4 Search Results for "Gallego Arias, Emilio Jesús"

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.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.ITP.2023.12
Lessons for Interactive Theorem Proving Researchers from a Survey of Coq Users

Authors: Ana de Almeida Borges, Annalí Casanueva Artís, Jean-Rémy Falleri, Emilio Jesús Gallego Arias, Érik Martin-Dorel, Karl Palmskog, Alexander Serebrenik, and Théo Zimmermann

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

Abstract
The Coq Community Survey 2022 was an online public survey of users of the Coq proof assistant conducted during February 2022. Broadly, the survey asked about use of Coq features, user interfaces, libraries, plugins, and tools, views on renaming Coq and Coq improvements, and also demographic data such as education and experience with Coq and other proof assistants and programming languages. The survey received 466 submitted responses, making it the largest survey of users of an interactive theorem prover (ITP) so far. We present the design of the survey, a summary of key results, and analysis of answers relevant to ITP technology development and usage. In particular, we analyze user characteristics associated with adoption of tools and libraries and make comparisons to adjacent software communities. Notably, we find that experience has significant impact on Coq user behavior, including on usage of tools, libraries, and integrated development environments.
Cite as

Ana de Almeida Borges, Annalí Casanueva Artís, Jean-Rémy Falleri, Emilio Jesús Gallego Arias, Érik Martin-Dorel, Karl Palmskog, Alexander Serebrenik, and Théo Zimmermann. Lessons for Interactive Theorem Proving Researchers from a Survey of Coq Users. In 14th International Conference on Interactive Theorem Proving (ITP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 268, pp. 12:1-12:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{dealmeidaborges_et_al:LIPIcs.ITP.2023.12,
  author =	{de Almeida Borges, Ana and Casanueva Art{\'\i}s, Annal{\'\i} and Falleri, Jean-R\'{e}my and Gallego Arias, Emilio Jes\'{u}s and Martin-Dorel, \'{E}rik and Palmskog, Karl and Serebrenik, Alexander and Zimmermann, Th\'{e}o},
  title =	{{Lessons for Interactive Theorem Proving Researchers from a Survey of Coq Users}},
  booktitle =	{14th International Conference on Interactive Theorem Proving (ITP 2023)},
  pages =	{12:1--12:18},
  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.2023.12},
  URN =		{urn:nbn:de:0030-drops-183875},
  doi =		{10.4230/LIPIcs.ITP.2023.12},
  annote =	{Keywords: Coq, Community, Survey, Statistical Analysis}
}
Document
DOI: 10.4230/LIPIcs.ICLP.2012.334
Logic Programming in Tabular Allegories

Authors: Emilio Jesús Gallego Arias and James B. Lipton

Published in: LIPIcs, Volume 17, Technical Communications of the 28th International Conference on Logic Programming (ICLP'12) (2012)

Abstract
We develop a compilation scheme and categorical abstract machine for execution of logic programs based on allegories, the categorical version of the calculus of relations. Operational and denotational semantics are developed using the same formalism, and query execution is performed using algebraic reasoning. Our work serves two purposes: achieving a formal model of a logic programming compiler and efficient runtime; building the base for incorporating features typical of functional programming in a declarative way, while maintaining 100% compatibility with existing Prolog programs.
Cite as

Emilio Jesús Gallego Arias and James B. Lipton. Logic Programming in Tabular Allegories. In Technical Communications of the 28th International Conference on Logic Programming (ICLP'12). Leibniz International Proceedings in Informatics (LIPIcs), Volume 17, pp. 334-347, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@InProceedings{gallegoarias_et_al:LIPIcs.ICLP.2012.334,
  author =	{Gallego Arias, Emilio Jes\'{u}s and B. Lipton, James},
  title =	{{Logic Programming in Tabular Allegories}},
  booktitle =	{Technical Communications of the 28th International Conference on Logic Programming (ICLP'12)},
  pages =	{334--347},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-43-9},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{17},
  editor =	{Dovier, Agostino and Santos Costa, V{\'\i}tor},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICLP.2012.334},
  URN =		{urn:nbn:de:0030-drops-36345},
  doi =		{10.4230/LIPIcs.ICLP.2012.334},
  annote =	{Keywords: Category Theory, Logic Programming, Lawvere Categories, Programming Language Semantics, Declarative Programming}
}
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