4 Search Results for "Néron, Pierre"


Document
Bel-Games: A Formal Theory of Games of Incomplete Information Based on Belief Functions in the Coq Proof Assistant

Authors: Pierre Pomeret-Coquot, Hélène Fargier, and Érik Martin-Dorel

Published in: LIPIcs, Volume 268, 14th International Conference on Interactive Theorem Proving (ITP 2023)


Abstract
Decision theory and game theory are both interdisciplinary domains that focus on modelling and {analyzing} decision-making processes. On the one hand, decision theory aims to account for the possible behaviors of an agent with respect to an uncertain situation. It thus provides several frameworks to describe the decision-making processes in this context, including that of belief functions. On the other hand, game theory focuses on multi-agent decisions, typically with probabilistic uncertainty (if any), hence the so-called class of Bayesian games. In this paper, we use the Coq/SSReflect proof assistant to formally prove the results we obtained in [Pierre Pomeret{-}Coquot et al., 2022]. First, we formalize a general theory of belief functions with finite support, and structures and solutions concepts from game theory. On top of that, we extend Bayesian games to the theory of belief functions, so that we obtain a more expressive class of games we refer to as Bel games; it makes it possible to better capture human behaviors with respect to lack of information. Next, we provide three different proofs of an extended version of the so-called Howson-Rosenthal’s theorem, showing that Bel games can be casted into games of complete information, i.e., without any uncertainty. We thus embed this class of games into classical game theory, enabling the use of existing algorithms.

Cite as

Pierre Pomeret-Coquot, Hélène Fargier, and Érik Martin-Dorel. Bel-Games: A Formal Theory of Games of Incomplete Information Based on Belief Functions in the Coq Proof Assistant. In 14th International Conference on Interactive Theorem Proving (ITP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 268, pp. 25:1-25:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{pomeretcoquot_et_al:LIPIcs.ITP.2023.25,
  author =	{Pomeret-Coquot, Pierre and Fargier, H\'{e}l\`{e}ne and Martin-Dorel, \'{E}rik},
  title =	{{Bel-Games: A Formal Theory of Games of Incomplete Information Based on Belief Functions in the Coq Proof Assistant}},
  booktitle =	{14th International Conference on Interactive Theorem Proving (ITP 2023)},
  pages =	{25:1--25:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-284-6},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{268},
  editor =	{Naumowicz, Adam and Thiemann, Ren\'{e}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2023.25},
  URN =		{urn:nbn:de:0030-drops-184001},
  doi =		{10.4230/LIPIcs.ITP.2023.25},
  annote =	{Keywords: Game of Incomplete Information, Belief Function Theory, Coq Proof Assistant, SSReflect Proof Language, MathComp Library}
}
Document
Confluence of Prefix-Constrained Rewrite Systems

Authors: Nirina Andrianarivelo and Pierre Réty

Published in: LIPIcs, Volume 108, 3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018)


Abstract
Prefix-constrained rewriting is a strict extension of context-sensitive rewriting. We study the confluence of prefix-constrained rewrite systems, which are composed of rules of the form L: l -> r where L is a regular string language that defines the allowed rewritable positions. The usual notion of Knuth-Bendix's critical pair needs to be extended using regular string languages, and the convergence of all critical pairs is not enough to ensure local confluence. Thanks to an additional restriction we get local confluence, and then confluence for terminating systems, which makes the word problem decidable. Moreover we present an extended Knuth-Bendix completion procedure, to transform a non-confluent prefix-constrained rewrite system into a confluent one.

Cite as

Nirina Andrianarivelo and Pierre Réty. Confluence of Prefix-Constrained Rewrite Systems. In 3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 108, pp. 6:1-6:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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@InProceedings{andrianarivelo_et_al:LIPIcs.FSCD.2018.6,
  author =	{Andrianarivelo, Nirina and R\'{e}ty, Pierre},
  title =	{{Confluence of Prefix-Constrained Rewrite Systems}},
  booktitle =	{3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018)},
  pages =	{6:1--6:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-077-4},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{108},
  editor =	{Kirchner, H\'{e}l\`{e}ne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2018.6},
  URN =		{urn:nbn:de:0030-drops-91762},
  doi =		{10.4230/LIPIcs.FSCD.2018.6},
  annote =	{Keywords: prefix-constrained term rewriting, confluence, critical pair}
}
Document
Counting Environments and Closures

Authors: Maciej Bendkowski and Pierre Lescanne

Published in: LIPIcs, Volume 108, 3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018)


Abstract
Environments and closures are two of the main ingredients of evaluation in lambda-calculus. A closure is a pair consisting of a lambda-term and an environment, whereas an environment is a list of lambda-terms assigned to free variables. In this paper we investigate some dynamic aspects of evaluation in lambda-calculus considering the quantitative, combinatorial properties of environments and closures. Focusing on two classes of environments and closures, namely the so-called plain and closed ones, we consider the problem of their asymptotic counting and effective random generation. We provide an asymptotic approximation of the number of both plain environments and closures of size n. Using the associated generating functions, we construct effective samplers for both classes of combinatorial structures. Finally, we discuss the related problem of asymptotic counting and random generation of closed environments and closures.

Cite as

Maciej Bendkowski and Pierre Lescanne. Counting Environments and Closures. In 3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 108, pp. 11:1-11:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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@InProceedings{bendkowski_et_al:LIPIcs.FSCD.2018.11,
  author =	{Bendkowski, Maciej and Lescanne, Pierre},
  title =	{{Counting Environments and Closures}},
  booktitle =	{3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018)},
  pages =	{11:1--11:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-077-4},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{108},
  editor =	{Kirchner, H\'{e}l\`{e}ne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2018.11},
  URN =		{urn:nbn:de:0030-drops-91817},
  doi =		{10.4230/LIPIcs.FSCD.2018.11},
  annote =	{Keywords: lambda-calculus, combinatorics, functional programming, mathematical analysis, complexity}
}
Document
Scopes Describe Frames: A Uniform Model for Memory Layout in Dynamic Semantics

Authors: Casper Bach Poulsen, Pierre Néron, Andrew Tolmach, and Eelco Visser

Published in: LIPIcs, Volume 56, 30th European Conference on Object-Oriented Programming (ECOOP 2016)


Abstract
Semantic specifications do not make a systematic connection between the names and scopes in the static structure of a program and memory layout, and access during its execution. In this paper, we introduce a systematic approach to the alignment of names in static semantics and memory in dynamic semantics, building on the scope graph framework for name resolution. We develop a uniform memory model consisting of frames that instantiate the scopes in the scope graph of a program. This provides a language-independent correspondence between static scopes and run-time memory layout, and between static resolution paths and run-time memory access paths. The approach scales to a range of binding features, supports straightforward type soundness proofs, and provides the basis for a language-independent specification of sound reachability-based garbage collection.

Cite as

Casper Bach Poulsen, Pierre Néron, Andrew Tolmach, and Eelco Visser. Scopes Describe Frames: A Uniform Model for Memory Layout in Dynamic Semantics. In 30th European Conference on Object-Oriented Programming (ECOOP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 56, pp. 20:1-20:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


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@InProceedings{bachpoulsen_et_al:LIPIcs.ECOOP.2016.20,
  author =	{Bach Poulsen, Casper and N\'{e}ron, Pierre and Tolmach, Andrew and Visser, Eelco},
  title =	{{Scopes Describe Frames: A Uniform Model for Memory Layout in Dynamic Semantics}},
  booktitle =	{30th European Conference on Object-Oriented Programming (ECOOP 2016)},
  pages =	{20:1--20:26},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-014-9},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{56},
  editor =	{Krishnamurthi, Shriram and Lerner, Benjamin S.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2016.20},
  URN =		{urn:nbn:de:0030-drops-61140},
  doi =		{10.4230/LIPIcs.ECOOP.2016.20},
  annote =	{Keywords: Dynamic semantics, scope graphs, memory layout, type soundness, operational semantics}
}
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