% solution for the 8 queens problem

% queens: true for column values of non-attacking queens

queens(C1, C2, C3, C4, C5, C6, C7, C8) :-
  col(C1), col(C2), col(C3), col(C4), col(C5), col(C6), col(C7), col(C8),
  dif(C1, C2, C3, C4, C5, C6, C7, C8),
  dif(1+C1, 2+C2, 3+C3, 4+C4, 5+C5, 6+C6, 7+C7, 8+C8),
  dif(1-C1, 2-C2, 3-C3, 4-C4, 5-C5, 6-C6, 7-C7, 8-C8).

% col: true for column values 1..8

col(1). col(2). col(3). col(4). col(5). col(6). col(7). col(8).

% dif: true if arguments are pairwise different
% \= means not identical, =\= means not numerically equal

dif(A, B, C, D, E, F, G, H) :-
  A =\= B, A =\= C, A =\= D, A =\= E, A =\= F, A =\= G, A =\= H,
           B =\= C, B =\= D, B =\= E, B =\= F, B =\= G, B =\= H,
                    C =\= D, C =\= E, C =\= F, C =\= G, C =\= H,
                             D =\= E, D =\= F, D =\= G, D =\= H,
                                      E =\= F, E =\= G, E =\= H,
                                               F =\= G, F =\= H,
                                                        G =\= H.

% main: backtracks queens for all solutions.

main :-
  queens(C1, C2, C3, C4, C5, C6, C7, C8),
  write(C1), write(' '), write(C2), write(' '),
  write(C3), write(' '), write(C4), write(' '),
  write(C5), write(' '), write(C6), write(' '),
  write(C7), write(' '), write(C8), write('\n'),
  fail.