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Deconstructing behavioural theories of mobility
, 2008
"... Abstract. We reexamine the standard structural operational semantics of the πcalculus with the view that both process structure and contextual observational power should play roles in describing the behavioural theory. To that end we provide a decomposition of the operational semantics of π which ..."
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Cited by 11 (2 self)
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Abstract. We reexamine the standard structural operational semantics of the πcalculus with the view that both process structure and contextual observational power should play roles in describing the behavioural theory. To that end we provide a decomposition of the operational semantics of π which allows for a systematic definition of labelled transitions. These are derived from the calculus ’ underlying reduction rules by following the contextsaslabels philosophy while being presented using the structural approach. Our novel transition system refines to a composite description of the standard early lts. We generalise our technique to higherorder and asynchronous variants.
SOS formats and metatheory: 20 years after
, 2007
"... 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 ..."
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Cited by 10 (5 self)
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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
Proof search specifications of bisimulation and modal logics for the πcalculus
 ACM Trans. on Computational Logic
"... We specify the operational semantics and bisimulation relations for the finite πcalculus within a logic that contains the ∇ quantifier for encoding generic judgments and definitions for encoding fixed points. Since we restrict to the finite case, the ability of the logic to unfold fixed points allo ..."
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Cited by 8 (6 self)
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We specify the operational semantics and bisimulation relations for the finite πcalculus within a logic that contains the ∇ quantifier for encoding generic judgments and definitions for encoding fixed points. Since we restrict to the finite case, the ability of the logic to unfold fixed points allows this logic to be complete for both the inductive nature of operational semantics and the coinductive nature of bisimulation. The ∇ quantifier helps with the delicate issues surrounding the scope of variables within πcalculus expressions and their executions (proofs). We shall illustrate several merits of the logical specifications permitted by this logic: they are natural and declarative; they contain no sideconditions concerning names of variables while maintaining a completely formal treatment of such variables; differences between late and open bisimulation relations arise from familar logic distinctions; the interplay between the three quantifiers (∀, ∃, and ∇) and their scopes can explain the differences between early and late bisimulation and between various modal operators based on bound input and output actions; and proof search involving the application of inference rules, unification, and backtracking can provide complete proof systems for onestep transitions, bisimulation, and satisfaction in modal logic. We also illustrate how one can encode the πcalculus with replications, in an extended logic with induction and coinduction.
General structural operational semantics through categorical logic (Extended Abstract)
, 2008
"... Certain principles are fundamental to operational semantics, regardless of the languages or idioms involved. Such principles include rulebased definitions and proof techniques for congruence results. We formulate these principles in the general context of categorical logic. From this general formul ..."
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Cited by 7 (6 self)
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Certain principles are fundamental to operational semantics, regardless of the languages or idioms involved. Such principles include rulebased definitions and proof techniques for congruence results. We formulate these principles in the general context of categorical logic. From this general formulation we recover precise results for particular language idioms by interpreting the logic in particular categories. For instance, results for firstorder calculi, such as CCS, arise from considering the general results in the category of sets. Results for languages involving substitution and name generation, such as the πcalculus, arise from considering the general results in categories of sheaves and group actions. As an extended example, we develop a tyft/tyxtlike rule format for open bisimulation in the πcalculus.
Representing and reasoning with operational semantics
 In: Proceedings of the Joint International Conference on Automated Reasoning
, 2006
"... The operational semantics of programming and specification languages is often presented via inference rules and these can generally be mapped into logic programminglike clauses. Such logical encodings of operational semantics can be surprisingly declarative if one uses logics that directly account ..."
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Cited by 7 (2 self)
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The operational semantics of programming and specification languages is often presented via inference rules and these can generally be mapped into logic programminglike clauses. Such logical encodings of operational semantics can be surprisingly declarative if one uses logics that directly account for termlevel bindings and for resources, such as are found in linear logic. Traditional theorem proving techniques, such as unification and backtracking search, can then be applied to animate operational semantic specifications. Of course, one wishes to go a step further than animation: using logic to encode computation should facilitate formal reasoning directly with semantic specifications. We outline an approach to reasoning about logic specifications that involves viewing logic specifications as theories in an objectlogic and then using a metalogic to reason about properties of those objectlogic theories. We motivate the principal design goals of a particular metalogic that has been built for that purpose.
A proof theoretic approach to operational semantics, in
 Proc. of the workshop on Algebraic Process Calculi: The First Twenty Five Years and Beyond
, 2005
"... Proof theory can be applied to the problem of specifying and reasoning about the operational semantics of process calculi. We overview some recent research in which λtree syntax is used to encode expressions containing bindings and sequent calculus is used to reason about operational semantics. The ..."
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Cited by 2 (0 self)
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Proof theory can be applied to the problem of specifying and reasoning about the operational semantics of process calculi. We overview some recent research in which λtree syntax is used to encode expressions containing bindings and sequent calculus is used to reason about operational semantics. There are various benefits of this proof theoretic approach for the πcalculus: the treatment of bindings can be captured with no side conditions; bisimulation has a simple and natural specification in which the difference between bound input and bound output is characterized using difference quantifiers; various modal logics for mobility can be specified declaratively; and simple logic programminglike deduction involving subsets of secondorder unification provides immediate implementations of symbolic bisimulation. These benefits should extend to other process calculi as well. As partial evidence of this, a simple λtree syntax extension to the tyft/tyxt rule format for namebinding and namepassing is possible that allows one to conclude that (open) bisimilarity is a congruence. Key words: operational semantics, proof theoretic specifications, λtree syntax, rule formats, πcalculus A number of frameworks have been used to formalize the semantics of process calculi and, more generally, programming languages. For example, algebra, category theory, and I/O automata have been used to provide formal settings for not only specifying but also reasoning about the operational semantics of calculi and languages. In this note, we overview recent results in making use of proof theory to encode and reason about such operational semantics. By the term “proof theory ” we refer the study of proofs for logics, particularly in the style initiated by Gentzen. 1 Support for this work comes from INRIA through the “Equipes Associées ” Slimmer and from the ACI grants GEOCAL and Rossignol.
Technical Report UCAMCLTR688
, 2007
"... Number 688 Computer Laboratory Namepassing process calculi: operational models and structural operational semantics ..."
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Number 688 Computer Laboratory Namepassing process calculi: operational models and structural operational semantics
The Australian National University
"... We specify the operational semantics and bisimulation relations for the finite πcalculus within a logic that contains the ∇ quantifier for encoding generic judgments and definitions for encoding fixed points. Since we restrict to the finite case, the ability of the logic to unfold fixed points allo ..."
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We specify the operational semantics and bisimulation relations for the finite πcalculus within a logic that contains the ∇ quantifier for encoding generic judgments and definitions for encoding fixed points. Since we restrict to the finite case, the ability of the logic to unfold fixed points allows this logic to be complete for both the inductive nature of operational semantics and the coinductive nature of bisimulation. The ∇ quantifier helps with the delicate issues surrounding the scope of variables within πcalculus expressions and their executions (proofs). We illustrate several merits of the logical specifications permitted by this logic: they are natural and declarative; they contain no sideconditions concerning names of variables while maintaining a completely formal treatment of such variables; differences between late and open bisimulation relations arise from familar logic distinctions; the interplay between the three quantifiers (∀, ∃, and ∇) and their scopes can explain the differences between early and late bisimulation and between various modal operators based on bound input and output actions; and proof search involving the application of inference rules, unification, and backtracking can provide complete proof systems for onestep transitions, bisimulation, and satisfaction in modal logic. We also illustrate how one can encode
MFPS 2012 Nominal SOS
"... Plotkin’s style of Structural Operational Semantics (SOS) has become a de facto standard in giving operational semantics to formalisms and process calculi. In many such formalisms and calculi, the concepts of names, variables and binders are essential ingredients. In this paper, we propose a formal ..."
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Plotkin’s style of Structural Operational Semantics (SOS) has become a de facto standard in giving operational semantics to formalisms and process calculi. In many such formalisms and calculi, the concepts of names, variables and binders are essential ingredients. In this paper, we propose a formal framework for dealing with names in SOS. The framework is based on the Nominal Logic of Gabbay and Pitts and hence is called Nominal SOS. We define nominal bisimilarity, an adaptation of the notion of bisimilarity that is aware of binding. We provide evidence of the expressiveness of the framework by formulating the early πcalculus and Abramsky’s lazy λcalculus within Nominal SOS. For both calculi we establish the operational correspondence with the original calculi. Moreover, in the context of the πcalculus, we prove that nominal bisimilarity coincides with Sangiorgi’s open bisimilarity and in the context of the λcalculus we prove that nominal bisimilarity coincides with Abramsky’s applicative bisimilarity. Keywords: SOS, Nominal SOS, Nominal calculi, λcalculus, πcalculus.
Characterizing contextual equivalence in calculi with passivation
 INFORMATION AND COMPUTATION
, 2011
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