SOS formats and meta-theory: 20 years after

Abstract

In 1981 Structural Operational Semantics (SOS) was introduced as a systematic way to define operational semantics of programming languages by a set of rules of a certain shape [G.D. Plotkin, A structural approach to operational semantics, Technical Report DAIMI ]. Subsequently, the format of SOS rules became the object of study. Using so-called Transition System Specifications (TSS's) several authors syntactically restricted the format of rules and showed several useful properties about the semantics induced by any TSS adhering to the format. This has resulted in a line of research proposing several syntactical rule formats and associated meta-theorems. Properties that are guaranteed by such rule formats range from well-definedness of the operational semantics and compositionality of behavioral equivalences to security-, time-and probability-related issues. In this paper, we provide an overview of SOS rule formats and meta-theorems formulated around them.

Transforming SOS Specifications to Linear Processes

“…A TSS defines a set of transitions, a so called transition relation; see, e.g., [2,30] for formal definitions thereof.…”

“…SOS meta-theory research is mainly aimed at proving useful properties about TSSs [2,30] such as congruence results [21], deriving equational theories [1], conservative extensions [19], and soundness of axioms [3]. Research on how to implement them is often underexposed.…”

“…Most of this work is performed with the Maude model checker [32]. Other authors have studied the link between the rewriting logic [24] and SOS both from a theoretical [8,15,26,17,30] as well as practical point of view [13,14,17,29,35,36].…”

Incremental Pattern-Based Coinduction for Process Algebra and Its Isabelle Formalization

“…Next we represent the meta-SOS notion of a transition-system specification [15,26]. Given any type α, the type α ftrans, of formal α-transitions, consists of pairs, written k l, with k, l :: α, where k is called the source and l the target.…”

Exploiting Algebraic Laws to Improve Mechanized Axiomatizations

“…These properties can either be validated using the semantics of the language with respect to a suitable notion of program equivalence, or they can be guaranteed a priori 'by design'. In particular, for languages equipped with a Structural Operational Semantics (SOS) [32,42,43], there are two closely related lines of work to achieve this goal: firstly, there is a rich body of syntactic rule formats that can guarantee the validity of certain algebraic properties; see [15,39] for recent surveys. Secondly, there are numerous results regarding the mechanical generation of ground-complete axiomatization of various behavioral equivalences and preorders for SOS language specifications in certain formats [3,5,18,22,30,46,47].…”