.Open Games

GAME::=Net{ N person game.
	Players::Sets. Some Players. 
	N::=No_of_players::=|Players|.
	Position: :Sets.
	moves::Position->@Position.
	moves::@Position->@Position=map[P:@Positions]{q:Position|| for some p:P, q in moves(p)}.
	State::Sets.
	win, loose,draw,undecided::State.
	value::Position->State.
	Won::=win./value.
	Lost::=loose./value.
	Drawn::=draw./value.
 	For all p:Position ( p in Won|Lost|Draw iff moves(p)={}).

	Winning, Loosing::@Position.
	Won==>Winning. Lost==>Loosing.
	No Winning & Loosing.
	Initial::@Position.
	loops::@= some p:positions( p in moves;do(moves) ).
}=::GAME.

SOLITAIRE::={ A game with one player were there may be a chance of winning and one initial state
	GAME and No_of_players=1.
	For all p:Loosing, p.moves==>Loosing.
	Draw={}.
	possible::@= Initial==>Winning and for all p:Winning, some p.moves & Winning.
 Rubik's cube is a patience game with loops.  Solitare card games have no loops.
 Rubik's cube has no Loosing positions, a single Won position, and a finite but large set of Winning positions.
	Call such a game a maze:
	maze::@= Winning=Position is Finite and |Won|=1.
}=::SOLITAIRE.

2_PERSON_GAME::=Net{
	|- GAME and No_of_players=2.
	black,white::Players.
	Winning::= 
		{  p:Position
		|| p in Won
		or p.moves==>Lost
		or for all q:p.moves, some r:q.moves (r in Winning)
		}.
	Loosing::= {  p:Position || p in Lost or some p.moves & Winning or for some q:p.moves, all r:q.moves (r in Loosing) }.
	play_alternately::@= For some State:Sets ( Position = Players >< State )
		and for all p:Position, q:moves(p) ( p.1st<>q.1st ).

}=::2_PERSON_GAME.

BOARD_GAME::=Net{
	|- GAME.
	Board::Sets.
	Type_of_piece::Sets.
	|- Position=Board->{empty}|Piece.
	|- Piece=Players><Type_of_piece.

 For Piece p, Board b,
		Add(p,b) ::=map[x:Position]{x'||x(b)=empty and x'(b)=p},
		Take(p,b) ::=map[x:Position]{x'||x(b)=p and x'(b)=empty},
		Move(p,b1,b2) ::=map[x:Position]
			{x'||x(b1)=p and x(b2)=empty and x'(b1)=empty and x'(b2)=p}.

}=::BOARD_GAME.

tictactoe::=$ Net{
	|- BOARDGAME(Position=>Grid).
	|- 2_PERSON_GAME(play_alternately).
	|- Type_of_piece={mark}.
	nought::Piece=(black,mark), cross::Piece=(white, mark).

	|- Board=1..3><1..3.
	Rows::={ {(r,c):Board||r:1..3}||c:1..3 },
	Cols::={ {(r,c):Board||c:1..3}||r:1..3 },
	Diagonals::={ {(1,1),(2,2),(3,3)} , {(1,3),(2,2),(3,1)}  }.

	|- Position=Player><Grid.

	Won::={p:Position
		|| for some X:Rows|Cols|Diagonals, q:{nought,cross}, all b:X	( Position(b)=q )
		}.
	()|- Won={p:Position
		|| for some X:Rows|Cols|Diagonals, q:{nought,cross}( X==>q./Position)
		}.

.Hole

}=::tictactoe.

.Close Games