A General Conservative Extension Theorem in Process Algebra
Chris Verhoef · 1993
this paper. Now that we have given some motivation for this paper we discuss its organization. In section 2 we recall some general SOS definitions of Verhoef [8]. We will provide a running example to elucidate the abstract notions. In section 3 we formally define the notions of operational and equational conservativity. Then we prove a general operational conservativity theorem, a general equational conservativity theorem and a simple corollary concerning completeness. Also here we provide our running example. In the next section we will recall some basic term rewriting terminology to prove the abovementioned reduction theorem on the ground Church-Rosser property modulo some equations. In section 5 we will give the reader an idea of the applicability of our general theorems. Surprisingly, we could not find any conservativity result in the literature for which our conservativity theorem could not be applied, as well. The last section contains concluding remarks and briefly discusses possible future work.