Lost qualifier should be added to type systems with viewpoint adaptation functionality.

[AndrewShf]

Imagine a standard lattice like this:

      TOP
       |
       |
       v
A      B       RDQ
       |
       |
       v
     BOTTOM

where TOP is the top type in the lattice, BOTTOM is the bottom type in the lattice and RDQ (receiver-dependent-qualifier) is for viewpoint adaptation.

Suppose this type system also supports viewpoint adaptation and a piece of code written like this:

   class Demo {
     @RDQ Object f;

    void adaptation(@Top Demo top) {
        top.f = new @A Object(); // allowed
    }
   }

This looks fine, top.f has type TOP |> RDQ = TOP by the viewpoint adaptation law and thus can be assigned by a subtype object (the @A Object)

However, if the method is invoked like this, we would lost our type safety.

@B Demo o;
adaptation(o);

In the above code o has type B and o.f has type B as well but in the method invocation, the field is assigned to a type A object which is not a subtype of type B.

This problem could cause serious type safety issues in some type systems, for example, the immutability type system.
We could add a lost qualifier (which was introduced in the Generic Universe Type paper) as the type when the top qualifier looking at a RDQ qualifier. In that case if the variable has type lost, assignment operation is forbidden.