Remove both the value and all duplicates of that value in a list in prolog

Question

I'm having some trouble removing values from a list in prolog. I have a list of colors and I want to add a list of colors to it and keep all the values that have no duplicate and remove the rest.

[green, red, blue, purple, yellow, brown, orange, black, purple]

so purple appears twice in this list and I want to remove both of them. This is the list I want to be returned.

[green, red, blue, yellow, brown, orange, black]

I currently have this to remove all the duplicates but I can't get both purples out.

mymember(X,[H|_]) :- X==H,!.
mymember(X,[_|T]) :- mymember(X,T).

not(A) :- \+ call(A).

set([],[]).
set([Head|Tail],[Head|Out]) :-
    not(mymember(Head,Tail)),
    set(Tail, Out).
set([Head|Tail],Out) :-
    mymember(Head,Tail),
    set(Tail, Out).

this is the result I get now:

[green, red, blue, yellow, brown, orange, black, purple]

Answer 1

The simple way...a one-liner:

singletons(Xs,Zs) :-
  findall( X , ( append(P,[X|S],Xs), \+member(X,P), \+member(X,S) ) , Zs )
  .

Answer 2

Stay pure by using tfilter/3 in combination with list_uniqmember_t/3!

list_uniqs(Es, Us) :-
   tfilter(list_uniqmember_t(Es), Es, Us).

The sample query given by the OP has the expected result:

?- list_uniqs([green,red,blue,purple,yellow,brown,orange,black,purple], Xs).
Xs = [green,red,blue,yellow,brown,orange,black]. % succeeds deterministically

Do we get logically sound answers for more general queries, too?

?- list_uniqs([A,B,A], []).
   A=B
;  false.

?- list_uniqs([A,B,A], [_]).
dif(A,B).

?- list_uniqs([A,B,A], [_,_]).
false.

?- list_uniqs([A,B,A], Xs).
   Xs = [] ,     A=B
;  Xs = [B], dif(A,B).

Yes! How about something a little more general?

?- list_uniqs([A,B,C],Xs).
   Xs = []     ,     A=B           ,     B=C
;  Xs = [C]    ,     A=B           , dif(B,C)
;  Xs = [B]    ,               A=C , dif(B,C)
;  Xs = [A]    ,           dif(A,C),     B=C 
;  Xs = [A,B,C], dif(A,B), dif(A,C), dif(B,C).

It works!