3 Search Results for "Genestier, Guillaume"

Document
DOI: 10.4230/LIPIcs.FSCD.2022.24
Encoding Type Universes Without Using Matching Modulo Associativity and Commutativity

Authors: Frédéric Blanqui

Published in: LIPIcs, Volume 228, 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)

Abstract
The encoding of proof systems and type theories in logical frameworks is key to allow the translation of proofs from one system to the other. The λΠ-calculus modulo rewriting is a powerful logical framework in which various systems have already been encoded, including type systems with an infinite hierarchy of type universes equipped with a unary successor operator and a binary max operator: Matita, Coq, Agda and Lean. However, to decide the word problem in this max-successor algebra, all the encodings proposed so far use rewriting with matching modulo associativity and commutativity (AC), which is of high complexity and difficult to integrate in usual algorithms for b-reduction and type-checking. In this paper, we show that we do not need matching modulo AC by enforcing terms to be in some special canonical form wrt associativity and commutativity, and by using rewriting rules taking advantage of this canonical form. This work has been implemented in the proof assistant Lambdapi.
Cite as

Frédéric Blanqui. Encoding Type Universes Without Using Matching Modulo Associativity and Commutativity. In 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 228, pp. 24:1-24:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{blanqui:LIPIcs.FSCD.2022.24,
  author =	{Blanqui, Fr\'{e}d\'{e}ric},
  title =	{{Encoding Type Universes Without Using Matching Modulo Associativity and Commutativity}},
  booktitle =	{7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)},
  pages =	{24:1--24:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-233-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{228},
  editor =	{Felty, Amy P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2022.24},
  URN =		{urn:nbn:de:0030-drops-163059},
  doi =		{10.4230/LIPIcs.FSCD.2022.24},
  annote =	{Keywords: logical framework, type theory, type universes, rewriting}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2020.31
Encoding Agda Programs Using Rewriting

Authors: Guillaume Genestier

Published in: LIPIcs, Volume 167, 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)

Abstract
We present in this paper an encoding in an extension with rewriting of the Edimburgh Logical Framework (LF) [Harper et al., 1993] of two common features: universe polymorphism and eta-convertibility. This encoding is at the root of the translator between Agda and Dedukti developped by the author.
Cite as

Guillaume Genestier. Encoding Agda Programs Using Rewriting. In 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 167, pp. 31:1-31:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

Copy BibTex To Clipboard

@InProceedings{genestier:LIPIcs.FSCD.2020.31,
  author =	{Genestier, Guillaume},
  title =	{{Encoding Agda Programs Using Rewriting}},
  booktitle =	{5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)},
  pages =	{31:1--31:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-155-9},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{167},
  editor =	{Ariola, Zena M.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2020.31},
  URN =		{urn:nbn:de:0030-drops-123530},
  doi =		{10.4230/LIPIcs.FSCD.2020.31},
  annote =	{Keywords: Logical Frameworks, Rewriting, Universe Polymorphism, Eta Conversion}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2019.9
Dependency Pairs Termination in Dependent Type Theory Modulo Rewriting

Authors: Frédéric Blanqui, Guillaume Genestier, and Olivier Hermant

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

Abstract
Dependency pairs are a key concept at the core of modern automated termination provers for first-order term rewriting systems. In this paper, we introduce an extension of this technique for a large class of dependently-typed higher-order rewriting systems. This extends previous results by Wahlstedt on the one hand and the first author on the other hand to strong normalization and non-orthogonal rewriting systems. This new criterion is implemented in the type-checker Dedukti.
Cite as

Frédéric Blanqui, Guillaume Genestier, and Olivier Hermant. Dependency Pairs Termination in Dependent Type Theory Modulo Rewriting. In 4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 131, pp. 9:1-9:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

Copy BibTex To Clipboard

@InProceedings{blanqui_et_al:LIPIcs.FSCD.2019.9,
  author =	{Blanqui, Fr\'{e}d\'{e}ric and Genestier, Guillaume and Hermant, Olivier},
  title =	{{Dependency Pairs Termination in Dependent Type Theory Modulo Rewriting}},
  booktitle =	{4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019)},
  pages =	{9:1--9:21},
  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.2019.9},
  URN =		{urn:nbn:de:0030-drops-105167},
  doi =		{10.4230/LIPIcs.FSCD.2019.9},
  annote =	{Keywords: termination, higher-order rewriting, dependent types, dependency pairs}
}
  • Refine by Author
  • 2 Blanqui, Frédéric
  • 2 Genestier, Guillaume
  • 1 Hermant, Olivier

  • Refine by Classification
  • 3 Theory of computation → Equational logic and rewriting
  • 3 Theory of computation → Type theory
  • 1 Theory of computation → Logic

  • Refine by Keyword
  • 1 Eta Conversion
  • 1 Logical Frameworks
  • 1 Rewriting
  • 1 Universe Polymorphism
  • 1 dependency pairs
  • Show More...

  • Refine by Type
  • 3 document

  • Refine by Publication Year
  • 1 2019
  • 1 2020
  • 1 2022

Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact