Use of Denotational Mathematics for the formal description of autonomous migration and polymorphism as prerequisites for mobility in home UbiHealth

In the home ubiquitous computing (UbiComp) environment the wirelessly and ad-hoc networked computing devices are connected with sensors and actuators monitoring, recording, and intervening in the performed activities. The unattended applications operating at this environment must be fault tolerant and redundant. However, the lack of standardization and the uncontrolled evolvement of the developed situations at home result in a hostile environment for computer applications. Also, the need to support the individual's mobility at home increases further the level of difficulty of the associated computing efforts. The individual's mobility is supported providing computing services which can migrate from the currently running device to the neighboring one in order to follow every inhabitant's disposition. Migration presupposes the selection of adequate policies supported by the suitable software infrastructure to exploit the conceptual implementation of polymorphism that allows the preservation of functionality while autonomously transferred to another computing device. This paper provides a formal description with Denotational Mathematics of the operational prerequisites of such an autonomous system that achieves the migration of applications for the continuous support of the individual's mobility. The infrastructure must be capable of enforcing strategies and policies related to migration either by transporting the supporting applications or by referencing them. The achievement of the provision of healthcare at the UbiComp home presupposes the continuous support of the individual's mobility.