valid_queen((Row, Col)) :-
Range = [1,2,3,4,5,6,7,8],
member(Row, Range), member(Col, Range).
valid_board([]).
valid_board([Head|Tail]) :- valid_queen(Head), valid_board(Tail).
rows([], []).
rows([(Row, _)|QueensTail], [Row|RowsTail]) :-
rows(QueensTail, RowsTail).
cols([], []).
cols([(_, Col)|QueensTail], [Col|ColsTail]) :-
cols(QueensTail, ColsTail).
diags1([], []).
diags1([(Row, Col)|QueensTail], [Diagonal|DiagonalsTail]) :-
Diagonal is Col - Row,
diags1(QueensTail, DiagonalsTail).
diags2([], []).
diags2([(Row, Col)|QueensTail], [Diagonal|DiagonalsTail]) :-
Diagonal is Col + Row,
diags2(QueensTail, DiagonalsTail).
eight_queens(Board) :-
length(Board, 8),
valid_board(Board),
rows(Board, Rows),
cols(Board, Cols),
diags1(Board, Diags1),
diags2(Board, Diags2),
fd_all_different(Rows),
fd_all_different(Cols),
fd_all_different(Diags1),
fd_all_different(Diags2).
| ?- listing.
diags2([], []).
diags2([(A, B)|C], [D|E]) :-
D is B + A,
diags2(C, E).
eight_queens(A) :-
length(A, 8),
valid_board(A),
rows(A, B),
cols(A, C),
diags1(A, D),
diags2(A, E),
fd_all_different(B),
fd_all_different(C),
fd_all_different(D),
fd_all_different(E).
cols([], []).
cols([(_, A)|B], [A|C]) :-
cols(B, C).
rows([], []).
rows([(A, _)|B], [A|C]) :-
rows(B, C).
diags1([], []).
diags1([(A, B)|C], [D|E]) :-
D is B - A,
diags1(C, E).
valid_queen((A, B)) :-
C = [1, 2, 3, 4, 5, 6, 7, 8],
member(A, C),
member(B, C).
valid_board([]).
valid_board([A|B]) :-
valid_queen(A),
valid_board(B).
(31 ms) yes
| ?- eight_queens([(1, A), (2, B), (3, C), (4, D), (5, E), (6, F), (7, G), (8, H)]).
A = 1
B = 5
C = 8
D = 6
E = 3
F = 7
G = 2
H = 4 ? a
