Structural Congruences and Structural Operational Semantics

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 theses two semantic specification frameworks. In this paper, we try to fill this gap by accommodating structural congruences inside transition system specifications. The Contributions of this paper can be summarized as follows: 1. Three interpretations of structural congruences in the SOS framework are presented; 2. The three interpretations are compared formally; 3. Syntactic criteria of a congruence format for structural congruences are given and proved correct; 4. Well-definedness criteria for transition system specifications with negative premises are extended to the setting with structural congruences; 5. Operational and equational conservative extensions of languages with structural congruences are studied.