Prolog: create a list of empty lists

Question

I'm working on creating a board used for the Bert Bos puzzle, and I'm trying to represent the board as a list of lists.

I need to create a list of empty lists ex [ [], [] , [] , [] ] but the problem is I need the exact number of empty lists provided from the input. So for example if I give create_board(4,X), it should return X= [ [], [], [], [] ].

Here is what I have so far

generate_board(0, [[]]) :- ! 
generate_board(N, [[] | T]) :-
  N =< 12, N >= 1,
  N is N-1.
  generate_board(N, T).

Answer 1

An easy way to create a list of a given length consisting of the same element, or just empty lists in this case, is to use maplist2:

 generate_board(Length, Board) :-
     length(Board, Length),
     maplist(=([]), Board).

Here, maplist(=([]), Board) will call =([], Element) (the canonical form of [] = Element) for each Element in Board, thus unifying each element with []:

| ?- generate_board(4, L).

L = [[],[],[],[]]

yes
| ?-

You can extend this concept to do a two-dimensional empty board. Think of the board as a list of rows (with length Length) and each row as a list of elements (with length Width):

generate_board(Length, Width, Board) :-
    length(Row, Width),
    maplist(=([]), Row),         % A row of empty lists, forming an empty row
    length(Board, Length),
    maplist(=(Row), Board).      % A list of empty rows

| ?- generate_board(4,3, L).

L = [[[],[],[]],[[],[],[]],[[],[],[]],[[],[],[]]]

yes
| ?-

Answer 2

Here is just the reason why your program did not work (apart from the . in place of ,). Because this fragment fails, also your original program fails. You have to generalize the visible part somehow.

:- op(950,fy,*).
*_.

generate_board(0, [[]]) :- ! 
generate_board(N, _/*[[] | T]*/) :-        % 2nd
  * N =< 12,                               % 2nd
  * N >= 1,                                % 2nd
  N is N-1,
  * generate_board(N, T).                  % 1st generalization

?- generate_board(4, B).

This method works for pure, monotonic Prolog programs. You have, however, used a cut which restricts generalization. In this case, one really has to pay attention not to generalize anything prior to the cut. The first generalization is thus the recursive goal. It is the very last goal in the clause. Only then, the other generalizations may take place

In your program without the cut, we could have generalized your program even further:

generate_board(0, _/*[[]]*/).
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