All partitions of a list in prolog

Question

I am coding in Prolog. I want to find all distinct partitions of a list. I look at a list as a set here. Each partition is a set of sets in which none is empty, the union of

Answer 1

part([Single], [[Single]]).

part([First|Others], [[First] | Result]) :-
    part(Others, Result).

part([First|Others], Result) :-
    part(Others, Temp),
    addElement(First, Temp, Result).

/* addElement(E, L, R) iff R is the same list of lists as L, except one of its sublist has an extra E in front */

addElement(Element, [FirstList | OtherLists], 
           [ [Element|FirstList] | OtherLists]).
addElement(Element, [FirstList | OtherLists], 
           [ FirstList | Temp] )
              :- addElement(Element, OtherLists, Temp).

Execution:

?- part([a,b,c,d],X).
X = [[a], [b], [c], [d]] ;
X = [[a], [b], [c, d]] ;
X = [[a], [b, c], [d]] ;
X = [[a], [c], [b, d]] ;
X = [[a], [b, c, d]] ;
X = [[a, b], [c], [d]] ;
X = [[b], [a, c], [d]] ;
X = [[b], [c], [a, d]] ;
X = [[a, b], [c, d]] ;
X = [[b], [a, c, d]] ;
X = [[a, b, c], [d]] ;
X = [[b, c], [a, d]] ;
X = [[a, c], [b, d]] ;
X = [[c], [a, b, d]] ;
X = [[a, b, c, d]] ;
false.