diff --git a/Babylon.hs b/Babylon.hs new file mode 100644 --- /dev/null +++ b/Babylon.hs @@ -0,0 +1,95 @@ +{- + Game playing module for Babylon + Pedro Vasconcelos, 2009 +-} +module Babylon where + +import List +import Maybe +import Data.Tree +import Control.Monad +import Minimax + +-- piece colors +data Color = White | Black | Green | Brown + deriving (Eq,Ord,Show,Enum) + +-- a game board is a list of stacks; +-- each stack is a list of colors +type Game = [[Color]] + +-- a move is given by a pair of indices +-- (i,j) means move stack i on top of stack j +type Move = (Int,Int) + +-- list of all colors +colors :: [Color] +colors = [White .. Brown] + +-- the initial game game: 4 colors x 3 pieces +-- each piece in a separate stack +initialGame :: Game +initialGame = [[c] | c<-colors, _<-[1..3]] + + +-- play a move and update the game +-- assumes the move is valid +play :: Game -> Move -> Game +play g (i,j) = let from = g!!i + (g', to:g'')= splitAt j g + in deleteIndex i (g' ++ (from++to):g'') + +-- delete element of a list at index i +deleteIndex :: Int -> [a] -> [a] +deleteIndex i xs = let (xs',x:xs'') = splitAt i xs + in xs' ++ xs'' + +-- list all valid moves of a given board +valid :: Game -> [Move] +valid g = [(i,j) | (xs,i)<-zip g [0..], (ys,j)<-zip g [0..], + i/=j && (head xs==head ys || length xs==length ys) + ] + + +-- a game position: a board labeled with an optional move +-- this is used to identify which move lead to which position +type Position = (Game, Maybe Move) + +-- subsequent positions from a given position +-- labelled with the first move; subsequent moves are not needed +-- optimization: reduces the branching factor +-- by removing "equivalent" child positions +positions :: Position -> [Position] +positions (g,m) + = nubBy (\x y->sort (fst x)==sort (fst y)) + [(play g m', mplus m (Just m')) | m'<-valid g] + +-- build the game tree from a starting position +gametree :: Position -> Tree Position +gametree p = Node p (map gametree (positions p)) + + +-- the static evaluation function +-- yields -1 if the position is a loss (no available moves); +-- yields 0 in other positions (unknown) +static :: Position -> Eval Position +static p@(g,m) | null (valid g) = Eval (-1) p + | otherwise = Eval 0 p + +-- dynamic evaluation to choose the best move +-- uses alpha-beta prunning minimax with a fixed ply-depth +dynamic :: Int -> Game -> Eval Position +dynamic depth game + = bbminimax (Eval (-1) undefined) (Eval 1 undefined) $ + fmap static $ + prune depth $ + gametree (game,Nothing) + + +-- get the best move from a given board (using the above) +bestmove :: Int -> Game -> Maybe Move +bestmove d g = snd $ fromEval (dynamic d g) + +bestmove' :: Int -> Game -> (Int, Maybe Move) +bestmove' d g = case dynamic d g of + Eval x (g,m) -> (x, m) diff --git a/LICENSE b/LICENSE new file mode 100644 --- /dev/null +++ b/LICENSE @@ -0,0 +1,674 @@ + GNU GENERAL PUBLIC LICENSE + Version 3, 29 June 2007 + + Copyright (C) 2007 Free Software Foundation, Inc. + Everyone is permitted to copy and distribute verbatim copies + of this license document, but changing it is not allowed. + + Preamble + + The GNU General Public License is a free, copyleft license for +software and other kinds of works. + + The licenses for most software and other practical works are designed +to take away your freedom to share and change the works. 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If not, see . + +Also add information on how to contact you by electronic and paper mail. + + If the program does terminal interaction, make it output a short +notice like this when it starts in an interactive mode: + + Copyright (C) + This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. + This is free software, and you are welcome to redistribute it + under certain conditions; type `show c' for details. + +The hypothetical commands `show w' and `show c' should show the appropriate +parts of the General Public License. Of course, your program's commands +might be different; for a GUI interface, you would use an "about box". + + You should also get your employer (if you work as a programmer) or school, +if any, to sign a "copyright disclaimer" for the program, if necessary. +For more information on this, and how to apply and follow the GNU GPL, see +. + + The GNU General Public License does not permit incorporating your program +into proprietary programs. If your program is a subroutine library, you +may consider it more useful to permit linking proprietary applications with +the library. If this is what you want to do, use the GNU Lesser General +Public License instead of this License. But first, please read +. diff --git a/Main.hs b/Main.hs new file mode 100644 --- /dev/null +++ b/Main.hs @@ -0,0 +1,264 @@ +{- + Main module and GUI for the Babylon game + Uses wxHaskell bindings to the wxWidgets toolkit + Pedro Vasconcelos, 2009 +-} +module Main where + +import Graphics.UI.WX hiding (play) +import Graphics.UI.WXCore +import Maybe +import Random + +import Babylon + +import Paths_babylon -- Cabal locations of image files + +data Player = Human | Computer deriving (Eq,Show) + +data Level = Easy | Medium | Hard | Hardest deriving (Eq,Show) + +levels :: [Level] +levels = [Easy, Medium, Hard, Hardest] + +main :: IO () +main = start gui + +-- start the GUI +gui :: IO () +gui = do f <- frame [text := "Babylon"] + status <- statusField [text:="Welcome to Babylon"] + pan <- panel f [] + + game <- shuffleIO initialGame + vgame <- varCreate game + vboard <- varCreate [] + vsel <- varCreate Nothing + vplayer <- varCreate Human + vlevel <- varCreate Medium + + bmps <- loadBitmaps + + game <- menuPane [text := "&Game"] + new<-menuItem game [text := "New", + help := "Restart the game" + ] + menuLine game + menuQuit game [help := "Quit this program", + on command := delBitmaps bmps >> close f] + opt <- menuPane [text := "Options"] + r0<-menuItem opt [text := "Human plays first", + help := "Choose starting player", + checkable:=True, checked := True] + menuLine opt + -- create radio buttons for AI level + rs<-sequence [menuRadioItem opt + [text := show level, + help := "Choose computer opponent level", + on command := varSet vlevel level] + | level<-levels] + + -- default: Medium level checked + set (rs!!1) [checked:=True] + + hlp <- menuHelp [] + rules<- menuItem hlp [text := "Rules", + help := "About the game rules", + on command := infoRules pan] + about <- menuAbout hlp [help := "About this program", + on command := infoAbout pan] + + -- name an action to update the status field & repaint the board + let updt = do updateStatus status vplayer vgame + repaint pan + + + set pan [on resize := repaint pan, + on paint := drawBoard bmps vgame vboard vsel, + on click := (\pt -> do ix<-getIndex vboard pt + humanPlay vplayer vgame vsel updt ix), + layout := space 700 300 + ] + + -- register a timer event to periodically play the computer + t <- timer f [interval := 2000, + on command := computerPlay vplayer vgame vlevel updt + ] + + set f [statusBar := [status], + menuBar := [game, opt, hlp], + layout := fill (widget pan) + ] + + -- set the handler for restarting the game + set new [on command := do game <- shuffleIO initialGame + flag <- get r0 checked + varSet vplayer (if flag then Human + else Computer) + varSet vgame game + varSet vsel Nothing + updt + ] + + + + +-- display an info dialog +infoAbout w + = infoDialog w "About Babylon" $ + init $ + unlines ["Written in Haskell using the wxWidgets toolkit", + "by Pedro Vasconcelos ", + "", + "Based on the board game by Bruno Faidutti", + "Published by FoxMind Games." + ] + +-- display the game rules +infoRules w + = infoDialog w "Rules of Babylon" $ + init $ + unlines ["Two players take turns moving stacks of colored tiles.", + "A move is valid provided that:", + "1) the stacks have same height; or", + "2) the stacks have the same top color.", + "The first player who cannot make a move loses the game!"] + +-- load bitmaps for the colored tiles +-- uses Cabal to for portable file paths +loadBitmaps + = sequence [do { f<-getDataFileName ("images/" ++ show c ++ ".png") + ; bitmapCreateLoad f wxBITMAP_TYPE_PNG } + | c<-colors] + +-- delete the bitmaps +delBitmaps bmps = sequence_ [bitmapDelete b | b<-bmps] + +-- update the status field +-- shows current player and checks for no available moves, i.e. game end +updateStatus status vplayer vgame + = do player <- varGet vplayer + game <- varGet vgame + let moves = valid game + case moves of + [] -> set status [text := show player ++ " loses (no moves available)"] + _ -> set status [text := show player ++ " to play"] + + +-- +-- main function to redraw the game board +-- +drawBoard bmps vgame vboard vsel dc (Rect x y w h) + = do game <- varGet vgame + rs <- drawStacks bmps game dc x' y' + varSet vboard rs + -- highlight the selection (if active) + sel <- varGet vsel + case sel of + Nothing -> return () + Just i -> drawRect dc (rs!!i) [pen:=penColored red 2, + brush:=brushTransparent] + where x'= x + 10 + y' = y + h`div`2 + +-- draw a list of tile stacks +-- returns the list of bounding boxes (rectangles) +drawStacks bmps [] dc x y + = return [] +drawStacks bmps (s:ss) dc x y + = do r<-drawStack bmps s dc x y + rs<-drawStacks bmps ss dc (x+rectWidth r+dx) y + return (r:rs) + where dx = 8 + +-- draw a single stack of tiles +drawStack bmps tiles dc x y + = do rs<-sequence [ do { drawBitmap dc b (pt x' y') False [] + ; sz <- bitmapGetSize b + ; return (rect (pt x' y') sz) + } + | (c,x',y')<-zip3 (reverse tiles) + [x,x+dx..] [y,y+dy..], + let b = bmps!!fromEnum c + ] + return (rectUnions rs) + where n = length tiles + dx = 4 + dy = -8 + +-- convert a screen positon into Just a tile index or Nothing +getIndex vboard pt + = do rs <- varGet vboard + return (listToMaybe [i | (i,r)<-zip [0..] rs, rectContains r pt]) + +-- +-- handle a mouse click and perform a human player move +-- `updt' is a continuation to update the board, etc. +-- +humanPlay vplayer vgame vsel updt Nothing + = return () +humanPlay vplayer vgame vsel updt (Just j) + = do player <- varGet vplayer + game <- varGet vgame + sel <- varGet vsel + case (player,sel) of + (Human, Nothing) -> do {varSet vsel (Just j); updt} + (Human, Just i) -> do varSet vsel Nothing + when ((i,j) `elem` valid game) $ + do varSet vgame (play game (i,j)) + varSet vplayer Computer + updt + _ -> return () + + + +-- +-- perform a computer opponent move +-- `updt' is a continuation to update the board, etc. +-- +computerPlay vplayer vgame vlevel updt + = do player <- varGet vplayer + game <- varGet vgame + level <- varGet vlevel + case player of + Human -> return () + Computer -> case bestmove' (depth level) game of + (_, Nothing) -> return () + (e, Just m) -> + do varSet vgame (play game m) + varSet vplayer Human + updt + + +-- show a move as a string +showMove :: Player -> Game -> Move -> String +showMove p g (i,j) = show p ++ ": " ++ show (g!!i) ++ " to " ++ show (g!!j) + + + +-- convert the difficulty level in the minimax analysis depth ("ply") +depth :: Level -> Int +depth Easy = 2 +depth Medium = 4 +depth Hard = 8 +depth Hardest = 12 -- optimal play (always wins as 2nd player) + + +-- an auxilary function to shuffle a list randomly +shuffleIO :: [a] -> IO [a] +shuffleIO xs = do g <- getStdGen + let (xs', g') = shuffle g xs (length xs) + setStdGen g' + return xs' + where + shuffle :: RandomGen g => g -> [a] -> Int -> ([a], g) + shuffle g xs n + | n>0 = let (k, g') = randomR (0,n-1) g + (xs',x:xs'') = splitAt k xs + (ys,g'') = shuffle g' (xs' ++ xs'') (n-1) + in (x:ys, g'') + | otherwise = ([],g) + + + + diff --git a/Minimax.hs b/Minimax.hs new file mode 100644 --- /dev/null +++ b/Minimax.hs @@ -0,0 +1,65 @@ +{- + Generic Minimax algorithm for game playing + Based in Bird & Wadler "Introduction to Functional Programming" + Pedro Vasconcelos, 2009 +-} +module Minimax where +import Data.Tree +--import Data.List + +-- annotate something with an evaluation estimate +data Eval a = Eval Int a deriving (Show) + +instance Eq (Eval a) where + (Eval x _) == (Eval y _) = x==y + +instance Ord (Eval a) where + compare (Eval x _) (Eval y _) = compare x y + +instance (Show a) => Num (Eval a) where + fromInteger = undefined + (+) = undefined + (-) = undefined + (*) = undefined + abs = undefined + signum= undefined + negate (Eval x a) = Eval (-x) a + +fromEval :: Eval a -> a +fromEval (Eval _ x) = x + + + +-- naive minimax algorithm +-- nodes are decorated with the static evaluation scores +minimax :: (Num a, Ord a) => Tree a -> a +minimax (Node n []) = n +minimax (Node n ts) = - minimum (map minimax ts) + + +-- branch-and-bound minimax (alpha-beta prunning) +-- nodes are decorated with the static evaluation scores +bbminimax :: (Num a, Ord a) => a -> a -> Tree a -> a +bbminimax a b (Node x []) = a `max` x `min` b +bbminimax a b (Node x ts) = cmx a ts + where + cmx a [] = a + cmx a (t:ts) | a'>=b = a' + | otherwise = cmx a' ts + where a' = -(bbminimax (-b) (-a) t) + + +-- some generic functions follow +-- prune a tree to a fixed depth +prune :: Int -> Tree a -> Tree a +prune n (Node x ts) + | n>0 = Node x (map (prune (n-1)) ts) + | otherwise = Node x [] + +-- breadth and depth of a tree +breadth :: Tree a -> Int +breadth (Node x ts) = length ts + +depth :: Tree a -> Int +depth (Node x []) = 1 +depth (Node x ts) = 1 + maximum (map depth ts) diff --git a/README b/README new file mode 100644 --- /dev/null +++ b/README @@ -0,0 +1,43 @@ +Babylon +------- + +This is an implementation of a simple two-player game +in Haskell using the wxWidgets GUI toolkit. +This program allows you to play against the computer plays using +the classical minimax algorithm with alpha-beta prunning +(based on Bird and Wadler's presentation in the "Introduction +to Functional Programming"). + +The rules of the game are very simple: +* there are 12 stone tablets in 4 colors (3 of each color) +* initially the stones are randomly placed on the table, + forming twelve 1-stone piles +* on his/her turn, a player moves one pile ontop of another + provided that they have the same height or the same top + color (or both) +* the first player who cannot perform a move loses the game. + +The game play very fast, typically under 5 mins; since there +are only 12 piles at the start, and each turn decrements one +pile, the game must finish in at most 11 moves. + +Note that there is a winning strategy for the second player, but +it does not appear to be a simple heuristic for it (?). +The computer will play the winning strategy at the hardest level, +so it will always win as a second player at this level. + +This was basically programmed in a single day as an experiment +using this wxWidgets (though I was experienced with Haskell). +I thought it would be a nice addition to show a simple but real +Haskell program. + +If you have any comments please drop me a line, + +Pedro Vasconcelos +pbv@dcc.fc.up.pt +Department of Computer Science +Faculty of Science, University of Porto, Portugal + + + + diff --git a/Setup.hs b/Setup.hs new file mode 100644 --- /dev/null +++ b/Setup.hs @@ -0,0 +1,2 @@ +import Distribution.Simple +main = defaultMain diff --git a/babylon.cabal b/babylon.cabal new file mode 100644 --- /dev/null +++ b/babylon.cabal @@ -0,0 +1,20 @@ +Name: babylon +Version: 0.1 +Cabal-Version: >= 1.2 +License: GPL +License-file: LICENSE +Author: Pedro Vasconcelos +Copyright: (c) 2009 Pedro Vasconcelos +Synopsis: An implementation of a simple 2-player board game +Description: The board game was originally designed by Bruno Faidutti (www.faidutti.com). + In this implementation you play against the computer. +Build-Type: Simple +Data-files: images/White.png images/Black.png images/Brown.png images/Green.png README +Category: Game + +Executable babylon + Build-Depends: base>= 3 && < 4, haskell98, containers, wx >= 0.11, wxcore >= 0.11 + Main-Is: Main.hs + Other-modules: Babylon Minimax + + diff --git a/images/Black.png b/images/Black.png new file mode 100644 Binary files /dev/null and b/images/Black.png differ diff --git a/images/Brown.png b/images/Brown.png new file mode 100644 Binary files /dev/null and b/images/Brown.png differ diff --git a/images/Green.png b/images/Green.png new file mode 100644 Binary files /dev/null and b/images/Green.png differ diff --git a/images/White.png b/images/White.png new file mode 100644 Binary files /dev/null and b/images/White.png differ