Notions of bisimulation and congruence formats for SOS with data

While studying the specification of the operational semantics of different programming languages and formalisms, one can observe the following three facts. First, Plotkin's style of Structural Operational Semantics has become a standard in defining operational semantics. Second, congruence with respect to some notion of bisimilarity is an interesting property for such languages and it is essential in reasoning. Third, there are numerous languages that contain an explicit data part in the state of the operational semantics. The first two facts have resulted in a line of research exploring syntactic formats of operational rules to derive the desired congruence property for free. However, the third point (in combination with the first two) is not sufficiently addressed and there is no standard congruence format for operational semantics with an explicit data state. In this article, we address this problem by studying the implications of the presence of a data state on the notion of bisimilarity. Furthermore, we propose a number of formats for congruence.