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Documents authored by Castellan, Simon

Document
DOI: 10.4230/LIPIcs.MFCS.2017.81
Distributed Strategies Made Easy

Authors: Simon Castellan, Pierre Clairambault, and Glynn Winskel

Published in: LIPIcs, Volume 83, 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)

Abstract
Distributed/concurrent strategies have been introduced as special maps of event structures. As such they factor through their "rigid images," themselves strategies. By concentrating on such "rigid image" strategies we are able to give an elementary account of distributed strategies and their composition, resulting in a category of games and strategies. This is in contrast to the usual development where composition involves the pullback of event structures explicitly and results in a bicategory. It is shown how, in this simpler setting, to extend strategies to probabilistic strategies; and indicated how through probability we can track nondeterministic branching behaviour, that one might otherwise think lost irrevocably in restricting attention to "rigid image" strategies.
Cite as

Simon Castellan, Pierre Clairambault, and Glynn Winskel. Distributed Strategies Made Easy. In 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 83, pp. 81:1-81:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{castellan_et_al:LIPIcs.MFCS.2017.81,
  author =	{Castellan, Simon and Clairambault, Pierre and Winskel, Glynn},
  title =	{{Distributed Strategies Made Easy}},
  booktitle =	{42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)},
  pages =	{81:1--81:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-046-0},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{83},
  editor =	{Larsen, Kim G. and Bodlaender, Hans L. and Raskin, Jean-Francois},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2017.81},
  URN =		{urn:nbn:de:0030-drops-81315},
  doi =		{10.4230/LIPIcs.MFCS.2017.81},
  annote =	{Keywords: Games, Strategies, Event Structures, Probability}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2017.12
Observably Deterministic Concurrent Strategies and Intensional Full Abstraction for Parallel-or

Authors: Simon Castellan, Pierre Clairambault, and Glynn Winskel

Published in: LIPIcs, Volume 84, 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)

Abstract
Although Plotkin’s parallel-or is inherently deterministic, it has a non-deterministic interpretation in games based on (prime) event structures - in which an event has a unique causal history - because they do not directly support disjunctive causality. General event structures can express disjunctive causality and have a more permissive notion of determinism, but do not support hiding. We show that (structures equivalent to) deterministic general event structures do support hiding, and construct a new category of games based on them with a deterministic interpretation of aPCFpor, an affine variant of PCF extended with parallel-or. We then exploit this deterministic interpretation to give a relaxed notion of determinism (observable determinism) on the plain event structures model. Putting this together with our previously introduced concurrent notions of well-bracketing and innocence, we obtain an intensionally fully abstract model of aPCFpor.
Cite as

Simon Castellan, Pierre Clairambault, and Glynn Winskel. Observably Deterministic Concurrent Strategies and Intensional Full Abstraction for Parallel-or. In 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 84, pp. 12:1-12:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{castellan_et_al:LIPIcs.FSCD.2017.12,
  author =	{Castellan, Simon and Clairambault, Pierre and Winskel, Glynn},
  title =	{{Observably Deterministic Concurrent Strategies and Intensional Full Abstraction for Parallel-or}},
  booktitle =	{2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)},
  pages =	{12:1--12:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-047-7},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{84},
  editor =	{Miller, Dale},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2017.12},
  URN =		{urn:nbn:de:0030-drops-77219},
  doi =		{10.4230/LIPIcs.FSCD.2017.12},
  annote =	{Keywords: Game semantics, parallel-or, concurrent games, event structures, full abstraction}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2016.32
Causality vs. Interleavings in Concurrent Game Semantics

Authors: Simon Castellan and Pierre Clairambault

Published in: LIPIcs, Volume 59, 27th International Conference on Concurrency Theory (CONCUR 2016)

Abstract
We investigate relationships between interleaving and causal notions of game semantics for concurrent programming languages, focusing on the existence of canonical compact causal representations of the interleaving game semantics of programs. We perform our study on an affine variant of Idealized Parallel Algol (IPA), for which we present two games model: and interleaving model (an adaptation of Ghica and Murawski’s fully abstract games model for IPA up to may-testing), and a causal model (a variant of Rideau and Winskel’s games on event structures). Both models are sound and adequate for affine IPA. Then, we relate the two models. First we give a causality-forgetting operation mapping functorially the causal model to the interleaving one. We show that from an interleaving strategy we can reconstruct a causal strategy, from which it follows that the interleaving model is the observational quotient of the causal one. Then, we investigate several reconstructions of causal strategies from interleaving ones, showing finally that there are programs which are inherently causally ambiguous, with several distinct minimal causal representations.
Cite as

Simon Castellan and Pierre Clairambault. Causality vs. Interleavings in Concurrent Game Semantics. In 27th International Conference on Concurrency Theory (CONCUR 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 59, pp. 32:1-32:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{castellan_et_al:LIPIcs.CONCUR.2016.32,
  author =	{Castellan, Simon and Clairambault, Pierre},
  title =	{{Causality vs. Interleavings in Concurrent Game Semantics}},
  booktitle =	{27th International Conference on Concurrency Theory (CONCUR 2016)},
  pages =	{32:1--32:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-017-0},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{59},
  editor =	{Desharnais, Jos\'{e}e and Jagadeesan, Radha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2016.32},
  URN =		{urn:nbn:de:0030-drops-61620},
  doi =		{10.4230/LIPIcs.CONCUR.2016.32},
  annote =	{Keywords: Game semantics, concurrency, causality, event structures}
}
Document
DOI: 10.4230/LIPIcs.TLCA.2015.138
Undecidability of Equality in the Free Locally Cartesian Closed Category

Authors: Simon Castellan, Pierre Clairambault, and Peter Dybjer

Published in: LIPIcs, Volume 38, 13th International Conference on Typed Lambda Calculi and Applications (TLCA 2015)

Abstract
We show that a version of Martin-Löf type theory with extensional identity, a unit type N1, Sigma, Pi, and a base type is a free category with families (supporting these type formers) both in a 1- and a 2-categorical sense. It follows that the underlying category of contexts is a free locally cartesian closed category in a 2-categorical sense because of a previously proved biequivalence. We then show that equality in this category is undecidable by reducing it to the undecidability of convertibility in combinatory logic.
Cite as

Simon Castellan, Pierre Clairambault, and Peter Dybjer. Undecidability of Equality in the Free Locally Cartesian Closed Category. In 13th International Conference on Typed Lambda Calculi and Applications (TLCA 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 38, pp. 138-152, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{castellan_et_al:LIPIcs.TLCA.2015.138,
  author =	{Castellan, Simon and Clairambault, Pierre and Dybjer, Peter},
  title =	{{Undecidability of Equality in the Free Locally Cartesian Closed Category}},
  booktitle =	{13th International Conference on Typed Lambda Calculi and Applications (TLCA 2015)},
  pages =	{138--152},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-87-3},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{38},
  editor =	{Altenkirch, Thorsten},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TLCA.2015.138},
  URN =		{urn:nbn:de:0030-drops-51602},
  doi =		{10.4230/LIPIcs.TLCA.2015.138},
  annote =	{Keywords: Extensional type theory, locally cartesian closed categories, undecidab- ility}
}
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