Prolog possible removal of elements in a list

Question

I have been asked to try to search for all possible outcomes of, removing any numbers from any single elements from a list.

For example, if I have a list X = [1,2,3]

Answer 1

You have to:

• select one item (number) from the list
• replace selected item with a number which is less than the selected item
• alternatively remove entirely the selected item

For example:

remove([N|Tail], [NX|Tail]):-
  succ(N1, N),
  between(1, N1, NX).
remove([_|Tail], Tail).
remove([N|Tail], [N|NTail]):-
  remove(Tail, NTail).

The first clause selects the first item in the list, and replaces that item with a number which is less than the item.

The second clause removes the item from the list (as shown in your examples when you subtract N to the selected item (N) it does not appear in the second list.

The third clause applies recursion, leaving the head item as-is and applies the procedure to the remaining list.

Answer 2

Here's another solution using append/3. I'm thinking @gusbro's answer is more elegant and/or efficient. But it's an alternative:

reduce(L, R) :-
    append(L1, [X|L2], L),
    (   X1 is X - 1,              % some element varies 1 to X-1
        between(1, X1, Y),
        append(L1, [Y|L2], R)
    ;   append(L1, L2, R)         % or the element is just removed
    ).