## SOS formats and meta-theory: 20 years after (2007)

Citations: | 11 - 5 self |

### BibTeX

@MISC{Mousavi07sosformats,

author = {Mohammadreza Mousavi and Michel A. Reniers and Jan Friso Groote},

title = { SOS formats and meta-theory: 20 years after},

year = {2007}

}

### OpenURL

### 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

### Citations

3682 | Communicating Sequential Processes
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Citation Context ...rovided that these new transitions and predicates do not change the behavioral equalities among old terms. 7 Generating Equational Theories Equational theories are central notions to process algebras =-=[8,19,71,90]-=-. They capture the basic intuition behind the algebra, and the models of the algebra 9 Note that although the notation ⊕ has been defined for TSS’s with a designated sort for labels (i.e., a TSS in tr... |

3463 |
Communication and Concurrency
- Milner
- 1989
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Citation Context ...rovided that these new transitions and predicates do not change the behavioral equalities among old terms. 7 Generating Equational Theories Equational theories are central notions to process algebras =-=[8,19,71,90]-=-. They capture the basic intuition behind the algebra, and the models of the algebra 9 Note that although the notation ⊕ has been defined for TSS’s with a designated sort for labels (i.e., a TSS in tr... |

1564 | The Stable Model Semantics for Logic Programming
- Gelfond, Lifschitz
- 1988
(Show Context)
Citation Context ...n the ntyft/ntyxt format (see Section 5) is guaranteed to have a well-defined semantics. This criterion, defined below for TSS’s in general, is called (strict) stratification and is originally due to =-=[55]-=- in logic programming. It is an important property of a format when it guarantees that every set of rules unequivocally defines a transition relation. Below we give a more general definition of strati... |

1385 | A structural approach to operational semantics - Plotkin - 2004 |

1071 | A calculus of mobile processes - Milner, Parrow, et al. - 1992 |

782 |
Security policies and security models
- Goguen, Meseguer
- 1982
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Citation Context ...he kernels of the MAUTO tool [28] and the Concurrency Workbench [38], respectively. 14 Other Meta-Results 14.1 Non-Interference Confidentiality is an important aspect of security and non-interference =-=[63]-=- is a well-studied means to guarantee end-to-end confidentiality. Non-interference means that a user with a lower confidentiality level cannot infer anything about the higher-level information by inte... |

707 | Concurrency and Automata on Infinite Sequences - Park - 1981 |

630 | A.C.: Language-based information-flow security - Sabelfeld, Myers |

520 | Algebraic Laws for Nondeterminism and Concurrency
- Henessy, Milner
- 1985
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Citation Context ...le the tyft format with closed terms is incomparable to the promoted tyft format, 40sthe positive subset of the promoted panth format is strictly more expressive than both. 12 Reasoning Techniques In =-=[69]-=-, a logical framework, nowadays called Hennessy-Milner logic after the authors’ names, is proposed. Hennessy-Milner logic can be used to reason about processes and characterize their equalities. The s... |

497 | The chemical abstract machine - Berry, Boudol - 1992 |

492 | The pi-Calculus: A Theory of Mobile Processes - Sangiorgi, Walker - 2003 |

432 | Bisimulation through probabilistic testing
- Larsen, Skou
- 1991
(Show Context)
Citation Context ... that, for reactive system, we mean p a → � µ and µ(q) = ρ and for generative system, we mean p � µ and µ(a, q) = ρ. Notions of bisimilarity for reactive and generative systems are defined as follows =-=[81,62,124]-=-. Definition 54 (Reactive Probabilistic Bisimilarity [81]) Let P and Q be arbitrary sets. Consider a relation R ⊆ P × Q. Then the lifting of R ⊆ (P → [0, 1]) × (Q → [0, 1]) , denoted by ≡R, is defined... |

389 | Process Algebra for Synchronous Communication
- Bergstra, Klop
- 1984
(Show Context)
Citation Context ...rovided that these new transitions and predicates do not change the behavioral equalities among old terms. 7 Generating Equational Theories Equational theories are central notions to process algebras =-=[8,19,71,90]-=-. They capture the basic intuition behind the algebra, and the models of the algebra 9 Note that although the notation ⊕ has been defined for TSS’s with a designated sort for labels (i.e., a TSS in tr... |

386 | Three Partition Refinement Algorithms - Paige, Tarjan - 1987 |

325 | Natural semantics
- Kahn
- 1987
(Show Context)
Citation Context ...ASF) Fig. 2. High-Level Architecture of Centaur used to pretty print the syntax in the editor. Semantics of languages can be specified in Typol which is a textual description of the natural semantics =-=[73]-=- which can be used to generate interpreters and debuggers. The syntactic manipulation part is implemented in Le-Lisp and the logical machine is written in Prolog. The interface between the two modules... |

323 | editors. Larch: Languages and Tools for Formal Specification
- Guttag, Horning
- 1993
(Show Context)
Citation Context ...rove confluence and termination of their rewrite systems (for the micro-steps on the way to making a complete operational transition). In [34] an implementation of the approach in the Larch 45sProver =-=[66]-=- is reported. Process Algebra Compiler (PAC) [37] is a tool that takes the signature and the SOS rules of a language and generates a scanner/parser as well as verification libraries targeted at the sp... |

315 | The Linear Time – Branching Time Spectrum
- Glabbeek
- 2001
(Show Context)
Citation Context ...uivalence (pre-order) to be compositional or in technical terms to be a congruence (pre-congruence). There is a myriad of notions of behavioral equivalence and pre-order in the concurrency literature =-=[57,59]-=-. Correspondingly, there are a number of rule formats guaranteeing these notions to be (pre-)congruences [65,23,22,61]. In the remainder, we confine ourselves to single-sorted frameworks. In such fram... |

210 |
The Concurrency Workbench: A Semanticsbased Tool for the Verification of Concurrent Systems
- Cleaveland, Parrow, et al.
- 1993
(Show Context)
Citation Context ...ted in LEX/YACC syntax and the verification libraries can be generated both in Lisp and in Standard ML which can then be compiled with the kernels of the MAUTO tool [28] and the Concurrency Workbench =-=[38]-=-, respectively. 14 Other Meta-Results 14.1 Non-Interference Confidentiality is an important aspect of security and non-interference [63] is a well-studied means to guarantee end-to-end confidentiality... |

201 |
Bisimulation can’t be traced
- Bloom, Istrail, et al.
- 1995
(Show Context)
Citation Context ...C(↔ R+(η,W B,BB,D) ) [22;61] AX [22,61] SBBNI SS,CT NIF [127] Generalized PANTH MS,CT,B,LA,CPY, NEG,INF,PRED C(↔ S ) [86] OC [87] Ready Simulation SS,CT,CPY,INF,NEG RM [50] GSOS SS,CT,CPY,NEG C(↔ S ) =-=[24]-=- AX [3], RM [123] FokkinkVerhoef MS,LT,B,LA, CPY,NEG,INF,PRED OC [51] PANTH SS,CT,LA,NWF, NEG,INF,PRED C(↔ S ) [143,48] NTyft (NTree) SS, CT,LA,NWF, CPY,NEG,INF C(↔ S ) [64,48] Probabilistic GSOS SS,C... |

201 |
Structured Operational Semantics and Bisimulation as a Congruence, Draft
- Groote, Vaandrager
- 1989
(Show Context)
Citation Context ...myriad of notions of behavioral equivalence and pre-order in the concurrency literature [57,59]. Correspondingly, there are a number of rule formats guaranteeing these notions to be (pre-)congruences =-=[65,23,22,61]-=-. In the remainder, we confine ourselves to single-sorted frameworks. In such frameworks, the arity of a function symbol can be conveniently expressed by a natural number (representing the number of p... |

194 |
CCS expressions finite state processes, and three problems of equivalence
- Kanellakis, Smolka
- 1990
(Show Context)
Citation Context ...gant and compact than those for other (weaker) notions; (2) For finite state processes, strong bisimilarity can be checked very efficiently in practice [108] while some weaker notions are intractable =-=[75]-=-; (3) Other (weaker) notions of behavioral equality can often be coded in strong bisimilarity [56]. So, it is not surprising that the first standard congruence format was geared toward strong bisimila... |

182 | The polyadic π-calculus: A tutorial
- Milner
- 1993
(Show Context)
Citation Context ..., yet important, instances of these concepts appear in different process algebras in the form of the recursion operator, the infinite sum operator and the time-integration operator (cf., for example, =-=[91]-=-, [82,117] and [13], respectively). Hence, it is interesting to accommodate the concept of names in the TSS framework. B The first step towards specifying the above-mentioned constructs is to allow fo... |

178 |
A temporal calculus of communicating systems
- Moller, Tofts
- 1990
(Show Context)
Citation Context ...e) temporal properties of programs and specifications. The extension of an operational semantics with time is usually realized by adding a time transition relation to the transition system (see e.g., =-=[94]-=-) or sometimes by annotating the action transitions with timing information. In the remainder, we only consider the former approach for it is the only approach studied in the SOS meta-theory. There ar... |

164 | Reactive, generative, and stratified models of probabilistic processes
- Glabbeek, Smolka, et al.
- 1995
(Show Context)
Citation Context ... that, for reactive system, we mean p a → � µ and µ(q) = ρ and for generative system, we mean p � µ and µ(a, q) = ρ. Notions of bisimilarity for reactive and generative systems are defined as follows =-=[81,62,124]-=-. Definition 54 (Reactive Probabilistic Bisimilarity [81]) Let P and Q be arbitrary sets. Consider a relation R ⊆ P × Q. Then the lifting of R ⊆ (P → [0, 1]) × (Q → [0, 1]) , denoted by ≡R, is defined... |

163 | Time Pro- cess Algebra
- Baeten, Bergstra, et al.
- 1990
(Show Context)
Citation Context |

159 | Rewriting logic as a logical and semantic framework
- Martí-Oliet, Meseguer
- 1993
(Show Context)
Citation Context ...tive to a class of assumptions) are proved in [123] for the above proof system. 43s13 Implementation 13.1 Term Rewriting Several authors have studied the, rather evident, link between rewriting logic =-=[83]-=- and SOS both from a theoretical [43,83–85] as well as practical point of view [30,31,140,142]. In [30], the outline of a translation from Modular SOS (MSOS) [97,96] to the Maude rewriting logic is gi... |

153 | A new approach to abstract syntax involving binders
- Gabbay, Pitts
- 1999
(Show Context)
Citation Context ...out freshness of names (or statements such as “name n does not appear free in term t”). In order to capture these notions, some capacities must be foreseen. The nominal techniques of Gabbay and Pitts =-=[53]-=- and the FOλ ∆∇ formalism of Miller and Tiu [88] provide good possibilities for incorporating these notions in the SOS meta-theory and the first attempt in this direction has been made by [147]. [45] ... |

153 | Miranda: a non-strict functional language with polymorphic types - Turner - 1985 |

143 | Centaur: The system
- Borras, Clément, et al.
- 1988
(Show Context)
Citation Context ...eck the premises of congruence and operational conservativity meta-theorems. Furthermore, it allows for animating programs based on their GSOS specifications. 13.2 Logic Programming (Centaur) Centaur =-=[26]-=- is a tool developed in the 1980’s within the group of the late Gilles Kahn at INRIA Sophia-Antipolis. It is described as a “generic interactive environment generator”, i.e., it provides an environmen... |

141 | Formal molecular biology
- Danos, Laneve
(Show Context)
Citation Context ...rsibility Reversible computations are known to have some interesting properties (such as being potentially dissipation free) and they can model several real-world phenomena such as biological systems =-=[40]-=-, chemical reactions [21] and quantum computation [118]. In [112], a general recipe is given for reversing the semantics in the SOS style. The technique is based on a subset of the de Simone format an... |

139 | Well-Founded Semantics Coincides with Three-Valued Stable Semantics - Przymusinski - 1989 |

131 | Structural operational semantics
- Aceto, Fokkink, et al.
(Show Context)
Citation Context ...ns imposed by these meta-theorems usually suggest particular forms of deduction rules to be safe for a particular purpose and hence these meta-theorems usually define what is called a rule format. In =-=[5]-=-, an excellent overview is provided for existing rule formats up to the date of publication (2001). Since then, more formats have been proposed and we felt that in order to keep track, the field of SO... |

122 | A calculus of mobile processes, parts I and II - Milner, Parrow, et al. - 1989 |

121 |
Transition system specifications with negative premises
- Groote
- 1993
(Show Context)
Citation Context ...sing syntactic restrictions on TSS’s one can deduce several interesting properties about their induced operational semantics. These properties range from well-definedness of the operational semantics =-=[64,25,60]-=- to security- [126,127] and probability-related issues [18,78]. The syntactic restrictions imposed by these meta-theorems usually suggest particular forms of deduction rules to be safe for a particula... |

120 | A Theory of Higher Order Communication Systems - Thomsen - 1995 |

115 | A congruence theorem for structured operational semantics with predicates and negative premises, Nordic
- Verhoef
- 1995
(Show Context)
Citation Context ...C(↔ p ) [18] De Simone SS,CT C(↔ S ) [42] PC(≤tr,f ) [138] Promoted PANTH SS, LT,LA,CPY, NEG,INF,PRED C(↔ S ,↔ HO ) [98] Fig. 1. A hierarchy of existing SOS formats PATH SS,CT,LA,CPY,INF,PRED C(↔ S ) =-=[14]-=- Extended Tyft MS,OT,LA,CPY,INF C(↔ ≡ ), CMP [54] Promoted Tyft SS, OT LA,CPY,NEG,INF,PRED C(↔ S ) [20] Tyft (Tree) SS, CT,LA,NWF,CPY,INF C(↔ S ) [65,46] PC(≤nn) [25], RM [49] Ziegler et. al. MS,CT,B,... |

114 | Proving congruence of bisimulation in functional programming languages
- Howe
- 1996
(Show Context)
Citation Context ... specifying the above-mentioned constructs is to allow for binding signatures. There have been a few attempts in this direction. Proposals for SOS frameworks with binding signatures are formulated in =-=[147,51,86,87,72,120,146]-=-. N Another related issue in this regard, is the concept of fresh names and freshness contexts. In the semantics and notions of behaviorial equivalence for some formalisms (such as the π-calculus), on... |

112 | The algebra of timed processes ATP: theory and application - Nicollin, Sifakis - 1994 |

97 |
Process algebra, volume 18 of Cambridge tracts
- Baeten, Weijland
- 1990
(Show Context)
Citation Context ...action labels, and a countable set of deduction rules. Then, the sub-format regular GSOS allows for generation of a complete and sound axiomatization, containing the Recursive Specification Principle =-=[16]-=- of bisimilarity. The restrictions that are covered by this regular GSOS format only allow for the specification of processes with a finite labelled transition system. Bloom [22] has shown that the ap... |

97 | The Maude 2.0 System
- CLAVEL, DURÁN, et al.
- 2003
(Show Context)
Citation Context ...ategies is given for the case of Ordered SOS specifications. Verdejo in [141] and Verdejo and Marti-Oliet in [139,140,142] report the implementation of a number of instances of SOS semantics in Maude =-=[36]-=-. Our approach is very close in essence to their work in that SOS deduction rules are interpreted as Maude conditional rewrite rules. In [102], some aspects of SOS meta-theory are implemented in Maude... |

94 | Full abstraction for a simple parallel programming language
- Hennessy, Plotkin
- 1979
(Show Context)
Citation Context ...w of SOS rule formats and meta-theorems formulated around them. Key words: Formal Semantics, Structural Operational Semantics, Rule Formats, Framework. 1 Introduction Structural Operational Semantics =-=[114,115,68]-=- has become the common way to define operational semantics. Operational semantics defines the possible 1 Corresponding Author. Also affiliated with Department of Electrical Engineering, Eindhoven Univ... |

92 | Turning SOS rules into equations
- ACETO, BLOOM, et al.
- 1994
(Show Context)
Citation Context ...,W B,BB,D) ) [22;61] AX [22,61] SBBNI SS,CT NIF [127] Generalized PANTH MS,CT,B,LA,CPY, NEG,INF,PRED C(↔ S ) [86] OC [87] Ready Simulation SS,CT,CPY,INF,NEG RM [50] GSOS SS,CT,CPY,NEG C(↔ S ) [24] AX =-=[3]-=-, RM [123] FokkinkVerhoef MS,LT,B,LA, CPY,NEG,INF,PRED OC [51] PANTH SS,CT,LA,NWF, NEG,INF,PRED C(↔ S ) [143,48] NTyft (NTree) SS, CT,LA,NWF, CPY,NEG,INF C(↔ S ) [64,48] Probabilistic GSOS SS,CT,CPY,N... |

76 | Syntax and defining equations for an interrupt mechanism in process algebra - Baeten, Bergstra, et al. |

74 | The meaning of negative premises in transition system specifications - Bol, Groote - 1996 |

74 |
Compositionality through an operational semantics of contexts
- Larsen, Xinxin
- 1990
(Show Context)
Citation Context ...it is shown that Hennessy-Milner logic is sound and adequate for strong bisimilarity, meaning that two processes are bisimilar if and only if they satisfy the same set of Hennessy-Milner formulae. In =-=[79,80]-=- a meta-theory is developed that allows for decomposing HennessyMilner formulae using the structure of terms in a generic way by examining deduction rules of the process language in the de Simone form... |

70 | The origins of structural operational semantics - Plotkin |

66 | A proof theory for generic judgments
- Miller, Tiu
- 2005
(Show Context)
Citation Context ...ame n does not appear free in term t”). In order to capture these notions, some capacities must be foreseen. The nominal techniques of Gabbay and Pitts [53] and the FOλ ∆∇ formalism of Miller and Tiu =-=[88]-=- provide good possibilities for incorporating these notions in the SOS meta-theory and the first attempt in this direction has been made by [147]. [45] adopts an alternative model of names and freshne... |

64 | Modular structural operational semantics
- Mosses
(Show Context)
Citation Context ...ations. Higher-order process calculi [27,125,121] are examples of formalisms exploiting this feature. Two other frameworks that use labels with some structure on them are the Modular SOS framework of =-=[96,97]-=- and the Enhanced Operational Semantics of [44]. The former assumes that labels are arrows of a category and thus comes equipped with composition and identity. The latter approach codes the derivation... |

61 |
Towards a Lambda-Calculus for Concurrent and Communicating Systems
- Boudol
(Show Context)
Citation Context ...els: Frameworks defined in [51,54,20,98] allow for arbitrary open terms as labels. Open terms are used as labels in a number of cases in transition system specifications. Higher-order process calculi =-=[27,125,121]-=- are examples of formalisms exploiting this feature. Two other frameworks that use labels with some structure on them are the Modular SOS framework of [96,97] and the Enhanced Operational Semantics of... |

59 | Bisimulation for Higher-order Process Calculi - Sangiorgi - 1996 |