Gamemaster General Game Playing hex Description Hex is a 2-player alternating move game played on a 9x9 hexagonally-connected board. On each step, one of the players places a colored marker on an open hexagon. The goal of the game is for the a player to form a path of markers of its color connecting one side of the board to the other. The goal of the red player is connect the upper left to the lower right, while the goal of the black player is to connect the upper right to the lower left. The game is interesting in that one of the two players must win; there is no possibility of a draw. The clever GDL encoding of the rules for this game is due to Peter Pham. Rulesheet %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% hex %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% metadata %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% role(red) role(black) base(cell(M,N,R)) :- row(M) & col(N) & role(R) base(connected(K,M,N)) :- succ(K,L) & row(M) & col(N) base(owner(K,R)) :- succ(K,L) & role(R) base(step(K)) :- succ(K,L) base(control(R)) :- role(R) action(place(M,N)) :- row(M) & col(N) action(update(J)) :- succ(J,K) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% init %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% init(step(1)) init(control(red)) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% legal %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% legal(place(M,N)) :- row(M) & col(N) & ~cell(M,N,red) & ~cell(M,N,black) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% operations %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% place(M,N) :: control(R) & step(K) ==> cell(M,N,R) & owner(K,R) & connected(K,M,N) place(M,N) :: control(R) & adjacent(M,N,P,Q) & connected(J,P,Q) & owner(J,R) ==> update(J) place(M,N) :: kerchunk update(J) :: connected(J,X,Y) & step(K) ==> ~connected(J,X,Y) & connected(K,X,Y) kerchunk :: step(M) & succ(M,N) ==> ~step(M) & step(N) kerchunk :: control(red) ==> ~control(red) & control(black) kerchunk :: control(black) ==> ~control(black) & control(red) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% goal %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% goal(red,100) :- redpath goal(red,0) :- ~redpath goal(black,100) :- blackpath goal(black,0) :- ~blackpath %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% terminal %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% terminal :- redpath terminal :- blackpath %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% Views %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% adjacent(J,K,J,N) :- nextcol(K,N) & row(J) adjacent(J,K,J,N) :- nextcol(N,K) & row(J) adjacent(J,K,M,K) :- nextrow(J,M) & col(K) adjacent(J,K,M,K) :- nextrow(M,J) & col(K) adjacent(J,K,M,N) :- nextrow(M,J) & nextcol(K,N) adjacent(J,K,M,N) :- nextrow(J,M) & nextcol(N,K) redpath :- connected(K,a,I) & connected(K,i,J) & owner(K,red) blackpath :- connected(K,I,1) & connected(K,J,9) & owner(K,black) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% Facts %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% row(a) row(b) row(c) row(d) row(e) row(f) row(g) row(h) row(i) col(1) col(2) col(3) col(4) col(5) col(6) col(7) col(8) col(9) nextrow(a,b) nextrow(b,c) nextrow(c,d) nextrow(d,e) nextrow(e,f) nextrow(f,g) nextrow(g,h) nextrow(h,i) nextcol(1,2) nextcol(2,3) nextcol(3,4) nextcol(4,5) nextcol(5,6) nextcol(6,7) nextcol(7,8) nextcol(8,9) succ(1,2) succ(2,3) succ(3,4) succ(4,5) succ(5,6) succ(6,7) succ(7,8) succ(8,9) succ(9,10) succ(10,11) succ(11,12) succ(12,13) succ(13,14) succ(14,15) succ(15,16) succ(16,17) succ(17,18) succ(18,19) succ(19,20) succ(20,21) succ(21,22) succ(22,23) succ(23,24) succ(24,25) succ(25,26) succ(26,27) succ(27,28) succ(28,29) succ(29,30) succ(30,31) succ(31,32) succ(32,33) succ(33,34) succ(34,35) succ(35,36) succ(36,37) succ(37,38) succ(38,39) succ(39,40) succ(40,41) succ(41,42) succ(42,43) succ(43,44) succ(44,45) succ(45,46) succ(46,47) succ(47,48) succ(48,49) succ(49,50) succ(50,51) succ(51,52) succ(52,53) succ(53,54) succ(54,55) succ(55,56) succ(56,57) succ(57,58) succ(58,59) succ(59,60) succ(60,61) succ(61,62) succ(62,63) succ(63,64) succ(64,65) succ(65,66) succ(66,67) succ(67,68) succ(68,69) succ(69,70) succ(70,71) succ(71,72) succ(72,73) succ(73,74) succ(74,75) succ(75,76) succ(76,77) succ(77,78) succ(78,79) succ(79,80) succ(80,81) succ(81,82) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Stylesheet //============================================================================== // Hex //============================================================================== function renderstate (state) {var step = compfindx('N',seq('step','N'),state,library); var role = compfindx('R',seq('control','R'),state,library); var table = document.createElement('table'); table.setAttribute('border','0'); var row = table.insertRow(0); var cell = row.insertCell(0); cell.setAttribute('align','center'); cell.setAttribute('style','font-size:20px'); cell.innerHTML = 'Step: ' + step; row = table.insertRow(1); var cell = row.insertCell(0); var board = renderboard(state); cell.appendChild(board); row = table.insertRow(2); var cell = row.insertCell(0); cell.setAttribute('align','center'); cell.setAttribute('style','font-size:20px'); if (compfindp('terminal',state,library)) {cell.innerHTML = 'Game over'} else {cell.innerHTML = 'Control: ' + role}; return table} function renderboard (state) {var canvas = document.createElement('canvas'); canvas.setAttribute('width','540px'); canvas.setAttribute('height','441px'); //drawhex(300, 0,canvas); //drawreddish(270, 20,canvas); //drawgrey(330, 20,canvas); drawhex(240, 40,canvas); //drawhex(300, 40,canvas); //drawgrey(360, 40,canvas); drawreddish(210, 60,canvas); drawgrey(270, 60,canvas); //drawhex(330, 60,canvas); //drawgrey(390, 60,canvas); drawreddish(180, 80,canvas); drawhex(240, 80,canvas); drawgrey(300, 80,canvas); //drawhex(360, 80,canvas); //drawgrey(420, 80,canvas); drawreddish(150,100,canvas); drawhex(210,100,canvas); drawhex(270,100,canvas); drawgrey(330,100,canvas); //drawhex(390,100,canvas); //drawgrey(450,100,canvas); drawreddish(120,120,canvas); drawhex(180,120,canvas); drawhex(240,120,canvas); drawhex(300,120,canvas); drawgrey(360,120,canvas); //drawhex(420,120,canvas); //drawgrey(480,120,canvas); drawreddish( 90,140,canvas); drawhex(150,140,canvas); drawhex(210,140,canvas); drawhex(270,140,canvas); drawhex(330,140,canvas); drawgrey(390,140,canvas); //drawhex(450,140,canvas); //drawgrey(510,140,canvas); drawreddish( 60,160,canvas); drawhex(120,160,canvas); drawhex(180,160,canvas); drawhex(240,160,canvas); drawhex(300,160,canvas); drawhex(360,160,canvas); drawgrey(420,160,canvas); //drawhex(480,160,canvas); //drawgrey(540,160,canvas); drawreddish( 30,180,canvas); drawhex( 90,180,canvas); drawhex(150,180,canvas); drawhex(210,180,canvas); drawhex(270,180,canvas); drawhex(330,180,canvas); drawhex(390,180,canvas); drawgrey(450,180,canvas); //drawhex(510,180,canvas); //drawgrey(570,180,canvas); drawhex( 0,200,canvas); drawhex( 60,200,canvas); drawhex(120,200,canvas); drawhex(180,200,canvas); drawhex(240,200,canvas); drawhex(300,200,canvas); drawhex(360,200,canvas); drawhex(420,200,canvas); drawhex(480,200,canvas); //drawhex(540,200,canvas); //drawhex(600,200,canvas); drawgrey( 30,220,canvas); drawhex( 90,220,canvas); drawhex(150,220,canvas); drawhex(210,220,canvas); drawhex(270,220,canvas); drawhex(330,220,canvas); drawhex(390,220,canvas); drawreddish(450,220,canvas); //drawreddish(510,220,canvas); //drawreddish(570,220,canvas); drawgrey( 60,240,canvas); drawhex(120,240,canvas); drawhex(180,240,canvas); drawhex(240,240,canvas); drawhex(300,240,canvas); drawhex(360,240,canvas); drawreddish(420,240,canvas); //drawreddish(480,240,canvas); //drawreddish(540,240,canvas); drawgrey( 90,260,canvas); drawhex(150,260,canvas); drawhex(210,260,canvas); drawhex(270,260,canvas); drawhex(330,260,canvas); drawreddish(390,260,canvas); //drawhex(450,260,canvas); //drawreddish(510,260,canvas); drawgrey(120,280,canvas); drawhex(180,280,canvas); drawhex(240,280,canvas); drawhex(300,280,canvas); drawreddish(360,280,canvas); //drawhex(420,280,canvas); //drawreddish(480,280,canvas); drawgrey(150,300,canvas); drawhex(210,300,canvas); drawhex(270,300,canvas); drawreddish(330,300,canvas); //drawhex(390,300,canvas); //drawreddish(450,300,canvas); drawgrey(180,320,canvas); drawhex(240,320,canvas); drawreddish(300,320,canvas); //drawhex(360,320,canvas); //drawreddish(420,320,canvas); drawgrey(210,340,canvas); drawreddish(270,340,canvas); //drawhex(330,340,canvas); //drawreddish(390,340,canvas); drawhex(240,360,canvas); //drawhex(300,360,canvas); //drawreddish(360,360,canvas); //drawgrey(270,380,canvas); //drawreddish(330,380,canvas); //drawhex(300,400,canvas); for (var i=0; i<state.length; i++) {if (state[i][0]=='cell') {var x = xpos(state[i][1],state[i][2]); var y = ypos(state[i][1],state[i][2]); if (state[i][3]=='red') {drawred(x,y,canvas)}; if (state[i][3]=='black') {drawblack(x,y,canvas)}}}; return canvas} function xpos (m,n) {return xm(m)+xn(n)} function ypos (m,n) {return 200+ym(m)-yn(n)} function xm (m) {if (m=='a') {return 0}; if (m=='b') {return 30}; if (m=='c') {return 60}; if (m=='d') {return 90}; if (m=='e') {return 120}; if (m=='f') {return 150}; if (m=='g') {return 180}; if (m=='h') {return 210}; if (m=='i') {return 240}; if (m=='j') {return 270}; if (m=='k') {return 300}; return 330} function ym (m) {if (m=='a') {return 0}; if (m=='b') {return 20}; if (m=='c') {return 40}; if (m=='d') {return 60}; if (m=='e') {return 80}; if (m=='f') {return 100}; if (m=='g') {return 120}; if (m=='h') {return 140}; if (m=='i') {return 160}; if (m=='j') {return 180}; if (m=='k') {return 200}; return 330} function yn (n) {if (n=='1') {return 0}; if (n=='2') {return 20}; if (n=='3') {return 40}; if (n=='4') {return 60}; if (n=='5') {return 80}; if (n=='6') {return 100}; if (n=='7') {return 120}; if (n=='8') {return 140}; if (n=='9') {return 160}; if (n=='10') {return 180}; if (n=='11') {return 200}; return 330} function xn (n) {if (n=='1') {return 0}; if (n=='2') {return 30}; if (n=='3') {return 60}; if (n=='4') {return 90}; if (n=='5') {return 120}; if (n=='6') {return 150}; if (n=='7') {return 180}; if (n=='8') {return 210}; if (n=='9') {return 240}; if (n=='10') {return 270}; if (n=='11') {return 300}; return 330} //------------------------------------------------------------------------------ // Drawing subroutines //------------------------------------------------------------------------------ function drawreddish (x,y,w) {var ctx = w.getContext('2d'); ctx.beginPath(); ctx.lineWidth=1; ctx.moveTo(x+10,y+ 0); ctx.lineTo(x+30,y+ 0); ctx.lineTo(x+40,y+20); ctx.lineTo(x+30,y+40); ctx.lineTo(x+10,y+40); ctx.lineTo( x+0,y+20); ctx.closePath(); ctx.fillStyle = "#fff0f0"; ctx.fill(); ctx.stroke()} function drawgrey (x,y,w) {var ctx = w.getContext('2d'); ctx.beginPath(); ctx.lineWidth=1; ctx.moveTo(x+10,y+ 0); ctx.lineTo(x+30,y+ 0); ctx.lineTo(x+40,y+20); ctx.lineTo(x+30,y+40); ctx.lineTo(x+10,y+40); ctx.lineTo( x+0,y+20); ctx.closePath(); ctx.fillStyle = "#dddddd"; ctx.fill(); ctx.stroke()} function drawhex (x,y,canvas) {drawline(x+ 0,y+20,x+10,y+ 0,canvas); drawline(x+10,y+ 0,x+30,y+ 0,canvas); drawline(x+30,y+ 0,x+40,y+20,canvas); drawline(x+40,y+20,x+30,y+40,canvas); drawline(x+30,y+40,x+10,y+40,canvas); drawline(x+10,y+40, x+0,y+20,canvas)} function drawred (x,y,w) {var ctx = w.getContext('2d'); ctx.beginPath(); ctx.lineWidth=2; ctx.arc(x+20,y+20,12,0,2*Math.PI,false); ctx.stroke(); ctx.fillStyle = "#ff8888"; ctx.fill();} function drawblack (x,y,w) {var ctx = w.getContext('2d'); ctx.beginPath(); ctx.lineWidth=2; ctx.arc(x+20,y+20,12,0,2*Math.PI,false); ctx.stroke(); ctx.fillStyle = "#888888"; ctx.fill();} function drawblank (x,y,w) {var ctx = w.getContext('2d'); ctx.beginPath(); ctx.lineWidth=2; ctx.arc(x+20,y+20,12,0,2*Math.PI,false); ctx.stroke(); ctx.fillStyle = "#ffffff"; ctx.fill();} function drawline(u,v,x,y,w) {var ctx = w.getContext('2d'); ctx.beginPath(); ctx.lineWidth=1; ctx.moveTo(u,v); ctx.lineTo(x,y); ctx.stroke()} function drawnode (node,x,y,canvas) {var mark = compfindx('X',seq('cell',node,'X'),state,library); if (mark=='red') {drawred(x,y,canvas); return true}; if (mark=='black') {drawblack(x,y,canvas); return true}; drawblank(x,y,canvas); return true} function drawtext (text,x,y,w) {var ctx = w.getContext('2d'); ctx.fillStyle = "#000000"; ctx.font="italic 14px Times" ctx.fillText(text,x+12,y+18); return true} function drawscore (text,x,y,w) {var ctx = w.getContext('2d'); ctx.fillStyle = "#000000"; ctx.font="28px Times" ctx.fillText(text,x+12,y+18); return true} //============================================================================== //============================================================================== //============================================================================== Ownership