Congruence for Structural Congruences

Structural congruences have been used to define the semantics and to capture inherent properties of language constructs. They have been used as an addendum to transition system specifications in Plotkin’s style of Structural Operational Semantics (SOS). However, there has been little theoretical work on establishing a formal link between these two semantic specification frameworks. In this paper, we give an interpretation of structural congruences inside the transition system specification framework. This way, we extend a number of well-behavedness meta-theorems for SOS (such as well-definedness of the semantics and congruence of bisimilarity) to the extended setting with structural congruences.