Rearranging variable_names

How to write in a standard conforming manner avs_term_rearranged(AVs, T, AVsR) with given AVs and T such that AVsR is a permutation of AVs with the elements arranged in same order as their variables occur in left-to-right order in T.

AVs is a list of elements of the form A = V where A is an atom designating a variable name like 'X' and V is a corresponding variable. Such lists are produced by read_term/2,3 with the read-option variable_names/1 (7.10.3). Additionally, the precise order of elements is not defined.

| ?- read_term(T,[variable_names(AVs)]).
A+B+A+_+C.

AVs = ['A'=A,'B'=B,'C'=C]
T = A+B+A+_+C

T is a term that contains all variables of AVs plus some more.

Note that in a standard conforming program one cannot rely on the term order for variables (7.2.1):

7.2.1 Variable

If X and Y are variables which are not identical then X term_precedes Y shall be implementation dependent except that during the creation of a sorted list (7.1.6.5, 8.10.3.1 j) the ordering shall remain constant.

NOTE — If X and Y are both anonymous variables then they are not identical terms (see 6.1.2 a).

Consider as an example from 8.4.3.4:

sort([f(U),U,U,f(V),f(U),V],L).
   Succeeds, unifying L with [U,V,f(U),f(V)] or
   [V,U,f(V),f(U)].
   [The solution is implementation dependent.]

So there are two possible ways how sort/2 will work, and one cannot even rely on the success of:

sort([f(U),U,U,f(V),f(U),V],L), sort(L, K), L == K.

As an example:

?- avs_term_rearranged(['A'=A,'B'=B,'C'=C], A+C+F+B, AVsR).
   AVsR = ['A'=A,'C'=C,'B'=B].

avs_term_rearranged(AVs, T, AVsR) :-
    term_variables(T, Vs),
    copy_term(Vs+AVs, Vs1+AVs1),
    bind_names(AVs1),
    build_vn_list(Vs, Vs1, AVsR).

bind_names([]).
bind_names([N=V|AVs]) :-
    N = V,
    bind_names(AVs).

build_vn_list([], [], []).
build_vn_list([V|Vs],[N|Ns],NVs) :-
    ( atom(N) ->
      NVs = [N=V|NVs1]
    ; var(N) ->
      NVs = NVs1
    ),
    build_vn_list(Vs, Ns, NVs1).