Prolog fd_domain is being undefined

Question

OK, so I am trying to code this simple sudoku solver for a school project. I am using SWI - Prolog, and I am using library clpfd.

The problem arises when I use domain/3 predicate. It is giving no syntax errors whatsover, only the program is returning "false" rather than the actual solution.

Excuse me for my Noobness, but I am completely new to Prolog and declarative languages.

Here is my full code:

:- use_module(library(clpfd)).

sudoku(Solution,Puzzle):-

    Solution = Puzzle,
    Solution =[[A1,A2,A3,A4,A5,A6,A7,A8,A9],
            [B1,B2,B3,B4,B5,B6,B7,B8,B9],
            [C1,C2,C3,C4,C5,C6,C7,C8,C9],
            [D1,D2,D3,D4,D5,D6,D7,D8,D9],
            [E1,E2,E3,E4,E5,E6,E7,E8,E9],
            [F1,F2,F3,F4,F5,F6,F7,F8,F9],
            [G1,G2,G3,G4,G5,G6,G7,G8,G9],
            [H1,H2,H3,H4,H5,H6,H7,H8,H9],
            [I1,I2,I3,I4,I5,I6,I7,I8,I9]],

    valid_domain(Puzzle,1,9),

    %Squares

    Sqr1 = [A1,A2,A3,B1,B2,B3,C1,C2,C3],
    Sqr2 = [A4,A5,A6,B4,B5,B6,C4,C5,C6],
    Sqr3 = [A7,A8,A9,B7,B8,B9,C7,C8,C9],
    Sqr4 = [D1,D2,D3,E1,E2,E3,F1,F2,F3],
    Sqr5 = [D4,D5,D6,E4,E5,E6,F4,F5,F6],
    Sqr6 = [D7,D8,D9,E7,E8,E9,F7,F8,F9],
    Sqr7 = [G1,G2,G3,H1,H2,H3,I1,I2,I3],
    Sqr8 = [G4,G5,G6,H4,H5,H6,I4,I5,I6],
    Sqr9 = [G7,G8,G9,H7,H8,H9,I7,I8,I9],


    %Rows

    Row1 = [A1,A2,A3,A4,A5,A6,A7,A8,A9],
    Row2 = [B1,B2,B3,B4,B5,B6,B7,B8,B9],
    Row3 = [C1,C2,C3,C4,C5,C6,C7,C8,C9],
    Row4 = [D1,D2,D3,D4,D5,D6,D7,D8,D9],
    Row5 = [E1,E2,E3,E4,E5,E6,E7,E8,E9],
    Row6 = [F1,F2,F3,F4,F5,F6,F7,F8,F9],
    Row7 = [G1,G2,G3,G4,G5,G6,G7,G8,G9],
    Row8 = [H1,H2,H3,H4,H5,H6,H7,H8,H9],
    Row9 = [I1,I2,I3,I4,I5,I6,I7,I8,I9],

    %Columns

    Col1 = [A1,B1,C1,D1,E1,F1,G1,H1,I1],
    Col2 = [A2,B2,C2,D2,E2,F2,G2,H2,I2],
    Col3 = [A3,B3,C3,D3,E3,F3,G3,H3,I3],
    Col4 = [A4,B4,C4,D4,E4,F4,G4,H4,I4],
    Col5 = [A5,B5,C5,D5,E5,F5,G5,H5,I5],
    Col6 = [A6,B6,C6,D6,E6,F6,G6,H6,I6],
    Col7 = [A7,B7,C7,D7,E7,F7,G7,H7,I7],
    Col8 = [A8,B8,C8,D8,E8,F8,G8,H8,I8],
    Col9 = [A9,B9,C9,D9,E9,F9,G9,H9,I9],

    valid([Row1, Row2, Row3, Row4, Row5, Row6, Row7, Row8, Row9, Col1, Col2, Col3, Col4, Col5, Col6, Col7, Col8, Col9, Sqr1, Sqr2, Sqr3, Sqr4, Sqr5, Sqr6, Sqr7, Sqr8, Sqr9]),

    show([Row1, Row2, Row3, Row4, Row5, Row6, Row7, Row8, Row9]).

valid_domain(List, Min, Max):-
    domain(List, Min, Max).  %HERE IS THE ERROR%

valid([]).
valid([H|T]):-
all_different(H),
valid(T).

show([]).
show([H,T]):-
    show_row(H),
    write('|'), nl,
    show(T).

show_row([]).
show_row([H,T]):-
    write('|'),
    write(H),
    show_row(T).

My Query:

sudoku(Solution, [4,8,7,_,5,_,_,6,_,
9,_,_,4,_,_,_,_,3,
2,_,6,_,8,9,5,_,_,
_,_,4,_,1,5,6,_,_,
1,_,_,_,_,4,_,5,_,
_,7,8,2,_,_,_,_,_,
_,_,_,_,_,8,_,7,_,
7,5,_,_,_,_,_,3,_,
_,2,_,_,3,7,4,1,_]).

Answer 1

SWI-Prolog library(clpfd) doesn't have domain/3.

Try

valid_domain(List, Min, Max):-
  List ins Min..Max.

and you should correct some typo:

show([H|T]):-
...
show_row([H|T]):-
...

EDIT: If you keep the 'list of list' representation, you should write

valid_domain(List, Min, Max) :-
  flatten(List, Temp), Temp ins Min..Max.

of course, uncomment the call. I was wrong suggesting to do.

EDIT: Since the input 'shapes' the data, adapt the Solutions variable:

sudoku(Solution,Puzzle):-
    Solution = Puzzle,
    Solution =
    [A1,A2,A3,A4,A5,A6,A7,A8,A9,
     B1,B2,B3,B4,B5,B6,B7,B8,B9,
     C1,C2,C3,C4,C5,C6,C7,C8,C9,
     D1,D2,D3,D4,D5,D6,D7,D8,D9,
     E1,E2,E3,E4,E5,E6,E7,E8,E9,
     F1,F2,F3,F4,F5,F6,F7,F8,F9,
     G1,G2,G3,G4,G5,G6,G7,G8,G9,
     H1,H2,H3,H4,H5,H6,H7,H8,H9,
     I1,I2,I3,I4,I5,I6,I7,I8,I9
    ],

    Solution ins 1..9,

    %Squares
    ...

and add label/1 before display:

    ...
    label(Solution),
    show([Row1, Row2, Row3, Row4, Row5, Row6, Row7, Row8, Row9]).

after all these corrections, I get

|4|8|7|3|5|1|9|6|2|
|9|1|5|4|2|6|7|8|3|
|2|3|6|7|8|9|5|4|1|
|3|9|4|8|1|5|6|2|7|
|1|6|2|9|7|4|3|5|8|
|5|7|8|2|6|3|1|9|4|
|6|4|3|1|9|8|2|7|5|
|7|5|1|6|4|2|8|3|9|
|8|2|9|5|3|7|4|1|6|