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lean.bib
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# To normalize:
# bibtool --preserve.key.case=on --preserve.keys=on --pass.comments=on --print.use.tab=off -s -i lean.bib -o lean.bib
@Book{ Avig14,
author = "Avigad, Jeremy and {de Moura}, Leonardo and Kong, Soonho",
title = {{Theorem Proving in Lean}},
year = "2014",
link = "\url{https://leanprover.github.io/tutorial/tutorial.pdf}",
publisher = "Carnegie Mellon University"
}
@Book{ Avig17,
author = "Avigad, Jeremy and Lewis, Robert Y. and {van Doorn},
Floris",
title = {{Logic and Proof}},
year = "2017",
link = "\url{https://avigad.github.io/logic_and_proof}",
publisher = "Carnegie Mellon University"
}
@InProceedings{ AvigadCarneiroHudon19,
author = {Jeremy Avigad and Mario M. Carneiro and Simon Hudon},
title = {Data Types as Quotients of Polynomial Functors},
booktitle = {10th International Conference on Interactive Theorem
Proving, {ITP} 2019, September 9-12, 2019, Portland, OR,
{USA}},
pages = {6:1--6:19},
year = {2019},
url = {https://doi.org/10.4230/LIPIcs.ITP.2019.6},
doi = {10.4230/LIPIcs.ITP.2019.6},
timestamp = {Fri, 27 Sep 2019 15:57:06 +0200},
biburl = {https://dblp.org/rec/conf/itp/AvigadCH19.bib},
bibsource = {dblp computer science bibliography, https://dblp.org},
website = {https://github.com/avigad/qpf}
}
@InProceedings{ Baanen20,
author = {Anne Baanen},
editor = {Nicolas Peltier and Viorica Sofronie{-}Stokkermans},
title = {A Lean Tactic for Normalising Ring Expressions with
Exponents (Short Paper)},
booktitle = {Automated Reasoning - 10th International Joint Conference,
{IJCAR} 2020, Paris, France, July 1-4, 2020, Proceedings,
Part {II}},
series = {Lecture Notes in Computer Science},
volume = {12167},
pages = {21--27},
publisher = {Springer},
year = {2020},
url = {https://doi.org/10.1007/978-3-030-51054-1\_2},
doi = {10.1007/978-3-030-51054-1\_2},
timestamp = {Thu, 06 Aug 2020 21:49:45 +0200},
biburl = {https://dblp.org/rec/conf/cade/Baanen20.bib},
bibsource = {dblp computer science bibliography, https://dblp.org},
tags = {about-mathlib, lean3}
}
@InProceedings{ Baanen22,
author = {Baanen, Anne},
title = {{Use and Abuse of Instance Parameters in the Lean
Mathematical Library}},
booktitle = {13th International Conference on Interactive Theorem
Proving (ITP 2022)},
pages = {4:1--4:20},
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/opus/volltexte/2022/16713},
urn = {urn:nbn:de:0030-drops-167131},
doi = {10.4230/LIPIcs.ITP.2022.4},
annote = {Keywords: formalization of mathematics, dependent type
theory, typeclasses, algebraic hierarchy, Lean prover},
tags = {about-mathlib, lean3}
}
@InProceedings{ BaanenBCD23,
author = {Anne Baanen and Alex J. Best and Nirvana Coppola and
Sander R. Dahmen},
editor = {Robbert Krebbers and Dmitriy Traytel and Brigitte Pientka
and Steve Zdancewic},
title = {Formalized Class Group Computations and Integral Points on
Mordell Elliptic Curves},
booktitle = {Proceedings of the 12th {ACM} {SIGPLAN} International
Conference on Certified Programs and Proofs, {CPP} 2023,
Boston, MA, USA, January 16-17, 2023},
pages = {47--62},
publisher = {{ACM}},
year = {2023},
url = {https://doi.org/10.1145/3573105.3575682},
doi = {10.1145/3573105.3575682},
tags = {formalization, lean3},
timestamp = {Fri, 13 Jan 2023 13:05:42 +0100},
biburl = {https://dblp.org/rec/conf/cpp/BaanenBCD23.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@Misc{ BaanenDahmenNarayananNuccio21,
title = {A formalization of {D}edekind domains and class groups of
global fields},
author = {Anne Baanen and Sander R. Dahmen and Ashvni Narayanan and
Filippo A. E. Nuccio},
year = {2021},
eprint = {2102.02600},
archiveprefix = {arXiv},
primaryclass = {cs.LO},
url = {https://arxiv.org/abs/2102.02600},
website = {https://github.com/lean-forward/class-number},
tags = {formalization, lean3},
note = {To be presented at ITP 2021}
}
@Booklet{ Best2021,
author = {Alexander Best},
title = {Automatically Generalizing Theorems Using Typeclasses},
howpublished = {EasyChair Preprint no. 6216},
url = {https://easychair.org/publications/preprint/KLfT},
year = {2021},
tags = {about-mathlib, lean3}
}
@Article{ BordgCavalleri2021,
author = {Anthony Bordg and Nicol{\`{o}} Cavalleri},
title = {Elements of Differential Geometry in Lean: {A} Report for
Mathematicians},
journal = {CoRR},
volume = {abs/2108.00484},
year = {2021},
url = {https://arxiv.org/abs/2108.00484},
eprinttype = {arXiv},
eprint = {2108.00484},
timestamp = {Thu, 05 Aug 2021 14:27:08 +0200},
biburl = {https://dblp.org/rec/journals/corr/abs-2108-00484.bib},
bibsource = {dblp computer science bibliography, https://dblp.org},
tags = {formalization, lean3}
}
@InProceedings{ Buch18,
author = {Ulrik Buchholtz and Floris {van Doorn} and Egbert Rijke},
title = {Higher Groups in Homotopy Type Theory},
booktitle = {Proceedings of the 33rd Annual {ACM/IEEE} Symposium on
Logic in Computer Science, {LICS} 2018, Oxford, UK, July
09-12, 2018},
pages = {205--214},
year = {2018},
crossref = {DBLP:conf/lics/2018},
url = {https://doi.org/10.1145/3209108.3209150},
doi = {10.1145/3209108.3209150}
}
@InProceedings{ BuzzardCommelinMassot20,
author = {Kevin Buzzard and Johan Commelin and Patrick Massot},
title = {Formalising perfectoid spaces},
booktitle = {Proceedings of the 9th {ACM} {SIGPLAN} International
Conference on Certified Programs and Proofs, {CPP} 2020,
New Orleans, LA, USA, January 20-21, 2020},
pages = {299--312},
year = {2020},
url = {https://doi.org/10.1145/3372885.3373830},
doi = {10.1145/3372885.3373830},
timestamp = {Thu, 23 Jan 2020 16:12:31 +0100},
biburl = {https://dblp.org/rec/conf/cpp/BuzzardCM20.bib},
bibsource = {dblp computer science bibliography, https://dblp.org},
website = {https://leanprover-community.github.io/lean-perfectoid-spaces/},
tags = {formalization, lean3}
}
@Misc{ BuzzardHLLFM21,
title = {Schemes in Lean},
author = {Kevin Buzzard and Chris Hughes and Kenny Lau and Amelia
Livingston and Ramon Fernández Mir and Scott Morrison},
year = {2021},
eprint = {2101.02602},
archiveprefix = {arXiv},
primaryclass = {math.AG},
url = {https://arxiv.org/abs/2101.02602},
tags = {formalization, lean3}
}
@InProceedings{ Carneiro19,
author = {Mario M. Carneiro},
title = {Formalizing Computability Theory via Partial Recursive
Functions},
booktitle = {10th International Conference on Interactive Theorem
Proving, {ITP} 2019, September 9-12, 2019, Portland, OR,
{USA}},
pages = {12:1--12:17},
year = {2019},
url = {https://doi.org/10.4230/LIPIcs.ITP.2019.12},
doi = {10.4230/LIPIcs.ITP.2019.12},
timestamp = {Fri, 27 Sep 2019 15:57:06 +0200},
biburl = {https://dblp.org/rec/conf/itp/Carneiro19.bib},
bibsource = {dblp computer science bibliography, https://dblp.org},
website = {https://github.com/leanprover-community/mathlib/tree/master/src/computability},
tags = {formalization, lean3}
}
@Misc{ CarneiroMaster,
author = {Mario Carneiro},
title = {The Type Theory of Lean},
eprint = {https://github.com/digama0/lean-type-theory/releases},
note = {Master thesis},
year = {2019},
abstract = {Meta-theoretic properties of Lean 3, including
soundness.},
tags = {about-lean, lean3}
}
@InProceedings{ Clune23,
author = {Joshua Clune},
editor = {Robbert Krebbers and Dmitriy Traytel and Brigitte Pientka
and Steve Zdancewic},
title = {A Formalized Reduction of Keller's Conjecture},
booktitle = {Proceedings of the 12th {ACM} {SIGPLAN} International
Conference on Certified Programs and Proofs, {CPP} 2023,
Boston, MA, USA, January 16-17, 2023},
pages = {90--101},
publisher = {{ACM}},
year = {2023},
url = {https://doi.org/10.1145/3573105.3575669},
doi = {10.1145/3573105.3575669},
tags = {formalization, lean3},
timestamp = {Fri, 13 Jan 2023 13:05:42 +0100},
biburl = {https://dblp.org/rec/conf/cpp/Clune23.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@InProceedings{ CommelinLewis21,
author = {Commelin, Johan and Lewis, Robert Y.},
title = {Formalizing the Ring of Witt Vectors},
year = {2021},
isbn = {9781450382991},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
url = {https://doi.org/10.1145/3437992.3439919},
doi = {10.1145/3437992.3439919},
abstract = {The ring of Witt vectors W R over a base ring R is an
important tool in algebraic number theory and lies at the
foundations of modern p-adic Hodge theory. W R has the
interesting property that it constructs a ring of
characteristic 0 out of a ring of characteristic p > 1,
and it can be used more specifically to construct from a
finite field containing ℤ/pℤ the corresponding
unramified field extension of the p-adic numbers ℚp
(which is unique up to isomorphism). We formalize the
notion of a Witt vector in the Lean proof assistant, along
with the corresponding ring operations and other algebraic
structure. We prove in Lean that, for prime p, the ring of
Witt vectors over ℤ/pℤ is isomorphic to the ring of
p-adic integers ℤp. In the process we develop idioms to
cleanly handle calculations of identities between
operations on the ring of Witt vectors. These calculations
are intractable with a naive approach, and require a proof
technique that is usually skimmed over in the informal
literature. Our proofs resemble the informal arguments
while being fully rigorous.},
booktitle = {Proceedings of the 10th ACM SIGPLAN International
Conference on Certified Programs and Proofs},
pages = {264–277},
numpages = {14},
keywords = {ring theory, formal math, proof assistant, Lean, number
theory},
location = {Virtual, Denmark},
series = {CPP 2021},
website = {https://leanprover-community.github.io/witt-vectors/},
tags = {formalization, lean3}
}
@InProceedings{ DahmenHolzlLewis19,
author = {Sander R. Dahmen and Johannes H{\"{o}}lzl and Robert Y.
Lewis},
title = {Formalizing the Solution to the Cap Set Problem},
booktitle = {10th International Conference on Interactive Theorem
Proving, {ITP} 2019, September 9-12, 2019, Portland, OR,
{USA}},
pages = {15:1--15:19},
year = {2019},
url = {https://doi.org/10.4230/LIPIcs.ITP.2019.15},
doi = {10.4230/LIPIcs.ITP.2019.15},
timestamp = {Mon, 23 Sep 2019 17:27:15 +0200},
biburl = {https://dblp.org/rec/conf/itp/DahmenHL19.bib},
bibsource = {dblp computer science bibliography, https://dblp.org},
website = {https://github.com/lean-forward/cap_set_problem},
tags = {formalization, lean3}
}
@InProceedings{ deFrutos22,
author = {de Frutos-Fern\'{a}ndez, Mar{\'\i}a In\'{e}s},
title = {{Formalizing the Ring of Ad\`{e}les of a Global Field}},
booktitle = {13th International Conference on Interactive Theorem
Proving (ITP 2022)},
pages = {14:1--14:18},
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/opus/volltexte/2022/16723},
urn = {urn:nbn:de:0030-drops-167232},
doi = {10.4230/LIPIcs.ITP.2022.14},
annote = {Keywords: formal math, algebraic number theory, class
field theory, Lean, mathlib},
tags = {formalization, lean3}
}
@Misc{ DeMoura15,
author = "{de Moura}, Leonardo and Avigad, Jeremy and Kong, Soonho
and Roux, Cody",
title = {{Elaboration in Dependent Type Theory}},
link = "\url{https://arxiv.org/pdf/1505.04324.pdf}",
year = "2015",
abstract = {Elaboration in Lean 2},
tags = {about-lean, lean2}
}
@InProceedings{ DeMouraKongAvigadVanDoornvonRaumer,
author = {Leonardo Mendonça {de Moura} and Soonho Kong and Jeremy
Avigad and Floris {van Doorn} and Jakob {von Raumer}},
title = {The Lean Theorem Prover (System Description)},
booktitle = {Automated Deduction - CADE-25 - 25th International
Conference on Automated Deduction, Berlin, Germany, August
1-7, 2015, Proceedings},
pages = {378--388},
year = {2015},
crossref = {DBLP:conf/cade/2015},
url = "\url{https://doi.org/10.1007/978-3-319-21401-6_26}",
doi = {10.1007/978-3-319-21401-6\_26},
timestamp = {Tue, 14 May 2019 10:00:39 +0200},
biburl = {https://dblp.org/rec/conf/cade/MouraKADR15.bib},
bibsource = {dblp computer science bibliography, https://dblp.org},
abstract = {System description of Lean 2},
tags = {about-lean, lean2}
}
@InProceedings{ deMouraUllrich2021,
author = "Moura, Leonardo de and Ullrich, Sebastian",
editor = "Platzer, Andr{\'e} and Sutcliffe, Geoff",
title = "The Lean 4 Theorem Prover and Programming Language",
booktitle = "Automated Deduction -- CADE 28",
year = "2021",
publisher = "Springer International Publishing",
address = "Cham",
pages = "625--635",
abstract = "Lean 4 is a reimplementation of the Lean interactive
theorem prover (ITP) in Lean itself. It addresses many
shortcomings of the previous versions and contains many new
features. Lean 4 is fully extensible: users can modify and
extend the parser, elaborator, tactics, decision
procedures, pretty printer, and code generator. The new
system has a hygienic macro system custom-built for ITPs.
It contains a new typeclass resolution procedure based on
tabled resolution, addressing significant performance
problems reported by the growing user base. Lean 4 is also
an efficient functional programming language based on a
novel programming paradigm called functional but in-place.
Efficient code generation is crucial for Lean users because
many write custom proof automation procedures in Lean
itself.",
isbn = "978-3-030-79876-5",
url = {https://link.springer.com/chapter/10.1007/978-3-030-79876-5_37},
tags = {lean4, about-lean}
}
@InProceedings{ DilliesMehta22,
author = {Dillies, Ya\"{e}l and Mehta, Bhavik},
title = {{Formalising Szemer\'{e}di’s Regularity Lemma in Lean}},
booktitle = {13th International Conference on Interactive Theorem
Proving (ITP 2022)},
pages = {9:1--9:19},
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/opus/volltexte/2022/16718},
urn = {urn:nbn:de:0030-drops-167185},
doi = {10.4230/LIPIcs.ITP.2022.9},
annote = {Keywords: Lean, formalisation, formal proof, graph theory,
combinatorics, additive combinatorics, Szemer\'{e}di’s
Regularity Lemma, Roth’s Theorem},
tags = {formalization, lean3}
}
@InProceedings{ Door16,
author = {Floris {van Doorn}},
title = {Constructing the propositional truncation using
non-recursive HITs},
booktitle = {Proceedings of the 5th {ACM} {SIGPLAN} Conference on
Certified Programs and Proofs, Saint Petersburg, FL, USA,
January 20-22, 2016},
pages = {122--129},
year = {2016},
crossref = {DBLP:conf/cpp/2016},
url = {https://doi.org/10.1145/2854065.2854076},
doi = {10.1145/2854065.2854076},
timestamp = {Tue, 06 Nov 2018 16:59:23 +0100},
biburl = {https://dblp.org/rec/bib/conf/cpp/Doorn16},
bibsource = {dblp computer science bibliography, https://dblp.org},
tags = {formalization, lean2}
}
@InProceedings{ Door17,
author = {Floris {van Doorn} and Jakob {von Raumer} and Ulrik
Buchholtz},
title = {Homotopy Type Theory in Lean},
booktitle = {Interactive Theorem Proving - 8th International
Conference, {ITP} 2017, Bras{\'{\i}}lia, Brazil, September
26-29, 2017, Proceedings},
pages = {479--495},
year = {2017},
crossref = {DBLP:conf/itp/2017},
url = "\url{https://doi.org/10.1007/978-3-319-66107-0_30}",
doi = {10.1007/978-3-319-66107-0\_30},
timestamp = {Tue, 14 May 2019 10:00:37 +0200},
biburl = {https://dblp.org/rec/bib/conf/itp/DoornRB17},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@InProceedings{ Door21,
author = {Floris {van Doorn}},
title = {{Formalized Haar Measure}},
booktitle = {12th International Conference on Interactive Theorem
Proving (ITP 2021)},
pages = {18:1--18:17},
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/opus/volltexte/2021/13913},
urn = {urn:nbn:de:0030-drops-139139},
doi = {10.4230/LIPIcs.ITP.2021.18},
annote = {Keywords: Haar measure, measure theory, Bochner integral,
Lean, interactive theorem proving, formalized mathematics},
tags = {formalization, lean3}
}
@InProceedings{ DoornMN23,
author = {Floris van Doorn and Patrick Massot and Oliver Nash},
editor = {Robbert Krebbers and Dmitriy Traytel and Brigitte Pientka
and Steve Zdancewic},
title = {Formalising the h-Principle and Sphere Eversion},
booktitle = {Proceedings of the 12th {ACM} {SIGPLAN} International
Conference on Certified Programs and Proofs, {CPP} 2023,
Boston, MA, USA, January 16-17, 2023},
pages = {121--134},
publisher = {{ACM}},
year = {2023},
url = {https://doi.org/10.1145/3573105.3575688},
doi = {10.1145/3573105.3575688},
tags = {formalization, lean3},
timestamp = {Fri, 13 Jan 2023 13:05:42 +0100},
biburl = {https://dblp.org/rec/conf/cpp/DoornMN23.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@Article{ DupuisLewisMacbeth22,
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/opus/volltexte/2022/16719},
urn = {urn:nbn:de:0030-drops-167191},
doi = {10.4230/LIPIcs.ITP.2022.10},
annote = {Keywords: Functional analysis, Lean, linear algebra,
semilinear, Hilbert space},
tags = {formalization, lean3}
}
@Article{ EURAM17,
author = {Gabriel Ebner and Sebastian Ullrich and Jared Roesch and
Jeremy Avigad and Leonardo {de Moura}},
title = {A metaprogramming framework for formal verification},
journal = {{PACMPL}},
volume = {1},
number = {{ICFP}},
pages = {34:1--34:29},
year = {2017},
url = {https://doi.org/10.1145/3110278},
doi = {10.1145/3110278},
timestamp = {Tue, 06 Nov 2018 12:51:05 +0100},
biburl = {https://dblp.org/rec/bib/journals/pacmpl/EbnerURAM17},
bibsource = {dblp computer science bibliography, https://dblp.org},
tags = {about-lean, lean3}
}
@Misc{ FernandezMir19,
author = {Ramon Fernández Mir},
title = {Schemes in Lean},
eprint = {https://www.imperial.ac.uk/media/imperial-college/faculty-of-engineering/computing/public/1819-ug-projects/Fernandez-I-MirR-Schemes-in-Lean.pdf},
note = {Project report},
year = {2019},
website = {https://github.com/ramonfmir/lean-scheme},
tags = {formalization, lean3}
}
@Article{ Gouezel2021,
author = {S{\'{e}}bastien Gou{\"{e}}zel},
title = {Formalizing the Gromov-Hausdorff space},
journal = {CoRR},
volume = {abs/2108.13660},
year = {2021},
url = {https://arxiv.org/abs/2108.13660},
eprinttype = {arXiv},
eprint = {2108.13660},
timestamp = {Fri, 03 Sep 2021 10:51:17 +0200},
biburl = {https://dblp.org/rec/journals/corr/abs-2108-13660.bib},
bibsource = {dblp computer science bibliography, https://dblp.org},
tags = {formalization, lean3}
}
@InProceedings{ Gouezel22,
author = {S{\'{e}}bastien Gou{\"{e}}zel},
editor = {Kevin Buzzard and Temur Kutsia},
title = {A Formalization of the Change of Variables Formula for
Integrals in mathlib},
booktitle = {Intelligent Computer Mathematics - 15th International
Conference, {CICM} 2022, Tbilisi, Georgia, September 19-23,
2022, Proceedings},
series = {Lecture Notes in Computer Science},
volume = {13467},
pages = {3--18},
publisher = {Springer},
year = {2022},
url = {https://doi.org/10.1007/978-3-031-16681-5\_1},
doi = {10.1007/978-3-031-16681-5\_1},
timestamp = {Mon, 19 Sep 2022 18:41:40 +0200},
biburl = {https://dblp.org/rec/conf/mkm/Gouezel22.bib},
bibsource = {dblp computer science bibliography, https://dblp.org},
tags = {formalization, lean3}
}
@Misc{ GusakovMehtaMiller21,
title = {Formalizing Hall's Marriage Theorem in Lean},
author = {Alena Gusakov and Bhavik Mehta and Kyle A. Miller},
year = {2021},
eprint = {2101.00127},
archiveprefix = {arXiv},
primaryclass = {math.CO},
url = {https://arxiv.org/abs/2101.00127},
tags = {formalization, lean3}
}
@InProceedings{ HanVanDoorn,
author = {Jesse Michael Han and Floris {van Doorn}},
title = {A formal proof of the independence of the continuum
hypothesis},
booktitle = {Proceedings of the 9th {ACM} {SIGPLAN} International
Conference on Certified Programs and Proofs, {CPP} 2020,
New Orleans, LA, USA, January 20-21, 2020},
pages = {353--366},
year = {2020},
url = {https://doi.org/10.1145/3372885.3373826},
doi = {10.1145/3372885.3373826},
timestamp = {Thu, 23 Jan 2020 16:12:31 +0100},
biburl = {https://dblp.org/rec/conf/cpp/HanD20.bib},
bibsource = {dblp computer science bibliography, https://dblp.org},
website = {https://flypitch.github.io/},
tags = {formalization, lean3}
}
@InProceedings{ HanVanDoorn19,
author = {Jesse Michael Han and Floris {van Doorn}},
title = {A Formalization of Forcing and the Unprovability of the
Continuum Hypothesis},
booktitle = {10th International Conference on Interactive Theorem
Proving, {ITP} 2019, September 9-12, 2019, Portland, OR,
{USA}},
pages = {19:1--19:19},
year = {2019},
crossref = {DBLP:conf/itp/2019},
url = {https://doi.org/10.4230/LIPIcs.ITP.2019.19},
doi = {10.4230/LIPIcs.ITP.2019.19},
timestamp = {Sat, 07 Sep 2019 02:31:13 +0200},
biburl = {https://dblp.org/rec/conf/itp/HanD19.bib},
bibsource = {dblp computer science bibliography, https://dblp.org},
tags = {formalization, lean3}
}
@Misc{ Huisinga19,
author = {Marc Huisinga},
title = {Formally Verified Insertion of Reference Counting
Instructions},
eprint = {https://pp.ipd.kit.edu/uploads/publikationen/huisinga19bachelorarbeit.pdf},
note = {Bachelor thesis},
year = {2019},
website = {https://github.com/mhuisi/rc-correctness},
tags = {about-lean, lean4}
}
@InCollection{ KjosHanssenNiraulaYoon22,
author = {Kjos-Hanssen, Bj{\o}rn and Niraula, Saroj and Yoon,
Soowhan},
title = {A parametrized family of {T}versky metrics connecting the
{J}accard distance to an analogue of the normalized
information distance},
booktitle = {L{FCS}: Logical foundations of computer science},
series = {Lecture Notes in Comput. Sci.},
publisher = {Springer, [Cham]},
tags = {formalization, lean3},
url = {https://arxiv.org/abs/2111.02498},
year = {2022}
}
@Booklet{ Kudryashov2021,
author = {Yury Kudryashov},
title = {Formalizing Rotation Number and Its Properties in Lean},
howpublished = {EasyChair Preprint no. 6168},
url = {https://easychair.org/publications/preprint/38w1},
year = {2021},
tags = {formalization, lean3}
}
@InProceedings{ Kudryashov22,
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/opus/volltexte/2022/16732},
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},
tags = {formalization, lean3}
}
@InProceedings{ LeeHurLopes19,
author = {Juneyoung Lee and Chung{-}Kil Hur and Nuno P. Lopes},
title = {AliveInLean: {A} Verified {LLVM} Peephole Optimization
Verifier},
booktitle = {Computer Aided Verification - 31st International
Conference, {CAV} 2019, New York City, NY, USA, July 15-18,
2019, Proceedings, Part {II}},
pages = {445--455},
year = {2019},
url = "\url{https://doi.org/10.1007/978-3-030-25543-5_25}",
doi = {10.1007/978-3-030-25543-5\_25},
timestamp = {Fri, 27 Mar 2020 08:45:57 +0100},
biburl = {https://dblp.org/rec/conf/cav/LeeHL19.bib},
bibsource = {dblp computer science bibliography, https://dblp.org},
website = {https://sf.snu.ac.kr/aliveinlean/}
}
@InProceedings{ Lewis17,
author = {Robert Y. Lewis},
title = {An Extensible Ad Hoc Interface between Lean and
Mathematica},
booktitle = {Proceedings of the Fifth Workshop on Proof eXchange for
Theorem Proving, PxTP 2017, Bras{\'{\i}}lia, Brazil, 23-24
September 2017},
pages = {23--37},
year = {2017},
url = {https://doi.org/10.4204/EPTCS.262.4},
doi = {10.4204/EPTCS.262.4},
timestamp = {Wed, 12 Sep 2018 01:05:13 +0200},
biburl = {https://dblp.org/rec/journals/corr/abs-1712-09288.bib},
bibsource = {dblp computer science bibliography, https://dblp.org},
website = {https://robertylewis.com/leanmm/},
tags = {about-mathlib, lean3}
}
@InProceedings{ Lewis19,
author = {Robert Y. Lewis},
title = {A formal proof of {H}ensel's lemma over the p-adic
integers},
booktitle = {Proceedings of the 8th {ACM} {SIGPLAN} International
Conference on Certified Programs and Proofs, {CPP} 2019,
Cascais, Portugal, January 14-15, 2019},
pages = {15--26},
year = {2019},
crossref = {DBLP:conf/cpp/2019},
url = {https://doi.org/10.1145/3293880.3294089},
doi = {10.1145/3293880.3294089},
timestamp = {Fri, 04 Jan 2019 10:46:45 +0100},
biburl = {https://dblp.org/rec/bib/conf/cpp/Lewis19},
bibsource = {dblp computer science bibliography, https://dblp.org},
tags = {formalization, lean3}
}
@InProceedings{ LewisMadelaine20,
author = {Robert Y. Lewis and Paul{-}Nicolas Madelaine},
title = {Simplifying Casts and Coercions},
booktitle = {Practical Aspects of Automated Reasoning, {PAAR} 2020},
year = {2020},
url = {https://arxiv.org/abs/2001.10594},
archiveprefix = {arXiv},
eprint = {2001.10594},
timestamp = {Thu, 30 Jan 2020 18:46:36 +0100},
biburl = {https://dblp.org/rec/journals/corr/abs-2001-10594.bib},
bibsource = {dblp computer science bibliography, https://dblp.org},
tags = {about-mathlib, lean3}
}
@Article{ LewisWu22,
author = {Robert Y. Lewis and Minchao Wu},
title = {A bi-directional extensible interface between Lean and
Mathematica},
journal = {{Journal of Automated Reasoning}},
volume = {66},
number = {1},
year = {2022},
url = {https://robertylewis.com/leanmm/lean_mm.pdf},
website = {https://robertylewis.com/leanmm},
doi = {https://doi.org/10.1007/s10817-021-09611-1},
tags = {about-mathlib, lean3}
}
@InProceedings{ Limperg21,
author = {Limperg, Jannis},
title = {A Novice-Friendly Induction Tactic for Lean},
year = {2021},
isbn = {9781450382991},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
url = {https://doi.org/10.1145/3437992.3439928},
doi = {10.1145/3437992.3439928},
abstract = {In theorem provers based on dependent type theory such as
Coq and Lean, induction is a fundamental proof method and
induction tactics are omnipresent in proof scripts. Yet the
ergonomics of existing induction tactics are not ideal:
they do not reliably support inductive predicates and
relations; they sometimes generate overly specific or
unnecessarily complex induction hypotheses; and they
occasionally choose confusing names for the hypotheses they
introduce. This paper describes a new induction tactic,
implemented in Lean 3, which addresses these issues. The
tactic is particularly suitable for educational use, but
experts should also find it more convenient than existing
induction tactics. In addition, the tactic serves as a
moderately complex case study for the metaprogramming
framework of Lean 3. The paper describes some difficulties
encountered during the implementation and suggests
improvements to the framework.},
booktitle = {Proceedings of the 10th ACM SIGPLAN International
Conference on Certified Programs and Proofs},
pages = {199–211},
numpages = {13},
keywords = {induction, Lean, tactic, type theory, metaprogramming},
location = {Virtual, Denmark},
series = {CPP 2021},
tags = {about-mathlib, lean3}
}
@InProceedings{ LimpergF23,
author = {Jannis Limperg and Asta Halkj{\ae}r From},
editor = {Robbert Krebbers and Dmitriy Traytel and Brigitte Pientka
and Steve Zdancewic},
title = {Aesop: White-Box Best-First Proof Search for Lean},
booktitle = {Proceedings of the 12th {ACM} {SIGPLAN} International
Conference on Certified Programs and Proofs, {CPP} 2023,
Boston, MA, USA, January 16-17, 2023},
pages = {253--266},
publisher = {{ACM}},
year = {2023},
url = {https://doi.org/10.1145/3573105.3575671},
doi = {10.1145/3573105.3575671},
tags = {lean4},
timestamp = {Fri, 13 Jan 2023 13:05:42 +0100},
biburl = {https://dblp.org/rec/conf/cpp/LimpergF23.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@Article{ Madelaine19,
author = {Paul{-}Nicolas Madelaine},
title = {Arithmetic and Casting in Lean},
url = {https://lean-forward.github.io/norm_cast/norm_cast.pdf},
year = {2019},
tags = {about-mathlib, lean3}
}
@InProceedings{ Mathlib,
title = {The {L}ean mathematical library},
booktitle = {Proceedings of the 9th {ACM} {SIGPLAN} International
Conference on Certified Programs and Proofs, {CPP} 2020,
New Orleans, LA, USA, January 20-21, 2020},
author = {{The mathlib community}},
pages = {367--381},
year = {2020},
url = {https://doi.org/10.1145/3372885.3373824},
doi = {10.1145/3372885.3373824},
timestamp = {Thu, 23 Jan 2020 16:12:31 +0100},
biburl = {https://dblp.org/rec/conf/cpp/X20.bib},
bibsource = {dblp computer science bibliography, https://dblp.org},
website = {https://leanprover-community.github.io/},
tags = {about-mathlib, lean3}
}
@InProceedings{ Mehta22,
author = {Bhavik Mehta},
editor = {Kevin Buzzard and Temur Kutsia},
title = {Formalising the Kruskal-Katona Theorem in Lean},
booktitle = {Intelligent Computer Mathematics - 15th International
Conference, {CICM} 2022, Tbilisi, Georgia, September 19-23,
2022, Proceedings},
series = {Lecture Notes in Computer Science},
volume = {13467},
pages = {75--91},
publisher = {Springer},
year = {2022},
url = {https://doi.org/10.1007/978-3-031-16681-5\_5},
doi = {10.1007/978-3-031-16681-5\_5},
timestamp = {Mon, 19 Sep 2022 18:41:39 +0200},
biburl = {https://dblp.org/rec/conf/mkm/Mehta22.bib},
bibsource = {dblp computer science bibliography, https://dblp.org},
tags = {formalization, lean3}
}
@InProceedings{ Mehta23,
author = {Bhavik Mehta},
editor = {Robbert Krebbers and Dmitriy Traytel and Brigitte Pientka
and Steve Zdancewic},
title = {Formalising Sharkovsky's Theorem (Proof Pearl)},
booktitle = {Proceedings of the 12th {ACM} {SIGPLAN} International
Conference on Certified Programs and Proofs, {CPP} 2023,
Boston, MA, USA, January 16-17, 2023},
pages = {267--274},
publisher = {{ACM}},
year = {2023},
url = {https://doi.org/10.1145/3573105.3575689},
doi = {10.1145/3573105.3575689},
tags = {formalization, lean3},
timestamp = {Fri, 13 Jan 2023 13:05:42 +0100},
biburl = {https://dblp.org/rec/conf/cpp/Mehta23.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@Article{ SelsamDeMoura16,
author = {Daniel Selsam and Leonardo {de Moura}},
title = {Congruence Closure in Intensional Type Theory},
booktitle = {Automated Reasoning - 8th International Joint Conference,
{IJCAR} 2016, Coimbra, Portugal, June 27 - July 2, 2016,
Proceedings},
pages = {99--115},
year = {2016},
crossref = {DBLP:conf/cade/2016},
url = "\url{https://doi.org/10.1007/978-3-319-40229-1_8}",
doi = {10.1007/978-3-319-40229-1\_8},
timestamp = {Wed, 06 Nov 2019 16:45:49 +0100},
biburl = {https://dblp.org/rec/conf/cade/SelsamM16.bib},
bibsource = {dblp computer science bibliography, https://dblp.org},
tags = {about-lean, lean2}
}
@Article{ SelsamHudonDeMoura20,
author = {Selsam, Daniel and Hudon, Simon and {de Moura}, Leonardo},
title = {Sealing Pointer-Based Optimizations behind Pure
Functions},
year = {2020},
issue_date = {August 2020},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
volume = {4},
number = {ICFP},
url = {https://doi.org/10.1145/3408997},
doi = {10.1145/3408997},
abstract = {Functional programming languages are particularly
well-suited for building automated reasoning systems, since
(among other reasons) a logical term is well modeled by an
inductive type, traversing a term can be implemented
generically as a higher-order combinator, and backtracking
search is dramatically simplified by persistent
datastructures. However, existing pure functional
programming languages all suffer a major limitation in
these domains: traversing a term requires time proportional
to the tree size of the term as opposed to its graph size.
This limitation would be particularly devastating when
building automation for interactive theorem provers such as
Lean and Coq, for which the exponential blowup of term-tree
sizes has proved to be both common and difficult to
prevent. All that is needed to recover the optimal scaling
is the ability to perform simple operations on the memory
addresses of terms, and yet allowing these operations to be
used freely would clearly violate the basic premise of
referential transparency. We show how to use dependent
types to seal the necessary pointer-address manipulations
behind pure functional interfaces while requiring only a
negligible amount of additional trust. We have implemented
our approach for the upcoming version (v4) of Lean, and our
approach could be adopted by other languages based on
dependent type theory as well.},
journal = {Proc. ACM Program. Lang.},
month = aug,
articleno = {115},
numpages = {20},
keywords = {interactive theorem proving, Lean, functional
programming},
tags = {about-lean, lean4}
}
@InProceedings{ SelsamLD17,
author = {Daniel Selsam and Percy Liang and David L. Dill},
title = {Developing Bug-Free Machine Learning Systems With Formal
Mathematics},
booktitle = {Proceedings of the 34th International Conference on
Machine Learning, {ICML} 2017, Sydney, NSW, Australia, 6-11
August 2017},
pages = {3047--3056},
year = {2017},
crossref = {DBLP:conf/icml/2017},
url = {http://proceedings.mlr.press/v70/selsam17a.html},
timestamp = {Wed, 29 May 2019 08:41:45 +0200},
biburl = {https://dblp.org/rec/bib/conf/icml/SelsamLD17},
bibsource = {dblp computer science bibliography, https://dblp.org},
website = {https://github.com/dselsam/certigrad}
}
@Misc{ SelsamUllrichDeMoura20,
author = {Daniel Selsam and Sebastian Ullrich and Leonardo {de
Moura}},
title = {Tabled Typeclass Resolution},
journal = {CoRR},
volume = {abs/2001.04301},
year = {2020},
url = {https://arxiv.org/abs/2001.04301},
archiveprefix = {arXiv},
eprint = {2001.04301},
timestamp = {Fri, 17 Jan 2020 14:07:30 +0100},
biburl = {https://dblp.org/rec/journals/corr/abs-2001-04301.bib},
bibsource = {dblp computer science bibliography, https://dblp.org},
tags = {about-lean, lean4}
}
@Misc{ StricklandBellumat19,
author = {Neil Strickland and Nicola Bellumat},
title = {Iterated chromatic localisation},
year = {2019},
eprint = {arXiv:1907.07801},
website = {https://github.com/NeilStrickland/itloc},
tags = {formalization, lean3}
}
@InProceedings{ TassarottiVBT21,
author = {Tassarotti, Joseph and Vajjha, Koundinya and Banerjee,
Anindya and Tristan, Jean-Baptiste},
title = {A Formal Proof of PAC Learnability for Decision Stumps},
year = {2021},
isbn = {9781450382991},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
url = {https://doi.org/10.1145/3437992.3439917},
doi = {10.1145/3437992.3439917},
abstract = {We present a formal proof in Lean of probably
approximately correct (PAC) learnability of the concept
class of decision stumps. This classic result in machine
learning theory derives a bound on error probabilities for
a simple type of classifier. Though such a proof appears
simple on paper, analytic and measure-theoretic subtleties
arise when carrying it out fully formally. Our proof is
structured so as to separate reasoning about deterministic
properties of a learning function from proofs of
measurability and analysis of probabilities.},
booktitle = {Proceedings of the 10th ACM SIGPLAN International
Conference on Certified Programs and Proofs},
pages = {5–17},
numpages = {13},
keywords = {probably approximately correct, interactive theorem
proving, decision stumps},
location = {Virtual, Denmark},
series = {CPP 2021},
tags = {formalization, lean3}