11 Search Results for "Lewis, Robert Y."

Document
DOI: 10.4230/LIPIcs.ITP.2024.10
Duper: A Proof-Producing Superposition Theorem Prover for Dependent Type Theory

Authors: Joshua Clune, Yicheng Qian, Alexander Bentkamp, and Jeremy Avigad

Published in: LIPIcs, Volume 309, 15th International Conference on Interactive Theorem Proving (ITP 2024)

Abstract
We present Duper, a proof-producing theorem prover for Lean based on the superposition calculus. Duper can be called directly as a terminal tactic in interactive Lean proofs, but is also designed with proof reconstruction for a future Lean hammer in mind. In this paper, we describe Duper’s underlying approach to proof search and proof reconstruction with a particular emphasis on the challenges of working in a dependent type theory. We also compare Duper’s performance to Metis' on pre-existing benchmarks to give evidence that Duper is performant enough to be useful for proof reconstruction in a hammer.
Cite as

Joshua Clune, Yicheng Qian, Alexander Bentkamp, and Jeremy Avigad. Duper: A Proof-Producing Superposition Theorem Prover for Dependent Type Theory. In 15th International Conference on Interactive Theorem Proving (ITP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 309, pp. 10:1-10:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{clune_et_al:LIPIcs.ITP.2024.10,
  author =	{Clune, Joshua and Qian, Yicheng and Bentkamp, Alexander and Avigad, Jeremy},
  title =	{{Duper: A Proof-Producing Superposition Theorem Prover for Dependent Type Theory}},
  booktitle =	{15th International Conference on Interactive Theorem Proving (ITP 2024)},
  pages =	{10:1--10:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-337-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{309},
  editor =	{Bertot, Yves and Kutsia, Temur and Norrish, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2024.10},
  URN =		{urn:nbn:de:0030-drops-207381},
  doi =		{10.4230/LIPIcs.ITP.2024.10},
  annote =	{Keywords: proof search, automatic theorem proving, interactive theorem proving, Lean, dependent type theory}
}
Document
DOI: 10.4230/LIPIcs.ITP.2024.37
Integrals Within Integrals: A Formalization of the Gagliardo-Nirenberg-Sobolev Inequality

Authors: Floris van Doorn and Heather Macbeth

Published in: LIPIcs, Volume 309, 15th International Conference on Interactive Theorem Proving (ITP 2024)

Abstract
We introduce an abstraction which allows arguments involving iterated integrals to be formalized conveniently in type-theory-based proof assistants. We call this abstraction the marginal construction, since it is connected to the marginal distribution in probability theory. The marginal construction gracefully handles permutations to the order of integration (Tonelli’s theorem in several variables), as well as arguments involving an induction over dimension. We implement the marginal construction and several applications in the language Lean. The most difficult of these applications, the Gagliardo-Nirenberg-Sobolev inequality, is a foundational result in the theory of elliptic partial differential equations and has not previously been formalized.
Cite as

Floris van Doorn and Heather Macbeth. Integrals Within Integrals: A Formalization of the Gagliardo-Nirenberg-Sobolev Inequality. In 15th International Conference on Interactive Theorem Proving (ITP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 309, pp. 37:1-37:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{vandoorn_et_al:LIPIcs.ITP.2024.37,
  author =	{van Doorn, Floris and Macbeth, Heather},
  title =	{{Integrals Within Integrals: A Formalization of the Gagliardo-Nirenberg-Sobolev Inequality}},
  booktitle =	{15th International Conference on Interactive Theorem Proving (ITP 2024)},
  pages =	{37:1--37:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-337-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{309},
  editor =	{Bertot, Yves and Kutsia, Temur and Norrish, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2024.37},
  URN =		{urn:nbn:de:0030-drops-207657},
  doi =		{10.4230/LIPIcs.ITP.2024.37},
  annote =	{Keywords: Sobolev inequality, measure theory, Lean, formalized mathematics}
}
Document
DOI: 10.4230/LIPIcs.WABI.2024.23
AlfaPang: Alignment Free Algorithm for Pangenome Graph Construction

Authors: Adam Cicherski, Anna Lisiecka, and Norbert Dojer

Published in: LIPIcs, Volume 312, 24th International Workshop on Algorithms in Bioinformatics (WABI 2024)

Abstract
The success of pangenome-based approaches to genomics analysis depends largely on the existence of efficient methods for constructing pangenome graphs that are applicable to large genome collections. In the current paper we present AlfaPang, a new pangenome graph building algorithm. AlfaPang is based on a novel alignment-free approach that allows to construct pangenome graphs using significantly less computational resources than state-of-the-art tools. The code of AlfaPang is freely available at https://github.com/AdamCicherski/AlfaPang.
Cite as

Adam Cicherski, Anna Lisiecka, and Norbert Dojer. AlfaPang: Alignment Free Algorithm for Pangenome Graph Construction. In 24th International Workshop on Algorithms in Bioinformatics (WABI 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 312, pp. 23:1-23:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{cicherski_et_al:LIPIcs.WABI.2024.23,
  author =	{Cicherski, Adam and Lisiecka, Anna and Dojer, Norbert},
  title =	{{AlfaPang: Alignment Free Algorithm for Pangenome Graph Construction}},
  booktitle =	{24th International Workshop on Algorithms in Bioinformatics (WABI 2024)},
  pages =	{23:1--23:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-340-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{312},
  editor =	{Pissis, Solon P. and Sung, Wing-Kin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2024.23},
  URN =		{urn:nbn:de:0030-drops-206673},
  doi =		{10.4230/LIPIcs.WABI.2024.23},
  annote =	{Keywords: pangenome, variation graph, genome alignment, population genomics}
}
Document
DOI: 10.4230/LIPIcs.SEA.2024.15
Determining Fixed-Length Paths in Directed and Undirected Edge-Weighted Graphs

Authors: Daniel Hambly, Rhyd Lewis, and Padraig Corcoran

Published in: LIPIcs, Volume 301, 22nd International Symposium on Experimental Algorithms (SEA 2024)

Abstract
In this paper, we examine the NP-hard problem of identifying fixed-length s-t paths in edge-weighted graphs - that is, a path of a desired length k from a source vertex s to a target vertex t. Many existing strategies look at paths whose lengths are determined by the number of edges in the path. We, however, look at the length of the path as the sum of the edge weights. Here, three exact algorithms for this problem are proposed: the first based on an integer programming (IP) formulation, the second a backtracking algorithm, and the third based on an extension of Yen’s algorithm. Analysis of these algorithms on random graphs shows that the backtracking algorithm performs best on smaller values of k, whilst the IP is preferable for larger values of k.
Cite as

Daniel Hambly, Rhyd Lewis, and Padraig Corcoran. Determining Fixed-Length Paths in Directed and Undirected Edge-Weighted Graphs. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 15:1-15:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{hambly_et_al:LIPIcs.SEA.2024.15,
  author =	{Hambly, Daniel and Lewis, Rhyd and Corcoran, Padraig},
  title =	{{Determining Fixed-Length Paths in Directed and Undirected Edge-Weighted Graphs}},
  booktitle =	{22nd International Symposium on Experimental Algorithms (SEA 2024)},
  pages =	{15:1--15:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-325-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{301},
  editor =	{Liberti, Leo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2024.15},
  URN =		{urn:nbn:de:0030-drops-203805},
  doi =		{10.4230/LIPIcs.SEA.2024.15},
  annote =	{Keywords: Graphs, paths, backtracking, integer programming, Yen’s algorithm}
}
Document
DOI: 10.4230/LIPIcs.ECRTS.2024.17
Response Time Analysis for Fixed-Priority Preemptive Uniform Multiprocessor Systems

Authors: Binqi Sun, Tomasz Kloda, and Marco Caccamo

Published in: LIPIcs, Volume 298, 36th Euromicro Conference on Real-Time Systems (ECRTS 2024)

Abstract
We present a response time analysis for global fixed-priority preemptive scheduling of constrained-deadline tasks upon a uniform multiprocessor where each processor can be characterized by a different speed. A fixed-priority scheduler assigns the jobs with the highest priorities to the fastest processors. Since determining whether all tasks can meet their deadlines is generally intractable even with identical processors, we propose two sufficient schedulability tests that calculate upper bounds on the task’s worst-case response time within polynomial and pseudo-polynomial time. The proposed tests leverage the linear programming model to upper bound the interference of the higher-priority tasks. Furthermore, we identify specific conditions and platforms upon which the problem can be solved more efficiently within linear time. These formulations are used to iteratively evaluate and refine possible solutions until a safe upper bound on the task’s worst-case response time is found. Additionally, we demonstrate that, with specific minor modifications, the proposed tests are compatible with Audsley’s optimal priority assignment. Experimental evaluations performed on synthetic task sets show that the proposed approach outperforms the state-of-the-art methods.
Cite as

Binqi Sun, Tomasz Kloda, and Marco Caccamo. Response Time Analysis for Fixed-Priority Preemptive Uniform Multiprocessor Systems. In 36th Euromicro Conference on Real-Time Systems (ECRTS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 298, pp. 17:1-17:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{sun_et_al:LIPIcs.ECRTS.2024.17,
  author =	{Sun, Binqi and Kloda, Tomasz and Caccamo, Marco},
  title =	{{Response Time Analysis for Fixed-Priority Preemptive Uniform Multiprocessor Systems}},
  booktitle =	{36th Euromicro Conference on Real-Time Systems (ECRTS 2024)},
  pages =	{17:1--17:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-324-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{298},
  editor =	{Pellizzoni, Rodolfo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECRTS.2024.17},
  URN =		{urn:nbn:de:0030-drops-203201},
  doi =		{10.4230/LIPIcs.ECRTS.2024.17},
  annote =	{Keywords: Real-time scheduling, Uniform multiprocessor, Response time analysis}
}
Document
DOI: 10.4230/DagMan.10.1.1
Current and Future Challenges in Knowledge Representation and Reasoning (Dagstuhl Perspectives Workshop 22282)

Authors: James P. Delgrande, Birte Glimm, Thomas Meyer, Miroslaw Truszczynski, and Frank Wolter

Published in: Dagstuhl Manifestos, Volume 10, Issue 1 (2024)

Abstract
Knowledge Representation and Reasoning is a central, longstanding, and active area of Artificial Intelligence. Over the years it has evolved significantly; more recently it has been challenged and complemented by research in areas such as machine learning and reasoning under uncertainty. In July 2022,sser a Dagstuhl Perspectives workshop was held on Knowledge Representation and Reasoning. The goal of the workshop was to describe the state of the art in the field, including its relation with other areas, its shortcomings and strengths, together with recommendations for future progress. We developed this manifesto based on the presentations, panels, working groups, and discussions that took place at the Dagstuhl Workshop. It is a declaration of our views on Knowledge Representation: its origins, goals, milestones, and current foci; its relation to other disciplines, especially to Artificial Intelligence; and on its challenges, along with key priorities for the next decade.
Cite as

James P. Delgrande, Birte Glimm, Thomas Meyer, Miroslaw Truszczynski, and Frank Wolter. Current and Future Challenges in Knowledge Representation and Reasoning (Dagstuhl Perspectives Workshop 22282). In Dagstuhl Manifestos, Volume 10, Issue 1, pp. 1-61, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@Article{delgrande_et_al:DagMan.10.1.1,
  author =	{Delgrande, James P. and Glimm, Birte and Meyer, Thomas and Truszczynski, Miroslaw and Wolter, Frank},
  title =	{{Current and Future Challenges in Knowledge Representation and Reasoning (Dagstuhl Perspectives Workshop 22282)}},
  pages =	{1--61},
  journal =	{Dagstuhl Manifestos},
  ISSN =	{2193-2433},
  year =	{2024},
  volume =	{10},
  number =	{1},
  editor =	{Delgrande, James P. and Glimm, Birte and Meyer, Thomas and Truszczynski, Miroslaw and Wolter, Frank},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagMan.10.1.1},
  URN =		{urn:nbn:de:0030-drops-201403},
  doi =		{10.4230/DagMan.10.1.1},
  annote =	{Keywords: Knowledge representation and reasoning, Applications of logics, Declarative representations, Formal logic}
}
Document
Position
DOI: 10.4230/TGDK.2.1.5
Standardizing Knowledge Engineering Practices with a Reference Architecture

Authors: Bradley P. Allen and Filip Ilievski

Published in: TGDK, Volume 2, Issue 1 (2024): Special Issue on Trends in Graph Data and Knowledge - Part 2. Transactions on Graph Data and Knowledge, Volume 2, Issue 1

Abstract
Knowledge engineering is the process of creating and maintaining knowledge-producing systems. Throughout the history of computer science and AI, knowledge engineering workflows have been widely used given the importance of high-quality knowledge for reliable intelligent agents. Meanwhile, the scope of knowledge engineering, as apparent from its target tasks and use cases, has been shifting, together with its paradigms such as expert systems, semantic web, and language modeling. The intended use cases and supported user requirements between these paradigms have not been analyzed globally, as new paradigms often satisfy prior pain points while possibly introducing new ones. The recent abstraction of systemic patterns into a boxology provides an opening for aligning the requirements and use cases of knowledge engineering with the systems, components, and software that can satisfy them best, however, this direction has not been explored to date. This paper proposes a vision of harmonizing the best practices in the field of knowledge engineering by leveraging the software engineering methodology of creating reference architectures. We describe how a reference architecture can be iteratively designed and implemented to associate user needs with recurring systemic patterns, building on top of existing knowledge engineering workflows and boxologies. We provide a six-step roadmap that can enable the development of such an architecture, consisting of scope definition, selection of information sources, architectural analysis, synthesis of an architecture based on the information source analysis, evaluation through instantiation, and, ultimately, instantiation into a concrete software architecture. We provide an initial design and outcome of the definition of architectural scope, selection of information sources, and analysis. As the remaining steps of design, evaluation, and instantiation of the architecture are largely use-case specific, we provide a detailed description of their procedures and point to relevant examples. We expect that following through on this vision will lead to well-grounded reference architectures for knowledge engineering, will advance the ongoing initiatives of organizing the neurosymbolic knowledge engineering space, and will build new links to the software architectures and data science communities.
Cite as

Bradley P. Allen and Filip Ilievski. Standardizing Knowledge Engineering Practices with a Reference Architecture. In Special Issue on Trends in Graph Data and Knowledge - Part 2. Transactions on Graph Data and Knowledge (TGDK), Volume 2, Issue 1, pp. 5:1-5:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@Article{allen_et_al:TGDK.2.1.5,
  author =	{Allen, Bradley P. and Ilievski, Filip},
  title =	{{Standardizing Knowledge Engineering Practices with a Reference Architecture}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{5:1--5:23},
  ISSN =	{2942-7517},
  year =	{2024},
  volume =	{2},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.2.1.5},
  URN =		{urn:nbn:de:0030-drops-198623},
  doi =		{10.4230/TGDK.2.1.5},
  annote =	{Keywords: knowledge engineering, knowledge graphs, quality attributes, software architectures, sociotechnical systems}
}
Document
DOI: 10.4230/LIPIcs.ITP.2022.10
Formalized functional analysis with semilinear maps

Authors: Frédéric Dupuis, Robert Y. Lewis, and Heather Macbeth

Published in: LIPIcs, Volume 237, 13th International Conference on Interactive Theorem Proving (ITP 2022)

Abstract
Semilinear maps are a generalization of linear maps between vector spaces where we allow the scalar action to be twisted by a ring homomorphism such as complex conjugation. In particular, this generalization unifies the concepts of linear and conjugate-linear maps. We implement this generalization in Lean’s mathlib library, along with a number of important results in functional analysis which previously were impossible to formalize properly. Specifically, we prove the Fréchet-Riesz representation theorem and the spectral theorem for compact self-adjoint operators generically over real and complex Hilbert spaces. We also show that semilinear maps have applications beyond functional analysis by formalizing the one-dimensional case of a theorem of Dieudonné and Manin that classifies the isocrystals over an algebraically closed field with positive characteristic.
Cite as

Frédéric Dupuis, Robert Y. Lewis, and Heather Macbeth. Formalized functional analysis with semilinear maps. In 13th International Conference on Interactive Theorem Proving (ITP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 237, pp. 10:1-10:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{dupuis_et_al:LIPIcs.ITP.2022.10,
  author =	{Dupuis, Fr\'{e}d\'{e}ric and Lewis, Robert Y. and Macbeth, Heather},
  title =	{{Formalized functional analysis with semilinear maps}},
  booktitle =	{13th International Conference on Interactive Theorem Proving (ITP 2022)},
  pages =	{10:1--10:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-252-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{237},
  editor =	{Andronick, June and de Moura, Leonardo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2022.10},
  URN =		{urn:nbn:de:0030-drops-167191},
  doi =		{10.4230/LIPIcs.ITP.2022.10},
  annote =	{Keywords: Functional analysis, Lean, linear algebra, semilinear, Hilbert space}
}
Document
DOI: 10.4230/LIPIcs.ITP.2022.23
Formalizing the Divergence Theorem and the Cauchy Integral Formula in Lean

Authors: Yury Kudryashov

Published in: LIPIcs, Volume 237, 13th International Conference on Interactive Theorem Proving (ITP 2022)

Abstract
I formalize a version of the divergence theorem for a function on a rectangular box that does not assume regularity of individual partial derivatives, only Fréchet differentiability of the vector field and integrability of its divergence. Then I use this theorem to prove the Cauchy-Goursat theorem (for some simple domains) and bootstrap complex analysis in the Lean mathematical library. The main tool is the GP-integral, a version of the Henstock-Kurzweil integral introduced by J. Mawhin in 1981. The divergence theorem for this integral does not require integrability of the divergence.
Cite as

Yury Kudryashov. Formalizing the Divergence Theorem and the Cauchy Integral Formula in Lean. In 13th International Conference on Interactive Theorem Proving (ITP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 237, pp. 23:1-23:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{kudryashov:LIPIcs.ITP.2022.23,
  author =	{Kudryashov, Yury},
  title =	{{Formalizing the Divergence Theorem and the Cauchy Integral Formula in Lean}},
  booktitle =	{13th International Conference on Interactive Theorem Proving (ITP 2022)},
  pages =	{23:1--23:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-252-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{237},
  editor =	{Andronick, June and de Moura, Leonardo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2022.23},
  URN =		{urn:nbn:de:0030-drops-167326},
  doi =		{10.4230/LIPIcs.ITP.2022.23},
  annote =	{Keywords: divergence theorem, Green’s theorem, Gauge integral, Cauchy integral formula, Cauchy-Goursat theorem, complex analysis}
}
Document
DOI: 10.4230/LIPIcs.ITP.2021.4
A Graphical User Interface Framework for Formal Verification

Authors: Edward W. Ayers, Mateja Jamnik, and W. T. Gowers

Published in: LIPIcs, Volume 193, 12th International Conference on Interactive Theorem Proving (ITP 2021)

Abstract
We present the "ProofWidgets" framework for implementing general user interfaces (UIs) within an interactive theorem prover. The framework uses web technology and functional reactive programming, as well as metaprogramming features of advanced interactive theorem proving (ITP) systems to allow users to create arbitrary interactive UIs for representing the goal state. Users of the framework can create GUIs declaratively within the ITP’s metaprogramming language, without having to develop in multiple languages and without coordinated changes across multiple projects, which improves development time for new designs of UI. The ProofWidgets framework also allows UIs to make use of the full context of the theorem prover and the specialised libraries that ITPs offer, such as methods for dealing with expressions and tactics. The framework includes an extensible structured pretty-printing engine that enables advanced interaction with expressions such as interactive term rewriting. We exemplify the framework with an implementation for the https://leanprover-community.github.io. The framework is already in use by hundreds of contributors to the Lean mathematical library.
Cite as

Edward W. Ayers, Mateja Jamnik, and W. T. Gowers. A Graphical User Interface Framework for Formal Verification. In 12th International Conference on Interactive Theorem Proving (ITP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 193, pp. 4:1-4:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

Copy BibTex To Clipboard

@InProceedings{ayers_et_al:LIPIcs.ITP.2021.4,
  author =	{Ayers, Edward W. and Jamnik, Mateja and Gowers, W. T.},
  title =	{{A Graphical User Interface Framework for Formal Verification}},
  booktitle =	{12th International Conference on Interactive Theorem Proving (ITP 2021)},
  pages =	{4:1--4:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-188-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{193},
  editor =	{Cohen, Liron and Kaliszyk, Cezary},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2021.4},
  URN =		{urn:nbn:de:0030-drops-138996},
  doi =		{10.4230/LIPIcs.ITP.2021.4},
  annote =	{Keywords: User Interfaces, ITP}
}
Document
DOI: 10.4230/LIPIcs.ITP.2019.15
Formalizing the Solution to the Cap Set Problem

Authors: Sander R. Dahmen, Johannes Hölzl, and Robert Y. Lewis

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

Abstract
In 2016, Ellenberg and Gijswijt established a new upper bound on the size of subsets of F^n_q with no three-term arithmetic progression. This problem has received much mathematical attention, particularly in the case q = 3, where it is commonly known as the cap set problem. Ellenberg and Gijswijt’s proof was published in the Annals of Mathematics and is noteworthy for its clever use of elementary methods. This paper describes a formalization of this proof in the Lean proof assistant, including both the general result in F^n_q and concrete values for the case q = 3. We faithfully follow the pen and paper argument to construct the bound. Our work shows that (some) modern mathematics is within the range of proof assistants.
Cite as

Sander R. Dahmen, Johannes Hölzl, and Robert Y. Lewis. Formalizing the Solution to the Cap Set Problem. In 10th International Conference on Interactive Theorem Proving (ITP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 141, pp. 15:1-15:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

Copy BibTex To Clipboard

@InProceedings{dahmen_et_al:LIPIcs.ITP.2019.15,
  author =	{Dahmen, Sander R. and H\"{o}lzl, Johannes and Lewis, Robert Y.},
  title =	{{Formalizing the Solution to the Cap Set Problem}},
  booktitle =	{10th International Conference on Interactive Theorem Proving (ITP 2019)},
  pages =	{15:1--15:19},
  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.2019.15},
  URN =		{urn:nbn:de:0030-drops-110703},
  doi =		{10.4230/LIPIcs.ITP.2019.15},
  annote =	{Keywords: formal proof, combinatorics, cap set problem, Lean}
}
  • Refine by Author
  • 2 Lewis, Robert Y.
  • 2 Macbeth, Heather
  • 1 Allen, Bradley P.
  • 1 Avigad, Jeremy
  • 1 Ayers, Edward W.
  • Show More...

  • Refine by Classification
  • 3 Theory of computation → Logic and verification
  • 2 Computing methodologies → Knowledge representation and reasoning
  • 2 Theory of computation → Type theory
  • 1 Applied computing → Computational genomics
  • 1 Computer systems organization → Real-time systems
  • Show More...

  • Refine by Keyword
  • 4 Lean
  • 1 Applications of logics
  • 1 Cauchy integral formula
  • 1 Cauchy-Goursat theorem
  • 1 Declarative representations
  • Show More...

  • Refine by Type
  • 11 document

  • Refine by Publication Year
  • 7 2024
  • 2 2022
  • 1 2019
  • 1 2021

Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact