How to define (and name) the corresponding safe term comparison predicates in ISO Prolog?

Question

Standard term order (ISO/IEC 13211-1 7.2 Term order) is defined over all terms — including variables. While there are good uses for this — think of the implement

Answer 1

This answer follows up on my previous one which presented safe_term_less_than/2.

What's next? A safe variant of compare/3—unimaginatively called scompare/3:

scompare(Ord, L, R) :-
   i_scompare_ord([L-R], Ord).

i_scompare_ord([], =).
i_scompare_ord([L-R|Ps], X) :-
   when((?=(L,R);nonvar(L),nonvar(R)), i_one_step_scompare_ord(L,R,Ps,X)).

i_one_step_scompare_ord(L, R, LRs, Ord) :-
   (  L == R
   -> scompare_ord(LRs, Ord)
   ;  term_itype(L, L_type),
      term_itype(R, R_type),
      compare(Rel, L_type, R_type),
      (  Rel \== (=)
      -> Ord = Rel
      ;  compound(L)
      -> L =.. [_|Ls],
         R =.. [_|Rs],
         phrase(args_args_paired(Ls,Rs), LRs0, LRs),
         i_scompare_ord(LRs0, Ord)
      ;  i_scompare_ord(LRs , Ord)
      )
   ).

The predicates term_itype/2 and args_args_paired//2 are the same as defined previously.