Rearranging variable_names

Solution 1:

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).

Solution 2:

Use term_variables/2 on T to obtain a list Xs with variables in the desired order. Then build a list with the elements of AVs, but in that order.

avs_term_rearranged(AVs, T, AVRs) :-
    term_variables(T, Xs),
    pick_in_order(AVs, Xs, AVRs).

pick_in_order([], [], []).
pick_in_order(AVs, [X|Xs], AVRs) :-
    ( pick(AVs, X, AV, AVs1) ->
        AVRs = [AV|AVRs1],
        pick_in_order(AVs1, Xs, AVRs1)
    ;
        pick_in_order(AVs, Xs, AVRs)
    ).

pick([AV|AVs], X, AX, DAVs) :-
    (_=V) = AV,
    ( V==X ->
        AX = AV,
        DAVs = AVs
    ;
        DAVs = [AV|DAVs1],
        pick(AVs, X, AX, DAVs1)
    ).

Notes:

• this is quadratic because pick/4 is linear
• term_variables/2 is not strictly necessary, you could traverse T directly