different/2 - does a pure, determinate definition

Question

different(Xs, Ys) :-
   member(X, Xs),
   non_member(X, Ys).
different(Xs, Ys) :-
   member(Y, Ys),
   non_member(Y, Xs).

While this definition using member/2 and non_member/2 is almost¹ perfect from a declarative viewpoint, it produces redundant solutions for certain queries and leaves choice points all around.

What is a definition that improves upon this (in a pure manner probably using if_/3 and (=)/3) such that exactly the same set of solutions is described by different/2 but is determinate at least for ground queries (thus does not leave any useless choice points open) and omits (if possible) any redundant answer?

---

¹ _{Actually, different([a|nonlist],[]), different([],[b|nonlist]) succeeds. It could equally fail. So a solution that fails for both is fine (maybe even finer).}

Answer 1

(Much inspired by @repeat's last answer, the names are still too clumsy)

different(Xs, Ys) :-
   if_(tnotexists_inlist_t(list_memberd_t(Ys), Xs),
      true,
      tnotexists_inlist_t(list_memberd_t(Xs), Ys)).

tnotexists_inlist_t(_P_2, [], false).
tnotexists_inlist_t(P_2, [E|Es], T) :-
   if_(call(P_2, E),
      tnotexists_inlist_t(P_2, Es, T),
      T = true).

Answer 2

Back to the roots! This variant is very close to the code given by the OP in the question.

The following is based on if_/3 and memberd_t/3.

different(Xs,Ys) :-
   if_(some_absent_t(Xs,Ys),
       true,
       some_absent_t(Ys,Xs,true)).

some_absent_t([]    ,_ ,false).
some_absent_t([X|Xs],Ys,Truth) :-
   if_(memberd_t(X,Ys), some_absent_t(Xs,Ys,Truth), Truth=true).

Here is a ground query:

?- different([4,2,3],[2,3,1]), different([1,2,3],[4,3,1]),
   different([1,4,3],[2,3,1]), different([1,2,3],[2,4,1]),
   different([1,2,4],[2,3,1]), different([1,2,3],[2,3,4]).
true.                                 % all subgoals succeed deterministically

And here's the (more general) query I used in previous answers:

?- different([A,B],[X,Y]).
      A=X ,               B=X ,           dif(Y,X)
;     A=X ,           dif(B,X), dif(B,Y)
;               A=Y ,               B=Y , dif(Y,X), dif(Y,X)
;               A=Y , dif(B,X), dif(B,Y), dif(Y,X)
; dif(A,X), dif(A,Y).