On relating type theories and set theories Types for Proofs and Programs, International Workshop TYPES '98, Lecture Notes in Computer Science, vol.1657, pp.1-1810, 1998. ,
DOI : 10.1007/3-540-48167-2_1
URL : http://www.cs.man.ac.uk/~petera/ts-st.ps.gz
Extensional equality in intensional type theory, Proceedings. 14th Symposium on Logic in Computer Science (Cat. No. PR00158), pp.412-420, 1999. ,
DOI : 10.1109/LICS.1999.782636
URL : http://www.cs.nott.ac.uk/~txa/publ/lics99.pdf
Distributive Lattices, 1974. ,
A Presheaf Model of Parametric Type Theory, Electronic Notes in Theoretical Computer Science, vol.319, pp.67-82, 2015. ,
DOI : 10.1016/j.entcs.2015.12.006
Type-theory in color, ACM SIGPLAN International Conference on Functional Programming , ICFP'13, pp.61-72, 2013. ,
A model of type theory in cubical sets, Proc. of 19th Int. Conf. on Types for Proofs and Programs, TYPES 2013, pp.107-128, 2014. ,
Nonabelian Algebraic Topology: Filtered Spaces, Crossed Complexes, Cubical Homotopy Groupoids, EMS Tracts in Mathematics . Europ. Math. Soc, vol.15, pp.10-4171, 2011. ,
DOI : 10.4171/083
Univalent universes for elegant models of homotopy types, 2014. arXiv preprint 1406.0058. URL: https ,
Internal type theory, Types for Proofs and Programs, International Workshop TYPES'95, pp.120-134, 1995. ,
DOI : 10.1007/3-540-61780-9_66
Sheaves and logic, Applications of Sheaves, pp.302-40110, 1979. ,
DOI : 10.1007/BFb0061296
Uniform fibrations and the Frobenius condition, 2015. arXiv preprint 1510.00669. URL: https://arxiv ,
Syntax and semantics of dependent types, Semantics and Logics of Computation of Publications of the Newton Institute, pp.79-130, 1997. ,
A Model of Type Theory in Cubical Sets, 2015. ,
Canonicity for cubical type theory, 2016. arXiv preprint 1607.04156. URL: https://arxiv ,
Lattices with involution, Transactions of the American Mathematical Society, vol.87, issue.2, pp.485-491, 1958. ,
DOI : 10.1090/S0002-9947-1958-0095135-X
ABSTRACT HOMOTOPY, Proc. Nat. Acad. Sci. USA, pp.1092-1096, 1955. ,
DOI : 10.1073/pnas.41.12.1092
The simplicial model of univalent foundations (after Voevodsky ,
A Cubical Approach to Synthetic Homotopy Theory, 2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science, pp.92-103 ,
DOI : 10.1109/LICS.2015.19
URL : https://hal.archives-ouvertes.fr/hal-01322397
An Intuitionistic Theory of Types: Predicative Part, Logic Colloquium '73, pp.73-11810, 1975. ,
DOI : 10.1016/S0049-237X(08)71945-1
An intuitionistic theory of types Twenty-Five Years of Constructive Type Theory, of Oxford Logic Guides, pp.127-172, 1998. ,
Nominal Sets: Names and Symmetry in Computer Science, volume 57 of Cambridge Tracts in Theoretical Computer Science, pp.10-1017, 2013. ,
DOI : 10.1017/CBO9781139084673
Nominal presentation of cubical sets models of type theory, Proc. of 20th Int. Conf. on Types for Proofs and Programs , TYPES 2014, pp.202-220, 2015. ,
Semantics of Type Theory: Correctness, Completeness and Independence Results, Progress in Theoretical Computer Science. Birkhäuser, 1991. ,
DOI : 10.1007/978-1-4612-0433-6
An algebraic weak factorisation system on 01-substitution sets: A constructive proof, 2014. arXiv preprint 1409 URL: https://arxiv.org/abs/1409.1829. 26 The Univalent Foundations Program. Homotopy Type Theory, 1829. ,
DOI : 10.4115/jla.2016.8.1
URL : http://logicandanalysis.org/index.php/jla/article/download/274/109
The equivalence axiom and univalent models of type theory (talk at CMU on feb, 2010. ,