Large-Scale Formal Proof for the Working Mathematician

Irrationality Criteria for Series by Erdős and Straus

Autori: Angeliki Koutsoukou-Argyraki, Wenda Li
Pubblicato in: Archive of Formal Proofs, 2020
Editore: Technical University of Munich

Undirected Graph Theory

Autori: Chelsea Edmonds
Pubblicato in: Archive of Formal Proofs, 2022
Editore: TUM

Szemerédi's Regularity Lemma

Autori: Chelsea Edmonds, Angeliki Koutsoukou-Argyraki, Lawrence C. Paulson
Pubblicato in: Archive of Formal Proofs, 2021, ISSN 2150-914x
Editore: TUM

The Nash-Williams Partition Theorem

Autori: Lawrence C. Paulson
Pubblicato in: Archive of Formal Proofs, 2020, ISSN 2150-914x
Editore: TUM

Grothendieck's Schemes in Algebraic Geometry

Autori: Anthony Bordg, Lawrence Paulson, Wenda Li
Pubblicato in: Archive of Formal Proofs, 2021, ISSN 2150-914x
Editore: TUM

Strict Omega Categories

Autori: Anthony Bordg, Adrián Doña Mateo
Pubblicato in: Archive of Formal Proofs, 2023
Editore: Technical University of Munich

Irrational numbers from THE BOOK

Autori: Lawrence C Paulson
Pubblicato in: Archive of Formal Proofs, 2022, ISSN 2150-914x
Editore: TUM

The Balog–Szemerédi–Gowers Theorem

Autori: Angeliki Koutsoukou-Argyraki, Mantas Bakšys, Chelsea Edmonds
Pubblicato in: Archive of Formal Proofs, 2022
Editore: TUM

Amicable Numbers

Autori: Angeliki Koutsoukou-Argyraki
Pubblicato in: Archive of Formal Proofs, 2020, ISSN 2150-914x
Editore: TUM

General Probabilistic Techniques for Combinatorics and the Lovasz Local Lemma

Autori: Chelsea Edmonds
Pubblicato in: Archive of Formal Proofs, 2023
Editore: TU Munich

Khovanskii's Theorem

Autori: Angeliki Koutsoukou-Argyraki, Lawrence C. Paulson
Pubblicato in: Archive of Formal Proofs, 2022
Editore: TUM

Isabelle Marries Dirac: a Library for Quantum Computation and Quantum Information

Autori: Anthony Bordg, Hanna Lachnitt and Yijun He
Pubblicato in: Archive of Formal Proofs, 2020, ISSN 2150-914x
Editore: TUM

Hypergraphs

Autori: Chelsea Edmonds
Pubblicato in: Archive of Formal Proofs, 2023
Editore: TU Munich

Wetzel's Problem and the Continuum Hypothesis

Autori: Lawrence C Paulson
Pubblicato in: Archive of Formal Proofs, 2022, ISSN 2150-914x
Editore: TUM

Euler's Polyhedron Formula

Autori: Lawrence C Paulson
Pubblicato in: Archive of Formal Proofs, 2023
Editore: TU Munich

Young's Inequality for Increasing Functions

Autori: Lawrence C Paulson
Pubblicato in: Archive of Formal Proofs, 2022, ISSN 2150-914x
Editore: TUM

The Plünnecke-Ruzsa Inequality

Autori: Angeliki Koutsoukou-Argyraki, Lawrence C. Paulson
Pubblicato in: 2022, ISSN 2150-914x
Editore: TUM

Ordinal Partitions

Autori: Lawrence C. Paulson
Pubblicato in: Archive of Formal Proofs, 2020, ISSN 2150-914x
Editore: TUM

Aristotle's Assertoric Syllogistic

Autori: Angeliki Koutsoukou-Argyraki
Pubblicato in: Archive of Formal Proofs, 2020, ISSN 2150-914x
Editore: TUM

The Transcendence of Certain Infinite Series

Autori: Angeliki Koutsoukou-Argyraki, Wenda Li
Pubblicato in: Archive of Formal Proofs, 2019, ISSN 2150-914x
Editore: TUM

The Prime Number Theorem

Autori: Manuel Eberl; Lawrence C. Paulson
Pubblicato in: Archive of Formal Proofs, 2018, ISSN 2150-914x
Editore: TUM

Octonions

Autori: Angeliki Koutsoukou-Argyraki
Pubblicato in: Archive of Formal Proofs, 2018, ISSN 2150-914x
Editore: TUM

Irrational Rapidly Convergent Series

Autori: Angeliki Koutsoukou-Argyraki; Wenda Li
Pubblicato in: Archive of Formal Proofs, 2018, ISSN 2150-914x
Editore: TUM

Zermelo Fraenkel Set Theory in Higher-Order Logic

Autori: Lawrence C. Paulson
Pubblicato in: Archive of Formal Proofs, 2019, ISSN 2150-914x
Editore: TUM

Fourier Series

Autori: Lawrence C. Paulson
Pubblicato in: Archive of Formal Proofs, 2019, ISSN 2150-914x
Editore: TUM

Quaternions

Autori: Lawrence C. Paulson
Pubblicato in: Archive of Formal Proofs, 2018, ISSN 2150-914x
Editore: TUM

An Isabelle/HOL formalisation of Green's Theorem

Autori: Mohammad Abdulaziz and Lawrence C. Paulson
Pubblicato in: Archive of Formal Proofs, 2018, ISSN 2150-914x
Editore: TUM

The Budan-Fourier Theorem and Counting Real Roots with Multiplicity

Autori: Wenda Li
Pubblicato in: Archive of Formal Proofs, 2018, ISSN 2150-914x
Editore: TUM

Evaluate Winding Numbers through Cauchy Indices

Autori: Wenda Li
Pubblicato in: Archive of Formal Proofs, 2017, ISSN 2150-914x
Editore: TUM

Count the Number of Complex Roots

Autori: Wenda Li
Pubblicato in: Archive of Formal Proofs, 2017, ISSN 2150-914x
Editore: TUM

Projective Geometry

Autori: Anthony Bordg
Pubblicato in: Archive of Formal Proofs, 2018, ISSN 2150-914x
Editore: TUM

The Localization of a Commutative Ring

Autori: Anthony Bordg
Pubblicato in: Archive of Formal Proofs, 2018, ISSN 2150-914x
Editore: TUM

The Theorem of Three Circles

Autori: Fox Thomson, Wenda Li
Pubblicato in: Archive of Formal Proofs, 2021, ISSN 2150-914x
Editore: TUM

Hypergraph Colouring Bounds

Autori: Chelsea Edmonds, Lawrence Paulson
Pubblicato in: Archive of Formal Proofs, 2023
Editore: TU Munich

Kneser's Theorem and the Cauchy–Davenport Theorem

Autori: Mantas Bakšys, Angeliki Koutsoukou-Argyraki
Pubblicato in: Archive of Formal Proofs, 2022
Editore: TUM

Fisher's Inequality: Linear Algebraic Proof Techniques for Combinatorics

Autori: Chelsea Edmonds, Lawrence C. Paulson
Pubblicato in: Archive of Formal Proofs, 2022, ISSN 2150-914x
Editore: TUM

Roth's Theorem on Arithmetic Progressions

Autori: Chelsea Edmonds, Angeliki Koutsoukou-Argyraki, Lawrence C. Paulson
Pubblicato in: Archive of Formal Proofs, 2021, ISSN 2150-914x
Editore: TUM

Polygonal Number Theorem

Autori: Kevin Lee, Zhengkun Ye, Angeliki Koutsoukou-Argyraki
Pubblicato in: Archive of Formal Proofs, 2023
Editore: Technical University of Munich

The Interpretation Lifting Theorem for C-Systems

Autori: Anthony Bordg
Pubblicato in: Theory and Applications of Categories, 2022, ISSN 1201-561X
Editore: R. Rosebrugh

Simple Type Theory is not too Simple: Grothendieck’s Schemes Without Dependent Types

Autori: Anthony Bordg, Lawrence Paulson, Wenda Li
Pubblicato in: Experimental Mathematics, 2022, ISSN 1058-6458
Editore: A K Peters Ltd.
DOI: 10.1080/10586458.2022.2062073

Formalising Szemerédi’s Regularity Lemma and Roth’s Theorem on Arithmetic Progressions in Isabelle/HOL

Autori: Chelsea Edmonds, Angeliki Koutsoukou-Argyraki, Lawrence C. Paulson
Pubblicato in: Journal of Automated Reasoning, 2023, ISSN 0168-7433
Editore: Kluwer Academic Publishers
DOI: 10.1007/s10817-022-09650-2

Formalising Mathematics – in Praxis; A Mathematician’s First Experiences with Isabelle/HOL and the Why and How of Getting Started

Autori: Angeliki Koutsoukou-Argyraki
Pubblicato in: Jahresbericht der Deutschen Mathematiker-Vereinigung, 2020, ISSN 0012-0456
Editore: Springer Verlag
DOI: 10.1365/s13291-020-00221-1

A Replication Crisis in Mathematics?

Autori: Anthony Bordg
Pubblicato in: The Mathematical Intelligencer, 2021, ISSN 0343-6993
Editore: Springer Verlag
DOI: 10.1007/s00283-020-10037-7

An Isabelle/HOL Formalisation of Green’s Theorem

Autori: Mohammad Abdulaziz, Lawrence C. Paulson
Pubblicato in: Journal of Automated Reasoning, 2018, ISSN 0168-7433
Editore: Kluwer Academic Publishers
DOI: 10.1007/s10817-018-9495-z

Deciding Univariate Polynomial Problems Using Untrusted Certificates in Isabelle/HOL

Autori: Wenda Li, Grant Olney Passmore, Lawrence C. Paulson
Pubblicato in: Journal of Automated Reasoning, Numero 62/1, 2019, Pagina/e 69-91, ISSN 0168-7433
Editore: Kluwer Academic Publishers
DOI: 10.1007/s10817-017-9424-6

Evaluating Winding Numbers and Counting Complex Roots Through Cauchy Indices in Isabelle/HOL

Autori: Wenda Li, Lawrence C. Paulson
Pubblicato in: Journal of Automated Reasoning, 2019, ISSN 0168-7433
Editore: Kluwer Academic Publishers
DOI: 10.1007/s10817-019-09521-3

Certified Quantum Computation in Isabelle/HOL

Autori: Anthony Bordg, Hanna Lachnitt, Yijun He
Pubblicato in: Journal of Automated Reasoning, 2020, ISSN 0168-7433
Editore: Kluwer Academic Publishers
DOI: 10.1007/s10817-020-09584-7

A formalised theorem in the partition calculus

Autori: Lawrence C. Paulson
Pubblicato in: Annals of Pure and Applied Logic, 2023, ISSN 0168-0072
Editore: Elsevier BV
DOI: 10.1016/j.apal.2023.103246

Formalizing Ordinal Partition Relations Using Isabelle/HOL

Autori: Mirna Džamonja, Angeliki Koutsoukou-Argyraki, Lawrence C. Paulson
Pubblicato in: Experimental Mathematics, 2021, ISSN 1058-6458
Editore: A K Peters Ltd.
DOI: 10.1080/10586458.2021.1980464

Irrationality and Transcendence Criteria for Infinite Series in Isabelle/HOL

Autori: Angeliki Koutsoukou-Argyraki; Wenda Li; Lawrence C. Paulson
Pubblicato in: Experimental Mathematics, 2021, ISSN 1058-6458
Editore: A K Peters Ltd.
DOI: 10.1080/10586458.2021.1980465

Ackermann’s Function in Iterative Form: A Proof Assistant Experiment

Autori: Lawrence C. Paulson
Pubblicato in: The Bulletin of Symbolic Logic, 2021, Pagina/e 1-10, ISSN 1079-8986
Editore: Association for Symbolic Logic
DOI: 10.1017/bsl.2021.47

Formalising Fisher’s Inequality: Formal Linear Algebraic Proof Techniques in Combinatorics

Autori: Chelsea Edmonds, Lawrence C. Paulson
Pubblicato in: 13th International Conference on Interactive Theorem Proving (ITP 2022), 2022, Pagina/e 11:1-11:19
Editore: Schloss Dagstuhl -- Leibniz-Zentrum für Informatik
DOI: 10.4230/lipics.itp.2022.11

LIME: Learning Inductive Bias for Primitives of Mathematical Reasoning

Autori: Yuhuai Wu, Markus Rabe, Wenda Li, Jimmy Ba, Roger Grosse, Christian Szegedy
Pubblicato in: ICML 2021 (International Conference on Machine Learning), 2021
Editore: Proceedings of Machine Learning Research

Encoding Dependently-Typed Constructions into Simple Type Theory

Autori: Anthony Bordg, Adrián Doña Mateo
Pubblicato in: Proceedings of the 12th ACM SIGPLAN International Conference on Certified Programs and Proofs, 2023
Editore: ACM
DOI: 10.1145/3573105.3575679

Thor: Wielding Hammers to Integrate Language Models and Automated Theorem Provers

Autori: Albert Q. Jiang, Wenda Li, Szymon Tworkowski, Konrad Czechowski, Tomasz Odrzygóźdź, Piotr Miłoś, Yuhuai Wu, Mateja Jamnik
Pubblicato in: Thirty-sixth Conference on Neural Information Processing Systems (NeurIPS 2022), 2022
Editore: Curran Associates

Formal Probabilistic Methods for Combinatorial Structures using the Lovász Local Lemma

Autori: Chelsea Edmonds, Lawrence C. Paulson
Pubblicato in: 2024
Editore: ACM
DOI: 10.1145/3636501.3636946

Nine Chapters of Analytic Number Theory in Isabelle/HOL

Autori: Manuel Eberl
Pubblicato in: 10th International Conference on Interactive Theorem Proving (ITP 2019), 2019
Editore: Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik
DOI: 10.4230/lipics.itp.2019.16

A Parallel Corpus of Natural Language and Isabelle Artefacts

Autori: Anthony Bordg, Yiannos Stathopoulos, Lawrence Paulson
Pubblicato in: Conference on Artificial Intelligence and Theorem Proving AITP 2022, 2022
Editore: AITP

IsarStep: a Benchmark for High-level Mathematical Reasoning

Autori: Wenda Li, Lei Yu, Yuhuai Wu, Lawrence C. Paulson
Pubblicato in: International Conference on Learning Representations, 2021
Editore: International Conference on Representation Learning

On Preserving the Computational Content of Mathematical Proofs: Toy Examples for a Formalising Strategy

Autori: Angeliki Koutsoukou-Argyraki
Pubblicato in: Connecting with Computability, 2021, ISBN 978-3-030-80048-2
Editore: Springer
DOI: 10.1007/978-3-030-80049-9_26

A Formalisation of the Balog–Szemerédi–Gowers Theorem in Isabelle/HOL

Autori: Angeliki Koutsoukou-Argyraki, Mantas Bakšys, Chelsea Edmonds
Pubblicato in: Proceedings of the 12th ACM SIGPLAN International Conference on Certified Programs and Proofs, 2023
Editore: ACM
DOI: 10.1145/3573105.3575680

Counting polynomial roots in Isabelle/HOL: a formal proof of the Budan-Fourier theorem

Autori: Wenda Li, Lawrence C. Paulson
Pubblicato in: Proceedings of the 8th ACM SIGPLAN International Conference on Certified Programs and Proofs - CPP 2019, Numero annual, 2019, Pagina/e 52-64, ISBN 9781-450362221
Editore: ACM Press
DOI: 10.1145/3293880.3294092

Draft, Sketch, and Prove: Guiding Formal Theorem Provers with Informal Proofs

Autori: Albert Qiaochu Jiang, Sean Welleck, Jin Peng Zhou, Timothee Lacroix, Jiacheng Liu, Wenda Li, Mateja Jamnik, Guillaume Lample, Yuhuai Wu
Pubblicato in: The Eleventh International Conference on Learning Representations (ICLR 2023), 2023
Editore: International Conference on Learning Representations

Elements of Differential Geometry in Lean: A Report for Mathematicians

Autori: Anthony Bordg, Nicolò Cavalleri
Pubblicato in: FMM 2021 – Fifth Workshop on Formal Mathematics for Mathematicians, 2021
Editore: Cornell University
DOI: 10.48550/arxiv.2108.00484

Algebraically Closed Fields in Isabelle/HOL

Autori: Paulo Emílio de Vilhena, Lawrence C. Paulson
Pubblicato in: Automated Reasoning - 10th International Joint Conference, IJCAR 2020, Paris, France, July 1–4, 2020, Proceedings, Part II, Numero 12167, 2020, Pagina/e 204-220, ISBN 978-3-030-51053-4
Editore: Springer International Publishing
DOI: 10.1007/978-3-030-51054-1_12

Bayesian Ranking for Strategy Scheduling in Automated Theorem Provers

Autori: Chaitanya Mangla, Sean Holden, Lawrence C. Paulson
Pubblicato in: Automated Reasoning. IJCAR 2022, 2022
Editore: Springer
DOI: 10.1007/978-3-031-10769-6_33

Univalent Foundations and the UniMath Library

Autori: Anthony Bordg
Pubblicato in: Reflections on the Foundations of Mathematics - Univalent Foundations, Set Theory and General Thoughts, 2018
Editore: Springer

Formalising Mathematics In Simple Type Theory

Autori: Lawrence C. Paulson
Pubblicato in: Reflections on the Foundations of Mathematics - Univalent Foundations, Set Theory and General Thoughts, 2018
Editore: Springer

A Modular First Formalisation of Combinatorial Design Theory

Autori: Chelsea Edmonds, Lawrence C. Paulson
Pubblicato in: Intelligent Computer Mathematics - 14th International Conference, CICM 2021, Timisoara, Romania, July 26–31, 2021, Proceedings, Numero 12833, 2021, Pagina/e 3-18, ISBN 978-3-030-81096-2
Editore: Springer International Publishing
DOI: 10.1007/978-3-030-81097-9_1

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