type-theory/resources/CCHM/main.bbl
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\begin{thebibliography}{10}
\bibitem{Aczel99}
P.~Aczel.
\newblock {On Relating Type Theories and Set Theories}.
\newblock In T.~Altenkirch, B.~Reus, and W.~Naraschewski, editors, {\em Types
for Proofs and Programs}, volume 1657 of {\em Lecture Notes in Computer
Science}, pages 1--18. Springer Verlag, Berlin, Heidelberg, New York, 1999.
\bibitem{Altenkirch99}
T.~Altenkirch.
\newblock {Extensional Equality in Intensional Type Theory}.
\newblock In {\em 14th Annual {IEEE} Symposium on Logic in Computer Science},
pages 412--420, 1999.
\bibitem{Balbes}
R.~Balbes and P.~Dwinger.
\newblock {\em {Distributive Lattices}}.
\newblock Abstract Space Publishing, 2011.
\bibitem{paramtt}
J.-P. Bernardy, T.~Coquand, and G.~Moulin.
\newblock {A Presheaf Model of Parametric Type Theory}.
\newblock {\em Electronic Notes in Theoretical Computer Science}, 319:67--82,
2015.
\bibitem{ttincolor}
J.-P. Bernardy and G.~Moulin.
\newblock {Type-theory in Color}.
\newblock {\em SIGPLAN Not.}, 48(9):61--72, September 2013.
\bibitem{BCH}
M.~Bezem, T.~Coquand, and S.~Huber.
\newblock {A Model of Type Theory in Cubical Sets}.
\newblock In R.~Matthes and A.~Schubert, editors, {\em 19th International
Conference on Types for Proofs and Programs (TYPES 2013)}, volume~26 of {\em
Leibniz International Proceedings in Informatics (LIPIcs)}, pages 107--128.
Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik, 2014.
\bibitem{Brown}
R.~Brown, P.J. Higgins, and R.~Sivera.
\newblock {\em {Nonabelian Algebraic Topology: Filtered Spaces, Crossed
Complexes, Cubical Homotopy Groupoids}}, volume~15 of {\em EMS tracts in
mathematics}.
\newblock European Mathematical Society, 2011.
\bibitem{Cisinski}
D.-C. {Cisinski}.
\newblock {Univalent universes for elegant models of homotopy types}.
\newblock {\em arXiv:1406.0058}, May 2014.
\newblock Preprint.
\bibitem{Dybjer96}
P.~Dybjer.
\newblock {Internal Type Theory}.
\newblock In {\em Lecture Notes in Computer Science}, pages 120--134. Springer
Verlag, Berlin, Heidelberg, New York, 1996.
\bibitem{Fourman-Scott}
M.~Fourman and D.~Scott.
\newblock Sheaves and logic.
\newblock In M.~Fourman, C.~Mulvey, and D.~Scott, editors, {\em {Applications
of Sheaves}}, volume 753 of {\em Lecture Notes in Mathematics}, pages
302--401. Springer Berlin Heidelberg, 1979.
\bibitem{GambinoSattler}
N.~{Gambino} and C.~{Sattler}.
\newblock {Uniform Fibrations and the Frobenius Condition}.
\newblock {\em arXiv:1510.00669}, October 2015.
\newblock Preprint.
\bibitem{Hofmann97}
M.~Hofmann.
\newblock Syntax and semantics of dependent types.
\newblock In A.M. Pitts and P.~Dybjer, editors, {\em Semantics and logics of
computation}, volume~14 of {\em Publ. Newton Inst.}, pages 79--130. Cambridge
University Press, Cambridge, 1997.
\bibitem{simonlic}
S.~Huber.
\newblock {\em {A Model of Type Theory in Cubical Sets}}.
\newblock Licentiate thesis, University of Gothenburg, May 2015.
\bibitem{Huber16}
S.~Huber.
\newblock Canonicity for cubical type theory.
\newblock {\em arXiv:1607.04156v1}, July 2016.
\newblock Preprint.
\bibitem{Kalman58}
J.~A. Kalman.
\newblock Lattices with involution.
\newblock {\em Transactions of the American Mathematical Society}, 87:485--491,
1958.
\bibitem{Kan55}
D.~M. Kan.
\newblock Abstract homotopy. {I}.
\newblock {\em Proceedings of the National Academy of Sciences of the United
States of America}, 41(12):1092--1096, 1955.
\bibitem{KL}
C.~{Kapulkin} and P.~{LeFanu Lumsdaine}.
\newblock {The Simplicial Model of Univalent Foundations (after {V}oevodsky)}.
\newblock {\em arXiv:1211.2851v4}, November 2012.
\newblock Preprint.
\bibitem{LicataBrunerie}
D.~R. Licata and G.~Brunerie.
\newblock {A Cubical Approach to Synthetic Homotopy Theory}.
\newblock In {\em 30th Annual {ACM/IEEE} Symposium on Logic in Computer
Science}, pages 92--103, 2015.
\bibitem{ML75}
P.~Martin-Löf.
\newblock An intuitionistic theory of types: predicative part.
\newblock In {\em Logic {C}olloquium '73 ({B}ristol, 1973)}, pages 73--118.
Studies in Logic and the Foundations of Mathematics, Vol. 80. North-Holland,
Amsterdam, 1975.
\bibitem{MLTT72}
P.~Martin-Löf.
\newblock An intuitionistic theory of types.
\newblock In G.~Sambin and J.~M. Smith, editors, {\em Twenty-five years of
constructive type theory ({V}enice, 1995)}, volume~36 of {\em Oxford Logic
Guides}, pages 127--172. Oxford University Press, 1998.
\bibitem{PittsBook}
A.~M. Pitts.
\newblock {\em {Nominal Sets: Names and Symmetry in Computer Science}}.
\newblock Cambridge University Press, New York, NY, USA, 2013.
\bibitem{Pitts}
A.~M. Pitts.
\newblock {Nominal Presentation of Cubical Sets Models of Type Theory}.
\newblock In H.~Herbelin, P.~Letouzey, and M.~Sozeau, editors, {\em 20th
International Conference on Types for Proofs and Programs (TYPES 2014)},
volume~39 of {\em Leibniz International Proceedings in Informatics (LIPIcs)},
pages 202--220. Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik, 2015.
\bibitem{Polonsky14}
Andrew Polonsky.
\newblock {Extensionality of lambda-*}.
\newblock In H.~Herbelin, P.~Letouzey, and M.~Sozeau, editors, {\em 20th
International Conference on Types for Proofs and Programs (TYPES 2014)},
volume~39 of {\em Leibniz International Proceedings in Informatics (LIPIcs)},
pages 221--250. Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik, 2015.
\bibitem{Streicher91}
T.~Streicher.
\newblock {\em {Semantics of Type Theory}}.
\newblock Progress in Theoretical Computer Science. Birkh{\"a}user Basel, 1991.
\bibitem{Swan}
A.~{Swan}.
\newblock {An Algebraic Weak Factorisation System on 01-Substitution Sets: A
Constructive Proof}.
\newblock {\em arXiv:1409.1829}, September 2014.
\newblock Preprint.
\bibitem{hott-book}
The {Univalent Foundations Program}.
\newblock {\em {Homotopy Type Theory: Univalent Foundations of Mathematics}}.
\newblock \url{http://homotopytypetheory.org/book}, Institute for Advanced
Study, 2013.
\bibitem{Voevodsky}
V.~{Voevodsky}.
\newblock {The equivalence axiom and univalent models of type theory. (Talk at
CMU on February 4, 2010)}.
\newblock {\em arXiv:1402.5556}, February 2014.
\newblock Preprint.
\end{thebibliography}