!TITLE Collecting together solutions
!KEY
When  there  are  many solutions to a problem, and when all those solutions are
required  to  be  collected  together,  this  can  be  achieved  by  repeatedly
backtracking  and gradually building up a list of the solutions.  The following
evaluable predicate is provided to automate this process.  Note, however,  that
this  is  the  simple version of this predicate and the implementation does not
match the sophistication of the equivalent in  DEC10  Prolog  (ie  the  logical
semantics  are  incorrect) - if this does not mean much to you then don't worry
about it.

bagof(X,P,Bag)
            Bag is a list of all X's such that P. Ie all the instantiations  of
            X  produced by backtracking through all possible solutions of P are
            gathered into the list Bag.  Since this list may contain  duplicate
            elements  it  is known, technically, as a bag; as opposed to a set,
            say, which would not allow duplicate elements.