Axiomatization of if-then-else over possibly non-halting programs and tests

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