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list - Prolog removing unique elements only

I want to return a list that removes all unique elements for example

remUniqueVals([1,1,2,2,3,4,4,5,6,6,6],Q).   
Q = [1,1,2,2,4,4,6,6,6].  

My problem is that currently I have code that returns

remUniqueVals([1,1,2,2,3,4,4,5,6,6,6],Q).  
Q = [1, 2, 4, 6, 6].

So that only the first instance of these non-unique values are returned. Here is my code:

remUniqueVals([], []).  
remUniqueVals([Q1|RestQ],[Q1|Xs]) :-        
   member(Q1,RestQ),  
   remUniqueVals(RestQ,Xs).  
remUniqueVals([Q1|RestQ],Xs) :-  
   remove(Q1,[Q1|RestQ], NewQ),  
   remUniqueVals(NewQ,Xs).  

I can see that member(Q1,RestQ) fails when it checks 1,2,4 the second time because they are now no longer in the list and so removes them. I'd like some helping solving this problem, my thoughts are to check member(Q1, PreviousQ), where this is the elements already in the final Q. Not sure how to go about implementing that though any help would be appreciated.

Update:

Ok so thanks for the suggestions I ended up going with this in the end:

remUniqueVals(_,[], []).  
remUniqueVals(_,[Q1|RestQ],[Q1|Xs]) :-        
   member(Q1,RestQ), 
   remUniqueVals(Q1,RestQ,Xs).  
remUniqueVals(PrevQ,[Q1|RestQ],[Q1|Xs]) :-        
   Q1 = PrevQ, 
   remUniqueVals(PrevQ,RestQ,Xs).  
remUniqueVals(PrevQ,[_|RestQ],Xs) :-  
   remUniqueVals(PrevQ,RestQ,Xs). 

remUniqueVals(0,[4,1,1,3,2,2,5,5],Q).
Q = [1, 1, 2, 2, 5, 5].

remUniqueVals(0, [A,B,C], [1,1]).
A = 1,
B = 1,
C = 1.
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1 Answer

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Prolog rules are read independently of each other, so you need one rule for the case where the element is unique and one where it is not. Provided the order of the elements is not relevant, you might use:

?- remUniqueVals([A,B,C], [1,1]).
A = B, B = 1,
dif(C, 1) ;
A = C, C = 1,
dif(B, 1),
dif(B, 1) ;
B = C, C = 1,
dif(A, 1),
dif(A, 1) ;
false.

?- remUniqueVals([1,1,2,2,3,4,4,5,6,6,6],Q).
Q = [1, 1, 2, 2, 4, 4, 6, 6, 6] ;
false.

remUniqueVals([], []).
remUniqueVals([Q1|RestQ],[Q1|Xs0]) :-
   memberd(Q1, RestQ),
   phrase(delall(Q1, RestQ, NewQ), Xs0, Xs),
   remUniqueVals(NewQ, Xs).
remUniqueVals([Q1|RestQ],Xs) :-
   maplist(dif(Q1), RestQ),
   remUniqueVals(RestQ,Xs).

memberd(X, [X|_Xs]).
memberd(X, [Y|Xs]) :-
   dif(X,Y),
   memberd(X, Xs).

delall(_X, [], []) --> [].
delall(X, [X|Xs], Ys) -->
   [X],
   delall(X, Xs, Ys).
delall(X, [Y|Xs], [Y|Ys]) -->
   {dif(X,Y)},
   delall(X, Xs, Ys).

Here is an alternate definition for memberd/2 which might be more efficient using if_/3:

memberd(E, [X|Xs]) :-
   if_(E = X, true, memberd(E, Xs) ).

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