2 Search Results for "Bréhard, Florent"

Document
DOI: 10.4230/LIPIcs.ITP.2025.36
Verifying Datalog Reasoning with Lean

Authors: Johannes Tantow, Lukas Gerlach, Stephan Mennicke, and Markus Krötzsch

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

Abstract
Datalog is an essential logical rule language with many applications, and modern rule engines compute logical consequences for Datalog with high performance and scalability. While Datalog is rather simple and, in principle, explainable by design, such sophisticated implementations and optimizations are hard to verify. We therefore propose a certificate-based approach to validate results of Datalog reasoners in a formally verified checker for Datalog proofs. Using the proof assistant Lean, we implement such a checker and verify its correctness against direct formalizations of the Datalog semantics. We propose two JSON encodings for Datalog proofs: one using the widely supported Datalog proof trees, and one using directed acyclic graphs for succinctness. To evaluate the practical feasibility and performance of our approach, we validate proofs that we obtain by converting derivation traces of an existing Datalog reasoner into our tool-independent format.
Cite as

Johannes Tantow, Lukas Gerlach, Stephan Mennicke, and Markus Krötzsch. Verifying Datalog Reasoning with Lean. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 36:1-36:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{tantow_et_al:LIPIcs.ITP.2025.36,
  author =	{Tantow, Johannes and Gerlach, Lukas and Mennicke, Stephan and Kr\"{o}tzsch, Markus},
  title =	{{Verifying Datalog Reasoning with Lean}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{36:1--36:19},
  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.2025.36},
  URN =		{urn:nbn:de:0030-drops-246342},
  doi =		{10.4230/LIPIcs.ITP.2025.36},
  annote =	{Keywords: Certifying Algorithms, Datalog, Formal Verification}
}
Document
DOI: 10.4230/LIPIcs.ITP.2019.8
A Certificate-Based Approach to Formally Verified Approximations

Authors: Florent Bréhard, Assia Mahboubi, and Damien Pous

Published in: LIPIcs, Volume 141, 10th International Conference on Interactive Theorem Proving (ITP 2019)

Abstract
We present a library to verify rigorous approximations of univariate functions on real numbers, with the Coq proof assistant. Based on interval arithmetic, this library also implements a technique of validation a posteriori based on the Banach fixed-point theorem. We illustrate this technique on the case of operations of division and square root. This library features a collection of abstract structures that organise the specfication of rigorous approximations, and modularise the related proofs. Finally, we provide an implementation of verified Chebyshev approximations, and we discuss a few examples of computations.
Cite as

Florent Bréhard, Assia Mahboubi, and Damien Pous. A Certificate-Based Approach to Formally Verified Approximations. In 10th International Conference on Interactive Theorem Proving (ITP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 141, pp. 8:1-8:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

Copy BibTex To Clipboard

@InProceedings{brehard_et_al:LIPIcs.ITP.2019.8,
  author =	{Br\'{e}hard, Florent and Mahboubi, Assia and Pous, Damien},
  title =	{{A Certificate-Based Approach to Formally Verified Approximations}},
  booktitle =	{10th International Conference on Interactive Theorem Proving (ITP 2019)},
  pages =	{8:1--8:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-122-1},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{141},
  editor =	{Harrison, John and O'Leary, John and Tolmach, Andrew},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2019.8},
  URN =		{urn:nbn:de:0030-drops-110638},
  doi =		{10.4230/LIPIcs.ITP.2019.8},
  annote =	{Keywords: approximation theory, Chebyshev polynomials, Banach fixed-point theorem, interval arithmetic, Coq}
}
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