Axiomatization of if-then-else over possibly non-halting programs and tests
Gayatri Panicker, K. V. Krishna, Purandar Bhaduri · International Journal of Algebra and Computation · 2017
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 [Formula: see text]-sets by considering the tests from an abstract [Formula: see text]-algebra. When the [Formula: see text]-algebra is an ada, the axiomatization is shown to be complete by obtaining a subdirect representation of [Formula: see text]-sets. Further, this paper considers the equality test with the if-then-else construct and gives a complete axiomatization through the notion of agreeable [Formula: see text]-sets.