Axiomatization of over possibly non-halting programs and tests.

In order to study the axiomatization of the construct over possibly non-halting programs and tests, this paper introduces the notion of -sets by considering the tests from an abstract -algebra. When the -algebra is an ada, the axiomatization is shown to be complete by obtaining a subdirect representation of -sets. Further, this paper considers the equality test with the construct and gives a complete axiomatization through the notion of agreeable -sets. [ABSTRACT FROM AUTHOR]