Abstract. In previous work, based on an original idea due to Saaltink, we proposed a unifying theory of undefined expressions in logics used for formally specifying software systems. In our current paper, we instantiate these ideas in Hoare and He's Unifying Theories of Programming, with each different treatment of undefinedness formalized as a UTP theory. In this setting, we show how to use classical logic to prove facts in a monotonic partial logic with guards, and we describe the guards for several different UTP theories. We show how classical logic can be used to prove semi-classical facts. We apply these ideas to the COMPASS Modelling Language (CML),w hi c hi sa ni n te g r a ti o no fVDMa ndC SPi ntheCircus tradition. We link CML, which uses McCarthy's left-to-right expression evaluation, and to VDM, which uses Jones's three-valued Logic of Partial Functions.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.