From Operational to Denotational Semantics

In this paper it is shown how operational semantic methods may be naturally extended to encompass many of the concepts of denotational semantics. This work builds on the standard development of an operational semantics as an interpreter and operational equivalence. The key addition is an operational ordering on sets of terms. From properties of this ordering a closure construction directly yields a fully abstract continuous cpo model. Furthermore, it is not necessary to construct the cpo, for principles such as soundness of xed-point induction may be obtained by direct reasoning from this new ordering. The end result is that traditional denotational techniques may be applied in a purely operational setting in a natural fashion, a matter of practical importance for developing semantics of realistic programming languages.