3 Search Results for "Vial, Pierre"

Document

DOI: 10.4230/LIPIcs.FSCD.2024.29

Böhm and Taylor for All!

Authors: Aloÿs Dufour and Damiano Mazza

Published in: LIPIcs, Volume 299, 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)

Abstract

Böhm approximations, used in the definition of Böhm trees, are a staple of the semantics of the lambda-calculus. Introduced more recently by Ehrhard and Regnier, Taylor approximations provide a quantitative account of the behavior of programs and are well-known to be connected to intersection types. The key relation between these two notions of approximations is a commutation theorem, roughly stating that Taylor approximations of Böhm trees are the same as Böhm trees of Taylor approximations. Böhm and Taylor approximations are available for several variants or extensions of the lambda-calculus and, in some cases, commutation theorems are known. In this paper, we define Böhm and Taylor approximations and prove the commutation theorem in a very general setting. We also introduce (non-idempotent) intersection types at this level of generality. From this, we show how the commutation theorem and intersection types may be applied to any calculus embedding in a sufficiently nice way into our general calculus. All known Böhm-Taylor commutation theorems, as well as new ones, follow by this uniform construction.

Cite as

Aloÿs Dufour and Damiano Mazza. Böhm and Taylor for All!. In 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 299, pp. 29:1-29:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{dufour_et_al:LIPIcs.FSCD.2024.29,
  author =	{Dufour, Alo\"{y}s and Mazza, Damiano},
  title =	{{B\"{o}hm and Taylor for All!}},
  booktitle =	{9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)},
  pages =	{29:1--29:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-323-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{299},
  editor =	{Rehof, Jakob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2024.29},
  URN =		{urn:nbn:de:0030-drops-203582},
  doi =		{10.4230/LIPIcs.FSCD.2024.29},
  annote =	{Keywords: Linear logic, Differential linear logic, Taylor expansion of lambda-terms, B\"{o}hm trees, Process calculi}
}

Document

DOI: 10.4230/LIPIcs.FSCD.2019.33

Sequence Types for Hereditary Permutators

Authors: Pierre Vial

Published in: LIPIcs, Volume 131, 4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019)

Abstract

The invertible terms in Scott’s model D_infty are known as the hereditary permutators. Equivalently, they are terms which are invertible up to beta eta-conversion with respect to the composition of the lambda-terms. Finding a type-theoretic characterization to the set of hereditary permutators was problem # 20 of TLCA list of problems. In 2008, Tatsuta proved that this was not possible with an inductive type system. Building on previous work, we use an infinitary intersection type system based on sequences (i.e., families of types indexed by integers) to characterize hereditary permutators with a unique type. This gives a positive answer to the problem in the coinductive case.

Cite as

Pierre Vial. Sequence Types for Hereditary Permutators. In 4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 131, pp. 33:1-33:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{vial:LIPIcs.FSCD.2019.33,
  author =	{Vial, Pierre},
  title =	{{Sequence Types for Hereditary Permutators}},
  booktitle =	{4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019)},
  pages =	{33:1--33:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-107-8},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{131},
  editor =	{Geuvers, Herman},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2019.33},
  URN =		{urn:nbn:de:0030-drops-105404},
  doi =		{10.4230/LIPIcs.FSCD.2019.33},
  annote =	{Keywords: hereditary permutators, B\"{o}hm trees, intersection types, coinduction, ridigity, sequence types, non-idempotent intersection}
}

Document

DOI: 10.4230/LIPIcs.FSCD.2017.24

Types as Resources for Classical Natural Deduction

Authors: Delia Kesner and Pierre Vial

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

Abstract

We define two resource aware typing systems for the lambda-mu-calculus based on non-idempotent intersection and union types. The non-idempotent approach provides very simple combinatorial arguments - based on decreasing measures of type derivations - to characterize head and strongly normalizing terms. Moreover, typability provides upper bounds for the length of head-reduction sequences and maximal reduction sequences.

Cite as

Delia Kesner and Pierre Vial. Types as Resources for Classical Natural Deduction. In 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 84, pp. 24:1-24:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{kesner_et_al:LIPIcs.FSCD.2017.24,
  author =	{Kesner, Delia and Vial, Pierre},
  title =	{{Types as  Resources for Classical Natural Deduction}},
  booktitle =	{2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)},
  pages =	{24:1--24:17},
  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.2017.24},
  URN =		{urn:nbn:de:0030-drops-77135},
  doi =		{10.4230/LIPIcs.FSCD.2017.24},
  annote =	{Keywords: lambda-mu-calculus, classical logic, intersection types, normalization}
}

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