Path-finding in a graph, acyclic path with cost

Source: PROLOG programming for artificial intelligence, 3rd Edition, Harlow, 2001, ISBN 0-201-40375-7.

Program source code: acyclic_path_2.pl

% Figure 9.21   Path-finding in a graph:  Path is 
% an acyclic path with cost Cost from A to Z in Graph.
 
:- op( 900, fy, not).
 
% path( A, Z, Graph, Path, Cost):
%    Path is an acyclic path with cost Cost from A to Z in Graph
 
path( A, Z, Graph, Path, Cost)  :-
  path1( A, [Z], 0, Graph, Path, Cost).
 
path1( A, [A | Path1], Cost1, Graph, [A | Path1], Cost1).
 
path1( A, [Y | Path1], Cost1, Graph, Path, Cost)  :-
   adjacent( X, Y, CostXY, Graph),
   not member( X, Path1),
   Cost2 is Cost1 + CostXY,
   path1( A, [X, Y | Path1], Cost2, Graph, Path, Cost).
 
% not Goal): negation as failure; 
%   Note: This is often available as a built-in predicate,
%   often written as prefix operator "\+", e.g. \+ likes(mary,snakes)
 
not Goal  :-
  Goal, !, fail
  ; 
  true.