SOS formats and meta-theory: 20 years after

Defining a formal (i.e., mathematical) semantics for computer languages is the first step towards developing rigorous techniques for reasoning about computerprograms and specifications in such a language. Structural Operational Semantics (SOS), introduced by Plotkin in 1981, has become a popular technique for defining formal semantics. In this thesis, we first review the basic concepts of SOS and the existing meta-results. Subsequently, we enhance the state of the art in this field by offering the following contributions:• developing a syntactic format guaranteeing a language construct to be commutative;• extending the existing congruence and well-definedness meta-results to the setting with equational specifications;• defining a more liberal notion of operational conservativity, called orthogonality,and formulating meta-theorems for it;• prototyping a framework for checking the premises of congruence and conservativity meta-theorems and animating programs according to their SOS specification;• defining notions of bisimulation with data and formulating syntactic rule formats guaranteeing congruence for these notions;• proposing syntactic rule formats for guaranteeing congruence of strong bisimilarity and higher-order bisimilarity in the setting of higher order processes.

/pdf/structuring-structural-operational-semantics-25401ecrvq.pdf

Structuring structural operational semantics

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 [113]. 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.

20 Years After

Groote and Vaandrager introduced the tyft/tyxt format for Transition System Specifications (TSSs), and established that for each TSS in this format that is well-founded, the bisimulation equivalence it induces is a congruence. In this paper, we construct for each TSS in tyft/tyxt format an equivalent TSS that consists of tree rules only. As a corollary we can give an affirmative answer to an open question, namely whether the well-foundedness condition in the congruence theorem for tyft/tyxt can be dropped. These results extend to tyft/tyxt with negative premises and predicates.

Ntyft/ntyxt rules reduce to ntree rules

Compositionality of Hennessy-Milner logic by structural operational semantics

We present a method for decomposing modal formulas for processes with the internal action @t. To decide whether a process algebra term satisfies a modal formula, one can check whether its subterms satisfy formulas that are obtained by decomposing the original formula. The decomposition uses the structural operational semantics that underlies the process algebra. We use this decomposition method to derive congruence formats for two weak and rooted weak semantics: branching and @h-bisimilarity.

https://www.cs.vu.nl/~wanf/pubs/dc-branching.pdf

Divide and congruence: From decomposition of modal formulas to preservation of branching and η -bisimilarity

Divide and Congruence Applied to η-Bisimulation

This paper presents a method for the decomposition of HML formulae. It can be used to decide whether a process algebra term satisfies a HML formula, by checking whether subterms satisfy certain formulae, obtained by decomposing the original formula. The method uses the structural operational semantics of the process algebra. The main contribution of this paper is that an earlier decomposition method from LARSEN [14] for the De Simone format is extended to the more general ntyft/ntyxt format without lookahead.

/pdf/compositionality-of-hennessy-milner-logic-through-structural-4wcehwnhcd.pdf

Compositionality of Hennessy-Milner Logic through Structural Operational Semantics

We present a method for decomposing modal formulas for processes with the internal action τ. To decide whether a process algebra term satisfies a modal formula, one can check whether its subterms satisfy formulas that are obtained by decomposing the original formula. The decomposition uses the structural operational semantics that underlies the process algebra. We use this decomposition method to derive congruence formats for branching and rooted branching bisimulation equivalence.

Paulien de Wind

Papers

Compositionality of Hennessy-Milner logic by structural operational semantics

Divide and congruence: From decomposition of modal formulas to preservation of branching and η -bisimilarity

Divide and Congruence Applied to η-Bisimulation

Compositionality of Hennessy-Milner Logic through Structural Operational Semantics

Divide and congruence: from decomposition of modalities to preservation of branching bisimulation