Modular SOS (MSOS) is a variant of conventional Structural Operational Semantics (SOS). Using MSOS, the transition rules for each construct of a programming language can be given incrementally, once and for all, and do not need reformulation when further constructs are added to the language. MSOS thus provides an exceptionally high degree of modularity in language descriptions, removing a shortcoming of the original SOS framework. After sketching the background and reviewing the main features of SOS, the paper explains the crucial differences between SOS and MSOS, and illustrates how MSOS descriptions are written. It also discusses standard notions of semantic equivalence based on MSOS. Appendix A shows how the illustrative MSOS rules given in the paper would be formulated in conventional SOS.

A novel form of labelled transition system is proposed, where the labels are the arrows of a category, and adjacent labels in computations are required to be composable. Such transition systems provide the foundations for modular SOS descriptions of programming languages. Three

Strategies are a powerful mechanism to control rule application in rule-based systems. For instance, different transition relations can be defined and then combined by means of strategies, giving rise to an effective tool to define the semantics of programming languages. We have endowed the Maude MSOS Tool (MMT), an executable environment for modular structural operational semantics, with the possibility of defining strategies over its transition rules, by combining MMT with the Maude strategy language interpreter prototype. The combination was possible due to Maude’s reflective capabilities. One possible use of MMT with strategies is to execute Ordered SOS specifications. We show how a particular form of strategy can be defined to represent an OSOS order and therefore execute, for instance, SOS specifications with negative premises. In this context, we also discuss how two known techniques for the representation of negative premises in OSOS become simplified in our setting.

Presheaf Semantics of SCCS with Finite Delay. September 1999. 37 pp. Appears in Hofmann, Rosolini and Pavlovic, editors, Category Theory and Computer Science: 8th International Conference, CTCS '99 Proceedings, ENTCS 29, 1999, 25 pp.