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Bibliography.bib
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@online{hott-in:agda,
author={Guillaume Brunerie
and Kuen-Bang {Hou (Favonia)}
and Evan Cavallo
and Eric Finster
and Jesper Cockx
and Christian Sattler
and Chris Jeris
and Michael Shulman
and others},
title={Homotopy Type Theory in {A}gda},
url={https://github.com/HoTT/HoTT-Agda}
}
@inproceedings{bauer17,
title={The HoTT Library: A formalization of homotopy type theory in Coq},
author={Bauer, Andrej and Gross, Jason and Lumsdaine, Peter LeFanu and Shulman, Michael and Sozeau, Matthieu and Spitters, Bas},
booktitle={Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs},
pages={164--172},
year={2017},
organization={ACM}
}
@article{lawvere64,
title={An elementary theory of the category of sets},
author={Lawvere, F. William},
journal={Proceedings of the national academy of sciences},
volume={52},
number={6},
pages={1506--1511},
year={1964},
publisher={National Acad Sciences}
}
@misc{altenkirch17,
title = {Introduction to Homotopy Type Theory},
author = {Thorsten Altenkirch},
howpublished = {Lecture notes for a course at EWSCS 2017}
}
@misc{voevodsky14,
title = {The Origins and Motivations of {Univalent} {Foundations}},
howpublished = {\url{https://www.ias.edu/ideas/2014/voevodsky-origins}},
note = {Accessed: 2018-04-17}
}
@inproceedings{delahaye00,
title={A tactic language for the system Coq},
author={Delahaye, David},
booktitle={International Conference on Logic for Programming Artificial Intelligence and Reasoning},
pages={85--95},
year={2000},
organization={Springer}
}
@book{lafont95,
title={Advances in linear logic},
author={Girard, Jean-Yves and Lafont, Yves and Regnier, Laurent},
volume={222},
year={1995},
publisher={Cambridge University Press}
}
@article{schreiber14,
title={Quantization via Linear homotopy types},
author={Schreiber, Urs},
journal={arXiv preprint arXiv:1402.7041},
year={2014}
}
@article{mellies09,
title={Categorical semantics of linear logic},
author={Mellies, Paul-Andr{\'e}},
journal={Panoramas et syntheses},
volume={27},
pages={15--215},
year={2009}
}
@article{lago12,
title={On multiplicative linear logic, modality and quantum circuits},
author={Lago, Ugo Dal and Faggian, Claudia},
journal={arXiv preprint arXiv:1210.0613},
year={2012}
}
@incollection{selinger10,
title={A survey of graphical languages for monoidal categories},
author={Selinger, Peter},
booktitle={New structures for physics},
pages={289--355},
year={2010},
publisher={Springer}
}
@inproceedings{vanderwalt12,
title={Engineering proof by reflection in Agda},
author={Van Der Walt, Paul and Swierstra, Wouter},
booktitle={Symposium on Implementation and Application of Functional Languages},
pages={157--173},
year={2012},
organization={Springer}
}
@book{kock06,
title={Synthetic differential geometry},
author={Kock, Anders},
volume={333},
year={2006},
publisher={Cambridge University Press}
}
@article{booij2017parametricity,
title={Parametricity, automorphisms of the universe, and excluded middle},
author={Booij, Auke Bart and Escard{\'o}, Mart{\'\i}n H{\"o}tzel and Lumsdaine, Peter LeFanu and Shulman, Michael},
journal={arXiv preprint arXiv:1701.05617},
year={2017}
}
@article{kraus2016notions,
title={Notions of Anonymous Existence in Martin-L$\backslash$" of Type Theory},
author={Kraus, Nicolai and Escard{\'o}, Mart{\'\i}n and Coquand, Thierry and Altenkirch, Thorsten},
journal={arXiv preprint arXiv:1610.03346},
year={2016}
}
@article{rabe2011kripke,
title={Kripke Semantics for Martin-Löf's Extensional Type Theory},
author={Rabe, Florian and Awodey, Steve},
journal={Logical Methods in Computer Science},
volume={7},
year={2011},
publisher={Episciences. org}
}
@misc{escardoagda,
title = {Some mathematical and computational developments in Haskell and Agda.},
author = {H{\"o}tzel Escard{\'o}, Mart{\'\i}n},
howpublished = {\url{http://www.cs.bham.ac.uk/~mhe/papers/index.html#ref:functional}},
note = {Accessed: 2018-04-17},
}
@Book{hottbook,
author = {The {Univalent Foundations Program}},
title = {Homotopy Type Theory: Univalent Foundations of Mathematics},
publisher = {\url{https://homotopytypetheory.org/book}},
address = {Institute for Advanced Study},
year = {2013}
}
@incollection{martinlof75,
title={An intuitionistic theory of types: Predicative part},
author={Martin-L{\"o}f, Per},
booktitle={Studies in Logic and the Foundations of Mathematics},
volume={80},
pages={73--118},
year={1975},
publisher={Elsevier}
}
@article{unimath,
title={UniMath: Univalent Mathematics},
author={Voevodsky, Vladimir and Ahrens, Benedikt and Grayson, Daniel and others},
journal={URL: https://github.com/UniMat},
year={2010}
}
@article{hedberg98,
title={A coherence theorem for Martin-L{\"o}f's type theory},
author={Hedberg, Michael},
journal={Journal of Functional Programming},
volume={8},
number={4},
pages={413--436},
year={1998},
publisher={Cambridge University Press}
}
@article{streicher93,
title={Investigations into intensional type theory},
author={Streicher, Thomas},
journal={Habilitiation Thesis, Ludwig Maximilian Universit{\"a}t},
year={1993}
}
@incollection{bauer13,
title={Intuitionistic mathematics and realizability in the physical world},
author={Bauer, Andrej},
booktitle={A Computable Universe: Understanding and Exploring Nature as Computation},
pages={143--157},
year={2013},
publisher={World Scientific}
}
@inproceedings{hudak07_haskell,
author = {Paul Hudak and John Hughes and Simon Peyton Jones
and Philip Wadler},
title = {A History of Haskell: Being Lazy With Class},
booktitle = {Proceedings of the third ACM SIGPLAN conference on
History of programming languages},
year = 2007,
pages = 1,
doi = {10.1145/1238844.1238856},
url = {https://doi.org/10.1145/1238844.1238856},
DATE_ADDED = {Fri Jun 16 11:23:03 2017},
month = {April},
publisher = {Microsoft Research},
}
@article{jupyter,
author = {{Jupyter Development Team}},
title = {{Jupyter} {Notebooks}. {A} Publishing Format for Reproducible Computational Workflows},
book = {Positioning and Power in Academic Publishing: Players, Agents and Agendas},
publisher = {IOS Press Ebooks},
pages = {87--90},
doi = {10.3233/978-1-61499-649-1-87}
}
@TechReport{leijen2001,
Author = {Leijen, Daan},
Title = {Parsec, a fast combinator parser},
Number = {35},
Institution = {Department of Computer Science, University of Utrecht (RUU)},
Month = {October},
Year = {2001},
% url = {https://web.archive.org/web/20120401040711/http://legacy.cs.uu.nl/daan/download/parsec/parsec.pdf}
}
@MISC{hutton96,
author = {Graham Hutton and Erik Meijer},
title = {Monadic Parser Combinators},
year = {1996},
number = {NOTTCS-TR-96-4},
institution = {Department of Computer Science, University of Nottingham},
url = {http://www.cs.nott.ac.uk/~pszgmh/monparsing.pdf}
}
@article{hutton98,
author = {Hutton, Graham and Meijer, Erik},
title = {Monadic Parsing in Haskell},
journal = {Journal of Functional Programming},
issue_date = {July 1998},
volume = {8},
number = {4},
month = jul,
year = {1998},
issn = {0956-7968},
pages = {437--444},
numpages = {8},
url = {http://dx.doi.org/10.1017/S0956796898003050},
doi = {10.1017/S0956796898003050},
acmid = {969598},
publisher = {Cambridge University Press},
address = {New York, NY, USA},
}
@inproceedings{Wadler90,
author = {Wadler, Philip},
title = {Comprehending Monads},
booktitle = {Proceedings of the 1990 ACM Conference on LISP and Functional Programming},
series = {LFP '90},
year = {1990},
isbn = {0-89791-368-X},
location = {Nice, France},
pages = {61--78},
numpages = {18},
url = {http://doi.acm.org/10.1145/91556.91592},
doi = {10.1145/91556.91592},
acmid = {91592},
publisher = {ACM},
address = {New York, NY, USA},
}
@misc{nlab,
author = {{nLab authors}},
title = {{{H}}ome{{P}}age},
howpublished = {\url{http://ncatlab.org/nlab/show/HomePage}},
note = {\href{http://ncatlab.org/nlab/revision/HomePage/262}{Revision 262}},
month = may,
year = 2018
}
@inproceedings{Wadler85,
author = {Wadler, Philip},
title = {How to Replace Failure by a List of Successes},
booktitle = {Proc. Of a Conference on Functional Programming Languages and Computer Architecture},
year = {1985},
isbn = {3-387-15975-4},
location = {Nancy, France},
pages = {113--128},
numpages = {16},
url = {http://dl.acm.org/citation.cfm?id=5280.5288},
acmid = {5288},
publisher = {Springer-Verlag New York, Inc.},
address = {New York, NY, USA},
}
@Misc{attoparsec,
author = {Bryan O'Sullivan},
title = {The attoparsec package},
howpublished = {\url{http://hackage.haskell.org/package/attoparsec}},
year = {2007--2016}
}
@book{maclane78,
author = {Saunders Mac Lane},
title = {Categories for the Working Mathematician},
year = 1978,
publisher = {Springer New York},
url = {https://doi.org/10.1007/978-1-4757-4721-8},
DATE_ADDED = {Sat Jul 22 17:28:44 2017},
doi = {10.1007/978-1-4757-4721-8},
pages = {nil},
series = {Graduate Texts in Mathematics},
}
@book{Hindley08,
author = {Hindley, J. Roger and Seldin, Jonathan P.},
title = {Lambda-Calculus and Combinators: An Introduction},
year = {2008},
isbn = {0521898854, 9780521898850},
edition = {2},
publisher = {Cambridge University Press},
address = {New York, NY, USA},
}
@article{dallago08,
title={The weak lambda calculus as a reasonable machine},
author={Dal Lago, Ugo and Martini, Simone},
journal={Theoretical Computer Science},
volume={398},
number={1-3},
pages={32--50},
year={2008},
publisher={Elsevier}
}
@unpublished{selinger13,
author = {Selinger, Peter},
title = {Lecture notes on the lambda calculus},
note = {Expository course notes, 120 pages. Available from
\arxiv{0804.3434}},
year = 2013,
filename = lambdanotes
}
@article{kamareddine01,
author = {Fairouz Kamareddine},
title = {Reviewing the classical and the de Bruijn notation for lambda-calculus and pure type systems},
journal = {Logic and Computation},
year = {2001},
volume = {11},
pages = {11--3}
}
@article{debruijn81,
author = {N.G. de Bruijn},
title = {Lambda calculus notation with nameless dummies, a tool for automatic formula manipulation, with application to the {C}hurch-{R}osser theorem},
journal = "Indagationes Mathematicae (Proceedings)",
volume = "75",
number = "5",
pages = "381 - 392",
year = "1972",
%note = "",
%issn = "1385-7258",
%doi = "http://dx.doi.org/10.1016/1385-7258(72)90034-0",
%url = "http://www.sciencedirect.com/science/article/pii/1385725872900340",
}
@book{haskell58,
author = {H. B. Curry and R. Feys},
title = {Combinatory Logic, Volume I},
publisher = {North-Holland},
year = {1958},
pages = {xvi+417},
note = {Second printing 1968}
}
@article{hofmann98,
title={The groupoid interpretation of type theory},
author={Hofmann, Martin and Streicher, Thomas},
journal={Twenty-five years of constructive type theory (Venice, 1995)},
volume={36},
pages={83--111},
year={1998}
}
@article{church40,
author = {Church, Alonzo},
groups = {public},
journal = {Journal of Symbolic Logic},
keywords = {type},
month = {June},
number = 2,
pages = {56-68},
title = {A Formulation of the Simple Theory of Types},
volume = 5,
year = 1940
}
@INPROCEEDINGS{tamsamani96,
author = {{Tamsamani}, Z.},
title = "{Equivalence de la théorie homotopique des $n$-groupoïdes et celle des espaces topologiques $n$-tronqués}",
keywords = {Mathematics - Algebraic Geometry},
booktitle = {eprint arXiv:alg-geom/9607010},
year = 1996,
month = jul,
adsurl = {http://adsabs.harvard.edu/abs/1996alg.geom..7010T},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
@inproceedings{licata13,
title={Calculating the fundamental group of the circle in homotopy type theory},
author={Licata, Daniel R and Shulman, Michael},
booktitle={Logic in Computer Science (LICS), 2013 28th Annual IEEE/ACM Symposium on},
pages={223--232},
year={2013},
organization={IEEE}
}
@article{berg11,
title={Types are weak $\omega$-groupoids},
author={Van Den Berg, Benno and Garner, Richard},
journal={Proceedings of the London Mathematical Society},
volume={102},
number={2},
pages={370--394},
year={2011},
publisher={Wiley Online Library}
}
@article{wadler15,
author = {Wadler, Philip},
title = {Propositions As Types},
journal = {Commun. ACM},
issue_date = {December 2015},
volume = {58},
number = {12},
month = nov,
year = {2015},
issn = {0001-0782},
pages = {75--84},
numpages = {10},
url = {http://doi.acm.org/10.1145/2699407},
doi = {10.1145/2699407},
acmid = {2699407},
publisher = {ACM},
address = {New York, NY, USA},
}
@article{curry34,
ISSN = {00278424},
URL = {http://www.jstor.org/stable/86796},
author = {H. B. Curry},
journal = {Proceedings of the National Academy of Sciences of the United States of America},
number = {11},
pages = {584-590},
publisher = {National Academy of Sciences},
title = {Functionality in Combinatory Logic},
volume = {20},
year = {1934}
}
@book{girard89,
author = {Girard, Jean-Yves and Taylor, Paul and Lafont, Yves},
title = {Proofs and Types},
year = {1989},
isbn = {0-521-37181-3},
publisher = {Cambridge University Press},
address = {New York, NY, USA},
}
@misc{barendsen94,
title={Introduction to lambda calculus},
author={Barendsen, Henk Barendregt Erik},
year={1994}
}
@book{barendregt84,
title={The lambda calculus: its syntax and semantics},
author={Barendregt, H.P.},
isbn={9780444867483},
lccn={84005966},
series={Studies in logic and the foundations of mathematics},
year={1984},
publisher={North-Holland}
}
@article{kashima00,
title = {A Proof of the Standardization Theorem in Lambda-Calculus},
author = {Kashima, Ryo},
year = {2000},
journal = {Tokyo Institute of Technology}
}
@book{maclane94,
title={Sheaves in Geometry and Logic: A First Introduction to Topos Theory},
author={Moerdijk, I. and MacLane, S.},
isbn={9780387977102},
lccn={lc91033709},
series={Universitext},
url={https://books.google.es/books?id=SGwwDerbEowC},
year={1994},
publisher={Springer New York}
}
@article{maclane42,
ISSN = {0003486X},
URL = {http://www.jstor.org/stable/1968966},
author = {Samuel Eilenberg and Saunders MacLane},
journal = {Annals of Mathematics},
number = {4},
pages = {757-831},
publisher = {Annals of Mathematics},
title = {Group Extensions and Homology},
volume = {43},
year = {1942}
}
@incollection{barendregt92,
author = {Barendregt, H. P.},
chapter = {Lambda Calculi with Types},
title = {Handbook of Logic in Computer Science (Vol. 2)},
editor = {Abramsky, S. and Gabbay, Dov M. and Maibaum, S. E.},
year = {1992},
isbn = {0-19-853761-1},
pages = {117--309},
numpages = {193},
url = {http://dl.acm.org/citation.cfm?id=162552.162561},
acmid = {162561},
publisher = {Oxford University Press, Inc.},
address = {New York, NY, USA},
}
@article{haskell98,
author = {Simon {Peyton-Jones} and others},
title = {The {Haskell} 98 Language and Libraries: The Revised Report},
journal = {Journal of Functional Programming},
volume = 13,
number = 1,
pages = {0--255},
month = {Jan},
year = 2003,
note = {\url{http://www.haskell.org/definition/}},
}
@online{gitsoftware,
author = {}
}
@article{hughes89,
author = {Hughes, J.},
title = {Why Functional Programming Matters},
journal = {Comput. J.},
issue_date = {April 1989},
volume = {32},
number = {2},
month = apr,
year = {1989},
issn = {0010-4620},
pages = {98--107},
numpages = {10},
url = {http://dx.doi.org/10.1093/comjnl/32.2.98},
doi = {10.1093/comjnl/32.2.98},
acmid = {63411},
publisher = {Oxford University Press},
address = {Oxford, UK},
}
@INPROCEEDINGS{mccune91,
author = {William W. McCune},
title = {Single axioms for groups and Abelian groups with various operations},
booktitle = {Preprint MCS-P270-1091, Mathematics and Computer Science Division,
Argonne National Laboratory, Argonne, IL},
year = {1991},
}
@article{pollack95,
author = {Robert Pollack},
title = {Polishing Up the {T}ait-{M}artin-{L}öf Proof of the {C}hurch-{R}osser Theorem},
year = {1995},
journal = {Proc. De Wintermöte, Chalmers University}
}
@article{curry46,
journal = {Journal of Symbolic Logic},
author = {Haskell B. Curry},
pages = {136--137},
title = {The Paradox of {K}leene and {R}osser},
number = {4},
publisher = {Association for Symbolic Logic},
year = {1946},
volume = {11}
}
@article{kleene35,
ISSN = {0003486X},
URL = {http://www.jstor.org/stable/1968646},
author = {S. C. Kleene and J. B. Rosser},
journal = {Annals of Mathematics},
number = {3},
pages = {630-636},
publisher = {Annals of Mathematics},
title = {The Inconsistency of Certain Formal Logics},
volume = {36},
year = {1935}
}
@article{turing37,
ISSN = {00224812},
URL = {http://www.jstor.org/stable/2268280},
author = {A. M. Turing},
journal = {The Journal of Symbolic Logic},
number = {4},
pages = {153-163},
publisher = {[Association for Symbolic Logic, Cambridge University Press]},
title = {Computability and λ-Definability},
volume = {2},
year = {1937}
}
@article{church36,
ISSN = {00029327, 10806377},
URL = {http://www.jstor.org/stable/2371045},
author = {Alonzo Church},
journal = {American Journal of Mathematics},
number = {2},
pages = {345-363},
publisher = {Johns Hopkins University Press},
title = {An Unsolvable Problem of Elementary Number Theory},
volume = {58},
year = {1936}
}
@article{tait67,
ISSN = {00224812},
URL = {http://www.jstor.org/stable/2271658},
author = {W. W. Tait},
journal = {The Journal of Symbolic Logic},
number = {2},
pages = {198-212},
publisher = {Association for Symbolic Logic},
title = {Intensional Interpretations of Functionals of Finite Type I},
volume = {32},
year = {1967}
}
@book{kunen11,
title={Set Theory},
author={Kunen, K.},
isbn={9781848900509},
series={Studies in logic},
url={https://books.google.es/books?id=Zn8ppwAACAAJ},
year={2011},
publisher={College Publications}
}
@Inbook{crossley75,
author="Crossley, J. N.",
editor="Crossley, John Newsome",
title="Reminiscences of logicians",
bookTitle="Algebra and Logic: Papers from the 1974 Summer Research Institute of the Australian Mathematical Society, Monash University, Australia",
year="1975",
publisher="Springer Berlin Heidelberg",
address="Berlin, Heidelberg",
pages="1--62",
isbn="978-3-540-37480-0",
doi="10.1007/BFb0062850",
url="https://doi.org/10.1007/BFb0062850"
}
@online{thecatsters,
title = {The catsters: course on category theory},
date = {2014},
organization = {Sheffield University},
author = {Eugenia Chang and Simon Willerton},
publisher = {Sheffield University},
url = {https://www.youtube.com/user/TheCatsters},
}
@Inbook{joyal91,
author="Joyal, Andr{\'e} and Street, Ross",
editor="Carboni, Aurelio and Pedicchio, Maria Cristina and Rosolini, Guiseppe",
title="An introduction to Tannaka duality and quantum groups",
bookTitle="Category Theory: Proceedings of the International Conference held in Como, Italy, July 22--28, 1990",
year="1991",
publisher="Springer Berlin Heidelberg",
address="Berlin, Heidelberg",
pages="413--492",
isbn="978-3-540-46435-8",
doi="10.1007/BFb0084235",
url="https://doi.org/10.1007/BFb0084235"
}
@book{lawvere09,
author = {Lawvere, F. William and Schanuel, Stephen H.},
title = {Conceptual Mathematics: A First Introduction to Categories},
year = {2009},
isbn = {0521894859, 9780521894852},
edition = {2nd},
publisher = {Cambridge University Press},
address = {New York, NY, USA},
}
@misc{Conor17,
author = {McBride, Conor},
title = {CS410 Advanced Functional Programming},
year = {2017},
publisher = {GitHub},
journal = {GitHub repository},
howpublished = {\url{https://github.com/pigworker/CS410-17}},
commit = {5bbcb3e3b254226163c26b26d42fa7b133f18e55}
}
@Manual{coq04,
title = {The Coq proof assistant reference manual},
author = {\mbox{The Coq development team}},
organization = {LogiCal Project},
note = {Version 8.0},
year = {2004},
url = "http://coq.inria.fr"
}
@book{nuprl86,
author = {Constable, R. L. and Allen, S. F. and Bromley, H. M. and Cleaveland, W. R. and Cremer, J. F. and Harper, R. W. and Howe, D. J. and Knoblock, T. B. and Mendler, N. P. and Panangaden, P. and Sasaki, J. T. and Smith, S. F.},
title = {Implementing Mathematics with the Nuprl Proof Development System},
year = {1986},
isbn = {0-13-451832-2},
publisher = {Prentice-Hall, Inc.},
address = {Upper Saddle River, NJ, USA},
}
@article{huber16,
author = {Simon Huber},
title = {Canonicity for Cubical Type Theory},
journal = {CoRR},
volume = {abs/1607.04156},
year = {2016},
url = {http://arxiv.org/abs/1607.04156},
timestamp = {Wed, 07 Jun 2017 14:40:19 +0200},
biburl = {http://dblp.uni-trier.de/rec/bib/journals/corr/Huber16},
bibsource = {dblp computer science bibliography, http://dblp.org}
}
@article{cohen16,
author = {Cyril Cohen and
Thierry Coquand and
Simon Huber and
Anders M{\"{o}}rtberg},
title = {Cubical Type Theory: a constructive interpretation of the univalence
axiom},
journal = {CoRR},
volume = {abs/1611.02108},
year = {2016},
url = {http://arxiv.org/abs/1611.02108},
timestamp = {Wed, 07 Jun 2017 14:41:32 +0200},
biburl = {http://dblp.uni-trier.de/rec/bib/journals/corr/CohenCHM16},
bibsource = {dblp computer science bibliography, http://dblp.org}
}
@article{awodey04,
title={Propositions as [types]},
author={Awodey, Steve and Bauer, Andrej},
journal={Journal of logic and computation},
volume={14},
number={4},
pages={447--471},
year={2004},
publisher={Oxford University Press}
}
@article{leinster10,
title={An informal introduction to topos theory},
author={Leinster, Tom},
journal={arXiv preprint arXiv:1012.5647},
year={2010}
}
@misc{bauer17,
author = {Steve Awodey and Andrej Bauer},
title = {Lecture notes: Introduction to categorical logic},
year = {2017},
howpublised = {https://www.andrew.cmu.edu/user/awodey/catlog/},
}
@misc{bishop67,
author = {Errett Bishop},
title = {A General Language},
year = {1967},
howpublised = {\url{https://u.cs.biu.ac.il/~katzmik/bishop18aa.pdf}},
}
@article{bishop67foundations,
title={Foundations of constructive analysis},
author={Bishop, Errett},
year={1967},
journal={{I}shi {P}ress {I}nternational},
}
@book{brouwer07,
title={Over de {G}rondslagen der {W}iskunde},
author={Brouwer, Luitzen Egbertus Jan},
year={1907},
}
@article{riehl2017type,
title={A type theory for synthetic $\infty$-categories},
author={Riehl, Emily and Shulman, Michael},
journal={arXiv preprint arXiv:1705.07442},
year={2017}
}
@article{lawvere1986taking,
title={Taking categories seriously},
author={Lawvere, F. William and others},
journal={Revista Colombiana de Matem{\'a}ticas, XX},
pages={147--178},
year={1986}
}
@book{troelstra2014,
title={Constructivism in mathematics},
author={Troelstra, Anne Sjerp and Van Dalen, Dirk},
volume={2},
year={2014},
publisher={Elsevier}
}
@article{riehl11,
title = {A leisurely introduction to simplicial sets},
journal = {Unpublished expository article available online at http://www. math. harvard. edu/∼ eriehl},
author = {Riehl, Emily},
year = {2011},
file = {ssets.pdf:/home/mario/Zotero/storage/3YE8I4VY/ssets.pdf:application/pdf}
}
@misc{redprl,
title={RedPRL--the People’s Refinement Logic},
author={Sterling, Jonathan and Gratzer, Danny and Rahli, Vincent and Morrison, Darin and Akentyev, Eugene and Tosun, Ayberk},
year={2016}
}
@book{nordstrom90,
title={Programming in Martin-L{\"o}f’s type theory},
author={Nordstr{\"o}m, Bengt and Petersson, Kent and Smith, Jan M},
volume={200},
year={1990},
publisher={Oxford University Press Oxford}
}
@book{goerss09,
title = {Simplicial homotopy theory},
urldate = {2017-10-15},
publisher = {Springer Science \& Business Media},
author = {Goerss, Paul G. and Jardine, John F.},
year = {2009},
}
@article{groth10,
author = {{Groth}, M.},
title = "{A short course on $\infty$-categories}",
journal = {ArXiv e-prints},
archivePrefix = "arXiv",
eprint = {1007.2925},
primaryClass = "math.AT",
keywords = {Mathematics - Algebraic Topology, Mathematics - Algebraic Geometry, Mathematics - Category Theory},
year = 2010,
month = jul,
}
@article{lawvere64,
title = {An {Elementary} {Theory} of the {Category} of {Sets}},
volume = {52},
issn = {0027-8424},
url = {https://www.ncbi.nlm.nih.gov/pmc/articles/PMC300477/},
number = {6},
urldate = {2017-10-25},
journal = {Proceedings of the National Academy of Sciences of the United States of America},
author = {Lawvere, F. William},
month = dec,
year = {1964},
pmid = {16591243},
pmcid = {PMC300477},
pages = {1506--1511}
}
@article{johnstone79,
title={On a topological topos},
author={Johnstone, Peter T},
journal={Proceedings of the London mathematical society},
volume={3},
number={2},
pages={237--271},
year={1979},
publisher={Wiley Online Library}
}
@book{vanoosten08,
title={Realizability: an introduction to its categorical side},
author={Van Oosten, Jaap},
volume={152},
year={2008},
publisher={Elsevier}
}
@inproceedings{escardo15,
title={The inconsistency of a {B}rouwerian continuity principle with the {C}urry--{H}oward interpretation},
author={H{\"o}tzel Escard{\'o}, Mart{\'\i}n and Xu, Chuangjie},
booktitle={{LIPI}cs-{Leibniz} {I}nternational {P}roceedings in {I}nformatics},
volume={38},
year={2015},
organization={Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik}
}
@incollection{martinlof08,
title={The Hilbert-Brouwer controversy resolved?},
author={Martin-L{\"o}f, Per},
booktitle={One hundred years of intuitionism (1907--2007)},
pages={243--256},
year={2008},
publisher={Springer}
}
@article{bauer2017five,
title={Five stages of accepting constructive mathematics},
author={Bauer, Andrej},
journal={Bulletin of the American Mathematical Society},
volume={54},
number={3},
pages={481--498},
year={2017}
}
@article{dubuc89,
title={Integraci{\'o}n de campos vectoriales y geometr{\'\i}a diferencial sint{\'e}tica},
author={Dubuc, Eduardo J},
journal={Revista de la Uni{\'o}n Matem{\'a}tica Argentina},
volume={35},
pages={151--162},
year={1989},
publisher={Uni{\'o}n Matem{\'a}tica Argentina}
}
@article{church32,
title={A set of postulates for the foundation of logic},
author={Church, Alonzo},
journal={Annals of mathematics},
pages={346--366},
year={1932},
publisher={JSTOR}
}
@article{lawvere309,
title = {Use of {Logical} {Operators} in mathematics},
author = {Lawvere, F. William},
journal = {{Lecture} notes in {Linear} {Algebra}, 309},
}
@article{lawvere06,
title = {Diagonal arguments and {Cartesian} {Closed} {Categories}},
author = {Lawvere, F. William},
journal = {Reprints in Theory and Applications of Categories},
year = {2016},
pages = {1--13}
}
@article{yanofsky03,
title = {A universal approach to {Self}-{Referential} {Paradoxes}, {Incompleteness} and {Fixed points}},
author = {Noson S. Yanofsky},
year = 2003,
pages = {15--17}
}
@book{awodey10,
title={Category theory},