4 Search Results for "Hondet, Gabriel"

Document
DOI: 10.4230/LIPIcs.CSL.2026.39
A Canonical Form for Universe Levels in Impredicative Type Theory

Authors: Yoan Géran

Published in: LIPIcs, Volume 363, 34th EACSL Annual Conference on Computer Science Logic (CSL 2026)

Abstract
The 0-imax-successor algebra, where imax: ℕ × ℕ → ℕ is the function defined by imax(n, 0) = 0 and imax(n, S(m)) = max(n, S(m)), is used to represent universe levels in impredicative type theory, in particular with universe polymorphism which introduces level variables, so it is present in proof systems such as Rocq and Lean. In particular, we need to know when two elements of this algebra are equivalent, and we may also want to decide the inequality. In this article, we introduce a canonical form for the terms of this algebra, and we provide a canonization algorithm. It permits deciding level equivalence by checking the canonical form equality, and also permits easily checking if a level is smaller than another one.
Cite as

Yoan Géran. A Canonical Form for Universe Levels in Impredicative Type Theory. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 39:1-39:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{geran:LIPIcs.CSL.2026.39,
  author =	{G\'{e}ran, Yoan},
  title =	{{A Canonical Form for Universe Levels in Impredicative Type Theory}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{39:1--39:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-411-6},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{363},
  editor =	{Guerrini, Stefano and K\"{o}nig, Barbara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2026.39},
  URN =		{urn:nbn:de:0030-drops-254640},
  doi =		{10.4230/LIPIcs.CSL.2026.39},
  annote =	{Keywords: universe levels, canonical form, impredicativity, imax algebra}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2021.20
Some Axioms for Mathematics

Authors: Frédéric Blanqui, Gilles Dowek, Émilie Grienenberger, Gabriel Hondet, and François Thiré

Published in: LIPIcs, Volume 195, 6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021)

Abstract
The λΠ-calculus modulo theory is a logical framework in which many logical systems can be expressed as theories. We present such a theory, the theory {U}, where proofs of several logical systems can be expressed. Moreover, we identify a sub-theory of {U} corresponding to each of these systems, and prove that, when a proof in {U} uses only symbols of a sub-theory, then it is a proof in that sub-theory.
Cite as

Frédéric Blanqui, Gilles Dowek, Émilie Grienenberger, Gabriel Hondet, and François Thiré. Some Axioms for Mathematics. In 6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 195, pp. 20:1-20:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{blanqui_et_al:LIPIcs.FSCD.2021.20,
  author =	{Blanqui, Fr\'{e}d\'{e}ric and Dowek, Gilles and Grienenberger, \'{E}milie and Hondet, Gabriel and Thir\'{e}, Fran\c{c}ois},
  title =	{{Some Axioms for Mathematics}},
  booktitle =	{6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021)},
  pages =	{20:1--20:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-191-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{195},
  editor =	{Kobayashi, Naoki},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2021.20},
  URN =		{urn:nbn:de:0030-drops-142581},
  doi =		{10.4230/LIPIcs.FSCD.2021.20},
  annote =	{Keywords: logical framework, axiomatic theory, dependent types, rewriting, interoperabilty}
}
Document
DOI: 10.4230/LIPIcs.TYPES.2020.6
Encoding of Predicate Subtyping with Proof Irrelevance in the λΠ-Calculus Modulo Theory

Authors: Gabriel Hondet and Frédéric Blanqui

Published in: LIPIcs, Volume 188, 26th International Conference on Types for Proofs and Programs (TYPES 2020)

Abstract
The λΠ-calculus modulo theory is a logical framework in which various logics and type systems can be encoded, thus helping the cross-verification and interoperability of proof systems based on those logics and type systems. In this paper, we show how to encode predicate subtyping and proof irrelevance, two important features of the PVS proof assistant. We prove that this encoding is correct and that encoded proofs can be mechanically checked by Dedukti, a type checker for the λΠ-calculus modulo theory using rewriting.
Cite as

Gabriel Hondet and Frédéric Blanqui. Encoding of Predicate Subtyping with Proof Irrelevance in the λΠ-Calculus Modulo Theory. In 26th International Conference on Types for Proofs and Programs (TYPES 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 188, pp. 6:1-6:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{hondet_et_al:LIPIcs.TYPES.2020.6,
  author =	{Hondet, Gabriel and Blanqui, Fr\'{e}d\'{e}ric},
  title =	{{Encoding of Predicate Subtyping with Proof Irrelevance in the \lambda\Pi-Calculus Modulo Theory}},
  booktitle =	{26th International Conference on Types for Proofs and Programs (TYPES 2020)},
  pages =	{6:1--6:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-182-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{188},
  editor =	{de'Liguoro, Ugo and Berardi, Stefano and Altenkirch, Thorsten},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2020.6},
  URN =		{urn:nbn:de:0030-drops-138853},
  doi =		{10.4230/LIPIcs.TYPES.2020.6},
  annote =	{Keywords: Predicate Subtyping, Logical Framework, PVS, Dedukti, Proof Irrelevance}
}
Document
System Description
DOI: 10.4230/LIPIcs.FSCD.2020.35
The New Rewriting Engine of Dedukti (System Description)

Authors: Gabriel Hondet and Frédéric Blanqui

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

Abstract
Dedukti is a type-checker for the λΠ-calculus modulo rewriting, an extension of Edinburgh’s logical framework LF where functions and type symbols can be defined by rewrite rules. It therefore contains an engine for rewriting LF terms and types according to the rewrite rules given by the user. A key component of this engine is the matching algorithm to find which rules can be fired. In this paper, we describe the class of rewrite rules supported by Dedukti and the new implementation of the matching algorithm. Dedukti supports non-linear rewrite rules on terms with binders using higher-order pattern-matching as in Combinatory Reduction Systems (CRS). The new matching algorithm extends the technique of decision trees introduced by Luc Maranget in the OCaml compiler to this more general context.
Cite as

Gabriel Hondet and Frédéric Blanqui. The New Rewriting Engine of Dedukti (System Description). In 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 167, pp. 35:1-35:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{hondet_et_al:LIPIcs.FSCD.2020.35,
  author =	{Hondet, Gabriel and Blanqui, Fr\'{e}d\'{e}ric},
  title =	{{The New Rewriting Engine of Dedukti}},
  booktitle =	{5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)},
  pages =	{35:1--35:16},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2020.35},
  URN =		{urn:nbn:de:0030-drops-123577},
  doi =		{10.4230/LIPIcs.FSCD.2020.35},
  annote =	{Keywords: rewriting, higher-order pattern-matching, decision trees}
}
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