Modularity in Structural Operational Semantics (extended Abstract)

Modularity is an important pragmatic aspect of semantic descriptions: good modu-larity is needed to allow the reuse of existing descriptions when extending or changing the described language. In denotational semantics, the issue of modularity has received much attention, and appropriate abstractions have been introduced, so that deenitions of semantic functions may be independent of the details of how computations are modelled. In structural operational semantics (SOS), however, this issue has largely been neglected, and SOS descriptions of programming languages typically exhibit rather poor modularity. This paper shows how to obtain a high degree of modularity in SOS. The main idea is quite simple: conngurations are restricted to pure syntax|enriched, as usual, with computed values|and all the usual semantic components of conngurations are incorporated in the labels on the transitions. Moreover, the labels are regarded as the arrows of a category, and are equipped with various language-independent operations, allowing the structure of labels to be abstracted from the rules used to specify transitions. It appears that the category of labels needed for describing a particular language may be obtained in a modular way using constructors that correspond to monad transformers. The reader is assumed to be familiar with basic notions of semantics and programming languages.