Prolog search for possible combination for subtracting 2 elements from a list

Question

This is an extended problem from this page. Prolog possible removal of elements in a list

For example, for a list X = [1,2,3], I can subtract like following:

sub

Answer 1

I would use 2 procedures.

The first one takes an item from the list, computes a number equal or lesser than it and then calls second procedure to subtract that number from another item in the remaining list.

You have to take care of border cases (if computed number is equal to item, then remove the item altogether), thus I use a different clause for those cases.

subt_comb([N|Tail], [NX|NTail]):-
  succ(N1, N),
  between(1, N1, NX),
  subt_comb1(Tail, NX, NTail).
subt_comb([N|Tail], NTail):-
  subt_comb1(Tail, N, NTail).
subt_comb([N|Tail], [N|NTail]):-
  subt_comb(Tail, NTail).

subt_comb1([M|Tail], N, [NM|Tail]):-
  M > N,
  NM is M - N.
subt_comb1([N|Tail], N, Tail).
subt_comb1([M|Tail], N, [M|NTail]):-
  subt_comb1(Tail, N, NTail).

Sample:

?- subt_comb([1,2,3], Y).
Y = [1, 3] ;
Y = [2, 2] ;
Y = [1, 1, 2] ;
Y = [1, 1] ;
false.