On implementing behavioral rewriting

Behavioral specification is an important algebraic method in software technology. A subtle aspect of behavioral specification is that operations may not be compatible with the behavioral (or observational) equivalence, meaning that the typical congruence inference rule may not be sound and, implicitly, that standard term rewriting cannot be used as is to execute behavioral specifications. Behavioral rewriting is an appropriate generalization of term rewriting which is already internally implemented in two behavioral specification and verification systems, CafeOBJ and BOBJ. In this paper we propose two alternative solutions to implement behavioral rewriting, on top of almost any standard term rewriting system, without modifying it internally.