instance Eq PrivateView where
  PV pub1 hs1 _ == PV pub2 hs2 _ = (pub1,hs1) == (pub2,hs2)


-- | recede rolls back 1 turn without rotating.
recede :: PublicInfo -> Move -> State -> State
recede lastpub (Hint _ _) st = st{ publicState = lastpub }
recede lastpub mv         st = St{ publicState = lastpub,
                                   pile        = if pileNum lastpub == 0 then [] else (head myHand, initAnn (gameSpec lastpub) $ ixDeck $ head $ head $ annotations $ publicState st) : pile st,
                                   hands       = case splitAt (index mv) $ if pileNum lastpub == 0 then myHand else tail myHand of (tk,dr) -> (tk ++ revealed (result $ publicState st) : dr) : tail (hands st)}
  where myHand = head $ hands st
-- | stateToStateHistory deduces the state history from the 'PublicState' history, the 'Move' history, and the current 'State'.
stateToStateHistory :: [PublicInfo] -> [Move] -> State -> [State]
stateToStateHistory []       []       st = [st]
stateToStateHistory (pi:pis) (mv:mvs) st = st : stateToStateHistory pis mvs (rotate (-1) $ recede pi mv st)

-- | @'EGS' f p ps@ usually behaves based on @p@, but it conducts the exhaustive search assuming that others behave based on @ps@ when the deck size is @f@ or below @f@.
data EndGameStrategy p ps = EGS {fromWhen::PublicInfo->Bool, myUsualStrategy::p, otherPlayers::ps}

instance (Monad m, Strategy p m, Strategies ps m) => Strategy (EndGameStrategy p ps) m where
  strategyName ms = return "EndGameStrategy"
  move pvs@(pv:_) mvs str@(EGS f p ps) | f (publicView pv)            = do (defaultMove, _) <- move pvs mvs p
                                                                           m <- endGameMove pvs mvs (ps, [EGS f p ps]) $ defaultMove : delete defaultMove (validMoves pv)
                                                                           return (m,str)
                                       | otherwise                    = do (m,_) <- move pvs mvs p
                                                                           return (m,str)

-- | 'EndGameMirrorStrategy' assumes that other players think in the same way as itself during endgame.
data EndGameMirrorStrategy p = EGMS (EndGameStrategy p [EndGameMirrorStrategy p])
egms :: (PublicInfo -> Bool) -- ^ from when to start the endgame search
     -> p                    -- ^ the default strategy used until endgame
     -> Int                  -- ^ number of players, including the resulting player
     -> EndGameMirrorStrategy p
egms from p nump = egms where egms = EGMS (EGS from p $ replicate (pred nump) egms)

instance (Monad m, Strategy p m) => Strategy (EndGameMirrorStrategy p) m where
  strategyName ms = return "EndGameMirrorStrategy"
  move pvs mvs (EGMS egs) = do (m, egs') <- move pvs mvs egs
                               return (m, EGMS egs')

endGameMove :: (Monad m, Strategies ps m) =>
               [PrivateView] -- ^ view history
               -> [Move]     -- ^ move history
               -> ps
               -> [Move]     -- ^ move candidates. More promising moves appear earlier.
               -> m Move
endGameMove pvs@(pv:tlpvs) mvs ps candidates = do
                                        let states = possibleStates pv
                                        scores <- mapM (evalMove states (map publicView tlpvs) mvs ps) candidates
                                        let asc = zip scores candidates
                                            pub = publicView pv
                                            achievable = moreStrictlyAchievableScore pub
                                            --  ToDo:  Also consider critical cards at the bottom deck.
                                        return $ case lookup (achievable * length states) asc of Nothing -> snd $ maximumBy (compare `on` fst) $ reverse asc
                                                                                                 Just k  -> k -- Stop search when the best possible score is found.

validMoves :: PrivateView -> [Move]
validMoves pv@PV{publicView=pub@PI{gameSpec=gs,hintTokens=hints},handsPV=tlHands}
  = map Play [0 .. pred myHandSize] ++ (if hints > 0 then ([ Hint hintedpl eck | hintedpl <- [1 .. numPlayers gs - 1], eck <- map Left (colors pub) ++ map Right [K1 .. K5], not (null $ filter (either (\c -> (==c).color) (\k -> (==k).number) eck) (tlHands !! pred hintedpl)) ] ++) else id) (if hints < 8 then (map Drop [0 .. pred myHandSize]) else [])
                  where myHandSize = length (head $ annotations pub)

evalMove :: (Monad m, Strategies ps m) => [(State, Int)] -> [PublicInfo] -> [Move] -> ps -> Move -> m Int
evalMove states pubs@(pub:_) mvs ps mv = fmap (sum . map (\(((eg,_,_),_),n) -> n * egToInt pub eg)) $ mapM (\(st,n) -> fmap (\a->(a,n)) $ tryAMove (stateToStateHistory pubs mvs st) mvs ps mv) states

-- | 'tryAMove' tries a 'Move' and then simulate the game to the end, using given 'Strategies'. Running this with empty history, such as @tryAMove [st] [] strs m@ is possible, but that assumes other strategies does not depend on the history.
tryAMove :: (Monad m, Strategies ps m) => [State] -> [Move] -> ps -> Move -> m ((EndGame, [State], [Move]),ps)
tryAMove states@(st:_) mvs strs mov = case proceed st mov of Nothing -> fail $ show mov ++ ": invalid move!"
                                                             Just st -> let nxt = rotate 1 st
                                                                        in case checkEndGame $ publicState nxt of Nothing -> runSilently (nxt:states) (mov:mvs) strs
                                                                                                                  Just eg -> return ((eg, nxt:states, mov:mvs), strs)

-- | 'EndGameMirrorLite' assumes that other players think in the same way as itself during endgame.
data EndGameMirrorLite p = EGML (EndGameLite p [EndGameMirrorLite p])
egml :: (PublicInfo -> Bool) -- ^ from when to start the endgame search
     -> p                    -- ^ the default strategy used until endgame
     -> Int                  -- ^ number of players, including the resulting player
     -> EndGameMirrorLite p
egml from p nump = egms where egms = EGML (egl from p $ replicate (pred nump) egms)

instance (Monad m, Strategy p m) => Strategy (EndGameMirrorLite p) m where
  strategyName ms = return "EndGameMirrorLite"
  move pvs mvs (EGML egs) = do (m, egs') <- move pvs mvs egs
                               return (m, EGML egs')

egl f p ps = EGL f p ps M.empty

-- | @'EGL' f p ps memory@ usually behaves based on @p@, but it conducts the exhaustive search assuming that others behave based on @ps@ when the deck size is @f@ or below @f@.
data EndGameLite p ps = EGL {fromWhenL::PublicInfo->Bool, myUsualStrategyL::p, otherPlayersL::ps, memory :: M.Map Key ([Move],[([State],ps,Int)])}
type Key = (Maybe Card, [Marks], [Move], [Card])

instance (Monad m, Strategy p m, Strategies ps m) => Strategy (EndGameLite p ps) m where
  strategyName ms = return "EndGameLite"
  move pvs mvs str@(EGL f p ps memory)
    | f pub     = do let statess = case M.lookup (resToMbC $ result $ publicView $ pvs !! pred numP, map marks $ head $ annotations pub, take (pred numP) mvs, map headC $ handsPV hdpv) memory of
                                     Just (_,tups) -> tups
                                     Nothing       -> [ (stateToStateHistory (map publicView tlpvs) mvs state, ps, n)  | (state, n) <- possibleStates hdpv ]
                     (_i, (mp,m)) <- endGameMoveLite statess pvs' mvs p
                     return (m, EGL f p ps mp)
    | otherwise = do (m,_) <- move pvs mvs p
                     return (m,str)
    where pvs'@(hdpv:tlpvs) = [ pv{publicView=pub{gameSpec=gs{rule=r{earlyQuit=True}}}} | pv@PV{publicView=pub@PI{gameSpec=gs@GS{rule=r}}}<- pvs ]
          pub = publicView hdpv
          numP = numPlayers $ gameSpec pub
endGameMoveLite :: (Monad m, Strategies ps m, Strategy p m) =>
               [([State],ps,Int)]   -- ^ possible pairs of the state history and the internal memory states of other players' strategies
               -> [PrivateView] -- ^ view history
               -> [Move]        -- ^ move history
               -> p             -- ^ default (recommended) strategy
               -> m (Int,  (M.Map Key ([Move], [([State],ps,Int)]),  Move))
endGameMoveLite statess pvs@(pv:_) mvs p = do
  (defaultMove, _) <- move pvs mvs p
  let candidateMoves = defaultMove : delete defaultMove (validMoves pv)
  tups <- mapM (evalMoveLite statess mvs p) candidateMoves
  let asc = zipWith (\(mp, score) mv -> (score, (mp,mv))) tups candidateMoves
      pub = publicView pv
      achievable = sum [ n | (_,_,n) <- statess ] * moreStrictlyAchievableScore pub
        --  ToDo:  Also consider critical cards at the bottom deck.
  return $ case lookup achievable asc of Nothing -> maximumBy (compare `on` fst) $ reverse asc
                                         Just k  -> (achievable, k) -- Stop search when the best possible score is found.

evalMoveLite :: (Monad m, Strategies ps m, Strategy p m) => [([State], ps, Int)] -> [Move] -> p -> Move -> m ( M.Map Key ([Move], [([State],ps,Int)]) , Int )
evalMoveLite statess@((st:_,_,_):_) mvs p mov = do
                                    roundResults <- mapM (\sts ->tryAMoveARound sts mvs mov) statess
                                    let pub = publicState st
                                        instantScore = sum [ egToInt pub eg * n | ((Just eg, _, _), _, n) <- roundResults ]
                                        roundResultMap = groupARound pub roundResults
                                    if M.null roundResultMap then return (roundResultMap, instantScore) else do
                                       let roundResults = M.elems roundResultMap
                                       scores <- sequence [ fmap fst $ endGameMoveLite stss (viewStates sts) moves p | (moves, stss@((sts,_,_):_)) <- roundResults ]
                                       return (roundResultMap, instantScore + sum scores)

groupARound :: PublicInfo -> [((Maybe EndGame, [State], [Move]),ps,Int)] -> M.Map Key ([Move], [([State],ps,Int)]) -- ToDo: IntMap could be used instead.
groupARound pub results = fmap procTip $ M.fromListWith (++) [ ( ( resToMbC $ result $ publicState $ stats !! pred numP,
                                                                   map marks $ head $ annotations $ publicState st,
                                                                   take (pred numP) movs,
                                                                   map headC $ tail $ hands st ),
                                                                 [r])
                                                             | r@((Nothing, stats@(st:_), movs), _, _) <- results ] where
                                          procTip :: [((Maybe EndGame, [State],[Move]),ps,Int)] -> ([Move], [([State],ps,Int)])
                                          procTip ts@(((_noth, _, mv), _, _) : _) = (mv, [ (stats, ps, n) | ((_nothing, stats, _), ps, n) <- ts ])
                                          numP = numPlayers $ gameSpec pub
-- total version of head, just in case of dealing with empty hand.
headC :: [Card] -> Card
headC = foldr const $ C Multicolor Empty


resToMbC :: Result -> Maybe Card
resToMbC None = Nothing
resToMbC r    = Just $ revealed r
tryAMoveARound :: (Monad m, Strategies ps m) => ([State],ps,Int) -> [Move] -> Move -> m ((Maybe EndGame, [State], [Move]),ps,Int)
tryAMoveARound (states@(st:_),strs,n) mvs mov = case proceed st mov of
                                                                     Nothing -> fail $ show mov ++ ": invalid move!"
                                                                     Just st -> let nxt = rotate 1 st
                                                                                in case checkEndGame $ publicState nxt of Nothing -> fmap (\(e,p) -> (e,p,n)) $ runARound (\_ _ -> return ()) (nxt:states) (mov:mvs) strs
                                                                                                                          Just eg -> return ((Just eg, nxt:states, mov:mvs), strs, n)

possibleStates :: PrivateView -> [(State, Int)]
possibleStates pv@PV{publicView=pub@PI{gameSpec=gs}}
  = [(St{ publicState = pub
        , pile = zipWith (\c i -> (c, initAnn gs i)) deck [ (numberOfCards (rule $ gameSpec pub) - pileNum pub) ..]
        , hands = hand : handsPV pv }
     , n)
    | ((hand, deck), n) <- uniqSort $ possiblePermutations pv ]
uniqSort :: (Eq a, Ord a) => [a] -> [(a,Int)]
uniqSort xs = map (\ys -> (head ys, length ys)) $ group $ sort xs
possiblePermutations :: PrivateView -> [([Card],[Card])]
possiblePermutations pv@PV{publicView=PI{annotations=anns:_}} = possiblePerms anns (invisibleCards pv)
invisibleCards :: PrivateView -> [Card]
invisibleCards PV{publicView=PI{annotations=anns}, invisibleBag=inv} = [ c | (k,v) <- IM.toList inv, c <- replicate v $ intToCard k ] -- x ++ [ C i k | (Just i, Just k) <- map marks anns ]
possiblePerms :: [Annotation] -> [Card] -> [([Card],[Card])]
possiblePerms [] cards = [([],cards)]
possiblePerms (Ann{marks = (Just i, Just k)} : anns) cards = [ (C i k : hand, deck) | (hand, deck) <- possiblePerms anns cards ]
possiblePerms (Ann{possibilities = (pi, pk)} : anns) cards = [ (card : hand, deck) | card@(C i k) <- cards, (pi .&. bit (colorToBitPos i)) * (pk .&. bit (numberToBitPos k)) /= 0, (hand, deck) <- possiblePerms anns $ delete card cards ]

-- | 'mkPV' is the constructor of PrivateView.
mkPV :: PublicInfo -> [[Card]] -> PrivateView
mkPV pub hs = PV pub hs $ foldr (IM.update (Just . pred)) (nonPublic pub) $ map cardToInt $ concat $ [ C c n | Ann{marks=(Just c, Just n)} <- head $ annotations pub ] : hs

prettyPV :: Verbosity -> PrivateView -> String
prettyPV v pv@PV{publicView=pub} = prettyPI pub ++ "\nYour hand:\n"
                                              ++ concat (replicate (length myAnn) $ wrap "+--+") ++ "\n"
--                                              ++ concat [ if markObviouslyPlayable v && isDefinitelyPlayable pv h then " _^" else " __" | h <- myAnn ] ++"\n"
                                              ++ concat (replicate (length myAnn) $ wrap "|**|") ++ "\n"
                                              ++ (if markHints v then showHintLine wrap $ map marks myAnn else "")
                                     -- x         ++ concat (replicate (length myHand) " ~~") ++ "\n"
-- x                                             ++ concat [ '+':shows d "-" | d <- [0 .. pred $ length myHand] ]
                                              ++ concat [ wrap $
                                                          '+':(if warnDoubleDrop v && isDoubleDrop pv (result pub) chopSet hp && d `elem` chopSet then ('D':) else
                                                               if markChops v && d `elem` chopSet then ('X':) else shows d)
                                                                      (if markObviouslyUseless  v && isDefinitelyUseless pv hp then ".+" else
                                                                       if markObviouslyPlayable v && isDefinitelyPlayable pv hp then "^+" else "-+") | (d,hp) <- zip [0..] myAnn ]
                                              ++"\n"
                                              ++ (if markPossibilities v then showPosLines $ map possibilities $ head $ annotations pub else "")
                                              ++ concat (zipWith3 (prettyHand v pub (ithPlayer $ numPlayers $ gameSpec pub)) [1..] (handsPV pv) (tail $ annotations pub))++"\n"
  where myAnn = head (annotations pub)
        wrap xs | markPossibilities v = "  "++xs++" "
                | otherwise           = xs
        chopSet = concat $ take 1 $ definiteChopss pv myAnn
prettySt :: (Int -> Int -> String) -> State -> String
prettySt ithP st@St{publicState=pub} = prettyPI pub ++ concat (zipWith3 (prettyHand verbose pub (ithP $ numPlayers $ gameSpec pub)) [0..] (hands st) (annotations pub))
verbose, quiet :: Verbosity
verbose = V{warnCritical=True, markUseless=True, markPlayable=True, markObviouslyUseless=True, markObviouslyPlayable=True, markHints=True, markPossibilities=True, markChops=True, warnDoubleDrop=True}
quiet   = V{warnCritical=False,markUseless=False,markPlayable=False,markObviouslyUseless=False,markObviouslyPlayable=False,markHints=False,markPossibilities=False,markChops=False,warnDoubleDrop=False}
prettyHand :: Verbosity -> PublicInfo -> (Int->String) -> Int -> [Card] -> [Annotation] -> String
prettyHand v pub ithPnumP i cards anns = "\n\n" ++ ithPnumP i ++ " hand:\n"
--                          ++ concat (replicate (length cards) " __") ++ " \n"
                          ++ concat [ wrap $
                                      if markUseless v && isUseless pub card then "+..+"
                                      else case (warnCritical v && tup==(Nothing,Nothing) && isCritical pub card, markPlayable v && isPlayable pub card) of
                                             (True, True)  -> "+!^+"
                                             (True, False) -> "+!!+"
                                             (False,True)  -> "+-^+"
                                             (False,False) -> "+--+"
                                    | (card, tup) <- zip cards hl ] ++"\n"
                          ++ concat [ wrap $ '|':shows card "|" | card <- cards ] ++"\n"
                          ++ (if markHints v then showHintLine wrap hl else "")
-- x                          ++ concat (replicate (length cards) "+--")
                          ++ concat [ wrap $
                                      '+':(if markChops v && d `elem` (concat $ take 1 $ obviousChopss pub anns) then ('X':) else ('-':))
                                             (if markObviouslyUseless  v && isObviouslyUseless  pub h then ".+" else
                                              if markObviouslyPlayable v && isObviouslyPlayable pub h then "^+" else "-+") | (d,h) <- zip [0..] ps ]++"\n"
                          ++ (if markPossibilities v then showPosLines ps else "")
                    where wrap xs | markPossibilities v = "  "++xs++" "
                                  | otherwise           = {- take 3 -} xs
                          hl = map marks anns
                          ps = map possibilities anns

showHintLine :: (String -> String) -> [Marks] -> String
showHintLine wrapper hl = concat [ wrapper $ '|' : maybe ' ' (head . show) mc : maybe ' ' (head . show . fromEnum) mk : "|" | (mc,mk) <- hl] ++ "\n"
showPosLines :: [Possibilities] -> String
showPosLines ps = concat [ ' ' : showColorPossibilities  cs | (cs,_) <- ps] ++ "\n"
               ++ concat [ showNumberPossibilities ns ++" " | (_,ns) <- ps]

showColorPossibilities, showNumberPossibilities :: Int -> String
showColorPossibilities  = reverse . showPossibilities ' ' colorkeys
showNumberPossibilities = reverse . showPossibilities ' ' "54321 "
colorkeys :: String
colorkeys = map (head . show) [maxBound, pred maxBound .. minBound::Color] -- colorkeys == "MBGRYW", but I just prefer to make this robust to changes in the order.
showPossibilities :: a -> [a] -> Int -> [a]
showPossibilities _     []     _   = []
showPossibilities blank (x:xs) pos = (if odd pos then x else blank) : showPossibilities blank xs (pos `div` 2)

colorPossibilities  :: Int -> [Color] -- The result is in the reverse order but I do not care.
colorPossibilities  = concat . showPossibilities [] (map (:[]) [maxBound, pred maxBound .. minBound])
numberPossibilities :: Int -> [Number] -- The result is in the reverse order but I do not care.
numberPossibilities = concat . showPossibilities [] (map (:[]) [K5,K4 .. K1])



-- | 'Verbosity' is the set of options used by verbose 'Strategy's
data Verbosity = V { warnCritical :: Bool -- ^ mark unhinted critical cards with "!!" ("!^" if it is playable and markPlayable==True.)
                   , markUseless  :: Bool -- ^ mark useless  cards with "..".
                   , markPlayable :: Bool -- ^ mark playable cards with "_^". ("!^" if it is unhinted critical and warnCritical==True.)
                   , markObviouslyUseless  :: Bool -- ^ mark useless  cards with "_." based on the hint marks.
                   , markObviouslyPlayable :: Bool -- ^ mark playable cards with "_^" based on the hint marks.
                   , markChops     :: Bool -- ^ mark the chop card(s) with "X". All obviously-useless cards will be marked, if any.
                   , warnDoubleDrop:: Bool -- ^ mark the chop card with "D" when dropping it is double-dropping.
                   , markHints     :: Bool -- ^ mark hints.
                   , markPossibilities :: Bool -- ^ mark more detailed hints based on the positive/negative hint history.
                                               --   markPossibilities == True && markHints == False is a reasonable choice, though markHints should still be informative for guessing other players' behavior.
                   } deriving (Read, Show, Eq, Generic)


{- This was too verbose
  = let
      showDeck 0 = "no card at the deck (the game will end in " ++ shows (fromJust $ deadline pub) " turn(s)), "
      showDeck 1 = "1 card at the deck, "
      showDeck n = shows n " cards at the deck, "
    in  "Turn "++ shows (turn pub) ": " ++ showDeck (pileNum pub) ++ shows (lives pub) " live(s) left, " ++ shows (hintTokens pub) " hint tokens;\n\n"
-}
showDeck pub = case deadline pub of
                 Nothing -> "Deck: " ++ shows (pileNum pub)  ",  "
                 Just 0  -> "Deck: 0 (no turn left),  "
                 Just 1  -> "Deck: 0 (1  turn left),  "
                 Just t  -> "Deck: 0 (" ++ shows t " turns left),  "

prettyPI :: PublicInfo -> String
prettyPI pub
  = "Turn: "++ shows (turn pub) ",  " ++ showDeck pub ++ "Lives: " ++ shows (lives pub) ",  Hints: " ++ shows (hintTokens pub) ";\n\n"
            ++ "played (" ++ shows (currentScore pub) " / " ++ shows (seeminglyAchievableScore pub) "):"
                         ++ concat [ "  " ++ concat ( [ show $ C c k | k <- [K1 .. achievedRank pub c] ] ++ replicate (possible - fromEnum playedMax) "__" ++ replicate (5 - possible) "XX")
                                   | c <- colors pub
                                   , let playedMax = achievedRank pub c
                                         possible  = fromEnum $ bestPossibleRank pub c
                                   ]
            ++ "\ndropped: " ++ concat [ '|' : concat (replicate n $ show $ intToCard ci) | (ci,n) <- IM.toList $ discarded pub ] ++"|\n"

view :: State -> PrivateView
view st = mkPV (publicState st) (tail $ hands st)

main :: IO ()
main = selfplay defaultGS

-- | 'selfplay' starts selfplay with yourself:)
--
--   Also,
--
-- > selfplay defaultGS{numPlayers=n}
--
--  (where 1<n<10) starts selfplay with youselves:D
selfplay :: GameSpec -> IO ()
selfplay gs
     = do g <- newStdGen
          ((finalSituation,_),_) <- start gs [] [stdio] g
          putStrLn $ prettyEndGame finalSituation

-- | 'prettyEndGame' can be used to pretty print the final situation.
prettyEndGame :: (EndGame, [State], [Move]) -> String
prettyEndGame (eg,sts@(st:_),mvs)
   = unlines $ recentEvents ithPlayerFromTheLast (map view sts) mvs :
               replicate 80 '!' :
               surround (replicate 40 '!') (show eg) :
               replicate 80 '!' :
               map (surround $ replicate 38 ' ' ++"!!") (lines $ prettySt ithPlayerFromTheLast st) ++
             [ replicate 80 '!' ]
surround :: [a] -> [a] -> [a]
surround ys xs = let len  = length xs
                     len2 =len `div` 2
                 in reverse (drop len2 ys) ++ xs ++ drop (len - len2) ys

type Peeker m = State -> [Move] -> m ()
peek :: Peeker IO
peek st []     = putStrLn $ prettySt ithPlayerFromTheLast st
peek st (mv:_) = putStrLn $ replicate 20 '-' ++ '\n' :
                            showTrial (const "") undefined (view st) mv ++ '\n' :
                            replicate 20 '-' ++ '\n' : prettySt ithPlayerFromTheLast st

-- | 'start' creates and runs a game. This is just the composition of 'createGame' and 'run'.
start :: (RandomGen g, Monad m, Strategies ps m) =>
       GameSpec -> [Peeker m] -> ps -> g -> m (((EndGame, [State], [Move]), ps), g)
start gs audience players gen = let
                         (st, g) = createGame gs gen
                       in fmap (\e -> (e,g)) $ run audience [st] [] players
startFromCards :: (Monad m, Strategies ps m) =>
       GameSpec -> [Peeker m] -> ps -> [Card] -> m ((EndGame, [State], [Move]), ps)
startFromCards gs audience players shuffled = let
                         st = createGameFromCards gs shuffled
                       in run audience [st] [] players
run :: (Monad m, Strategies ps m) => [Peeker m] -> [State] -> [Move] -> ps -> m ((EndGame, [State], [Move]), ps)
run audience states moves players = do
                              ((mbeg, sts, mvs), ps) <- runARound (\sts@(st:_) mvs -> let myOffset = turn (publicState st) in mapM_ (\p -> p st mvs) audience >> broadcast (zipWith rotate [-myOffset, 1-myOffset ..] sts) mvs players (myOffset `mod` numPlayers (gameSpec $ publicState st)) >> return ()) states moves players
                              case mbeg of Nothing -> run audience sts mvs ps
                                           Just eg -> return ((eg, sts, mvs), ps)

-- | 'runSilently' is a light variant of 'run' that does not broadcast the process. This is useful for simulating the game within a strategy.
runSilently :: (Monad m, Strategies ps m) => [State] -> [Move] -> ps -> m ((EndGame, [State], [Move]), ps)
runSilently states moves players = do
                              ((mbeg, sts, mvs), ps) <- runARound (\_ _ -> return ()) states moves players
                              case mbeg of Nothing -> runSilently sts mvs ps
                                           Just eg -> return ((eg, sts, mvs), ps)

-- | The 'Strategy' class is exactly the interface that
--   AI researchers defining their algorithms have to care about.
class Monad m => Strategy p m where
      -- | 'strategyName' is just the name of the strategy. The designer of the instance should choose one.
      strategyName :: m p -> m String

      -- | 'move' is the heart of the strategy. It takes the history of observations and moves, and selects a 'Move'.
      --   Because the full history is available, your algorithm can be stateless, but still there is the option to design it in the stateful manner.
      move :: [PrivateView] -- ^ The history of 'PrivateView's, new to old.
                   -> [Move]     -- ^ The history of 'Move's, new to old.
                   -> p          -- ^ The strategy's current state. This can be isomorphic to @()@ if the strategy does not have any parameter.
                   -> m (Move, p) -- ^ 'move' returns the pair of the Move and the next state, wrapped with monad m that is usually either IO or Identity.
                                  --   The next state can be the same as the current one unless the algorithm is learning on-line during the game.

      -- | 'observe' is called during other players' turns. It allows (mainly) human players to think while waiting.
      --
      --   It is arguable whether algorithms running on the same machine may think during other players' turn, especially when the game is timed.
      observe :: [PrivateView] -- ^ The history of 'PrivateView's, new to old.
                 -> [Move]     -- ^ The history of 'Move's, new to old.
                 -> p          -- ^ The strategy's current state. This can be isomorphic to @()@ if the strategy does not have any parameter.
                 -> m ()
      observe _pvs _moves _st = return () -- The default does nothing.
{-
                 -> m ((), p)  -- ^ 'observe' returns the next state, wrapped with monad m that is usually either IO or Identity.
                               --   The next state can be the same as the current one unless the algorithm is learning on-line during the game.
      observe _pvs _moves st = return ((),st) -- The default does nothing.
-}


-- StrategyDict should be used instead of class Strategy, maybe.

-- | 'StrategyDict' is a dictionary implementation of class 'Strategy'. It can be used instead if you like.
data StrategyDict m s = SD{sdName :: String, sdMove :: Mover s m, sdObserve :: Observer s m, sdState :: s}
type Mover    s m = [PrivateView] -> [Move] -> s -> m (Move, s)
type Observer s m = [PrivateView] -> [Move] -> s -> m ()
mkSD :: (Monad m, Typeable s, Strategy s m) => String -> s -> StrategyDict m s
mkSD name s = SD{sdName=name, sdMove=move, sdObserve=observe, sdState=s}
instance Monad m => Strategy (StrategyDict m s) m where
  strategyName mp = do p <- mp
                       return $ sdName p
  move    pvs mvs s = sdMove s pvs mvs (sdState s) >>= \ (m, nexts) -> return (m, s{sdState=nexts})
  observe pvs mvs s = sdObserve s pvs mvs $ sdState s


-- Should DynamicStrategy be limited to IO?
type DynamicStrategy m = StrategyDict m Dynamic
mkDS :: (Monad m, Typeable s, Strategy s m) => String -> s -> DynamicStrategy m
mkDS name s = mkDS' $ mkSD name s
mkDS' :: (Monad m, Typeable s) => StrategyDict m s -> DynamicStrategy m
mkDS' gs = SD{sdName    = sdName gs,
              sdMove    = \pvs mvs dyn -> fmap (\(m,p)->(m, toDyn p)) $ sdMove gs pvs mvs (fromDyn dyn (error "mkDS': impossible")),
              sdObserve = \pvs mvs dyn -> sdObserve gs pvs mvs (fromDyn dyn (error "mkDS': impossible")),
              sdState   = toDyn $ sdState gs}


-- | The 'Strategies' class defines the list of 'Strategy's. If all the strategies have the same type, one can use the list instance.
--   I (Susumu) guess that in most cases one can use 'Dynamic' in order to force the same type, but just in case, the tuple instance is also provided. (Also, the tuple instance should be more handy.)
--
--   The strategies are used in order, cyclically.
--   The number of strategies need not be the same as 'numPlayers', though the latter should be a divisor of the former.
--   For normal play, they should be the same. 
--   If only one strategy is provided, that means selfplay, though this is not desired because all the hidden info can be memorized. (In order to avoid such cheating, the same strategy should be repeated.)
--   If there are twice as many strategies as 'numPlayers', the game will be "Pair Hanabi", like "Pair Go" or "Pair Golf" or whatever. (Maybe this is also interesting.)
class Strategies ps m where
   runARound :: ([State] -> [Move] -> m ()) -> [State] -> [Move] -> ps -> m ((Maybe EndGame, [State], [Move]), ps)
   broadcast :: [State] -> [Move] -> ps -> Int -> m ([State], Int)
{- Abolished in order to avoid confusion due to overlapping instances. When necessary, use a singleton list instead.
instance {-# OVERLAPS #-} (Strategy p1 m, Monad m) => Strategies p1 m where
   runARound states moves p = runATurn states moves p
-}
instance (Strategies p1 m, Strategies p2 m, Monad m) => Strategies (p1,p2) m where
   runARound hook states moves (p,ps) = runARound hook states moves p >>= \(tup@(mbeg,sts,mvs), p') -> case mbeg of
                                                               Nothing -> do (tups,ps') <- runARound hook sts mvs ps
                                                                             return (tups, (p',ps'))
                                                               _       -> return (tup, (p',ps))
   broadcast states moves (p1,p2) offset = do (sts, ofs) <- broadcast states moves p1 offset
                                              broadcast sts moves p2 ofs
instance (Strategy p m, Monad m) => Strategies [p] m where
--   runARound hook states moves []     = return ((Nothing, states, moves), [])
   runARound _    _      _     []     = error "It takes at least one algorithm to play Hanabi!"
   runARound hook states moves [p]    = hook states moves >> runATurn states moves p >>= \(tup, p') -> return (tup, [p'])
   runARound hook states moves (p:ps) = hook states moves >> runATurn states moves p >>= \(tup@(mbeg,sts,mvs), p') -> case mbeg of
                                                               Nothing -> do (tups,ps') <- runARound hook sts mvs ps
                                                                             return (tups, (p':ps'))
                                                               _       -> return (tup, (p':ps))
   broadcast _      _     []     _   = error "It takes at least one algorithm to play Hanabi!"
   broadcast states moves [p]    ofs = when (ofs/=0) (observe (viewStates states) moves p) >> return (map (rotate 1) states, pred ofs)
   broadcast states moves (p:ps) ofs = when (ofs/=0) (observe (viewStates states) moves p) >> broadcast (map (rotate 1) states) moves ps (pred ofs)

viewStates :: [State] -> [PrivateView]
viewStates = map view . zipWith rotate [0..]

runATurn :: (Strategy p m, Monad m) => [State] -> [Move] -> p -> m ((Maybe EndGame, [State], [Move]), p)
runATurn states moves p = let alg = move (viewStates states) moves p in
                                     do (mov, p') <- alg
                                        case proceed (head states) mov of
                                          Nothing -> do name <- strategyName (fmap snd alg)
                                                        error $ show mov ++ " by " ++ name ++ ": invalid move!"  -- 'strategyName' exists in order to blame stupid algorithms:) 
                                                                                                                 -- (but seriously, this could end with failure. There is a safety net for human players.)
                                          Just st -> let nxt = rotate 1 st
                                                     in return ((checkEndGame $ publicState nxt, nxt:states, mov:moves), p')

-- | Verbose makes a player verbose. It is useful to monitor the viewpoint of a specific player.
data Verbose p = Verbose {unV :: p, verbV :: Verbosity} deriving (Read, Show)
instance (Strategy p m, MonadIO m) => Strategy (Verbose p) m where
    strategyName mp = do name <- strategyName $ fmap unV mp
                         return $ if name == "Blind" then "STDIO" else "Verbose " ++ name
    move views@(_:_) moves (Verbose p verb) = let alg = move views moves p in
                                              do name <- strategyName (fmap (\a -> Verbose (snd a) verb) alg)
                                                 liftIO $ putStrLn $ what'sUp verb name views moves
                                                 (mv,p') <- alg
                                                 -- liftIO $ putStrLn $ "Move is " ++ show mv -- This is redundant because of echo back.
                                                 return (mv, Verbose p' verb)
    observe _     []    _ = return ()
    observe (v:_) (m:_) (Verbose _ verb) = liftIO $ putStrLn $ what'sUp1 verb v m

what'sUp :: Verbosity -> String -> [PrivateView] -> [Move] -> String
what'sUp verb name views@(v:_) moves = replicate 20 '-' ++ '\n' :
                                  recentEvents ithPlayer views moves ++ '\n' :
                                  replicate 20 '-' ++ '\n' :
                                  "Algorithm: " ++ name ++ '\n' :
                                  prettyPV verb v ++ "\nYour turn.\n"
what'sUp1 :: Verbosity -> PrivateView -> Move -> String
what'sUp1 verb v m = replicate 20 '-' ++ '\n' :
                showTrial (const "") undefined v m ++ '\n' :
                replicate 20 '-' ++ '\n' :
                prettyPV verb v

recentEvents :: (Int -> Int -> String) -> [PrivateView] -> [Move] -> String
recentEvents ithP vs@(v:_) ms = unlines $ reverse $ zipWith3 (showTrial $ ithP nump) [pred nump, nump-2..0] vs ms
   where nump = numPlayers $ gameSpec $ publicView v

showTrial :: (Int -> String) -> Int -> PrivateView -> Move -> String
showTrial ithP i v m = ithP i ++ " move: " ++ replicate (length (ithP 2) - length (ithP i)) ' ' ++ show m ++
                                                        case result $ publicView v of Discard c -> ", which revealed "++shows c "."
                                                                                      Success c -> ", which succeeded revealing "++shows c "."
                                                                                      Fail    c -> ", which failed revealing " ++ shows c "."
                                                                                      _         -> "."

ithPlayer :: Int -> Int -> String
ithPlayer _ 0 = "Your"
ithPlayer _ i = "The " ++ ith i ++"next player's"
ith :: Int -> String
ith 1 = ""
ith 2 = "2nd "
ith 3 = "3rd "
ith i = shows i "th "
ithPlayerFromTheLast :: Int -> Int -> String
ithPlayerFromTheLast nump j = "The " ++ ith (nump-j) ++"last player's"


newtype Replay = Replay String deriving (Read, Show)
instance (MonadIO m) => Strategy Replay m where
  strategyName _ = return "Replay"
  move (v:_) _ (Replay xs) = case splitAt 2 xs of ("","") -> do mov <- liftIO $ repeatReadingAMoveUntilSuccess stdin stdout v
                                                                return (mov, Replay "")
                                                  (tk,dr) -> return (read tk, Replay dr)


type STDIO = Verbose Blind
stdio :: Verbose Blind
stdio = Verbose Blind verbose
data Blind = Blind
instance (MonadIO m) => Strategy Blind m where
    strategyName _ = return "Blind"
    move (v:_) _ _ = do mov <- liftIO $ repeatReadingAMoveUntilSuccess stdin stdout v
                        return (mov, Blind)
data ViaHandles = VH {hin :: Handle, hout :: Handle, verbVH :: Verbosity}
instance (MonadIO m) => Strategy ViaHandles m where
    strategyName _ = return "via handles"
    move views@(v:_) moves vh = liftIO $ do hPutStrLn (hout vh) $ what'sUp (verbVH vh) "via handles" views moves
                                            mov <- repeatReadingAMoveUntilSuccess (hin vh) (hout vh) v
                                            return (mov, vh)

repeatReadingAMoveUntilSuccess :: Handle -> Handle -> PrivateView -> IO Move
repeatReadingAMoveUntilSuccess hin hout v = do
    str <- hGetLine hin
    case reads str of [(mv, rest)] | all isSpace rest -> if isMoveValid v mv then return mv else hPutStrLn hout "Invalid Move" >> repeatReadingAMoveUntilSuccess hin hout v
                      _            -> hPutStr hout ("Parse error.\n"++help) >> repeatReadingAMoveUntilSuccess hin hout v

-- | 'createGameFromCards' deals cards and creates the initial state.
createGameFromCards :: GameSpec -> [Card] -> State
createGameFromCards gs cards = splitCons (numPlayers gs) [] [ (c, initAnn gs i) | (c,i) <- zip cards [0..] ]
           where splitCons 0 hnds stack
                   = St {publicState = PI {gameSpec   = gs,
                                            pileNum    = initialPileNum gs,
                                            played     = IM.fromAscList [ (i,            Empty) | i <- [0 .. pred $ numColors $ rule gs] ],
                                            discarded  = IM.fromList    [ (cardToInt $ C i k, 0) | i <- take (numColors $ rule gs) [White .. Multicolor],
                                                                                                   k <- [K1 ..K5] ],
                                            nonPublic  = cardMap $ rule gs,
                                            turn       = 0,
                                            lives      = numBlackTokens $ rule gs,
                                            hintTokens = 8,
                                            deadline   = Nothing,
                                            annotations = map (map snd) hnds,
                                            result     = None
                                           },
                           pile  = stack,
                           hands = map (map fst) hnds
                          }
                 splitCons n hnds stack = case splitAt (handSize gs) stack of (tk,dr) -> splitCons (pred n) (tk:hnds) dr
initAnn gs i = Ann{ixDeck=i, marks=(Nothing, Nothing), possibilities=unknown gs}
createGame :: RandomGen g => GameSpec -> g -> (State, g) -- Also returns the new RNG state, in order not to require safe 'split' for collecting statistics. RNG is only used for initial shuffling.
createGame gs gen = (createGameFromCards gs shuffled, g) where
                 (shuffled, g) = createDeck (rule gs) gen
createDeck :: RandomGen g => Rule -> g -> ([Card], g)
createDeck r gen = shuffle (cardBag r) gen


numAssoc :: [(Number, Int)]
numAssoc = zip [K1 ..K5] [3,2,2,2,1]
cardAssoc :: Rule -> [(Card,Int)]
cardAssoc rule = take (5 * numColors rule) $
               [ (C i k, n) | i <- [White .. pred Multicolor], (k,n) <- numAssoc ] ++ [ (C Multicolor k, n) | (k, n) <- zip [K1 ..K5] (numMulticolors rule) ]
cardBag :: Rule -> [Card]
cardBag rule = concat         [ replicate n c | (c,n) <- cardAssoc rule ]
cardMap :: Rule -> IM.IntMap Int
cardMap rule = IM.fromList [ (cardToInt c, n) | (c,n) <- cardAssoc rule ]
unknown :: GameSpec -> Possibilities
unknown gs = (64 - bit (6 - numColors (rule gs)),  31)

shuffle :: RandomGen g => [c] -> g -> ([c], g)
shuffle xs = shuf [] xs $ length xs
shuf :: RandomGen g => [a] -> [a] -> Int -> g -> ([a], g)
shuf result _  0 gen  = (result, gen)
shuf result xs n gen  = let (i,  g)    = randomR (0, pred n) gen
                            (nth,rest) = pickNth i xs
                        in shuf (nth:result) rest (pred n) g

-- | 'isMoveValid' can be used to check if the candidate Move is compliant to the rule under the current situation. Each player can decide it based on the current 'PrivateView' (without knowing the full state).
isMoveValid :: PrivateView -> Move -> Bool
isMoveValid PV{publicView=pub} (Drop ix) = hintTokens pub < 8 && length (head $ annotations pub) > ix && ix >= 0
isMoveValid PV{publicView=pub} (Play ix) = length (head $ annotations pub) > ix && ix >= 0
isMoveValid PV{publicView=pub,handsPV=tlHands} (Hint hintedpl eck)
                                         = hintTokens pub > 0 &&
                                           hintedpl > 0 && hintedpl < numPlayers (gameSpec pub) &&    -- existing player other than the current
                                           not (null $ filter willBeHinted (tlHands !! pred hintedpl))
    where willBeHinted :: Card -> Bool
          willBeHinted = either (\c -> (==c).color) (\k -> (==k).number) eck
pickNth :: Int -> [a] -> (a, [a])
pickNth    n   xs = case splitAt n xs of (tk,nth:dr) -> (nth,tk++dr)
replaceNth :: Int -> a -> [a] -> (a, [a])
replaceNth n x xs = case splitAt n xs of (tk,nth:dr) -> (nth,tk++x:dr)    -- = updateNth n (const x) xs
updateNth :: Int -> (a -> a) -> [a] -> (a, [a])
updateNth  n f xs = case splitAt n xs of (tk,nth:dr) -> (nth,tk++f nth:dr)

-- | 'proceed' updates the state based on the current player's Move, without rotating.
proceed :: State -> Move -> Maybe State
proceed st@(St{publicState=pub@PI{gameSpec=gS}}) mv = if (isMoveValid (view st) mv) then return (prc mv) else Nothing where

  -- only used by Drop and Play
  (nth, droppedHand) = pickNth (index mv) playersHand where playersHand = head $ hands st
  (_  , droppedAnn)  = pickNth (index mv) playersAnn  where playersAnn  = head $ annotations pub
  (nextHand,nextAnn,nextPile, nextPileNum) = case pile st of []   -> (        droppedHand,         droppedAnn, [], 0)
                                                             d:ps -> (fst d : droppedHand, snd d : droppedAnn, ps, pred $ pileNum pub)
  nextHands = nextHand : tail (hands st)
  nextAnns  = nextAnn : tail (annotations pub)
  nextDeadline = case deadline pub of Nothing | nextPileNum==0 && not (prolong $ rule $ gameSpec pub) -> Just $ numPlayers gS
                                              | otherwise                                             -> Nothing
                                      Just i  -> Just $ pred i
  prc (Drop _) = st{pile = nextPile,
                    hands = nextHands,
                    publicState = pub{pileNum = nextPileNum,
                                      discarded = IM.update (Just . succ) (cardToInt nth) $ discarded pub,
                                      nonPublic = IM.update (Just . pred) (cardToInt nth) $ nonPublic pub,
                                      turn       = succ $ turn pub,
                                      hintTokens = succ $ hintTokens pub,
                                      annotations = nextAnns,
                                      deadline   = nextDeadline,
                                      result     = Discard nth}}
  prc (Play i) | failure   = let newst@St{publicState=newpub} = prc (Drop i) in newst{publicState=newpub{hintTokens = hintTokens pub, lives = pred $ lives pub, result = Fail nth}}
               | otherwise = st{pile = nextPile,
                                hands = nextHands,
                                publicState = pub{pileNum = nextPileNum,
                                                  played = IM.update (Just . succ) (fromEnum $ color nth) (played pub),
                                                  nonPublic = IM.update (Just . pred) (cardToInt nth) $ nonPublic pub,
                                                  turn       = succ $ turn pub,
                                                  hintTokens = if hintTokens pub < 8 && number nth == K5 then succ $ hintTokens pub else hintTokens pub,
                                                  annotations = nextAnns,
                                                  deadline   = nextDeadline,
                                                  result = Success nth}}
    where failure = not $ isPlayable pub nth
  prc (Hint hintedpl eik) = st{publicState = pub{hintTokens = pred $ hintTokens pub,
                                                 turn       = succ $ turn pub,
                                                 annotations = snd $ updateNth hintedpl newAnns (annotations pub),
                                                 deadline   = case deadline pub of Nothing -> Nothing
                                                                                   Just i  -> Just $ pred i,
                                                 result     = None}}
    where newAnns hs = zipWith zipper (hands st !! hintedpl) hs
          zipper (C ir ka) ann@Ann{marks=(mi,mk),possibilities=(c,n)}
            = case eik of Left  i | i == ir -> ann{marks=(Just i, mk), possibilities = (bit ibit, n)}
                                  |otherwise-> ann{possibilities = (clearBit c ibit, n)}
                            where ibit = colorToBitPos i
                          Right k | k == ka -> ann{marks=(mi, Just k), possibilities = (c, bit kbit)}
                                  |otherwise-> ann{possibilities = (c, clearBit n kbit)}
                            where kbit = numberToBitPos k


-- | @'rotate' num@ rotates the first person by @num@ (modulo the number of players).
rotate :: Int -> State -> State
rotate num st@(St{publicState=pub@PI{gameSpec=gS}}) = st{hands       = rotateList $ hands st,
                                                         publicState = pub{annotations = rotateList $ annotations pub}}
    where rotateList xs = case splitAt (num `mod` numPlayers gS) xs of (tk,dr) -> dr++tk

-- | 'EndGame' represents the game score, along with the info of how the game ended.
--   It is not just @Int@ in order to distinguish 'Failure' (disaster / no life) from @'Soso' 0@ (not playing any card), though @'Soso' 0@ does not look more attractive than 'Failure'.
data EndGame = Failure | Soso Int | Perfect deriving (Show,Read,Eq,Generic)

egToInt _   Failure  = 0
egToInt _   (Soso n) = n
egToInt pub Perfect  = 5 * numColors (rule $ gameSpec pub)

checkEndGame :: PublicInfo -> Maybe EndGame
checkEndGame pub | lives pub == 0                                      = Just Failure
                 | all (==K5) [ achievedRank pub k | k <- colors pub ] = Just Perfect
                 | deadline pub == Just 0 ||
                   (earlyQuit (rule $ gameSpec pub) && currentScore pub == seeminglyAchievableScore pub)
                                                                       = Just $ Soso $ IM.foldr (+) 0 $ fmap fromEnum $ played pub
                 | hintTokens pub == 0 && null (head $ annotations pub) = Just Failure -- No valid play is possible for the next player. This can happen when prolong==True.
                 | otherwise                                           = Nothing