Definition of a path/trail/walk

Question

Many predicates define some kind of an acyclic path built from edges defined via a binary relation, quite similarly to defining transitive closure. A generic definition is t

Answer 1

How about defining path/4 like this?

path(R_2, Xs, A,Z) :-                   % A path `Xs` from `A` to `Z` is ...
   walk(R_2, Xs, A,Z),                  % ... a walk `Xs` from `A` to `Z` ...
   all_dif(Xs).                         % ... with no duplicates in `Xs`.

To aid universal termination, we swap the two goals in above conjunction ...

path(R_2, Xs, A,Z) :-
   all_dif(Xs),                         % enforce disequality ASAP
   walk(R_2, Xs, A,Z).

... and use the following lazy implementation of all_dif/1:

all_dif(Xs) :-                          % enforce pairwise term inequality
   freeze(Xs, all_dif_aux(Xs,[])).      % (may be delayed)

all_dif_aux([], _).
all_dif_aux([E|Es], Vs) :-               
   maplist(dif(E), Vs),                 % is never delayed
   freeze(Es, all_dif_aux(Es,[E|Vs])).  % (may be delayed)

walk/4 is defined like path/4 and path/5 given by the OP:

:- meta_predicate walk(2, ?, ?, ?).
walk(R_2, [X0|Xs], X0,X) :-
   walk_from_to_step(Xs, X0,X, R_2).

:- meta_predicate walk_from_to_step(?, ?, ?, 2).
walk_from_to_step([], X,X, _).
walk_from_to_step([X1|Xs], X0,X, R_2) :-
   call(R_2, X0,X1),
   walk_from_to_step(Xs, X1,X, R_2).

IMO above path/4 is simpler and more approachable, particularly for novices. Would you concur?