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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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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.
Information and Computation 207 (2009) 258–283 Contents lists available at ScienceDirect
"... Information and Computation journal homepage: www.elsevier.com/locate/ic ..."
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Bialgebraic Operational Semantics and Modal Logic (extended abstract)
"... A novel, general approach is proposed to proving the compositionality of process equivalences on languages defined by Structural Operational Semantics (SOS). The approach, based on modal logic, is inspired by the simple observation that if the set of formulas satisfied by a process can be derived fr ..."
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A novel, general approach is proposed to proving the compositionality of process equivalences on languages defined by Structural Operational Semantics (SOS). The approach, based on modal logic, is inspired by the simple observation that if the set of formulas satisfied by a process can be derived from the corresponding sets for its subprocesses, then the logical equivalence is a congruence. Striving for generality, SOS rules are modeled categorically as bialgebraic distributive laws for some notions of process syntax and behaviour, and modal logics are modeled via coalgebraic polyadic modal logic. Compositionality is proved by providing a suitable notion of behaviour for the logic together with a dual distributive law, reflecting the one modeling the SOS specification. Concretely, the dual laws may appear as SOSlike rules where logical formulas play the role of processes, and their behaviour models logical decomposition over process syntax. The approach can be used either to proving compositionality for specific languages or for defining SOS congruence formats.
Biinductive Structural Semantics (Extended Abstract)
"... We propose a simple ordertheoretic generalization of settheoretic inductive definitions. This generalization covers inductive, coinductive and biinductive definitions and is preserved by abstraction. This allows the structural operational semantics to describe simultaneously the finite/terminati ..."
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We propose a simple ordertheoretic generalization of settheoretic inductive definitions. This generalization covers inductive, coinductive and biinductive definitions and is preserved by abstraction. This allows the structural operational semantics to describe simultaneously the finite/terminating and infinite/diverging behaviors of programs. This is illustrated on the structural bifinitary small/bigstep trace/relational/operational semantics of the callbyvalue λcalculus.
SOS 2007 Preliminary Version Biinductive Structural Semantics
"... We propose a simple ordertheoretic generalization of settheoretic inductive de nitions. This generalization covers inductive, coinductive and biinductive de nitions and is preserved by abstraction. This allows the structural operational semantics to describe simultaneously the nite/terminating a ..."
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We propose a simple ordertheoretic generalization of settheoretic inductive de nitions. This generalization covers inductive, coinductive and biinductive de nitions and is preserved by abstraction. This allows the structural operational semantics to describe simultaneously the nite/terminating and innite/diverging behaviors of programs. This is illustrated on the structural bi nitary small/bigstep trace/relational/operational semantics of the callbyvalue λcalculus.