28 Search Results for "Herbelin, Hugo"

Volume

LIPIcs, Volume 39

20th International Conference on Types for Proofs and Programs (TYPES 2014)

TYPES 2014, May 12-15, 2014, Paris, France

Editors: Hugo Herbelin, Pierre Letouzey, and Matthieu Sozeau

Document
DOI: 10.4230/LIPIcs.FSCD.2026.5
Not Choosing Is Still a Choice: Constructive mathematics without any choice

Authors: Martin Baillon, Yannick Forster, Dominik Kirst, Assia Mahboubi, and Pierre-Marie Pédrot

Published in: LIPIcs, Volume 378, 11th International Conference on Formal Structures for Computation and Deduction (FSCD 2026)

Abstract
The axiom of choice (AC) states that every total relation contains a function. It enjoys a pivotal role in both classical and constructive dialects of mathematics. In the former, it is seen as a useful closure property invoked especially in set-theoretic contexts, in the latter it is seen either as a tautology, following from a constructive reading of totality proofs, or as a taboo, as by an extensional reading of totality proofs it enforces full classical logic. It has therefore been debated how much of AC should be accepted in constructive foundations and authors like Richman argued for "Constructive mathematics without choice" where even countable choice, not immediately jeopardising constructive reasoning, is avoided. With this paper, we propose a continuation of Richman’s programme of more radical extent and systematically study constructive foundations absent of countable, unique, or quantifier-free choice principles as well as the spurious fragments of (the actual) AC in form of extensionality principles: "Constructive mathematics without any choice" We argue that such a minimalistic setting is advantageous, for instance for studies in constructive reverse mathematics and synthetic computability theory. Apart from these programmatic considerations and a careful encyclopedia of choice principles, we revisit and refine several results from the literature: We show that already the partition principle (a consequence of AC of unknown strength) implies the excluded middle, that already logically decidable (inductive) equality of propositions implies proof irrelevance, and that function inversion principles such as the Cantor-Bernstein theorem not only rely on the excluded middle but also on unique choice. To the best of our knowledge, the latter is the first reverse mathematics result regarding the full axiom of unique choice, enabled by our minimal setting. Implementing such a minimalistic foundation, the proofs of all our results have been mechanised with the Rocq prover.
Cite as

Martin Baillon, Yannick Forster, Dominik Kirst, Assia Mahboubi, and Pierre-Marie Pédrot. Not Choosing Is Still a Choice: Constructive mathematics without any choice. In 11th International Conference on Formal Structures for Computation and Deduction (FSCD 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 378, pp. 5:1-5:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{baillon_et_al:LIPIcs.FSCD.2026.5,
  author =	{Baillon, Martin and Forster, Yannick and Kirst, Dominik and Mahboubi, Assia and P\'{e}drot, Pierre-Marie},
  title =	{{Not Choosing Is Still a Choice: Constructive mathematics without any choice}},
  booktitle =	{11th International Conference on Formal Structures for Computation and Deduction (FSCD 2026)},
  pages =	{5:1--5:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-433-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{378},
  editor =	{Pfenning, Frank},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2026.5},
  URN =		{urn:nbn:de:0030-drops-263553},
  doi =		{10.4230/LIPIcs.FSCD.2026.5},
  annote =	{Keywords: Axiom of Choice, Constructive Mathematics, Type Theory}
}
Document
DOI: 10.4230/LIPIcs.ECOOP.2026.2
Automatic Layout of Railroad Diagrams

Authors: Shardul Chiplunkar and Clément Pit-Claudel

Published in: LIPIcs, Volume 372, 40th European Conference on Object-Oriented Programming (ECOOP 2026)

Abstract
Railroad diagrams (also called "syntax diagrams") are a common, intuitive visualization of grammars, but limited tooling and a lack of formal attention to their layout mostly confines them to hand-drawn documentation. We present the first formal treatment of railroad diagram layout along with a principled, practical implementation. We characterize the problem as compiling a diagram language (specifying conceptual components and how they connect and compose) to a layout language (specifying basic graphical shapes and their sizes and positions). We then implement a compiler that performs line wrapping to meet a target width, as well as vertical alignment and horizontal justification per user-specified policies. We frame line wrapping as optimization, where we describe principled dimensions of optimality and implement corresponding heuristics. For front-end evaluation, we show that our diagram language is well-suited for common applications by describing how regular expressions and Backus-Naur form can be compiled to it. For back-end evaluation, we argue that our compiler is practical by comparing its output to diagrams laid out by hand and by other tools.
Cite as

Shardul Chiplunkar and Clément Pit-Claudel. Automatic Layout of Railroad Diagrams. In 40th European Conference on Object-Oriented Programming (ECOOP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 372, pp. 2:1-2:31, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{chiplunkar_et_al:LIPIcs.ECOOP.2026.2,
  author =	{Chiplunkar, Shardul and Pit-Claudel, Cl\'{e}ment},
  title =	{{Automatic Layout of Railroad Diagrams}},
  booktitle =	{40th European Conference on Object-Oriented Programming (ECOOP 2026)},
  pages =	{2:1--2:31},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-423-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{372},
  editor =	{Krebbers, Robbert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2026.2},
  URN =		{urn:nbn:de:0030-drops-260982},
  doi =		{10.4230/LIPIcs.ECOOP.2026.2},
  annote =	{Keywords: syntax diagram, graph layout, line wrapping, pretty-printing}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.FSCD.2025.1
Computation First: Rebuilding Constructivism with Effects (Invited Talk)

Authors: Liron Cohen

Published in: LIPIcs, Volume 337, 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)

Abstract
Constructive logic and type theory have traditionally been grounded in pure, effect-free model of computation. This paper argues that such a restriction is not a foundational necessity but a historical artifact, and it advocates for a broader perspective of effectful constructivism, where computational effects, such as state, non-determinism, and exceptions, are directly and internally embedded in the logical and computational foundations. We begin by surveying examples where effects reshape logical principles, and then outline three approaches to effectful constructivism, focusing on realizability models: Monadic Combinatory Algebras, which extend classical partial combinatory algebras with effectful computation; Evidenced Frames, a flexible semantic structure capable of uniformly capturing a wide range of effects; and Effectful Higher-Order Logic (EffHOL), a syntactic approach that directly translates logical propositions into specifications for effectful programs. We further illustrate how concrete type theories can internalize effects, via the family of type theories TT^□_C. Together, these works demonstrate that effectful constructivism is not merely possible but a natural and robust extension of traditional frameworks.
Cite as

Liron Cohen. Computation First: Rebuilding Constructivism with Effects (Invited Talk). In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 1:1-1:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{cohen:LIPIcs.FSCD.2025.1,
  author =	{Cohen, Liron},
  title =	{{Computation First: Rebuilding Constructivism with Effects}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{1:1--1:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-374-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{337},
  editor =	{Fern\'{a}ndez, Maribel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2025.1},
  URN =		{urn:nbn:de:0030-drops-236167},
  doi =		{10.4230/LIPIcs.FSCD.2025.1},
  annote =	{Keywords: Effectful constructivism, realizability, type theory, monadic combinatory algebras, evidenced frame}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.FSCD.2025.2
Vehicle: Bridging the Embedding Gap in the Verification of Neuro-Symbolic Programs (Invited Talk)

Authors: Matthew L. Daggitt, Wen Kokke, Robert Atkey, Ekaterina Komendantskaya, Natalia Slusarz, and Luca Arnaboldi

Published in: LIPIcs, Volume 337, 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)

Abstract
Neuro-symbolic programs, i.e. programs containing both machine learning components and traditional symbolic code, are becoming increasingly widespread. Finding a general methodology for verifying such programs is challenging due to both the number of different tools involved and the intricate interface between the "neural" and "symbolic" program components. In this paper we present a general decomposition of the neuro-symbolic verification problem into parts, and examine the problem of the embedding gap that occurs when one tries to combine proofs about the neural and symbolic components. To address this problem we then introduce Vehicle - standing as an abbreviation for a "verification condition language" - an intermediate programming language interface between machine learning frameworks, automated theorem provers, and dependently-typed formalisations of neuro-symbolic programs. Vehicle allows users to specify the properties of the neural components of neuro-symbolic programs once, and then safely compile the specification to each interface using a tailored typing and compilation procedure. We give a high-level overview of Vehicle’s overall design, its interfaces and compilation & type-checking procedures, and then demonstrate its utility by formally verifying the safety of a simple autonomous car controlled by a neural network, operating in a stochastic environment with imperfect information.
Cite as

Matthew L. Daggitt, Wen Kokke, Robert Atkey, Ekaterina Komendantskaya, Natalia Slusarz, and Luca Arnaboldi. Vehicle: Bridging the Embedding Gap in the Verification of Neuro-Symbolic Programs (Invited Talk). In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 2:1-2:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{daggitt_et_al:LIPIcs.FSCD.2025.2,
  author =	{Daggitt, Matthew L. and Kokke, Wen and Atkey, Robert and Komendantskaya, Ekaterina and Slusarz, Natalia and Arnaboldi, Luca},
  title =	{{Vehicle: Bridging the Embedding Gap in the Verification of Neuro-Symbolic Programs}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{2:1--2:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-374-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{337},
  editor =	{Fern\'{a}ndez, Maribel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2025.2},
  URN =		{urn:nbn:de:0030-drops-236172},
  doi =		{10.4230/LIPIcs.FSCD.2025.2},
  annote =	{Keywords: Neural Network Verification, Types, Interactive Theorem Provers}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2025.32
Interpolation as Cut-Introduction: On the Computational Content of Craig-Lyndon Interpolation

Authors: Alexis Saurin

Published in: LIPIcs, Volume 337, 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)

Abstract
Analyzing Maehara’s method for proving Craig’s interpolation theorem, we extract a "proof relevant" interpolation theorem for first-order LL in the sense that if π is a cut-free sequent proof of A⊢ B, we can find a formula C in the common vocabulary of A and B and proofs π₁,π₂ of A⊢ C and C⊢ B respectively such that π₁ composed with π₂ cut-reduces to π. As a direct corollary, we get similar proof relevant interpolation results for LJ and LK using linear translations. This refined interpolation is then rephrased in terms of a cut-introduction process synthetizing the interpolant. Finally, we analyze the computational content of interpolation by proving an interpolation result for Curien and Herbelin’s Duality of Computation.
Cite as

Alexis Saurin. Interpolation as Cut-Introduction: On the Computational Content of Craig-Lyndon Interpolation. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 32:1-32:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{saurin:LIPIcs.FSCD.2025.32,
  author =	{Saurin, Alexis},
  title =	{{Interpolation as Cut-Introduction: On the Computational Content of Craig-Lyndon Interpolation}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{32:1--32:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-374-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{337},
  editor =	{Fern\'{a}ndez, Maribel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2025.32},
  URN =		{urn:nbn:de:0030-drops-236478},
  doi =		{10.4230/LIPIcs.FSCD.2025.32},
  annote =	{Keywords: Classical Logic, Interpolation, Cut Elimination, Linear Logic, Sequent calculus, System L}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2025.27
What Does It Take to Certify a Conversion Checker?

Authors: Meven Lennon-Bertrand

Published in: LIPIcs, Volume 337, 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)

Abstract
We report on a detailed exploration of the properties of conversion (definitional equality) in dependent type theory, with the goal of certifying decision procedures for it. While in that context the property of normalisation has attracted the most light, we instead emphasize the importance of injectivity properties, showing that they alone are both crucial and sufficient to certify most desirable properties of conversion checkers. We also explore the certification of a fully untyped conversion checker, with respect to a typed specification, and show that the story is mostly unchanged, although the exact injectivity properties needed are subtly different.
Cite as

Meven Lennon-Bertrand. What Does It Take to Certify a Conversion Checker?. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 27:1-27:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{lennonbertrand:LIPIcs.FSCD.2025.27,
  author =	{Lennon-Bertrand, Meven},
  title =	{{What Does It Take to Certify a Conversion Checker?}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{27:1--27:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-374-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{337},
  editor =	{Fern\'{a}ndez, Maribel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2025.27},
  URN =		{urn:nbn:de:0030-drops-236428},
  doi =		{10.4230/LIPIcs.FSCD.2025.27},
  annote =	{Keywords: Dependent types, Bidirectional typing, Certified software}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2025.29
Linear Logic Using Negative Connectives

Authors: Dale Miller

Published in: LIPIcs, Volume 337, 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)

Abstract
In linear logic, the invertibility of a connective’s right-introduction rule is equivalent to the non-invertibility of its left-introduction rule. This duality motivates the concept of polarity: a connective is termed negative if its right-introduction rule is invertible, and positive otherwise. A two-sided sequent calculus for first-order linear logic featuring only negative connectives exhibits a compelling proof theory. Proof search in such a system unfolds through alternating phases of invertible (right-introduction) rules and non-invertible (left-introduction) rules, mirroring the processes of goal-reduction and backchaining, respectively. These phases are formalized here using the framework of multifocused proofs. We analyze linear logic by dissecting it into three sublogics: L₀ (first-order intuitionistic logic with conjunction, implication, and universal quantification); L₁ (an extension of L₀ incorporating linear implication which preserves its intuitionistic nature); and L₂ (which includes multiplicative falsity ⊥ and encompasses classical linear logic). It is worth noting that the single-conclusion restriction on sequents, a constraint imposed by Gentzen, is not a prerequisite for defining intuitionistic logic proofs within this framework, as it emerges naturally by restricting the formulas to those of L₀ and L₁. While multifocused proofs of L₂ sequents can accommodate parallel applications of left-introduction rules, proofs of L₀ and L₁ sequents cannot leverage such parallel rule applications. This notion of parallelism within proofs enables a novel approach to handling disjunctions and existential quantifiers in the natural deduction system for intuitionistic logic.
Cite as

Dale Miller. Linear Logic Using Negative Connectives. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 29:1-29:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{miller:LIPIcs.FSCD.2025.29,
  author =	{Miller, Dale},
  title =	{{Linear Logic Using Negative Connectives}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{29:1--29:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-374-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{337},
  editor =	{Fern\'{a}ndez, Maribel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2025.29},
  URN =		{urn:nbn:de:0030-drops-236442},
  doi =		{10.4230/LIPIcs.FSCD.2025.29},
  annote =	{Keywords: Linear logic, multifocused proofs, sequent calculus}
}
Document
DOI: 10.4230/LIPIcs.CSL.2025.32
A Mixed Linear and Graded Logic: Proofs, Terms, and Models

Authors: Victoria Vollmer, Danielle Marshall, Harley Eades III, and Dominic Orchard

Published in: LIPIcs, Volume 326, 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)

Abstract
Graded modal logics generalise standard modal logics via families of modalities indexed by an algebraic structure whose operations mediate between the different modalities. The graded "of-course" modality !_r captures how many times a proposition is used and has an analogous interpretation to the of-course modality from linear logic; the of-course modality from linear logic can be modelled by a linear exponential comonad and graded of-course can be modelled by a graded linear exponential comonad. Benton showed in his seminal paper on Linear/Non-Linear logic that the of-course modality can be split into two modalities connecting intuitionistic logic with linear logic, forming a symmetric monoidal adjunction. Later, Fujii et al. demonstrated that every graded comonad can be decomposed into an adjunction and a "strict action". We give a similar result to Benton, leveraging Fujii et al.’s decomposition, showing that graded modalities can be split into two modalities connecting a graded logic with a graded linear logic. We propose a sequent calculus, its proof theory and categorical model, and a natural deduction system which we show is isomorphic to the sequent calculus system. Interestingly, our system can also be understood as Linear/Non-Linear logic composed with an action that adds the grading, further illuminating the shared principles between linear logic and a class of graded modal logics.
Cite as

Victoria Vollmer, Danielle Marshall, Harley Eades III, and Dominic Orchard. A Mixed Linear and Graded Logic: Proofs, Terms, and Models. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 32:1-32:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{vollmer_et_al:LIPIcs.CSL.2025.32,
  author =	{Vollmer, Victoria and Marshall, Danielle and Eades III, Harley and Orchard, Dominic},
  title =	{{A Mixed Linear and Graded Logic: Proofs, Terms, and Models}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{32:1--32:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-362-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{326},
  editor =	{Endrullis, J\"{o}rg and Schmitz, Sylvain},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2025.32},
  URN =		{urn:nbn:de:0030-drops-227892},
  doi =		{10.4230/LIPIcs.CSL.2025.32},
  annote =	{Keywords: linear logic, graded modal logic, adjoint decomposition}
}
Document
DOI: 10.4230/LIPIcs.CSL.2025.40
Completeness of First-Order Bi-Intuitionistic Logic

Authors: Dominik Kirst and Ian Shillito

Published in: LIPIcs, Volume 326, 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)

Abstract
We provide a succinct and verified completeness proof for first-order bi-intuitionistic logic, relative to constant domain Kripke semantics. By doing so, we make up for the almost-50-year-old substantial mistakes in Rauszer’s foundational work, detected but unresolved by Shillito two years ago. Moreover, an even earlier but historically neglected proof by Klemke has been found to contain at least local errors by Olkhovikov and Badia, that remained unfixed due to the technical complexity of Klemke’s argument. To resolve this unclear situation once and for all, we give a succinct completeness proof, based on and dualising a standard proof for constant domain intuitionistic logic, and verify our constructions using the Coq proof assistant to guarantee correctness.
Cite as

Dominik Kirst and Ian Shillito. Completeness of First-Order Bi-Intuitionistic Logic. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 40:1-40:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kirst_et_al:LIPIcs.CSL.2025.40,
  author =	{Kirst, Dominik and Shillito, Ian},
  title =	{{Completeness of First-Order Bi-Intuitionistic Logic}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{40:1--40:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-362-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{326},
  editor =	{Endrullis, J\"{o}rg and Schmitz, Sylvain},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2025.40},
  URN =		{urn:nbn:de:0030-drops-227979},
  doi =		{10.4230/LIPIcs.CSL.2025.40},
  annote =	{Keywords: bi-intuitionistic logic, first-order logic, completeness, Coq proof assistant}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2024.26
On the Logical Structure of Some Maximality and Well-Foundedness Principles Equivalent to Choice Principles

Authors: Hugo Herbelin and Jad Koleilat

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

Abstract
We study the logical structure of Teichmüller-Tukey lemma, a maximality principle equivalent to the axiom of choice and show that it corresponds to the generalisation to arbitrary cardinals of update induction, a well-foundedness principle from constructive mathematics classically equivalent to the axiom of dependent choice. From there, we state general forms of maximality and well-foundedness principles equivalent to the axiom of choice, including a variant of Zorn’s lemma. A comparison with the general class of choice and bar induction principles given by Brede and the first author is initiated.
Cite as

Hugo Herbelin and Jad Koleilat. On the Logical Structure of Some Maximality and Well-Foundedness Principles Equivalent to Choice Principles. In 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 299, pp. 26:1-26:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{herbelin_et_al:LIPIcs.FSCD.2024.26,
  author =	{Herbelin, Hugo and Koleilat, Jad},
  title =	{{On the Logical Structure of Some Maximality and Well-Foundedness Principles Equivalent to Choice Principles}},
  booktitle =	{9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)},
  pages =	{26:1--26:15},
  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.2024.26},
  URN =		{urn:nbn:de:0030-drops-203551},
  doi =		{10.4230/LIPIcs.FSCD.2024.26},
  annote =	{Keywords: axiom of choice, Teichm\"{u}ller-Tukey lemma, update induction, constructive reverse mathematics}
}
Document
Complete Volume
DOI: 10.4230/LIPIcs.TYPES.2014
LIPIcs, Volume 39, TYPES'14, Complete Volume

Authors: Hugo Herbelin, Pierre Letouzey, and Matthieu Sozeau

Published in: LIPIcs, Volume 39, 20th International Conference on Types for Proofs and Programs (TYPES 2014)

Abstract
LIPIcs, Volume 39, TYPES'14, Complete Volume
Cite as

20th International Conference on Types for Proofs and Programs (TYPES 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 39, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@Proceedings{herbelin_et_al:LIPIcs.TYPES.2014,
  title =	{{LIPIcs, Volume 39, TYPES'14, Complete Volume}},
  booktitle =	{20th International Conference on Types for Proofs and Programs (TYPES 2014)},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-88-0},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{39},
  editor =	{Herbelin, Hugo and Letouzey, Pierre and Sozeau, Matthieu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2014},
  URN =		{urn:nbn:de:0030-drops-55047},
  doi =		{10.4230/LIPIcs.TYPES.2014},
  annote =	{Keywords: Applicative (Functional) Programming, Software/Program Verification, Specifying and Verifying and Reasoning about Programs, Mathematical Logic}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.TYPES.2014.i
Front Matter, Table of Contents, Preface, Authors Index

Authors: Hugo Herbelin, Pierre Letouzey, and Matthieu Sozeau

Published in: LIPIcs, Volume 39, 20th International Conference on Types for Proofs and Programs (TYPES 2014)

Abstract
Front Matter, Table of Contents, Preface, Authors Index
Cite as

20th International Conference on Types for Proofs and Programs (TYPES 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 39, pp. i-x, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{herbelin_et_al:LIPIcs.TYPES.2014.i,
  author =	{Herbelin, Hugo and Letouzey, Pierre and Sozeau, Matthieu},
  title =	{{Front Matter, Table of Contents, Preface, Authors Index}},
  booktitle =	{20th International Conference on Types for Proofs and Programs (TYPES 2014)},
  pages =	{i--x},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-88-0},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{39},
  editor =	{Herbelin, Hugo and Letouzey, Pierre and Sozeau, Matthieu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2014.i},
  URN =		{urn:nbn:de:0030-drops-54888},
  doi =		{10.4230/LIPIcs.TYPES.2014.i},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Authors Index}
}
Document
DOI: 10.4230/LIPIcs.TYPES.2014.1
Terminal Semantics for Codata Types in Intensional Martin-Löf Type Theory

Authors: Benedikt Ahrens and Régis Spadotti

Published in: LIPIcs, Volume 39, 20th International Conference on Types for Proofs and Programs (TYPES 2014)

Abstract
We study the notions of relative comonad and comodule over a relative comonad. We use these notions to give categorical semantics for the coinductive type families of streams and of infinite triangular matrices and their respective cosubstitution operations in intensional Martin-Löf type theory. Our results are mechanized in the proof assistant Coq.
Cite as

Benedikt Ahrens and Régis Spadotti. Terminal Semantics for Codata Types in Intensional Martin-Löf Type Theory. In 20th International Conference on Types for Proofs and Programs (TYPES 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 39, pp. 1-26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{ahrens_et_al:LIPIcs.TYPES.2014.1,
  author =	{Ahrens, Benedikt and Spadotti, R\'{e}gis},
  title =	{{Terminal Semantics for Codata Types in Intensional Martin-L\"{o}f Type Theory}},
  booktitle =	{20th International Conference on Types for Proofs and Programs (TYPES 2014)},
  pages =	{1--26},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-88-0},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{39},
  editor =	{Herbelin, Hugo and Letouzey, Pierre and Sozeau, Matthieu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2014.1},
  URN =		{urn:nbn:de:0030-drops-54891},
  doi =		{10.4230/LIPIcs.TYPES.2014.1},
  annote =	{Keywords: relative comonad, Martin-L\"{o}f type theory, coinductive type, computer theorem proving}
}
Document
DOI: 10.4230/LIPIcs.TYPES.2014.27
A Calculus of Constructions with Explicit Subtyping

Authors: Ali Assaf

Published in: LIPIcs, Volume 39, 20th International Conference on Types for Proofs and Programs (TYPES 2014)

Abstract
The calculus of constructions can be extended with an infinite hierarchy of universes and cumulative subtyping. Subtyping is usually left implicit in the typing rules. We present an alternative version of the calculus of constructions where subtyping is explicit. We avoid problems related to coercions and dependent types by using the Tarski style of universes and by adding equations to reflect equality.
Cite as

Ali Assaf. A Calculus of Constructions with Explicit Subtyping. In 20th International Conference on Types for Proofs and Programs (TYPES 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 39, pp. 27-46, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{assaf:LIPIcs.TYPES.2014.27,
  author =	{Assaf, Ali},
  title =	{{A Calculus of Constructions with Explicit Subtyping}},
  booktitle =	{20th International Conference on Types for Proofs and Programs (TYPES 2014)},
  pages =	{27--46},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-88-0},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{39},
  editor =	{Herbelin, Hugo and Letouzey, Pierre and Sozeau, Matthieu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2014.27},
  URN =		{urn:nbn:de:0030-drops-54904},
  doi =		{10.4230/LIPIcs.TYPES.2014.27},
  annote =	{Keywords: type theory, calculus of constructions, universes, cumulativity, subtyping}
}
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