Rewriting logic is a flexible and expressive logical framework that unifies denotational semantics and SOS in a novel way, avoiding their respective limitations and allowing very succinct semantic definitions. The fact that a rewrite theory’s axioms include both equations and rewrite rules provides a very useful “abstraction knob” to find the right balance between abstraction and observability in semantic definitions. Such semantic definitions are directly executable as interpreters in a rewriting logic language such as Maude, whose generic formal tools can be used to endow those interpreters with powerful program analysis capabilities.

This work describes the formal semantics of SCHEME 1 as an equational theory in the MAUDE rewriting system. The semantics is based on continuations and is highly modular. We briefly investigate the relationship between our methodology for defining programming languages and other semantic formalisms. We conclude by showing some performance results of the interpreter obtained for free from the executable specification.

Abstract. Modularity is a pragmatic property of specifications that is not easy to achieve. For instance, it has been left as an open problem by Plotkin in his 81 Aarhus lecture notes where Structural Operational Semantics (SOS) was defined. This open problem has been solved only recently by Mosses with Modular SOS (MSOS), a framework that extends labelled transitions systems with a label category where the semantic information is encapsulated inside its arrows. This extension gave rise to arrow-labelled transition systems that allow MSOS specifications to be made modular, that is, extended monotonically. The objective of this paper is to present the Maude MSOS Tool, a Maude implementation of MSOS. Maude is a fast implementation of rewriting logic, a reflective logic that has been shown as a generic framework which can represent many logics, specification languages and models of computation. It is precisely the reflective capabilities of rewriting logic implemented in the Maude system that allow us to create an executable environment for MSOS: Maude MSOS Tool. 1

Abstract. This work describes the formal semantics of Scheme 1 as an equational theory in the Maude rewriting system. The semantics is based on continuations and is highly modular. We briefly investigate the relationship between our methodology for defining programming languages and other semantic formalisms. We conclude by showing some performance results of the interpreter obtained for free from the executable specification. 1