% =================================================================
:- pred constr(bool).
:- mode constr(in).
:- ignore constr/1.
% =================================================================
% Program. 
% Delete all multiple copies on lists leaving one copy only.
:- pred list_deletecopies(list(int),list(int)).
:- mode list_deletecopies(in,out).

list_deletecopies([],[]).
list_deletecopies([X],[X]).
list_deletecopies([X,X|T], ResT) :- cons(X,T,XT), list_deletecopies(XT,ResT).
list_deletecopies([X,Y|T], [X|ResT]) :- constr(~(X=Y)), cons(Y,T,YT),
      list_deletecopies(YT,ResT1), deleteall(X,ResT1,ResT).

% all elements X are deleted from a list, producing a new list.
:- pred deleteall(int,list(int),list(int)).
:- mode deleteall(in,in,out).

deleteall(X,[],[]).
deleteall(X,[X|T],Res) :- deleteall(X,T,Res).
deleteall(X,[H|T],[H|ResT]) :- constr(~(X=H)), deleteall(X,T,ResT).

:- pred cons(int,list(int),list(int)).
:- mode cons(in,in,out).
cons(H,T,[H|T]).

% =================================================================
% catamorphism
:- pred listmember(int,list(int),bool).
:- mode listmember(in,in,out).
:- cata listmember/3-2.

listmember(X,[],Res) :- constr(~Res).
listmember(X,[Y|Ys],B) :-
      constr( B=ite(X=Y,true,B1) ) ,
      listmember(X,Ys,B1).
%  
% =================================================================
% Verification.
% Property:
:- pred ff1.
ff1 :- 
   constr(~(SL=SS)), 
   listmember(X,L,SL), listmember(X,S,SS),  
   list_deletecopies(L,S).

:- spec deleteall(X,L,L1) ==> listmember(Y,L,LS), listmember(Y,L1,L1S) => constr(true).

:- spec cons(H,T,HT) ==> listmember(X,T,TN), listmember(X,HT,HTN) => constr(true).

% =================================================================
:- query ff1/0.
% =================================================================