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Automata with group actions
 In LICS
, 2011
"... Abstract—Our motivating question is a MyhillNerode theorem for infinite alphabets. We consider several kinds of those: alphabets whose letters can be compared only for equality, but also ones with more structure, such as a total order or a partial order. We develop a framework for studying such alp ..."
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Cited by 17 (5 self)
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Abstract—Our motivating question is a MyhillNerode theorem for infinite alphabets. We consider several kinds of those: alphabets whose letters can be compared only for equality, but also ones with more structure, such as a total order or a partial order. We develop a framework for studying such alphabets, where the key role is played by the automorphism group of the alphabet. This framework builds on the idea of nominal sets of Gabbay and Pitts; nominal sets are the special case of our framework where letters can be only compared for equality. We use the framework to uniformly generalize to infinite alphabets parts of automata theory, including decidability results. In the case of letters compared for equality, we obtain automata equivalent in expressive power to finite memory automata, as defined by Francez and Kaminski. I.
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.
Nominal renaming sets
"... Abstract. Nominal techniques are based on the idea of sets with a finitelysupported atomspermutation action. We consider the idea of nominal renaming sets, which are sets with a finitelysupported atomsrenaming action; renamings can identify atoms, permutations cannot. We show that nominal renaming ..."
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Cited by 4 (2 self)
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Abstract. Nominal techniques are based on the idea of sets with a finitelysupported atomspermutation action. We consider the idea of nominal renaming sets, which are sets with a finitelysupported atomsrenaming action; renamings can identify atoms, permutations cannot. We show that nominal renaming sets exhibit many of the useful qualities found in (permutative) nominal sets; an elementary setsbased presentation, inductive datatypes of syntax up to binding, cartesian closure, and being a topos. Unlike is the case for nominal sets, the notion of namesabstraction coincides with functional abstraction. Thus we obtain a concrete presentation of sheaves on
Automata theory in nominal sets
, 2012
"... Abstract. We study languages over infinite alphabets equipped with some structure that can be tested by recognizing automata. We develop a framework for studying such alphabets and the ensuing automata theory, where the key role is played by an automorphism group of the alphabet. In the process, we ..."
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Cited by 2 (1 self)
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Abstract. We study languages over infinite alphabets equipped with some structure that can be tested by recognizing automata. We develop a framework for studying such alphabets and the ensuing automata theory, where the key role is played by an automorphism group of the alphabet. In the process, we generalize nominal sets due to Gabbay and Pitts.
Abstract Effects and ProofRelevant Logical Relations
"... We introduce a novel variant of logical relations that maps types not merely to partial equivalence relations on values, as is commonly done, but rather to a proofrelevant generalisation thereof, namely setoids. The objects of a setoid establish that values inhabit semantic types, whilst its morph ..."
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Cited by 1 (1 self)
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We introduce a novel variant of logical relations that maps types not merely to partial equivalence relations on values, as is commonly done, but rather to a proofrelevant generalisation thereof, namely setoids. The objects of a setoid establish that values inhabit semantic types, whilst its morphisms are understood as proofs of semantic equivalence. The transition to proofrelevance solves two wellknown problems caused by the use of existential quantification over future worlds in traditional Kripke logical relations: failure of admissibility, and spurious functional dependencies. We illustrate the novel format with two applications: a directstyle validation of Pitts and Stark’s equivalences for “new” and a denotational semantics for a regionbased effect system that supports type abstraction in the sense that only externally visible effects need to be tracked; nonobservable internal modifications, such as the reorganisation of a search tree or lazy initialisation, can count as ‘pure’ or ‘read only’. This ‘fictional purity’ allows clients of a module soundly to validate more effectbased program equivalences than would be possible with traditional effect systems.
Full Abstraction for Nominal Scott Domains
"... We develop a domain theory within nominal sets and present programming language constructs and results that can be gained from this approach. The development is based on the concept of orbitfinite subset, that is, a subset of a nominal sets that is both finitely supported and contained in finitely m ..."
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We develop a domain theory within nominal sets and present programming language constructs and results that can be gained from this approach. The development is based on the concept of orbitfinite subset, that is, a subset of a nominal sets that is both finitely supported and contained in finitely many orbits. This concept appears prominently in the recent research programme of Bojańczyk et al. on automata over infinite languages, and our results establish a connection between their work and a characterisation of topological compactness discovered, in a quite different setting, by Winskel and Turner as part of a nominal domain theory for concurrency. We use this connection to derive a notion of Scott domain within nominal sets. The functionals for existential quantification over names and ‘definite description ’ over names turn out to be compact in the sense appropriate for nominal Scott domains. Adding them, together with parallelor, to a programming language for recursively defined higherorder functions with name abstraction and locally scoped names, we prove a full abstraction result for nominal Scott domains analogous to Plotkin’s classic result about PCF and conventional Scott domains: two program phrases have the same observable operational behaviour in all contexts if and only if they denote equal elements of the nominal Scott domain model. This is the first full abstraction result we know of for higherorder functions with local names that uses a domain theory based on ordinary extensional functions, rather than using the more intensional approach of game semantics.
MFPS 2008 A categorical model of the Fusion calculus
"... We provide a categorical presentation of the Fusion calculus. Working in a suitable category of presheaves, we describe the syntax as initial algebra of a signature endofunctor, and the semantics as coalgebras of a “behaviour ” endofunctor. To this end, we first give a new, congruencefree presentat ..."
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We provide a categorical presentation of the Fusion calculus. Working in a suitable category of presheaves, we describe the syntax as initial algebra of a signature endofunctor, and the semantics as coalgebras of a “behaviour ” endofunctor. To this end, we first give a new, congruencefree presentation of the Fusion calculus; then, the behaviour endofunctor is constructed by adding in a systematic way a notion of “state ” to the intuitive endofunctor induced by the LTS. Coalgebras can be given a concrete presentation as “stateful indexed labelled transition systems”; the bisimilarity over these systems is a congruence, and corresponds to hyperequivalence. Then, we model the labelled transition system of Fusion by as abstract categorical rules. As a consequence, we get a semantics for the Fusion calculus which is both compositional and fully abstract: two processes have the same semantics iff they are bisimilar, that is, hyperequivalent. 1