How to convert vectors to arrays in ECLiPSe (CLP)?

I have to solve Sudoku puzzles in the format of a vector containing 9 vectors (of length 9 each). Seeing as vectors are linked lists in Prolog, I figured the search would go faster if I transformed the puzzles in a 2D array format first.

Example puzzle:

puzzle(P) :- P = 
[[_,_,8,7,_,_,_,_,6],
[4,_,_,_,_,9,_,_,_],
[_,_,_,5,4,6,9,_,_],

[_,_,_,_,_,3,_,5,_],
[_,_,3,_,_,7,6,_,_],
[_,_,_,_,_,_,_,8,9],

[_,7,_,4,_,2,_,_,5],
[8,_,_,9,_,5,_,2,3],
[2,_,9,3,_,8,7,6,_]].

I'm using ECLiPSe CLP to implement a solver. The best I've come up with so far is to write a domain like this:

domain(P):-
  dim(P,[9,9]),
  P[1..9,1..9] :: 1..9.

and a converter for the puzzle (parameter P is the given puzzle and Sudoku is the new defined grid with the 2D array). But I'm having trouble linking the values from the given initial puzzle to my 2D array.

convertVectorsToArray(Sudoku,P):-
  ( for(I,1,9),
      param(Sudoku,P)
    do
      ( for(J,1,9),
          param(Sudoku,P,I)
        do
          Sudoku[I,J] is P[I,J]
      )
  ).

Before this, I tried using array_list (http://eclipseclp.org/doc/bips/kernel/termmanip/array_list-2.html), but I kept getting type errors. How I did it before:

convertVectorsToArray(Sudoku,P):-
  ( for(I,1,9),
      param(Sudoku,P)
    do
      ( for(J,1,9),
          param(Sudoku,P,I)
        do
          A is Sudoku[I],
          array_list(A,P[I])
      )
  ).

When my Sudoku finally outputs the example puzzle P in the following format:

Sudoku = []([](_Var1, _Var2, 8, 7, ..., 6), [](4, ...), ...)

then I'll be happy.

update

I tried again with the array_list; it almost works with the following code:

convertVectorsToArray(Sudoku,P):-
  ( for(I,1,9),
      param(Sudoku,P)
    do
      X is Sudoku[I],
      Y is P[I],
      write(I),nl,
      write(X),nl,
      write(Y),nl,
      array_list(X, Y)
  ).

The writes are there to see how the vectors/arrays look like. For some reason, it stops at the second iteration (instead of 9 times) and outputs the rest of the example puzzle as a vector of vectors. Only the first vector gets assigned correctly.

update2

While I'm sure the answer given by jschimpf is correct, I also figured out my own implementation:

convertVectorsToArray(Sudoku,[],_).
convertVectorsToArray(Sudoku,[Y|Rest],Count):-
  X is Sudoku[Count],
  array_list(X, Y),
  NewCount is Count + 1,
  convertVectorsToArray(Sudoku,Rest,NewCount).

Thanks for the added explanation on why it didn't work before though!

The easiest solution is to avoid the conversion altogether by writing your puzzle specification directly as a 2-D array. An ECLiPSe "array" is simply a structure with the functor '[]'/N, so you can write:

puzzle(P) :- P = [](
    [](_,_,8,7,_,_,_,_,6),
    [](4,_,_,_,_,9,_,_,_),
    [](_,_,_,5,4,6,9,_,_),

    [](_,_,_,_,_,3,_,5,_),
    [](_,_,3,_,_,7,6,_,_),
    [](_,_,_,_,_,_,_,8,9),

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

You can then use this 2-D array directly as the container for your domain variables:

sudoku(P) :-
    puzzle(P),
    P[1..9,1..9] :: 1..9,
    ...

However, if you want to keep your list-of-lists puzzle specification, and convert that to an array-of-arrays format, you can use array_list/2. But since that only works for 1-D arrays, you have to convert the nesting levels individually:

listoflists_to_matrix(Xss, Xzz) :-
    % list of lists to list of arrays
    ( foreach(Xs,Xss), foreach(Xz,Xzs) do
        array_list(Xz, Xs)
    ),
    % list of arrays to array of arrays
    array_list(Xzz, Xzs).

As for the reason your own code didn't work: this is due to the subscript notation P[I]. This

requires P to be an array (you were using it on lists)
works only in contexts where an arithmetic expression is expected, e.g. the right hand side of is/2, in arithmetic constraints, etc.