14 Search Results for "Larchey-Wendling, Dominique"

Document
DOI: 10.4230/LIPIcs.CSL.2026.16
On the Entailment Problem in Dynamic Separation Logic with Inductive Definitions

Authors: Nicolas Peltier

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

Abstract
Separation Logic (SL) is a well-established framework for reasoning about programs that manipulate dynamic memory. To express and verify properties of custom recursive data structures, SL is extended with spatial predicates defined by user-specified inductive rules. Many verification problems reduce to deciding entailments between formulas involving these predicates. While the general entailment problem is undecidable, a broad class of inductive rules - known as PCE (Progressing, Connected, and Established) - has been identified for which entailment is decidable. In this work, we extend the study of the entailment problem to Dynamic Separation Logic (DSL), an extension of SL that includes dynamic modalities for reasoning about actions on the heap and store. We show that entailment in DSL remains decidable for PCE rules by proving that dynamic modalities can be automatically eliminated.
Cite as

Nicolas Peltier. On the Entailment Problem in Dynamic Separation Logic with Inductive Definitions. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 16:1-16:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{peltier:LIPIcs.CSL.2026.16,
  author =	{Peltier, Nicolas},
  title =	{{On the Entailment Problem in Dynamic Separation Logic with Inductive Definitions}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{16:1--16:20},
  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.2026.16},
  URN =		{urn:nbn:de:0030-drops-254402},
  doi =		{10.4230/LIPIcs.CSL.2026.16},
  annote =	{Keywords: Separation logic, Dynamic logic, Entailment problem}
}
Document
DOI: 10.4230/LIPIcs.ITP.2025.3
A Formal Proof of Complexity Bounds on Diophantine Equations

Authors: Jonas Bayer and Marco David

Published in: LIPIcs, Volume 352, 16th International Conference on Interactive Theorem Proving (ITP 2025)

Abstract
We present a universal construction of Diophantine equations with bounded complexity in Isabelle/HOL. This is a formalization of our own work in number theory [Jonas Bayer et al., 2025]. Hilbert’s Tenth Problem was answered negatively by Yuri Matiyasevich, who showed that there is no general algorithm to decide whether an arbitrary Diophantine equation has a solution. However, the problem remains open when generalized to the field of rational numbers, or contrarily, when restricted to Diophantine equations with bounded complexity, characterized by the number of variables ν and the degree δ. If every Diophantine set can be represented within the bounds (ν, δ), we say that this pair is universal, and it follows that the corresponding class of equations is undecidable. In a separate mathematics article, we have determined the first non-trivial universal pair for the case of integer unknowns. In this paper, we contribute a formal verification of this new result. In doing so, we markedly extend the Isabelle AFP entry on multivariate polynomials [Christian Sternagel et al., 2010], formalize parts of a number theory textbook [Melvyn B. Nathanson, 1996], and develop classical theory on Diophantine equations [Yuri Matiyasevich and Julia Robinson, 1975] in Isabelle. In addition, our work includes metaprogramming infrastructure designed to efficiently handle complex definitions of multivariate polynomials. Our mathematical draft has been formalized while the mathematical research was ongoing, and benefited largely from the help of the theorem prover. We reflect on how the close collaboration between mathematician and computer is an uncommon but promising modus operandi.
Cite as

Jonas Bayer and Marco David. A Formal Proof of Complexity Bounds on Diophantine Equations. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 3:1-3:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{bayer_et_al:LIPIcs.ITP.2025.3,
  author =	{Bayer, Jonas and David, Marco},
  title =	{{A Formal Proof of Complexity Bounds on Diophantine Equations}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{3:1--3:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-396-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{352},
  editor =	{Forster, Yannick and Keller, Chantal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.3},
  URN =		{urn:nbn:de:0030-drops-246023},
  doi =		{10.4230/LIPIcs.ITP.2025.3},
  annote =	{Keywords: Diophantine Equations, Hilbert’s Tenth Problem, Isabelle/HOL}
}
Document
DOI: 10.4230/LIPIcs.ITP.2025.13
Barendregt’s Theory of the λ-Calculus, Refreshed and Formalized

Authors: Adrienne Lancelot, Beniamino Accattoli, and Maxime Vemclefs

Published in: LIPIcs, Volume 352, 16th International Conference on Interactive Theorem Proving (ITP 2025)

Abstract
Barendregt’s book on the untyped λ-calculus refines the inconsistent view of β-divergence as representation of the undefined via the key concept of head reduction. In this paper, we put together recent revisitations of some key theorems laid out in Barendregt’s book, and we formalize them in the Abella proof assistant. Our work provides a compact and refreshed presentation of the core of the book. The formalization faithfully mimics pen-and-paper proofs. Two interesting aspects are the manipulation of contexts for the study of contextual equivalence and a formal alternative to the informal trick at work in Takahashi’s proof of the genericity lemma. As a by-product, we obtain an alternative definition of contextual equivalence that does not mention contexts.
Cite as

Adrienne Lancelot, Beniamino Accattoli, and Maxime Vemclefs. Barendregt’s Theory of the λ-Calculus, Refreshed and Formalized. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 13:1-13:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{lancelot_et_al:LIPIcs.ITP.2025.13,
  author =	{Lancelot, Adrienne and Accattoli, Beniamino and Vemclefs, Maxime},
  title =	{{Barendregt’s Theory of the \lambda-Calculus, Refreshed and Formalized}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{13:1--13:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-396-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{352},
  editor =	{Forster, Yannick and Keller, Chantal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.13},
  URN =		{urn:nbn:de:0030-drops-246114},
  doi =		{10.4230/LIPIcs.ITP.2025.13},
  annote =	{Keywords: lambda-calculus, head reduction, equational theory}
}
Document
DOI: 10.4230/LIPIcs.ITP.2025.10
An Isabelle/HOL Formalization of Semi-Thue and Conditional Semi-Thue Systems

Authors: Dohan Kim

Published in: LIPIcs, Volume 352, 16th International Conference on Interactive Theorem Proving (ITP 2025)

Abstract
We present a formalized framework for semi-Thue and conditional semi-Thue systems for studying monoids and their word problem using the Isabelle/HOL proof assistant. We provide a formalized decision procedure for the word problem of monoids if they are finitely presented by complete semi-Thue systems. In particular, we present a new formalized method for checking confluence using (conditional) critical pairs for certain conditional semi-Thue systems. We propose and formalize an inference system for generating conditional equational theories and Thue congruences using conditional semi-Thue systems. Then we provide a new formalized decision procedure for the word problem of monoids which have finite complete (reductive) conditional presentations.
Cite as

Dohan Kim. An Isabelle/HOL Formalization of Semi-Thue and Conditional Semi-Thue Systems. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 10:1-10:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{kim:LIPIcs.ITP.2025.10,
  author =	{Kim, Dohan},
  title =	{{An Isabelle/HOL Formalization of Semi-Thue and Conditional Semi-Thue Systems}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{10:1--10:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-396-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{352},
  editor =	{Forster, Yannick and Keller, Chantal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.10},
  URN =		{urn:nbn:de:0030-drops-246081},
  doi =		{10.4230/LIPIcs.ITP.2025.10},
  annote =	{Keywords: semi-Thue systems, conditional semi-Thue systems, conditional string rewriting, monoids, word problem}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2025.17
Mechanized Undecidability of Higher-Order Beta-Matching

Authors: Andrej Dudenhefner

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

Abstract
Higher-order β-matching is the following decision problem: given two simply typed λ-terms, can the first term be instantiated to be β-equivalent to the second term? This problem was formulated by Huet in the 1970s and shown undecidable by Loader in 2003 by reduction from λ-definability. The present work provides a novel undecidability proof for higher-order β-matching, in an effort to verify this result by means of a proof assistant. Rather than starting from λ-definability, the presented proof encodes a restricted form of string rewriting as higher-order β-matching. The particular approach is similar to Urzyczyn’s undecidability result for intersection type inhabitation. The presented approach has several advantages. First, the proof is simpler to verify in full detail due to the simple form of rewriting systems, which serve as a starting point. Second, undecidability of the considered problem in string rewriting is already certified using the Coq proof assistant. As a consequence, we obtain a certified many-one reduction from the Halting Problem to higher-order β-matching. Third, the presented approach identifies a uniform construction which shows undecidability of higher-order β-matching, λ-definability, and intersection type inhabitation. The presented undecidability proof is mechanized in the Coq proof assistant and contributed to the existing Coq Library of Undecidability Proofs.
Cite as

Andrej Dudenhefner. Mechanized Undecidability of Higher-Order Beta-Matching. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 17:1-17:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{dudenhefner:LIPIcs.FSCD.2025.17,
  author =	{Dudenhefner, Andrej},
  title =	{{Mechanized Undecidability of Higher-Order Beta-Matching}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{17:1--17:15},
  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.2025.17},
  URN =		{urn:nbn:de:0030-drops-236323},
  doi =		{10.4230/LIPIcs.FSCD.2025.17},
  annote =	{Keywords: lambda-calculus, simple types, undecidability, higher-order matching, mechanization, Coq}
}
Document
DOI: 10.4230/LIPIcs.TYPES.2024.2
Constructive Substitutes for Kőnig’s Lemma

Authors: Dominique Larchey-Wendling

Published in: LIPIcs, Volume 336, 30th International Conference on Types for Proofs and Programs (TYPES 2024)

Abstract
We propose weaker but constructively provable variants of the contrapositive of Kőnig’s lemma. We derive those from a generalization of the FAN theorem for inductive bars to inductive covers, for which we give a concise proof. We compare the positive, negative and sequential characterizations of covers and bars in classical and constructive contexts, giving precise accounts of the role played by the axioms of excluded middle and dependent choice. As an application, we discuss some examples where the use of Kőnig’s lemma can be replaced by one of our weaker variants to obtain fully constructive accounts of results or proofs that could otherwise appear as inherently classical.
Cite as

Dominique Larchey-Wendling. Constructive Substitutes for Kőnig’s Lemma. In 30th International Conference on Types for Proofs and Programs (TYPES 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 336, pp. 2:1-2:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{larcheywendling:LIPIcs.TYPES.2024.2,
  author =	{Larchey-Wendling, Dominique},
  title =	{{Constructive Substitutes for K\H{o}nig’s Lemma}},
  booktitle =	{30th International Conference on Types for Proofs and Programs (TYPES 2024)},
  pages =	{2:1--2:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-376-8},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{336},
  editor =	{M{\o}gelberg, Rasmus Ejlers and van den Berg, Benno},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2024.2},
  URN =		{urn:nbn:de:0030-drops-233644},
  doi =		{10.4230/LIPIcs.TYPES.2024.2},
  annote =	{Keywords: K\H{o}nig’s lemma, FAN theorem, constructive mathematics, inductive covers, inductive bars, almost full relations, inductive type theory, Coq}
}
Artifact
Software
DOI: 10.4230/artifacts.23151
Constructive substitutes for König's lemma (artifact)

Authors: Dominique Larchey-Wendling

Abstract
Cite as

Dominique Larchey-Wendling. Constructive substitutes for König's lemma (artifact) (Software). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@misc{dagstuhl-artifact-23151,
   title = {{Constructive substitutes for K\"{o}nig's lemma (artifact)}}, 
   author = {Larchey-Wendling, Dominique},
   note = {Software, NARCO (ANR-21-CE48-0011), swhId: \href{https://archive.softwareheritage.org/swh:1:dir:611c848b0dbc19c9de20744122776440c00e413d;origin=https://github.com/DmxLarchey/Constructive-Konig;visit=swh:1:snp:b2a4befb410e99c74039905ec69fe72e1c266b84;anchor=swh:1:rev:f0445fb756d1bf8a6bb54a9574a6056ef16720db}{\texttt{swh:1:dir:611c848b0dbc19c9de20744122776440c00e413d}} (visited on 2025-07-03)},
   url = {https://github.com/DmxLarchey/Constructive-Konig},
   doi = {10.4230/artifacts.23151},
}
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)

Copy BibTex To Clipboard

@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.CSL.2025.42
Unifying Sequent Systems for Gödel-Löb Provability Logic via Syntactic Transformations

Authors: Tim S. Lyon

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

Abstract
We demonstrate the inter-translatability of proofs between the most prominent sequent-based formalisms for Gödel-Löb provability logic. In particular, we consider Sambin and Valentini’s sequent system GL_{seq}, Shamkanov’s non-wellfounded and cyclic sequent systems GL_∞ and GL_{circ}, Poggiolesi’s tree-hypersequent system CSGL, and Negri’s labeled sequent system G3GL. Shamkanov provided proof-theoretic correspondences between GL_{seq}, GL_∞, and GL_{circ}, and Goré and Ramanayake showed how to transform proofs between CSGL and G3GL, however, the exact nature of proof transformations between the former three systems and the latter two systems has remained an open problem. We solve this open problem by showing how to restructure tree-hypersequent proofs into an end-active form and introduce a novel linearization technique that transforms such proofs into linear nested sequent proofs. As a result, we obtain a new proof-theoretic tool for extracting linear nested sequent systems from tree-hypersequent systems, which yields the first cut-free linear nested sequent calculus LNGL for Gödel-Löb provability logic. We show how to transform proofs in LNGL into a certain normal form, where proofs repeat in stages of modal and local rule applications, and which are translatable into GL_{seq} and G3GL proofs. These new syntactic transformations, together with those mentioned above, establish full proof-theoretic correspondences between GL_{seq}, GL_∞, GL_{circ}, CSGL, G3GL, and LNGL while also giving (to the best of the author’s knowledge) the first constructive proof mappings between structural (viz. labeled, tree-hypersequent, and linear nested sequent) systems and a cyclic sequent system.
Cite as

Tim S. Lyon. Unifying Sequent Systems for Gödel-Löb Provability Logic via Syntactic Transformations. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 42:1-42:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{lyon:LIPIcs.CSL.2025.42,
  author =	{Lyon, Tim S.},
  title =	{{Unifying Sequent Systems for G\"{o}del-L\"{o}b Provability Logic via Syntactic Transformations}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{42:1--42:23},
  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.2025.42},
  URN =		{urn:nbn:de:0030-drops-227992},
  doi =		{10.4230/LIPIcs.CSL.2025.42},
  annote =	{Keywords: Cyclic proof, G\"{o}del-L\"{o}b logic, Labeled sequent, Linear nested sequent, Modal logic, Non-wellfounded proof, Proof theory, Proof transformation, Tree-hypersequent}
}
Document
DOI: 10.4230/LIPIcs.CSL.2024.29
The Kleene-Post and Post’s Theorem in the Calculus of Inductive Constructions

Authors: Yannick Forster, Dominik Kirst, and Niklas Mück

Published in: LIPIcs, Volume 288, 32nd EACSL Annual Conference on Computer Science Logic (CSL 2024)

Abstract
The Kleene-Post theorem and Post’s theorem are two central and historically important results in the development of oracle computability theory, clarifying the structure of Turing reducibility degrees. They state, respectively, that there are incomparable Turing degrees and that the arithmetical hierarchy is connected to the relativised form of the halting problem defined via Turing jumps. We study these two results in the calculus of inductive constructions (CIC), the constructive type theory underlying the Coq proof assistant. CIC constitutes an ideal foundation for the formalisation of computability theory for two reasons: First, like in other constructive foundations, computable functions can be treated via axioms as a purely synthetic notion rather than being defined in terms of a concrete analytic model of computation such as Turing machines. Furthermore and uniquely, CIC allows consistently assuming classical logic via the law of excluded middle or weaker variants on top of axioms for synthetic computability, enabling both fully classical developments and taking the perspective of constructive reverse mathematics on computability theory. In the present paper, we give a fully constructive construction of two Turing-incomparable degrees à la Kleene-Post and observe that the classical content of Post’s theorem seems to be related to the arithmetical hierarchy of the law of excluded middle due to Akama et. al. Technically, we base our investigation on a previously studied notion of synthetic oracle computability and contribute the first consistency proof of a suitable enumeration axiom. All results discussed in the paper are mechanised and contributed to the Coq library of synthetic computability.
Cite as

Yannick Forster, Dominik Kirst, and Niklas Mück. The Kleene-Post and Post’s Theorem in the Calculus of Inductive Constructions. In 32nd EACSL Annual Conference on Computer Science Logic (CSL 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 288, pp. 29:1-29:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{forster_et_al:LIPIcs.CSL.2024.29,
  author =	{Forster, Yannick and Kirst, Dominik and M\"{u}ck, Niklas},
  title =	{{The Kleene-Post and Post’s Theorem in the Calculus of Inductive Constructions}},
  booktitle =	{32nd EACSL Annual Conference on Computer Science Logic (CSL 2024)},
  pages =	{29:1--29:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-310-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{288},
  editor =	{Murano, Aniello 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.CSL.2024.29},
  URN =		{urn:nbn:de:0030-drops-196728},
  doi =		{10.4230/LIPIcs.CSL.2024.29},
  annote =	{Keywords: Constructive mathematics, Computability theory, Logical foundations, Constructive type theory, Interactive theorem proving, Coq proof assistant}
}
Document
DOI: 10.4230/LIPIcs.ITP.2023.21
Proof Pearl: Faithful Computation and Extraction of μ-Recursive Algorithms in Coq

Authors: Dominique Larchey-Wendling and Jean-François Monin

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

Abstract
Basing on an original Coq implementation of unbounded linear search for partially decidable predicates, we study the computational contents of μ-recursive functions via their syntactic representation, and a correct by construction Coq interpreter for this abstract syntax. When this interpreter is extracted, we claim the resulting OCaml code to be the natural combination of the implementation of the μ-recursive schemes of composition, primitive recursion and unbounded minimization of partial (i.e., possibly non-terminating) functions. At the level of the fully specified Coq terms, this implies the representation of higher-order functions of which some of the arguments are themselves partial functions. We handle this issue using some techniques coming from the Braga method. Hence we get a faithful embedding of μ-recursive algorithms into Coq preserving not only their extensional meaning but also their intended computational behavior. We put a strong focus on the quality of the Coq artifact which is both self contained and with a line of code count of less than 1k in total.
Cite as

Dominique Larchey-Wendling and Jean-François Monin. Proof Pearl: Faithful Computation and Extraction of μ-Recursive Algorithms in Coq. In 14th International Conference on Interactive Theorem Proving (ITP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 268, pp. 21:1-21:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{larcheywendling_et_al:LIPIcs.ITP.2023.21,
  author =	{Larchey-Wendling, Dominique and Monin, Jean-Fran\c{c}ois},
  title =	{{Proof Pearl: Faithful Computation and Extraction of \mu-Recursive Algorithms in Coq}},
  booktitle =	{14th International Conference on Interactive Theorem Proving (ITP 2023)},
  pages =	{21:1--21:17},
  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.2023.21},
  URN =		{urn:nbn:de:0030-drops-183963},
  doi =		{10.4230/LIPIcs.ITP.2023.21},
  annote =	{Keywords: Unbounded linear search, \mu-recursive functions, computational contents, Coq, extraction, OCaml}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2021.18
Synthetic Undecidability of MSELL via FRACTRAN Mechanised in Coq

Authors: Dominique Larchey-Wendling

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

Abstract
We present an alternate undecidability proof for entailment in (intuitionistic) multiplicative sub-exponential linear logic (MSELL). We contribute the result and its mechanised proof to the Coq library of synthetic undecidability. The result crucially relies on the undecidability of the halting problem for two counters Minsky machines, which we also hand out to the library. As a seed of undecidability, we start from FRACTRAN halting which we (many-one) reduce to Minsky machines termination by implementing Euclidean division using two counters only. We then give an alternate presentation of those two counters machines as sequent rules, where computation is performed by proof-search, and halting reduced to provability. We use this system called non-deterministic two counters Minsky machines to describe and compare both the legacy reduction to linear logic, and the more recent reduction to MSELL. In contrast with that former MSELL undecidability proof, our correctness argument for the reduction uses trivial phase semantics in place of a focused calculus.
Cite as

Dominique Larchey-Wendling. Synthetic Undecidability of MSELL via FRACTRAN Mechanised in Coq. In 6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 195, pp. 18:1-18:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

Copy BibTex To Clipboard

@InProceedings{larcheywendling:LIPIcs.FSCD.2021.18,
  author =	{Larchey-Wendling, Dominique},
  title =	{{Synthetic Undecidability of MSELL via FRACTRAN Mechanised in Coq}},
  booktitle =	{6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021)},
  pages =	{18:1--18:20},
  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.2021.18},
  URN =		{urn:nbn:de:0030-drops-142568},
  doi =		{10.4230/LIPIcs.FSCD.2021.18},
  annote =	{Keywords: Undecidability, computability theory, many-one reduction, Minsky machines, Fractran, sub-exponential linear logic, Coq}
}
Document
DOI: 10.4230/LIPIcs.CSL.2021.21
Church’s Thesis and Related Axioms in Coq’s Type Theory

Authors: Yannick Forster

Published in: LIPIcs, Volume 183, 29th EACSL Annual Conference on Computer Science Logic (CSL 2021)

Abstract
"Church’s thesis" (CT) as an axiom in constructive logic states that every total function of type ℕ → ℕ is computable, i.e. definable in a model of computation. CT is inconsistent both in classical mathematics and in Brouwer’s intuitionism since it contradicts weak Kőnig’s lemma and the fan theorem, respectively. Recently, CT was proved consistent for (univalent) constructive type theory. Since neither weak Kőnig’s lemma nor the fan theorem is a consequence of just logical axioms or just choice-like axioms assumed in constructive logic, it seems likely that CT is inconsistent only with a combination of classical logic and choice axioms. We study consequences of CT and its relation to several classes of axioms in Coq’s type theory, a constructive type theory with a universe of propositions which proves neither classical logical axioms nor strong choice axioms. We thereby provide a partial answer to the question as to which axioms may preserve computational intuitions inherent to type theory, and which certainly do not. The paper can also be read as a broad survey of axioms in type theory, with all results mechanised in the Coq proof assistant.
Cite as

Yannick Forster. Church’s Thesis and Related Axioms in Coq’s Type Theory. In 29th EACSL Annual Conference on Computer Science Logic (CSL 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 183, pp. 21:1-21:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

Copy BibTex To Clipboard

@InProceedings{forster:LIPIcs.CSL.2021.21,
  author =	{Forster, Yannick},
  title =	{{Church’s Thesis and Related Axioms in Coq’s Type Theory}},
  booktitle =	{29th EACSL Annual Conference on Computer Science Logic (CSL 2021)},
  pages =	{21:1--21:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-175-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{183},
  editor =	{Baier, Christel and Goubault-Larrecq, Jean},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2021.21},
  URN =		{urn:nbn:de:0030-drops-134552},
  doi =		{10.4230/LIPIcs.CSL.2021.21},
  annote =	{Keywords: Church’s thesis, constructive type theory, constructive reverse mathematics, synthetic computability theory, Coq}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2019.27
Hilbert’s Tenth Problem in Coq

Authors: Dominique Larchey-Wendling and Yannick Forster

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

Abstract
We formalise the undecidability of solvability of Diophantine equations, i.e. polynomial equations over natural numbers, in Coq’s constructive type theory. To do so, we give the first full mechanisation of the Davis-Putnam-Robinson-Matiyasevich theorem, stating that every recursively enumerable problem - in our case by a Minsky machine - is Diophantine. We obtain an elegant and comprehensible proof by using a synthetic approach to computability and by introducing Conway’s FRACTRAN language as intermediate layer.
Cite as

Dominique Larchey-Wendling and Yannick Forster. Hilbert’s Tenth Problem in Coq. In 4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 131, pp. 27:1-27:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

Copy BibTex To Clipboard

@InProceedings{larcheywendling_et_al:LIPIcs.FSCD.2019.27,
  author =	{Larchey-Wendling, Dominique and Forster, Yannick},
  title =	{{Hilbert’s Tenth Problem in Coq}},
  booktitle =	{4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019)},
  pages =	{27:1--27:20},
  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.2019.27},
  URN =		{urn:nbn:de:0030-drops-105342},
  doi =		{10.4230/LIPIcs.FSCD.2019.27},
  annote =	{Keywords: Hilbert’s tenth problem, Diophantine equations, undecidability, computability theory, reduction, Minsky machines, Fractran, Coq, type theory}
}
  • Refine by Type
  • 13 Document/PDF
  • 8 Document/HTML
  • 1 Artifact

  • Refine by Publication Year
  • 1 2026
  • 8 2025
  • 1 2024
  • 1 2023
  • 2 2021
  • Show More...

  • Refine by Author
  • 5 Larchey-Wendling, Dominique
  • 3 Forster, Yannick
  • 2 Kirst, Dominik
  • 1 Accattoli, Beniamino
  • 1 Bayer, Jonas
  • Show More...

  • Refine by Series/Journal
  • 13 LIPIcs

  • Refine by Classification
  • 6 Theory of computation → Type theory
  • 4 Theory of computation → Constructive mathematics
  • 4 Theory of computation → Logic and verification
  • 3 Theory of computation → Models of computation
  • 2 Theory of computation → Lambda calculus
  • Show More...

  • Refine by Keyword
  • 7 Coq
  • 2 Coq proof assistant
  • 2 FAN theorem
  • 2 Fractran
  • 2 Kőnig’s lemma
  • Show More...

Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact