% predicates that return positions in 8 directions from the given position
% north(Pos,NorthOfPos)
north([X,Y], [X, YN]) :- YN is Y - 1.

% south(Pos,SouthOfPos)
south([X,Y], [X, YS]) :- YS is Y + 1.

% west(Pos,WestOfPos)
west([X,Y], [XW, Y]) :- XW is X - 1.

% east(Pos,WestOfPos)
east([X,Y], [XW, Y]) :- XW is X + 1.

% diagonal positions are obtained from the major directions
% northEast(Pos,NorthEastOfPos)
northEast(Pos,NorthEastOfPos) :-
        north(Pos,NorthOfPos),
        east(NorthOfPos,NorthEastOfPos).