Meta SOS - A Maude Based SOS Meta-Theory Framework

Meta SOS is a software framework designed to integrate the results from the meta-theory of structural operational semantics (SOS). These results include deriving semantic properties of language constructs just by syntactically analyzing their rule-based definition, as well as automatically deriving sound and ground-complete axiomatizations for languages, when considering a notion of behavioural equivalence. This paper describes the Meta SOS framework by blending aspects from the meta-theory of SOS, details on their implementation in Maude, and running examples.Comment: In Proceedings EXPRESS/SOS 2013, arXiv:1307.690

Robustness of Equations Under Operational Extensions

Sound behavioral equations on open terms may become unsound after conservative extensions of the underlying operational semantics. Providing criteria under which such equations are preserved is extremely useful; in particular, it can avoid the need to repeat proofs when extending the specified language. This paper investigates preservation of sound equations for several notions of bisimilarity on open terms: closed-instance (ci-)bisimilarity and formal-hypothesis (fh-)bisimilarity, both due to Robert de Simone, and hypothesis-preserving (hp-)bisimilarity, due to Arend Rensink. For both fh-bisimilarity and hp-bisimilarity, we prove that arbitrary sound equations on open terms are preserved by all disjoint extensions which do not add labels. We also define slight variations of fh- and hp-bisimilarity such that all sound equations are preserved by arbitrary disjoint extensions. Finally, we give two sets of syntactic criteria (on equations, resp. operational extensions) and prove each of them to be sufficient for preserving ci-bisimilarity.Comment: In Proceedings EXPRESS'10, arXiv:1011.601

Bisimilarity of Open Terms in Stream GSOS

Stream GSOS is a specification format for operations and calculi on infinite sequences. The notion of bisimilarity provides a canonical proof technique for equivalence of closed terms in such specifications. In this paper, we focus on open terms, which may contain variables, and which are equivalent whenever they denote the same stream for every possible instantiation of the variables. Our main contribution is to capture equivalence of open terms as bisimilarity on certain Mealy machines, providing a concrete proof technique. Moreover, we introduce an enhancement of this technique, called bisimulation up-to substitutions, and show how to combine it with other up-to techniques to obtain a powerful method for proving equivalence of open terms

The Way We Were: Structural Operational Semantics Research in Perspective

This position paper on the (meta-)theory of Structural Operational Semantic (SOS) is motivated by the following two questions: (1) Is the (meta-)theory of SOS dying out as a research field? (2) If so, is it possible to rejuvenate this field with a redefined purpose? In this article, we will consider possible answers to those questions by first analysing the history of the EXPRESS/SOS workshops and the data concerning the authors and the presentations featured in the editions of those workshops as well as their subject matters. The results of our quantitative and qualitative analyses all indicate a diminishing interest in the theory of SOS as a field of research. Even though `all good things must come to an end', we strive to finish this position paper on an upbeat note by addressing our second motivating question with some optimism. To this end, we use our personal reflections and an analysis of recent trends in two of the flagship conferences in the field of Programming Languages (namely POPL and PDLI) to draw some conclusions on possible future directions that may rejuvenate research on the (meta-)theory of SOS. We hope that our musings will entice members of the research community to breathe new life into a field of research that has been kind to three of the authors of this article.Comment: In Proceedings EXPRESS/SOS2023, arXiv:2309.0578

Bisimulation of Labeled State-to-Function Transition Systems of Stochastic Process Languages

Labeled state-to-function transition systems, FuTS for short, admit multiple transition schemes from states to functions of finite support over general semirings. As such they constitute a convenient modeling instrument to deal with stochastic process languages. In this paper, the notion of bisimulation induced by a FuTS is proposed and a correspondence result is proven stating that FuTS-bisimulation coincides with the behavioral equivalence of the associated functor. As generic examples, the concrete existing equivalences for the core of the process algebras ACP, PEPA and IMC are related to the bisimulation of specific FuTS, providing via the correspondence result coalgebraic justification of the equivalences of these calculi.Comment: In Proceedings ACCAT 2012, arXiv:1208.430

Lean and Full Congruence Formats for Recursion

In this paper I distinguish two (pre)congruence requirements for semantic equivalences and preorders on processes given as closed terms in a system description language with a recursion construct. A lean congruence preserves equivalence when replacing closed subexpressions of a process by equivalent alternatives. A full congruence moreover allows replacement within a recursive specification of subexpressions that may contain recursion variables bound outside of these subexpressions. I establish that bisimilarity is a lean (pre)congruence for recursion for all languages with a structural operational semantics in the ntyft/ntyxt format. Additionally, it is a full congruence for the tyft/tyxt format.Comment: To appear in: Proc. LICS'17, Reykjavik, Iceland, IEE

A Coalgebraic Semantics for Imperative Programming Languages

In the theory of programming languages, one often takes two complementary perspectives. In operational semantics, one defines and reasons about the behaviour of programs; and in denotational semantics, one abstracts away implementation details, and reasons about programs as mathematical objects or denotations. The denotational semantics should be compositional, meaning that denotations of programs are determined by the denotations of their parts. It should also be adequate with respect to operational equivalence: programs with the same denotation should be behaviourally indistinguishable. One often has to prove adequacy and compositionality independently for different languages, and the proofs are often laborious and repetitive. These proofs were provided systematically in the context of process algebras by the mathematical operational semantics framework of Turi and Plotkin – which represented transition systems as coalgebras, and program syntax by free algebras; operational specifications were given by distributive laws of syntax over behaviour. By framing the semantics on this abstract level, one derives denotational and operational semantics which are guaranteed to be adequate and compositional for a wide variety of examples. However, despite speculation on the possibility, it is hard to apply the framework to programming languages, because one obtains undesirably fine-grained behavioural equivalences, and unconventional notions of operational semantics. Moreover, the behaviour of these languages is often formalised in a different way – such as computational effects, which may be thought of as an interface between programs and external factors such as non-determinism or a variable store; and comodels, or transition systems which implement these effects. This thesis adapts the mathematical operational semantics framework to provide semantics for various classes of programming languages. After identifying the need for such an adaptation, we show how program behaviour may be characterised by final coalgebras in suitably order- enriched Kleisli categories. We define both operational and denotational semantics, first for languages with syntactic effects, and then for languages with effects and/or comodels given by a Lawvere theory. To ensure adequacy and compositionality, we define concrete and abstract operational rule-formats for these languages, based on the idea of evaluation-in-context; we give syntactic and then categorical proofs that those properties are guaranteed by operational specifications in these rule-formats.Open Acces

A Declarative Validator for GSOS Languages

Rule formats can quickly establish meta-theoretic properties of process algebras. It is then desirable to identify domain-specific languages (DSLs) that can easily express rule formats. In prior work, we have developed Lang-n-Change, a DSL that includes convenient features for browsing language definitions and retrieving information from them. In this paper, we use Lang-n-Change to write a validator for the GSOS rule format, and we augment Lang-n-Change with suitable macros on our way to do so. Our GSOS validator is concise, and amounts to a few lines of code. We have used it to validate several concurrency operators as adhering to the GSOS format. Moreover, our code expresses the restrictions of the format declaratively.Comment: In Proceedings PLACES 2023, arXiv:2304.0543