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19
About permutation algebras, (pre)sheaves and named sets
 In Higher Order and Symbolic Computation
, 2006
"... Abstract. In this paper, we survey some wellknown approaches proposed as general models for calculi dealing with names (like e.g. process calculi with namepassing). We focus on (pre)sheaf categories, nominal sets, permutation algebras and named sets. We study the relationships among these models, w ..."
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Cited by 20 (4 self)
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Abstract. In this paper, we survey some wellknown approaches proposed as general models for calculi dealing with names (like e.g. process calculi with namepassing). We focus on (pre)sheaf categories, nominal sets, permutation algebras and named sets. We study the relationships among these models, which allow for transferring techniques and constructions from one model to the other.
Bialgebraic Methods and Modal Logic in Structural Operational Semantics
 Electronic Notes in Theoretical Computer Science
, 2007
"... Bialgebraic semantics, invented a decade ago by Turi and Plotkin, is an approach to formal reasoning about wellbehaved structural operational semantics (SOS). An extension of algebraic and coalgebraic methods, it abstracts from concrete notions of syntax and system behaviour, thus treating various ..."
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Cited by 14 (3 self)
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Bialgebraic semantics, invented a decade ago by Turi and Plotkin, is an approach to formal reasoning about wellbehaved structural operational semantics (SOS). An extension of algebraic and coalgebraic methods, it abstracts from concrete notions of syntax and system behaviour, thus treating various kinds of operational descriptions in a uniform fashion. In this paper, bialgebraic semantics is combined with a coalgebraic approach to modal logic in a novel, general approach to proving the compositionality of process equivalences for languages defined by structural operational semantics. To prove compositionality, one provides a notion of behaviour for logical formulas, and defines an SOSlike specification of modal operators which reflects the original SOS specification of the language. This approach can be used to define SOS congruence formats as well as to prove compositionality for specific languages and equivalences. Key words: structural operational semantics, coalgebra, bialgebra, modal logic, congruence format 1
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 14 (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
Processes as formal power series: a coinductive approach to denotational semantics
 TCS
, 2006
"... We characterize must testing equivalence on CSP in terms of the unique homomorphism from the Moore automaton of CSP processes to the final Moore automaton of partial formal power series over a certain semiring. The final automaton is then turned into a CSPalgebra: operators and fixpoints are define ..."
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Cited by 12 (1 self)
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We characterize must testing equivalence on CSP in terms of the unique homomorphism from the Moore automaton of CSP processes to the final Moore automaton of partial formal power series over a certain semiring. The final automaton is then turned into a CSPalgebra: operators and fixpoints are defined, respectively, via behavioural differential equations and simulation relations. This structure is then shown to be preserved by the final homomorphism. As a result, we obtain a fully abstract compositional model of CSP phrased in purely settheoretical terms.
Symmetries, local names and dynamic (de)allocation of names
 Information and Computation
"... The semantics of namepassing calculi is often defined employing coalgebraic models over presheaf categories. This elegant theory lacks finiteness properties, hence it is not apt to implementation. Coalgebras over named sets, called historydependent automata, are better suited for the purpose due t ..."
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Cited by 9 (3 self)
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The semantics of namepassing calculi is often defined employing coalgebraic models over presheaf categories. This elegant theory lacks finiteness properties, hence it is not apt to implementation. Coalgebras over named sets, called historydependent automata, are better suited for the purpose due to locality of names. A theory of behavioural functors for named sets is still lacking: the semantics of each language has been given in an adhoc way, and algorithms were implemented only for the picalculus. Existence of the final coalgebra for the picalculus was never proved. We introduce a language of accessible functors to specify historydependent automata in a modular way, leading to a clean formulation and a generalisation of previous results, and to the proof of existence of a final coalgebra in a wide range of cases. 1
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 9 (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.
Generalized Coiteration Schemata
, 2003
"... Coiterative functions can be explained categorically as final coalgebraic morphisms, once coinductive types are viewed as final coalgebras. However, the coiteration schema which arises in this way is too rigid to accommodate directly many interesting classes of circular specifications. In this paper ..."
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Cited by 9 (0 self)
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Coiterative functions can be explained categorically as final coalgebraic morphisms, once coinductive types are viewed as final coalgebras. However, the coiteration schema which arises in this way is too rigid to accommodate directly many interesting classes of circular specifications. In this paper, building on the notion of T coiteration introduced by the third author and capitalizing on recent work on bialgebras by TuriPlotkin and Bartels, we introduce and illustrate various generalized coiteration patterns. First we show that, by choosing the appropriate monad T , T coiteration captures naturally a wide range of coiteration schemata, such as the duals of primitive recursion and courseofvalue iteration, and mutual coiteration. Then we show that, in the more structured categorical setting of bialgebras, T coiteration captures guarded coiterations schemata, i.e. specifications where recursive calls appear guarded by predefined algebraic operations.
Modeling Fresh Names in the πcalculus Using Abstractions
, 2004
"... In this paper, we model fresh names in the #calculus using abstractions with respect to a new binding operator #. Both the theory and the metatheory of the #calculus benefit from this simple extension. The operational semantics of this new calculus is finitely branching. Bisimulation can be given ..."
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Cited by 2 (0 self)
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In this paper, we model fresh names in the #calculus using abstractions with respect to a new binding operator #. Both the theory and the metatheory of the #calculus benefit from this simple extension. The operational semantics of this new calculus is finitely branching. Bisimulation can be given without mentioning any constraint on names, thus allowing for a straightforward definition of a coalgebraic semantics, within a category of coalgebras over permutation algebras. Following previous work by Montanari and Pistore, we present also a finite representation for finitary processes and a finite state verification procedure for bisimilarity, based on the new notion of #automaton.
Comparing HigherOrder Encodings in Logical Frameworks and Tile Logic
, 2001
"... In recent years, logical frameworks and tile logic have been separately proposed by our research groups, respectively in Udine and in Pisa, as suitable metalanguages with higherorder features for encoding and studying nominal calculi. This paper discusses the main features of the two approaches, tr ..."
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Cited by 1 (1 self)
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In recent years, logical frameworks and tile logic have been separately proposed by our research groups, respectively in Udine and in Pisa, as suitable metalanguages with higherorder features for encoding and studying nominal calculi. This paper discusses the main features of the two approaches, tracing di#erences and analogies on the basis of two case studies: late #calculus and lazy simply typed #calculus.