Semantics, Modularity, and Rewriting Logic Mosses 1 Modularity in Denotational Semantics Sition Relation Involving Semantic Action Arguments from a X : ! : X a X X and Its Reeexive-transitive Closure

A complete formal semantic description of a practical programming language (such as Java) is likely to be a lengthy document, regardless of which semantic framework is being used. Good modularity of the description is important to the person(s) developing it, to facilitate reuse, change, and extension. Unfortunately, the conventional versions of the major semantic frameworks have rather poor modularity. In this paper, we rst recall some approaches that improve the modularity of denotational semantics, namely action semantics, modular monadic semantics, and a hybrid framework that combines these: modular monadic action semantics. We then address the issue of modularity in operational semantics, which appears to have received comparatively little attention so far, and report on some preliminary investigations of how one might achieve the same kind of modularity in structural operational semantics as the use of monad transformers can provide in denotational semantics|this is the main technical contribution of the paper. Finally, we brieey consider the representation of structural operational semantics in rewriting logic, and speculate on the possibility of using it to interpret programs in the described language. Providing powerful meta-tools for such semantics-based interpretation is an interesting potential application of rewriting logic; good modularity of the semantic descriptions may be crucial for the practicality of using the tools. Much of the paper consists of (very) simple examples of semantic descriptions in the various frameworks, illustrating the degree of reformulation needed when extending the described language|a strong indicator of modularity. Throughout, it is assumed that the reader has some familiarity with the concepts and notation of denotational and structural operational semantics. Familiarity with the basic notions of monads and monad transformers is not a prerequisite. It is well-known 5,12,13,22] that the cause of poor modularity in conventional denotational semantic descriptions is the unrestricted use of (typed)-notation to specify semantic entities. When the described language is extended with unanticipated new constructs, the domains of denotations may need to be changed, and then the description of the old constructs may have to be completely reformulated to adapt it to the new domains. A small-scale illustration of the poor extensibility in denotational semantics is provided in Appendix A. Action semantics 15,16,18,23] improves the modularity of denotational semantics by taking denotations to be so-called actions, which are expressed using a xed action notation consisting of various primitives and combinators|a few of them are listed in Appendix B. The primary interpretation of action notation is, …