Sudoku solver in prolog

sudoku9.pl

valid([]).
valid([Head|Tail]) :- fd_all_different(Head), valid(Tail).

sudoku9(Puzzle, Solution) :-
  Solution = Puzzle,

  Puzzle = [S11, S12, S13, S14, S15, S16, S17, S18, S19,
            S21, S22, S23, S24, S25, S26, S27, S28, S29,
            S31, S32, S33, S34, S35, S36, S37, S38, S39,
            S41, S42, S43, S44, S45, S46, S47, S48, S49,
            S51, S52, S53, S54, S55, S56, S57, S58, S59,
            S61, S62, S63, S64, S65, S66, S67, S68, S69,
            S71, S72, S73, S74, S75, S76, S77, S78, S79,
            S81, S82, S83, S84, S85, S86, S87, S88, S89,
            S91, S92, S93, S94, S95, S96, S97, S98, S99],

  fd_domain(Solution, 1, 9),

  Row1 = [S11, S12, S13, S14, S15, S16, S17, S18, S19],
  Row2 = [S21, S22, S23, S24, S25, S26, S27, S28, S29],
  Row3 = [S31, S32, S33, S34, S35, S36, S37, S38, S39],
  Row4 = [S41, S42, S43, S44, S45, S46, S47, S48, S49],
  Row5 = [S51, S52, S53, S54, S55, S56, S57, S58, S59],
  Row6 = [S61, S62, S63, S64, S65, S66, S67, S68, S69],
  Row7 = [S71, S72, S73, S74, S75, S76, S77, S78, S79],
  Row8 = [S81, S82, S83, S84, S85, S86, S87, S88, S89],
  Row9 = [S91, S92, S93, S94, S95, S96, S97, S98, S99],

  Col1 = [S11, S21, S31, S41, S51, S61, S71, S81, S91],
  Col2 = [S12, S22, S32, S42, S52, S62, S72, S82, S92],
  Col3 = [S13, S23, S33, S43, S53, S63, S73, S83, S93],
  Col4 = [S14, S24, S34, S44, S54, S64, S74, S84, S94],
  Col5 = [S15, S25, S35, S45, S55, S65, S75, S85, S95],
  Col6 = [S16, S26, S36, S46, S56, S66, S76, S86, S96],
  Col7 = [S17, S27, S37, S47, S57, S67, S77, S87, S97],
  Col8 = [S18, S28, S38, S48, S58, S68, S78, S88, S98],
  Col9 = [S19, S29, S39, S49, S59, S69, S79, S89, S99],

  Squ1 = [S11, S12, S13, S21, S22, S23, S31, S32, S33],
  Squ2 = [S14, S15, S16, S24, S25, S26, S34, S35, S36],
  Squ3 = [S17, S18, S19, S27, S28, S29, S37, S38, S39],
  Squ4 = [S41, S42, S43, S51, S52, S53, S61, S62, S63],
  Squ5 = [S44, S45, S46, S54, S55, S56, S64, S65, S66],
  Squ6 = [S47, S48, S49, S57, S58, S59, S67, S68, S69],
  Squ7 = [S71, S72, S73, S81, S82, S83, S91, S92, S93],
  Squ8 = [S74, S75, S76, S84, S85, S86, S94, S95, S96],
  Squ9 = [S77, S78, S79, S87, S88, S89, S97, S98, S99],

  valid([Row1, Row2, Row3, Row4, Row5, Row6, Row7, Row8, Row9,
         Col1, Col2, Col3, Col4, Col5, Col6, Col7, Col8, Col9,
         Squ1, Squ2, Squ3, Squ4, Squ5, Squ6, Squ7, Squ8, Squ9]),
  
  nl,
  format('~w~w~w|~w~w~w|~w~w~w~n', Row1),
  format('~w~w~w|~w~w~w|~w~w~w~n', Row2),
  format('~w~w~w|~w~w~w|~w~w~w~n', Row3),
  write('---|---|---'), nl,
  format('~w~w~w|~w~w~w|~w~w~w~n', Row4),
  format('~w~w~w|~w~w~w|~w~w~w~n', Row5),
  format('~w~w~w|~w~w~w|~w~w~w~n', Row6),
  write('---|---|---'), nl,
  format('~w~w~w|~w~w~w|~w~w~w~n', Row7),
  format('~w~w~w|~w~w~w|~w~w~w~n', Row8),
  format('~w~w~w|~w~w~w|~w~w~w~n', Row9).