Invariant properties in a dialog system

Dialog systems are servers for an interface; graphical interfaces are one such. They are like operating systems in the concepts they provide. From a functional point of view, they maintain the interface for the application, permit concurrent execution of programs attached to graphical objects on the interface, and provide services with which a user (or programs) can edit objects of the interface. This paper formulates the invariant properties which need to be satisfied by the various components of a dialog system. These properties involve treatment of object relationships in regard to their layout, the activation and execution of programs attached to objects, and the concurrency model supported by the dialog system. In order to keep detail to the essential, we consider a simple model of dialogs and use the Z notation for the formal design of the system.