list a ::= Nil | Cons a (list a) ; ;;

if c t f = case c of True -> t; False -> f end;

utSetEmpty = Nil;

utSetIsEmpty s = case s of
                    Nil -> True;
                    Cons x xs -> False
                 end;

utSetSingleton x = Cons x Nil;

utSetFromList l
   = letrec
        rmdup = \rl -> case rl of
                      Nil -> Nil;
                      Cons x xs -> case xs of
                                      Nil -> Cons x Nil;
                                      Cons y ys -> case x==y of
                                         True -> Cons x (rmdup ys);
                                         False -> Cons x (Cons y (rmdup ys))
                                                   end
                                   end
                   end;
        sort = \sl -> 
        letrec
        insert = \a l -> case l of
                            Nil -> Cons a Nil;
                            Cons bb xx -> case a <= bb of
                                            True -> Cons a (Cons bb xx);
                                            False -> Cons bb (insert a xx)    
                                          end
                         end

        in          case sl of
                        Nil -> Nil;
                        Cons a x -> insert a (sort x)
                     end
       in  rmdup (sort l);

utSetToList xs = xs;

utSetUnion seta setb
 = case seta of 
     Nil -> Nil;
     Cons a as -> case setb of
                    Nil -> Nil;
                    Cons b bs ->
       case a <  b of
         True -> Cons a (utSetUnion as setb);
         False -> case a == b of
           True-> Cons a (utSetUnion as bs);
           False -> Cons b (utSetUnion seta bs)
         end end end end;