% The 8-queens problem.  Place 8 queens on a chessboard such that
% none can capture any other.
%
% Get all solutions (don't worry about isomorphic solutions).
%
% board([8,5,1]) means that queens are on the first 3 rows: 
% (row 1, col 1), (row 2, col 5), (row 3, col 8).
%
%      1 2 3 4 5 6 7 8
%   1 |x| | | | | | | |
%   2 | | | | |x| | | |
%   3 | | | | | | | |x|
%   4 | | | | | | | | |
%   5 | | | | | | | | |
%   6 | | | | | | | | |
%   7 | | | | | | | | |
%   8 | | | | | | | | |
%
% For other board sizes/number of queens, change 'pick' property and
% the denial in the passive list.
%

make_evaluable(_-_, $DIFF(_,_)).
make_evaluable(_+_, $SUM(_,_)).
make_evaluable(_==_, $EQ(_,_)).

set(hyper_res).
set(prolog_style_variables).
assign(max_proofs,-1).       % get all solutions
set(sos_stack).              % depth-first search
clear(print_kept).
clear(demod_history).

list(usable).

-board(B) |
     -pick(New_col) |
     % check that new queen is consistent with all preceding rows.
     -$TRUE(ok(B, 1, New_col)) | 
     board([New_col|B]).

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

end_of_list.

list(sos).
board([]).
end_of_list.

list(passive).
-board([X1,X2,X3,X4,X5,X6,X7,X8]) | $Ans([X1,X2,X3,X4,X5,X6,X7,X8]).
% -board([X1,X2,X3,X4,X5]) | $Ans([X1,X2,X3,X4,X5]).
end_of_list.

list(demodulators).
ok([], X, Y) = $T.
ok([H|T], Rows_back, New_col) =
        $IF(H == New_col,
            $F,
            $IF(H-Rows_back == New_col,
                $F,
                $IF(H+Rows_back == New_col,
                    $F,
                    ok(T, Rows_back+1, New_col)))).
end_of_list.