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

Modularity is an important pragmatic aspect of semantic descriptions. In denotational semantics, the issue of modularity has received much attention, and appropriate abstractions have been introduced, so that definitions 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 -- for instance, extending the described language may entail a complete reformulation of the description of the original constructs. A propos

These notes give an overview of the main frameworks that have been developed for specifying the formal semantics of programming languages. Some of the pragmatic aspects of semantic descriptions are discussed, including modularity, and potential applicability to visual and modelling languages. References to the literature provide starting points for further study.

Various logic-based frameworks have been proposed for specifying the operational semantics of programming languages and concurrent systems, including inference systems in the styles advocated by Plotkin and by Kahn, Horn logic, equational specifications, reduction systems for evaluation contexts, rewriting logic, and tile logic. We consider

Abstract: Most approaches to formal semantics are based on the assumption that all the constructs of a language are defined together. The details of the definition of each construct can (and usually do) depend on which other constructs are included in the given language. This limits reuse of definitions of common constructs. programming construct is defined separately and independently. The semantics of a full language is obtained by translating its constructs into the basic abstract constructs, whose definitions are thus reused verbatim. The frameworks of Modular SOS and Action Semantics can both be used in conjunction with the proposed approach. Some illustrations are given. Key Words: semantics of programming languages, action semantics, structural operational semantics, modularity

Abstract. Formal descriptions of syntax are quite popular: regular and context-free grammars have become accepted as useful for documenting the syntax of programming languages, as well as for generating efficient parsers; attribute grammars allow parsing to be linked with typechecking and code generation; and regular expressions are extensively used for searching and transforming text. In contrast, formal semantic descriptions are widely regarded as being of interest only to theoreticians. This paper surveys the main frameworks available for describing the dynamic semantics of programming languages. It assesses the potential and actual uses of semantic descriptions, and considers practical aspects, such as comprehensibility, modularity, and extensibility, which are especially significant when describing full-scale languages. It concludes by suggesting that the provision of mature tools for transforming practical semantic descriptions into reasonably efficient compilers and interpreters would significantly increase the popularity of formal semantics. The paper is intended to be accessible to all computer scientists. Familiarity with the details of particular semantic frameworks is not required, although some understanding of the general concepts of formal semantics is assumed. 1

Modular SOS (MSOS) is a simple variant of conventional Structural Operational Semantics (SOS). Using MSOS, the transition rules for each construct of a programming language can be given definitively, once and for all, and never need reformulation when further constructs are added to the language. MSOS thus provides an exceptionally high degree of modularity in language descriptions, thereby removing a shortcoming of the original SOS framework. This

Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent BRICS Notes Series publications. Copies may be obtained by contacting: BRICS