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references.bib
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% Please do not open this file with BibDesk. It screws up git diffs.
@Book{Euclid,
author = {Euclid},
title = {Elements, {V}ols.\ 1--13},
publisher = {Elsevier},
year = {300 {BC}}}
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Author = {Andrej Bauer and Paul Taylor},
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Volume = 19,
Year = 2009}
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Number = 664,
Series = {Lecture Notes in Computer Science},
Title = {{Inductive Definitions in the System {Coq} - Rules and Properties}},
Year = 1993}
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author = {Kent Petersson and Dan Synek},
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volume = 389,
series = {Lecture Notes in Computer Science},
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publisher = {Springer}}
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Author = {Peter Dybjer},
Journal = {Journal of Symbolic Logic},
Number = {2},
Pages = {525--549},
Title = {A general formulation of simultaneous inductive-recursive definitions in type theory},
Volume = {65},
Year = {2000}}
@incollection{Dybjer:1991,
Author = {Peter Dybjer},
Booktitle = {Logical Frameworks},
Editor = {Gerard Huet and Gordon Plotkin},
Pages = {280--30},
Publisher = {Cambridge University Press},
Title = {Inductive sets and families in {M}artin-{L}{\"o}f's type theory and their set-theoretic semantics},
Year = 1991}
@incollection{CoquandPaulin,
Author = {Thierry Coquand and Christine Paulin},
Booktitle = {COLOG-88 (Tallinn, 1988)},
Pages = {50--66},
Publisher = {Springer},
Series = {Lecture Notes in Computer Science},
Title = {Inductively defined types},
Volume = {416},
Year = {1990}}
@incollection{PfenningPaulinMohring,
Author = {Frank Pfenning and Christine Paulin-Mohring},
Booktitle = {Mathematical Foundations of Programming Semantics, 5th International
Conference, Tulane University, New Orleans, Louisiana, USA,
March 29 -- April 1, 1989, Proceedings},
Number = {442},
Pages = {209--228},
Editor = {Michael G. Main and Austin Melton and Michael W. Mislove and David A. Schmidt},
Publisher = {Springer},
Series = {Lecture Notes in Computer Science},
Title = {Inductively defined types in the calculus of constructions},
Year = {1990}}
@inproceedings{martin-lof-hauptsatz,
Author = {Per Martin-L{\"{o}}f},
Booktitle = {Proceedings of the Second Scandinavian Logic Symposium (University of Oslo 1970)},
Pages = {179--216},
Publisher = {North-Holland},
Series = {Studies in Logic and the Foundations of Mathematics},
Title = {Hauptsatz for the intuitionistic theory of iterated inductive definitions},
Volume = {63},
Year = {1971}}
@book{WR:PM,
Address = {New York},
Author = {Whitehead, Alfred North and Russell, Bertrand},
Pages = {xlvi+410},
Publisher = {Cambridge University Press},
Title = {Principia mathematica to {$^{\ast} 56$}},
Year = {1962}}
@book{TroelstraII,
Address = {Amsterdam},
Author = {Troelstra, Anne Sjerp and van Dalen, Dirk},
Isbn = {0-444-70358-6},
Note = {An introduction},
Pages = {i--xviii and 345--880 and I--LII},
Publisher = {North-Holland Publishing Co.},
Series = {Studies in Logic and the Foundations of Mathematics},
Title = {Constructivism in mathematics. {V}ol. {II}},
Volume = {123},
Year = {1988}}
@book{TroelstraI,
Address = {Amsterdam},
Author = {Troelstra, Anne Sjerp and van Dalen, Dirk},
Isbn = {0-444-70266-0; 0-444-70506-6},
Note = {An introduction},
Pages = {xx+342+XIV},
Publisher = {North-Holland Publishing Co.},
Series = {Studies in Logic and the Foundations of Mathematics},
Title = {Constructivism in mathematics. {V}ol. {I}},
Volume = {121},
Year = {1988}}
@article{martin2006100,
Author = {Martin-L{\"o}f, Per},
Journal = {The Computer Journal},
Number = {3},
Pages = {345--350},
Publisher = {BCS},
Title = {100 years of {Z}ermelo's axiom of choice: what was the problem with it?},
Volume = {49},
Year = {2006}}
@inproceedings{aczel2002collection,
Author = {Aczel, Peter and Gambino, Nicola},
Booktitle = {Types for Proofs and Programs, International Workshop, TYPES
2000, Durham, UK, December 8-12, 2000, Selected Papers},
Editor = {Paul Callaghan and Zhaohui Luo and James McKinna and Robert Pollack},
Pages = {1--23},
Publisher = {Springer},
series = {Lecture Notes in Computer Science},
volume = 2277,
Title = {Collection principles in dependent type theory},
Year = 2002}
@InCollection{maietti2005toward,
author = {Maietti, Maria Emilia and Sambin, Giovanni},
title = {Toward a minimalist foundation for constructive mathematics},
booktitle = {From Sets and Types to Topology and Analysis: Practicable Foundations for Constructive Mathematics},
publisher = {Clarendon Press},
year = 2005,
editor = {Laura Crosilla and Peter Schuster},
volume = 48,
series = {Oxford Logic Guides},
pages = {91--114}}
@phdthesis{Spiwack,
Author = {Arnaud Spiwack},
School = {{\'Ecole Polytechnique, Palaiseau, France}},
Title = {A Journey Exploring the Power and Limits of Dependent Type Theory},
Year = 2011}
@article{Palmgren:FT,
Author = {Palmgren, Erik},
Doi = {10.1016/j.topol.2007.01.018},
Issn = {0166-8641},
Journal = {Topology and its Applications},
Number = {9},
Pages = {1854--1880},
Title = {A constructive and functorial embedding of locally compact metric spaces into locales},
Url = {http://dx.doi.org/10.1016/j.topol.2007.01.018},
Volume = {154},
Year = {2007}
}
@unpublished{forsbergfinite,
Author = {Forsberg, Fredrik Nordvall and Setzer, Anton},
Note = {\url{http://cs.swan.ac.uk/~csfnf/papers/indind_finite.pdf}},
Title = {A finite axiomatisation of inductive-inductive definitions},
Year = 2012}
@article{lawvere:adjinfound,
Author = {F. William Lawvere},
Journal = {Reprints in Theory and Applications of Categories},
Note = {Reprinted from Dialectica {\bf 23} (1969)},
Pages = {1--16},
Title = {Adjointness in Foundations},
Volume = {16},
Year = {2006}}
@book{somma,
Author = {Giovanni Sommaruga},
Number = {290},
Publisher = {Kluwer},
Series = {Synthese Library},
Title = {History and Philosophy of Constructive Type Theory},
Year = {2010}}
@book{kamar,
Author = {Fairouz Kamareddine and Twan Laan and Rob Nederpelt},
Number = {29},
Publisher = {Kluwer},
Series = {Applied Logic},
Title = {A Modern Perspective on Type Theory: From its Origins until Today},
Year = {2004}}
@book{beeson,
Author = {Beeson, Michael},
Publisher = {Springer},
Title = {Foundations of Constructive Mathematics},
Year = 1985}
@book{heyting1966intuitionism,
Author = {Heyting, Arend},
Publisher = {North-Holland Pub. Co.},
Series = {Studies in logic and the foundations of mathematics},
Title = {Intuitionism: an introduction},
Year = {1966}}
@InProceedings{Scott70,
author = {Dana Scott},
title = {Constructive Validity},
booktitle = {Symposium on Automatic Demonstration},
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publisher = {Springer-Verlag}}
@article{Richman:reals,
Author = {Richman, Fred},
Doi = {10.1002/malq.200710024},
Journal = {Mathematical Logic Quarterly},
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Title = {Real numbers and other completions},
Url = {http://dx.doi.org/10.1002/malq.200710024},
Volume = {54},
Year = {2008}}
@ARTICLE{Richman00thefundamental,
author = {Fred Richman},
title = {The fundamental theorem of algebra: a constructive development without choice},
journal = {Pacific Journal of Mathematics},
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volume = 196,
number = 1,
pages = {213--230}
}
@techreport{HoTTbook,
Author = {The Univalent Foundations Program},
Institution = {Institute for Advanced Study},
Title = {Homotopy type theory: Univalent foundations of mathematics},
Year = {2013}}
@incollection{AczelCZF,
Address = {Amsterdam},
Author = {Aczel, Peter},
Booktitle = {Logic {C}olloquium '77},
Editor = {A. MacIntyre and L. Pacholski and J. Paris},
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Publisher = {North-Holland},
Series = {Studies in Logic and the Foundations of Mathematics},
Title = {The type theoretic interpretation of constructive set theory},
Volume = {96},
Year = {1978}}
@book{JoyalMoerdijk1995,
Author = {Joyal, A. and Moerdijk, I.},
Doi = {10.1017/CBO9780511752483},
Pages = {viii+123},
Publisher = {Cambridge University Press},
Series = {London Mathematical Society Lecture Note Series},
Title = {Algebraic set theory},
Url = {http://dx.doi.org/10.1017/CBO9780511752483},
Volume = {220},
Year = {1995}}
@book{PM2,
Address = {Cambridge},
Author = {Whitehead, Alfred North and Russell, Bertrand},
Publisher = {Cambridge University Press},
Title = {Principia mathematica, 3 vol.s},
Year = {1910--1913; Second edition, 1925--1927}}
@book{Lawvere/Rosenburgh,
Address = {Cambridge},
Author = {Lawvere, F. William and Rosebrugh, Robert},
Doi = {10.1017/CBO9780511755460},
Isbn = {0-521-80444-2; 0-521-01060-8},
Pages = {xiv+261},
Publisher = {Cambridge University Press},
Title = {Sets for mathematics},
Url = {http://dx.doi.org/10.1017/CBO9780511755460},
Year = {2003}}
@article{modalTT,
Author = {Valeria de Paiva and Rajeev Gor{\'e} and Michael Mendler},
Journal = {Journal of Logic and Computation},
Keywords = {Editorial introduction to special issue.},
Number = {4},
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Title = {Modalities in constructive logics and type theories},
Volume = {14},
Year = {2004}}
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Author = {Georges Gonthier and Andrea Asperti and Jeremy Avigad and Yves Bertot and Cyril Cohen and Fran{\c c}ois Garillot and St{\'e}phane Le Roux and Assia Mahboubi and Russell O'Connor and Sidi Ould Biha and Ioana Pasca and Laurence Rideau and Alexey Solovyev and Enrico Tassi and Laurent Thery},
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Year = 2013}
@misc{wikipedia-groups,
Author = {Wikipedia},
Month = {April},
Title = {Homotopy groups of spheres},
Url = {http://en.wikipedia.org/wiki/Homotopy_groups_of_spheres\#Table},
Year = 2013}
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Author = {Bridges, Douglas and Ishihara, Hajime and Schuster, Peter},
Booktitle = {Computer Science Logic, 16th International Workshop, CSL
2002, 11th Annual Conference of the EACSL, Edinburgh, Scotland,
UK, September 22-25, 2002, Proceedings},
Editor = {Julian C. Bradfield},
Publisher = {Springer},
series = {Lecture Notes in Computer Science},
volume = {2471},
Pages = {89--102},
Title = {Compactness and continuity, constructively revisited},
Year = {2002}}
@inproceedings{EscardoSimpson:01,
Author = {Mart\'{\i}n H{\"o}tzel Escard{\'o} and Alex K. Simpson},
Booktitle = {16th Annual IEEE Symposium on Logic in Computer Science,
Boston, Massachusetts, USA, June 16-19, 2001, Proceedings},
Publisher = {IEEE Computer Society},
Pages = {115--125},
Title = {A Universal Characterization of the Closed Euclidean Interval},
Year = {2001}}
@book{knuth74:_surreal_number,
Author = {Knuth, Donald Ervin},
Publisher = {Addison-Wesley},
Title = {Surreal Numbers},
Year = 1974}
@article{Diaconescu,
Author = {Diaconescu, Radu},
Journal = {Proceedings of the American Mathematical Society},
Pages = {176--178},
Title = {Axiom of choice and complementation},
Volume = {51},
Year = {1975}}
@book{Bishop1967,
Address = {New York},
Author = {Bishop, Erret},
Pages = {xiii+370},
Publisher = {McGraw-Hill Book Co.},
Title = {Foundations of constructive analysis},
Year = {1967}}
@techreport{aczel2001notes,
author = {Peter Aczel and Michael Rathjen},
title = {Notes on Constructive Set Theory},
institution = {Institut Mittag--Leffler Preprint},
volume = {40},
year = 2000
}
@article{MoerdijkPalmgren2002,
Author = {Moerdijk, Ieke and Palmgren, Erik},
Doi = {10.1016/S0168-0072(01)00079-3},
Journal = {Annals of Pure and Applied Logic},
Number = {1--3},
Pages = {155--201},
Title = {Type theories, toposes and constructive set theory: predicative aspects of {AST}},
Url = {http://dx.doi.org/10.1016/S0168-0072(01)00079-3},
Volume = {114},
Year = {2002}}
@book{jacobs1999categorical,
Author = {Bart Jacobs},
Publisher = {Elsevier},
Title = {Categorical logic and type theory},
Series = {Studies in Logic and the Foundations of Mathematics},
Volume = {141},
Year = {1999}}
@unpublished{Universe-poly,
Author = {Vladimir Voevodsky},
Note = {\url{http://uf-ias-2012.wikispaces.com/file/view/Universe+polymorphic+type+sytem.pdf}},
Title = {A universe polymorphic type system},
Year = 2012}
@inproceedings{Altenkirch1999,
Author = {Thorsten Altenkirch},
Booktitle = {14th Annual IEEE Symposium on Logic in Computer Science,
Trento, Italy, July 2--5, 1999},
Pages = {412--420},
Title = {Extensional Equality in Intensional Type Theory},
Year = {1999}}
@Misc{pelayo2013preliminary,
Author = {Pelayo, {\'A}lvaro and Voevodsky, Vladimir and Warren, Michael A},
Note = {\href{http://arxiv.org/abs/1302.1207/}{arXiv:1302.1207}},
Title = {A preliminary univalent formalization of the {$p$}-adic numbers},
Year = {2013}}
@article{Wilander2010,
Author = {Wilander, Olov},
Doi = {10.1017/S0960129510000071},
Journal = {Mathematical Structures in Computer Science},
Number = {4},
Pages = {563--576},
Title = {Setoids and universes},
Url = {http://dx.doi.org/10.1017/S0960129510000071},
Volume = {20},
Year = {2010},
Bdsk-Url-1 = {http://dx.doi.org/10.1017/S0960129510000071}}
@book{Mines/R/R:1988,
Author = {Ray Mines and Fred Richman and Wim Ruitenburg},
Publisher = {Springer-Verlag},
Title = {A course in constructive algebra},
Year = 1988}
@Unpublished{coquand2012constructive,
author = {Bruno Barras and Thierry Coquand and Simon Huber},
title = {A Generalization of {T}akeuti-{G}andy Interpretation},
note = {\url{http://uf-ias-2012.wikispaces.com/file/view/semi.pdf}},
year = 2013}
@Misc{RijkeSpitters,
Author = {Egbert Rijke and Bas Spitters},
Title = {Sets in homotopy type theory},
Year = 2013,
note={\href{http://arxiv.org/abs/1305.3835/}{arXiv:1305.3835}}}
@article{hedberg1998coherence,
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