references.bib

% 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}}}

@article{BauerTaylor09,
	Author = {Andrej Bauer and Paul Taylor},
	Journal = {Mathematical structures in computer science},
	Number = 4,
	Pages = {757--838},
	Title = {The {D}edekind reals in abstract {S}tone duality},
	Volume = 19,
	Year = 2009}

@inproceedings{Moh93,
	Author = {Christine Paulin-Mohring},
	Booktitle = {Proceedings of the conference {T}yped {L}ambda {C}alculi and {A}pplications},
	Editor = {Marc Bezem and Jan Friso Groote},
	Number = 664,
	Series = {Lecture Notes in Computer Science},
	Title = {{Inductive Definitions in the System {Coq} - Rules and Properties}},
	Year = 1993}


@InProceedings{PeterssonSynek,
  author =       {Kent Petersson and Dan Synek},
  title =        {A Set Constructor for Inductive Sets in {M}artin-{L{\"o}f}'s Type Theory},
  booktitle = {Category Theory and Computer Science, Manchester, UK, September 5--8, 1989, Proceedings},
  year =      1989,
  editor =    {David H. Pitt and David E. Rydeheard and Peter Dybjer and Andrew M. Pitts and Axel Poign{\'e}},
  volume =    389,
  series =    {Lecture Notes in Computer Science},
  pages =     {128--140},
  publisher = {Springer}}

@article{Dybjer:2000,
	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},
  year =      1970,
  editor =    {M. Laudet and D. Lacombe and L. Nolin and M. Sch{\"u}tzenberger},
  volume =    125,
  pages =     {237--275},
  publisher = {Springer-Verlag}}

@article{Richman:reals,
	Author = {Richman, Fred},
	Doi = {10.1002/malq.200710024},
	Journal = {Mathematical Logic Quarterly},
	Number = {1},
	Pages = {98--108},
	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},
    year = 2000,
    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},
	Pages = {55--66},
	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},
	Pages = {439--446},
	Title = {Modalities in constructive logics and type theories},
	Volume = {14},
	Year = {2004}}

@inproceedings{gonthier,
	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},
	Booktitle = {Interactive Theorem Proving},
	Title = {A Machine-Checked Proof of the Odd Order Theorem},
	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}

@inproceedings{bridges2002compactness,
	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 {E}uclidean 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{https://ncatlab.org/ufias2012/files/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{https://ncatlab.org/ufias2012/files/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,
	Author = {Hedberg, Michael},
	Journal = {Journal of Functional Programming},
	Number = {4},
	Pages = {413--436},
	Publisher = {Cambridge Univ Press},
	Title = {A coherence theorem for {M}artin-{L\"o}f's type theory},
	Volume = {8},
	Year = {1998}}

@InProceedings{krausgeneralizations,
  author =       {Kraus, Nicolai and Escard{\'o}, Mart{\i}n and Coquand, Thierry and Altenkirch, Thorsten},
  title =        {Generalizations of {H}edberg's Theorem},
  booktitle = {11th International Conference, Typed Lambda Calculus and Applications 2013, Eindhoven, The Netherlands, June 26--28, 2013. Proceedings},
  year =      2013,
  editor =    {Masahito Hasegawa},
  volume =    7941,
  series =    {Lecture Notes in Computer Science},
  pages =     {173--188},
  publisher = {Springer Berlin Heidelberg}}

@article{rezk01css,
	Author = {Rezk, Charles},
	Note = {\href{https://arxiv.org/abs/math.AT/9811037}{arXiv:math.AT/9811037}},
	Issn = {0002-9947},
	Journal = {Transactions of the American Mathematical Society},
	Number = 3,
	Pages = {973--1007},
	Title = {A model for the homotopy theory of homotopy theory},
	Volume = 353,
	Year = 2001}

@Misc{bsp12infncats,
	Author = {Clark Barwick and Christopher Schommer-Pries},
	note = {\href{http://arxiv.org/abs/1112.0040/}{arXiv:1112.0040}},
	Title = {On the Unicity of the Homotopy Theory of Higher Categories},
	Year = 2011}

@incollection{hs:gpd-typethy,
	Address = {New York},
	Author = {Hofmann, Martin and Streicher, Thomas},
	Booktitle = {Twenty-five years of constructive type theory ({V}enice, 1995)},
        Editor = {Giovanni Sambin and Jan M. Smith},
	Mrclass = {03B15 (68N15 68Q55)},
	Mrnumber = {MR1686862},
	Pages = {83--111},
	Publisher = {Oxford University Press},
	Series = {Oxford Logic Guides},
	Title = {The groupoid interpretation of type theory},
	Volume = 36,
	Year = 1998}

@article{bg:type-wkom,
	Author = {van den Berg, Benno and Garner, Richard},
	Doi = {10.1112/plms/pdq026},
	eprint = {http://plms.oxfordjournals.org/content/102/2/370.full.pdf+html},
	Journal = {Proceedings of the London Mathematical Society},
	Number = {2},
	Pages = {370--394},
	Title = {Types are weak $\omega$-groupoids},
	Url = {http://plms.oxfordjournals.org/content/102/2/370.abstract},
	Volume = {102},
	Year = {2011},
	Bdsk-Url-1 = {http://plms.oxfordjournals.org/content/102/2/370.abstract},
	Bdsk-Url-2 = {http://dx.doi.org/10.1112/plms/pdq026}}

@article{pll:wkom-type,
	Author = {Lumsdaine, Peter Le{F}anu},
	Journal = {Typed lambda calculi and applications},
	Note = {\href{http://arxiv.org/abs/0812.0409/}{arXiv:0812.0409}},
	Pages = {1--19},
	Title = {Weak $\omega$-categories from intensional type theory},
	Url = {http://www.springerlink.com/index/k5w4n04273035095.pdf},
	Volume = {6},
	Year = {2010},
	Bdsk-Url-1 = {http://www.springerlink.com/index/k5w4n04273035095.pdf}}

@inproceedings{lh:canonicity,
	Acmid = {2103697},
	Address = {New York, NY, USA},
	Author = {Licata, Daniel R. and Harper, Robert},
	Booktitle = {Proceedings of the 39th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages},
	Doi = {10.1145/2103656.2103697},
	Isbn = {978-1-4503-1083-3},
	Keywords = {category theory, dependent types, homotopy type theory, type theory},
	Location = {Philadelphia, PA, USA},
	Pages = {337--348},
	Publisher = {ACM},
	Title = {Canonicity for 2-dimensional type theory},
	Url = {http://doi.acm.org/10.1145/2103656.2103697},
	Year = {2012}}

@article{garner:depprod,
	Author = {Garner, Richard},
	Coden = {APALD7},
	Doi = {10.1016/j.apal.2008.12.003},
	Issn = {0168-0072},
	Journal = {Annals of Pure and Applied Logic},
	Mrclass = {03B15},
	Mrnumber = {2525970 (2010m:03016)},
	Number = {1},
	Pages = {1--12},
	Title = {On the strength of dependent products in the type theory of {M}artin-{L}\"of},
	Url = {http://dx.doi.org/10.1016/j.apal.2008.12.003},
	Volume = {160},
	Year = {2009},
	Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.apal.2008.12.003}}

@Misc{klv:ssetmodel,
	Author = {Chris Kapulkin and Peter LeFanu Lumsdaine and Vladimir Voevodsky},
	note = {\href{http://arxiv.org/abs/1211.2851/}{arXiv:1211.2851}},
	Title = {The Simplicial Model of Univalent Foundations},
	Year = 2012}



@InProceedings{ls:pi1s1,
  author =       {Daniel R. Licata and Michael Shulman},
  title =        {Calculating the Fundamental Group of the Circle in Homotopy Type Theory},
  booktitle = {LICS 2013: Proceedings of the Twenty-Eighth Annual
                  ACM/IEEE Symposium on Logic in Computer Science},
  year =      2013}

@article{ab:bracket-types,
	Author = {Awodey, Steven and Bauer, Andrej},
	Doi = {10.1093/logcom/14.4.447},
	Issn = {0955-792X},
	Journal = {Journal of Logic and Computation},
	Mrclass = {03B15 (03B20 03B45 18C50)},
	Mrnumber = {MR2081047 (2005d:03015)},
	Number = {4},
	Pages = {447--471},
	Title = {Propositions as [types]},
	Url = {http://dx.doi.org/10.1093/logcom/14.4.447},
	Volume = {14},
	Year = {2004},
	Bdsk-Url-1 = {http://dx.doi.org/10.1093/logcom/14.4.447}}

@unpublished{ls:hits,
	Author = {Peter LeFanu Lumsdaine and Michael Shulman},
	Note = {arXiv:1705.07088},
	Title = {Semantics of higher inductive types},
	Year = 2017}

@incollection{howard:pat,
	Author = {Howard, William A.},
	Booktitle = {To H.B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism},
	Editor = {Seldin, Jonathan P.; Hindley, J. Roger},
	Note = {original paper manuscript from 1969},
	Pages = {479--490},
	Publisher = {Academic Press},
	Title = {The formulae-as-types notion of construction},
	Year = {1980}}

@book{lurie:higher-topoi,
	Author = {Jacob Lurie},
	Note = {\href{http://arxiv.org/abs/math.CT/0608040}{arXiv:math.CT/0608040}},
	Number = {170},
	Publisher = {Princeton University Press},
	Series = {Annals of Mathematics Studies},
	Title = {Higher topos theory},
	Year = {2009}}

@article{blass:freealg,
	Author = {Blass, Andreas},
	Journal = {Fundamenta Mathematicae},
	Language = {eng},
	Number = {2},
	Pages = {117--160},
	Publisher = {Institute of Mathematics Polish Academy of Sciences},
	Title = {Words, free algebras, and coequalizers},
	Url = {http://eudml.org/doc/211359},
	Volume = {117},
	Year = {1983},
	Bdsk-Url-1 = {http://eudml.org/doc/211359}}


@article{gitik:unc-sing,
	Author = {Gitik, Moti},
	Coden = {ISJMAP},
	Doi = {10.1007/BF02760939},
	Issn = {0021-2172},
	Journal = {Israel Journal of Mathematics},
	Mrclass = {03E35 (03E10)},
	Mrnumber = {MR576462 (81h:03096)},
	Mrreviewer = {F. R. Drake},
	Number = {1--2},
	Pages = {61--88},
	Title = {All uncountable cardinals can be singular},
	Url = {http://dx.doi.org/10.1007/BF02760939},
	Volume = {35},
	Year = {1980}}

@book{constable+86nuprl-book,
	Author = {Robert L. Constable and Stuart F. Allen and H. M. Bromley and W. R. Cleaveland and J. F. Cremer and Robert W. Harper and Douglas J. Howe and T. B. Knoblock and N. P. Mendler and P. Panangaden and James T. Sasaki and Scott F. Smith},
	Publisher = {Prentice Hall},
	Title = {Implementing Mathematics with the {NuPRL} Proof Development System},
	Year = 1986}

@inproceedings{altenkirch+07ott,
	Author = {Thorsten Altenkirch and Conor McBride and Wouter Swierstra},
	Booktitle = {Proceedings of the ACM Workshop Programming Languages meets
               Program Verification, PLPV 2007, Freiburg, Germany, October
               5, 2007},
        Editor = {Aaron Stump and Hongwei Xi},
	Title = {Observational Equality, Now!},
	Year = 2007}

@phdthesis{hofmann:thesis,
	Author = {Hofmann, Martin},
	School = {University of Edinburgh},
	Title = {Extensional concepts in intensional type theory},
	Year = {1995}}

@incollection{hofmann:syntax-and-semantics,
	Address = {Cambridge},
	Author = {Hofmann, Martin},
	Booktitle = {Semantics and logics of computation},
	Doi = {10.1017/CBO9780511526619.004},
	Mrclass = {03B70 (68N15 68Q55)},
	Mrnumber = 1629519,
	Pages = {79--130},
	Publisher = {Cambridge University Press},
	Series = {Publictions of the Newton Institute},
	Title = {Syntax and semantics of dependent types},
	Url = {http://dx.doi.org/10.1017/CBO9780511526619.004},
	Volume = 14,
	Year = 1997}

@book{martin-lof:bibliopolis,
	Author = {Martin-L{\"o}f, Per},
	Isbn = {88-7088-105-9},
	Mrclass = {03B15 (03F50 03F55)},
	Mrnumber = {769301 (86j:03005)},
	Mrreviewer = {M. M. Richter},
	Pages = {iv+91},
	Publisher = {Bibliopolis},
	Series = {Studies in Proof Theory},
	Note = {Notes by Giovanni Sambin of a series of lectures given in Padua, June 1980},
	Title = {Intuitionistic type theory},
	Volume = {1},
	Year = {1984}}

@article{coquand:paradox,
	Author = {Coquand, Thierry},
	Journal = {BIT Numerical Mathematics},
	Number = {1},
	Pages = {10--14},
	Publisher = {Springer},
	Title = {The paradox of trees in type theory},
	Volume = {32},
	Year = {1992}}

@book{conway:onag,
	Author = {Conway, John H.},
	Isbn = {1-56881-127-6},
	Mrclass = {00A08 (05-01 91A05)},
	Mrnumber = {MR1803095 (2001j:00008)},
	Pages = {xii+242},
	Publisher = {A K Peters Ltd.},
	Title = {On numbers and games},
	Year = {1976}}

@article{Goedel-T-1958,
	Author = {G{\"o}del, Kurt},
	Issn = {0012-2017},
	Journal = {Dialectica. International Journal of Philosophy},
	Mrclass = {02.00},
	Mrnumber = {0102482 (21 \#1275)},
	Mrreviewer = {E. W. Beth},
	Pages = {280--287},
	Title = {{\"U}ber eine bisher noch nicht ben{\"u}tzte {E}rweiterung des finiten {S}tandpunktes},
	Volume = {12},
	Year = {1958}}

@article{Tait-1966,
	Author = {Tait, William W.},
	Issn = {0022-4812},
	Journal = {The Journal of Symbolic Logic},
	Mrclass = {02.32},
	Mrnumber = {0219400 (36 \#2483)},
	Mrreviewer = {G. Kreisel},
	Pages = {198--212},
	Title = {Intensional interpretations of functionals of finite type. {I}},
	Volume = {32},
	Year = {1967}}

@incollection{Martin-Lof-1972,
	Author = {Martin-L{\"o}f, Per},
	Booktitle = {Twenty-five years of constructive type theory ({V}enice, 1995)},
	Mrclass = {03B15 (03F55)},
	Mrnumber = 1686864,
	Pages = {127--172},
	Publisher = {Oxford University Press},
        Editor = {Giovanni Sambin and Jan M. Smith},
	Series = {Oxford Logic Guides},
	Title = {An intuitionistic theory of types},
	Volume = 36,
	Year = 1998}

@incollection{Martin-Lof-1973,
	Author = {Martin-L{\"o}f, Per},
	Booktitle = {Logic Colloquium '73, Proceedings of the Logic Colloquium},
	Editor = {H.E. Rose and J.C. Shepherdson},
	Mrclass = {02C15 (02D99)},
	Mrnumber = {0387009 (52 \#7856)},
	Mrreviewer = {Horst Luckhardt},
	Pages = {73--118},
	Publisher = {North-Holland},
	Series = {Studies in Logic and the Foundations of Mathematics},
	Title = {An intuitionistic theory of types: predicative part},
	Volume = 80,
	Year = 1975}

@incollection{Martin-Lof-1979,
	Author = {Martin-L{\"o}f, Per},
	Booktitle = {Logic, Methodology and Philosophy of Science VI, Proceedings of the Sixth International Congress of Logic, Methodology and Philosophy of Science, Hannover 1979},
        Editor = {L. Jonathan Cohen and Jerzy {Łoś} and Helmut Pfeiffer and Klaus-Peter Podewski},
	Doi = {10.1016/S0049-237X(09)70189-2},
	Mrclass = {03F50 (03B70 03F55 68Q45)},
	Mrnumber = {682410 (85d:03112)},
	Mrreviewer = {B. H. Mayoh},
	Pages = {153--175},
	Publisher = {North-Holland},
	Series = {Studies in Logic and the Foundations of Mathematics},
	Title = {Constructive mathematics and computer programming},
	Url = {http://dx.doi.org/10.1016/S0049-237X(09)70189-2},
	Volume = 104,
	Year = 1982}

@book{deBruijn-1973,
	Author = {de Bruijn, Nicolaas Govert},
	Mrclass = {68A40},
	Mrnumber = {0416132 (54 \#4208)},
	Mrreviewer = {Charles G. Morgan},
	Note = {S{\'e}minaire de Math{\'e}matiques Sup{\'e}rieures, No. 52 ({\'E}t{\'e} 1971)},
	Pages = {62},
	Publisher = {Les Presses de l'Universit\'e de Montr\'eal, Montreal, Quebec},
	Title = {A{UTOMATH}, a language for mathematics},
	Year = {1973}}

@book{Streicher-1991,
	Author = {Streicher, Thomas},
	Doi = {10.1007/978-1-4612-0433-6},
	Isbn = {0-8176-3594-7},
	Mrclass = {68Q55 (03B40 03B70 03F50 06B35 68Q65)},
	Mrnumber = {1134134 (93d:68042)},
	Mrreviewer = {John C. Mitchell},
	Pages = {xii+298},
	Publisher = {Birkh\"auser Boston Inc.},
	Series = {Progress in Theoretical Computer Science},
	Title = {Semantics of type theory},
	Url = {http://dx.doi.org/10.1007/978-1-4612-0433-6},
	Year = 1991}

@article{Hilbert-1925,
	Author = {Hilbert, David},
	Coden = {MAANA},
	Doi = {10.1007/BF01206605},
	Issn = {0025-5831},
	Journal = {Mathematische Annalen},
	Mrclass = {Contributed Item},
	Mrnumber = {1512272},
	Number = {1},
	Pages = {161--190},
	Title = {\"{U}ber das {U}nendliche},
	Url = {http://dx.doi.org/10.1007/BF01206605},
	Volume = {95},
	Year = {1926},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/BF01206605}}

@article{lawvere:etcs-long,
	Author = {Lawvere, F. William},
	Issn = {1201-561X},
	Journal = {Reprints in Theory and Applications of Categories},
	Mrclass = {03A05 (00B60 03E99 18B05)},
	Mrnumber = {MR2177727 (2006g:03009)},
	Note = {Reprinted and expanded from Proc. Nat. Acad. Sci. U.S.A. {\bf 52} (1964), With comments by the author and Colin McLarty},
	Pages = {1--35},
	Title = {An elementary theory of the category of sets (long version) with commentary},
	Volume = {11},
	Year = {2005}}

@inproceedings{ags:it-hott,
 author = {Awodey, Steve and Gambino, Nicola and Sojakova, Kristina},
 title = {Inductive Types in Homotopy Type Theory},
 booktitle = {Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science},
 year = {2012},
 isbn = {978-0-7695-4769-5},
 eprint = 	 {arXiv:1201.3898},
 pages = {95--104},
 numpages = {10},
 url = {http://dx.doi.org/10.1109/LICS.2012.21},
 doi = {10.1109/LICS.2012.21},
 acmid = {2359495},
 publisher = {IEEE Computer Society}
} 

@inproceedings{mp:wftrees,
	Author = {Moerdijk, Ieke and Palmgren, Erik},
	Booktitle = {Proceedings of the {W}orkshop on {P}roof {T}heory and {C}omplexity, {PTAC}'98 ({A}arhus)},
	Coden = {APALD7},
	Issn = {0168-0072},
	Journal = {Annals of Pure and Applied Logic},
	Mrclass = {03B15 (03G30 18A15 18B25)},
	Mrnumber = {MR1778939 (2001j:03016)},
	Mrreviewer = {Carsten Butz},
	Pages = {189--218},
	Title = {Wellfounded trees in categories},
	Volume = {104},
	Year = {2000}}

@article{mvdb:wtypes,
author = {van den Berg, Benno and Moerdijk, Ieke},
title = {W-types in homotopy type theory},
journal = {Mathematical Structures in Computer Science},
volume = {25},
issue = {Special Issue 05},
month = {6},
year = {2015},
issn = {1469-8072},
pages = {1100--1115},
numpages = {16},
doi = {10.1017/S0960129514000516},
URL = {http://journals.cambridge.org/article_S0960129514000516},
}

@inproceedings{DBLP:conf/lop/ConstableM85,
	Author = {Robert L. Constable and N. P. Mendler},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Booktitle = {Logics of Programs, Conference, {B}rooklyn College, {J}une 17--19, 1985, Proceedings},
	Ee = {http://dx.doi.org/10.1007/3-540-15648-8_5},
        Series = {Lecture Notes in Computer Science},
        Volume = 193,
        Editor = {Rohit Parikh},
	Pages = {61--78},
	Title = {Recursive Definitions in Type Theory},
	Year = 1985}

@incollection{Con85,
	Author = {Constable, Robert L.},
	Booktitle = {Annals of Mathematics},
	Note = {Reprinted from \emph{Topics in the Theory of Computation}, Selected Papers of the International Conference on Foundations of Computation Theory, FCT '83},
	Pages = {21--37},
	Publisher = {Elsevier Science Publishers, B.V. (North-Holland)},
	Title = {Constructive Mathematics as a Programming Logic {I}: Some Principles of Theory},
	Volume = 24,
	Year = 1985}

@Misc{ToenVezzosi02,
	Author = {Bertrand To\"en and Gabriele Vezzosi},
	note = {\href{http://arxiv.org/abs/math/0207028/}{arXiv:math/0207028}},
	Title = {Homotopical Algebraic Geometry {I}: Topos theory},
	Year = 2002}

@unpublished{Rezk05,
	Author = {Charles Rezk},
	Note = {\url{http://www.math.uiuc.edu/~rezk/homotopy-topos-sketch.pdf}},
	Title = {Toposes and homotopy toposes},
	Url = {http://www.math.uiuc.edu/~rezk/homotopy-topos-sketch.pdf},
	Year = 2005}

@book{bertot+10coq,
	Author = {Yves Bertot and Pierre Cast\'{e}ran},
	Publisher = {Springer-Verlag},
	Series = {EATCS Texts in Theoretical Computer Science},
	Title = {Interactive Theorem Proving and Program Development: {C}oq'{A}rt: The Calculus of Inductive Constructions},
	Year = 2010}

@book{nordstrom+90mltt,
	Author = {Bengt Nordstr\"{o}m and Kent Petersson and Jan Smith},
	Url = {http://www.cs.chalmers.se/Cs/Research/Logic/book/},
	Publisher = {Oxford University Press},
	Title = {Programming in Martin-L\"{o}f's Type Theory},
	Year = 1990}

@book{Coq,
	Author = {{Coq Development Team}},
	Publisher = {INRIA-Rocquencourt},
	Title = {The {C}oq Proof Assistant Reference Manual},
	Year = {2012}}

@phdthesis{norell2007towards,
	Author = {Norell, Ulf},
	School = {{Chalmers, G\"oteborg University}},
	Title = {Towards a practical programming language based on dependent type theory},
	Year = {2007}}

@incollection{Tait-1968,
	Address = {Amsterdam},
	Author = {Tait, William W.},
	Booktitle = {Logic, {M}ethodology and {P}hilos. {S}ci. {III} ({P}roc. {T}hird {I}nternat. {C}ongr., {A}msterdam, 1967)},
	Mrclass = {02.70},
	Mrnumber = {0256877 (41 \#1533)},
	Mrreviewer = {G. Kreisel},
	Pages = {185--199},
	Publisher = {North-Holland},
	Title = {Constructive reasoning},
	Year = {1968}}

@book{Pierce-TAPL,
	Author = {Benjamin C. Pierce},
	Errata = {http://www.cis.upenn.edu/~bcpierce/tapl/errata.txt},
	Homepage = {http://www.cis.upenn.edu/~bcpierce/tapl},
	Publisher = {MIT Press},
	Title = {Types and Programming Languages},
	Year = 2002}

@article{AW,
	Author = {Steve Awodey and Michael A. Warren},
	Journal = {Mathematical Proceedings of the Cambridge Philosophical Society},
	Pages = {45--55},
	Title = {Homotopy theoretic models of identity types},
	Volume = {146},
	Year = {2009}}

@book{Bourbaki,
	Author = {Nicolas Bourbaki},
	Publisher = {Hermann, Paris},
	Title = {Theory of Sets},
	Year = {1968}}

@article{carboni,
	Author = {Aurelio Carboni},
	Journal = {Journal of Pure and Applied Algebra},
	Pages = {117--148},
	Title = {Some free constructions in realizability and proof theory},
	Volume = {103},
	Year = {1995}}

@article{Church1932,
	Author = {Alonzo Church},
	Journal = {Annals of Mathematics},
	Pages = {346--366},
	Title = {A set of postulates for the foundation of logic 1},
	Volume = {33},
	Year = {1932}}

@article{Church:1933cl,
	Author = {Alonzo Church},
	Journal = {Annals of Mathematics},
	Pages = {839--864},
	Title = {A set of postulates for the foundation of logic 2},
	Volume = {34},
	Year = {1933}}

@article{Church:1940tu,
	Author = {Alonzo Church},
	Journal = {Journal of Symbolic Logic},
	Pages = {56--68},
	Title = {A formulation of the simple theory of types},
	Volume = {5},
	Year = {1940}}

@book{Church:1941tc,
	Author = {Alonzo Church},
	Publisher = {Princeton University Press},
	Title = {The Calculi of Lambda Conversion},
	Year = {1941}}

@article{kolmogorov,
	Author = {Andrey Kolmogorov},
	Journal = {Mathematische Zeitschrift},
	Pages = {58--65},
	Title = {Zur {D}eutung der intuitionistischen {L}ogik},
	Volume = {35},
	Year = {1932}}

@article{Russell:1908,
	Author = {Bertand Russell},
	Journal = {American Journal of Mathematics},
	Pages = {222--262},
	Title = {Mathematical logic based on the theory of types},
	Volume = 30,
	Year = 1908}

@phdthesis{mw:thesis,
	Author = {Michael A. Warren},
	School = {Carnegie Mellon University},
	Title = {Homotopy Theoretic Aspects of Constructive Type Theory},
	Year = {2008}}

@unpublished{VV,
	Author = {Vladimir Voevodsky},
	Date-Modified = {2013-05-12 19:02:35 +0000},
	Note = {\url{http://www.math.ias.edu/~vladimir/Site3/Univalent_Foundations_files/Hlambda_short_current.pdf}},
	Title = {A very short note on the homotopy {$\lambda$}-calculus},
	Year = 2006}

@article{blanc:eqv-log,
	Author = {Blanc, Georges},
	Coden = {AMLGAN},
	Doi = {10.1007/BF02011874},
	Issn = {0003-9268},
	Journal = {Archiv f{\"u}r Mathematische Logik und Grundlagenforschung},
	Mrclass = {03G30 (18A15)},
	Mrnumber = {MR539867 (80m:03109)},
	Mrreviewer = {Marta C. Bunge},
	Number = {3-4},
	Pages = {131--137},
	Title = {\'{E}quivalence naturelle et formules logiques en th{\'e}orie des cat{\'e}gories},
	Url = {http://dx.doi.org/10.1007/BF02011874},
	Volume = {19},
	Year = {1978/79},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/BF02011874}}

@incollection{freyd:invar-eqv,
	Author = {Freyd, Peter},
	Booktitle = {Algebra, topology, and category theory (a collection of papers in honor of {S}amuel {E}ilenberg)},
	Mrclass = {18C10 (02H10)},
	Mrnumber = {MR0412249 (54 \#376)},
	Mrreviewer = {J. Lambek},
	Pages = {55--61},
	Publisher = {Academic Press},
	Title = {Properties invariant within equivalence types of categories},
	Year = {1976}}

@unpublished{makkai:folds,
	Author = {Michael Makkai},
	Note = {\url{http://www.math.mcgill.ca/makkai/folds/}},
	Title = {First order logic with dependent sorts, with applications to category theory},
	Year = {1995}}

@misc{makkai:comparing,
	Author = {Michael Makkai},
	Howpublished = {\url{http://www.math.mcgill.ca/makkai/}},
	Month = {August},
	Title = {On comparing definitions of weak $n$-category},
	Year = {2001}}

@incollection{jt:strong-stacks,
	Address = {Berlin},
	Author = {Joyal, Andr{\'e} and Tierney, Myles},
	Booktitle = {Category Theory. Proceedings of the International Conference held in Como, Italy, July 22–28, 1990},
        Editr = {Aurelio Carboni and Maria Cristina Pedicchio and Guiseppe Rosolini},
	Mrclass = {18G55 (18B25)},
	Mrnumber = {MR1173014 (93h:18019)},
	Mrreviewer = {Kimmo I. Rosenthal},
	Pages = {213--236},
	Publisher = {Springer},
	Series = {Lecture Notes in Mathematics},
	Title = {Strong stacks and classifying spaces},
	Volume = {1488},
	Year = {1991}}

@article{bunge:stacks-morita-internal,
	Author = {Bunge, Marta},
	Coden = {CTGDBR},
	Issn = {0008-0004},
	Journal = {Cahiers de Topologie et G\'eom\'etrie Diff\'erentielle},
	Mrclass = {18B25 (14F05)},
	Mrnumber = {MR558106 (81f:18018)},
	Mrreviewer = {A. Preller},
	Number = {4},
	Pages = {401--436},
	Title = {Stack completions and {M}orita equivalence for categories in a topos},
	Volume = {20},
	Year = {1979}}

@Misc{aks:rezk,
	Author = {Benedikt Ahrens and Krzysztof Kapulkin and Michael Shulman},
	note = {\href{http://arxiv.org/abs/1303.0584/}{arXiv:1303.0584}},
	Title = {Univalent categories and the {R}ezk completion},
	Year = {2013}}

@unpublished{palmgren:cetcs,
	Author = {Erik Palmgren},
	Note = {\url{http://www.math.uu.se/~palmgren/cetcs.pdf}},
	Title = {Constructivist and Structuralist Foundations: {B}ishop's and {L}awvere's Theories of Sets},
	Year = {2009}}

@article{taylor:ordinals,
	Author = {Taylor, Paul},
	Coden = {JSYLA6},
	Issn = {0022-4812},
	Journal = {The Journal of Symbolic Logic},
	Mrclass = {03E70 (03F55)},
	Mrnumber = {MR1412506 (97j:03102)},
	Mrreviewer = {Wim Ruitenburg},
	Number = {3},
	Pages = {705--744},
	Title = {Intuitionistic sets and ordinals},
	Volume = {61},
	Year = {1996}}

@book{hatcher02topology,
	Author = {Allen Hatcher},
	Note = {\url{http://www.math.cornell.edu/~hatcher/AT/ATpage.html}},
	Publisher = {Cambridge University Press},
	Title = {Algebraic Topology},
	Year = {2002}}

@book{elephant,
	Author = {Peter T. Johnstone},
	Number = {43},
	Publisher = {Oxford Science Publications},
	Series = {Oxford Logic Guides},
	Title = {Sketches of an Elephant: A Topos Theory Compendium: Volumes 1 and 2},
	Year = {2002}}

@inproceedings{bergner:infty-one,
	Author = {Julia E. Bergner},
	Booktitle = {Towards Higher Categories},
	Editor = {John C.~Baez and J.~Peter May},
	eprint = {arXiv:math.CT/0610239},
	Pages = {69--83},
	Publisher = {Springer},
	Series = {The IMA Volumes in Mathematics and its Applications},
	Title = {A survey of $(\infty, 1)$-categories},
	Volume = 152,
	Year = 2009}

@article{Moggi89,
	Author = {Eugenio Moggi},
	Journal = {Information and Computation},
	Pages = {55--92},
	Title = {Notions of Computation and Monads},
	Volume = {93},
	Year = {1989}}

@article{QGFTinCHoTT12,
	Author = {Urs Schreiber and Michael Shulman},
	Journal = {Quantum Physics and Logic},
	Title = {Quantum gauge field theory in cohesive homotopy type theory},
	Year = 2012}

@article{Huet80,
	Acmid = 322230,
	Author = {Huet, G{\'e}rard},
	Doi = {10.1145/322217.322230},
	Issn = {0004-5411},
	Issue_Date = {Oct. 1980},
	Journal = {Journal of the ACM},
	Number = 4,
	Numpages = 25,
	Pages = {797--821},
	Publisher = {ACM},
	Title = {Confluent Reductions: Abstract Properties and Applications to Term Rewriting Systems: Abstract Properties and Applications to Term Rewriting Systems},
	Url = {http://doi.acm.org/10.1145/322217.322230},
	Volume = 27,
	Year = 1980}

@article{Nordstrom88,
	Author = {Nordstr{\"o}m, Bengt},
	Doi = {10.1007/BF01941137},
	Issn = {0006-3835},
	Journal = {BIT Numerical Mathematics},
	Keywords = {D.2.1; D.2.4; D.3.1; F.3.1; F.3.3; recursion; well-founded induction; programming logic; fixed point; termination proof},
	Language = {English},
	Number = {3},
	Pages = {605--619},
	Publisher = {Kluwer Academic Publishers},
	Title = {Terminating general recursion},
	Url = {http://dx.doi.org/10.1007/BF01941137},
	Volume = {28},
	Year = {1988},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/BF01941137}}

@article{Gentzen36,
	Author = {Gentzen, Gerhard},
	Doi = {10.1007/BF01565428},
	Issn = {0025-5831},
	Journal = {Mathematische Annalen},
	Language = {German},
	Number = {1},
	Pages = {493--565},
	Publisher = {Springer-Verlag},
	Title = {{Die Widerspruchsfreiheit der reinen Zahlentheorie}},
	Url = {http://dx.doi.org/10.1007/BF01565428},
	Volume = {112},
	Year = {1936},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/BF01565428}}

@article{Paulson86,
	Author = {Lawrence C. Paulson},
	Bibsource = {DBLP, http://dblp.uni-trier.de},
	Ee = {http://dx.doi.org/10.1016/S0747-7171(86)80002-5},
	Journal = {Journal of Symbolic Computation},
	Number = {4},
	Pages = {325--355},
	Title = {Constructing Recursion Operators in Intuitionistic Type Theory},
	Volume = {2},
	Year = {1986}}

@misc{AKL13,
	Author = {Jeremy Avigad and Krzysztof Kapulkin and Peter LeFanu Lumsdaine},
	Note = {\href{http://arxiv.org/abs/1304.0680/}{arXiv:1304.0680}},
	Title = {Homotopy limits in {C}oq},
	Year = {2013}}

@misc{Streicher93,
	Author = {Thomas Streicher},
	Note = {Habilitationsschrift, Ludwig-Maximilians-Universit\"at M\"unchen},
	Title = {Investigations into intensional type theory},
	Year = 1993}

@ARTICLE{lawvere:metric-spaces,
  author = {F. William Lawvere},
  title = {Metric spaces, generalized logic, and closed categories},
  journal = {Rendiconti del Seminario Matematico e Fisico di Milano},
  year = {1974},
  volume = {43},
  pages = {135--166},
  note = {Reprinted as Reprints in Theory and Applications of Categories 1:1--37, 2002.}
}

@Article{Angiuli13,
  author = 	 {Carlo Angiuli},
  title = 	 {The $(\infty,1)$-accidentopos model of unintentional type theory\index{type theory!unintentional}\index{unintentional type theory}\index{mistaken identity type}\index{type!mistaken identity}},
  journal = 	 {Sigbovik '13},
  year = 	 2013,
  month = 	 {April 1}}

@misc{BauerAcceptanceVideo,
 title = {Five Stages of Accepting Constructive Mathematics\index{stages, five, of accepting constructive mathematics}},
 author = {Andrej Bauer},
 note = {\url{http://video.ias.edu/members/1213/0318-AndrejBauer}},
 year = {2013}
}

@Book{Taylor99,
  author = 	 {Paul Taylor},
  title = 	 {Practical Foundations of Mathematics},
  publisher = 	 {Cambridge University Press},
  year = 	 1999}

@inproceedings{CDP14,
	Author = {Jesper Cockx and Dominique Devriese and Frank Piessens},
	Booktitle = {Proceedings of the 19th ACM SIGPLAN International Conference on Functional Programming, ICFP 2014, Gothenburg, Sweden, September 1-3, 2014},
	Title = {Pattern matching without {K}},
	Year = 2014
}

@inproceedings{Coquand92Pattern,
title={Pattern matching with dependent types},
author={Coquand, Thierry},
booktitle={Proceedings of the Workshop on Types for Proofs and Programs},
pages={71--83},
year={1992}
}