H. Barendregt, Lambda calculi with types, Handbook of Logic in Computer Science, pp.117-309, 1992.
DOI : 10.1017/cbo9781139032636

B. Barras, Auto-validation d'un système de preuves avec familles inductives, 1999.

B. Barras and B. Grégoire, On the Role of Type Decorations in the Calculus of Inductive Constructions, Computer Science Logic, number 3634 in Lecture Notes in Computer Science, pp.151-166, 2005.
DOI : 10.1007/11538363_12

M. Boespflug and G. Burel, CoqInE: Translating the calculus of inductive constructions into the ??-calculus modulo, Proof Exchange for Theorem Proving?Second International Workshop, p.44, 2012.
URL : https://hal.archives-ouvertes.fr/hal-01126128

D. Cousineau and G. Dowek, Embedding pure type systems in the lambda-Picalculus modulo, Typed Lambda Calculi and Applications , number 4583 in Lecture Notes in Computer Science, pp.102-117, 2007.

H. Geuvers and F. Wiedijk, A Logical Framework with Explicit Conversions, Electronic Notes in Theoretical Computer Science, vol.199, pp.33-47, 2008.
DOI : 10.1016/j.entcs.2007.11.011

R. Harper and R. Pollack, Type checking, universe polymorphism, and typical ambiguity in the calculus of constructions draft, TAP- SOFT'89, number 352 in Lecture Notes in Computer Science, pp.241-256, 1989.
DOI : 10.1007/3-540-50940-2_39

R. Harper and R. Pollack, Type checking with universes, Theoretical Computer Science, vol.89, issue.1, pp.107-136, 1991.
DOI : 10.1016/0304-3975(90)90108-T

H. Herbelin and A. Spiwack, The Rooster and the Syntactic Bracket, 19th International Conference on Types for Proofs and Programs (TYPES 2013), volume 26 of Leibniz International Proceedings in Informatics (LIPIcs), pp.169-187, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01097919

M. Lasson, Réalisabilité et paramétricité dans les systèmes de types purs, 2012.

Z. Luo and . Cc, Laboratory for Foundations of Computer Science Report ECS-LFCS-88-58, 1988.

Z. Luo, ECC, an extended calculus of constructions, [1989] Proceedings. Fourth Annual Symposium on Logic in Computer Science, pp.386-395, 1989.
DOI : 10.1109/LICS.1989.39193

Z. Luo, Computation and Reasoning: A Type Theory for Computer Science, 1994.

Z. Luo, Notes on universes in type theory Lecture notes for a talk at Institute for Advanced Study, p.2012

G. Martin-löf and . Sambin, Intuitionistic type theory, Bibliopolis Naples, vol.17, 1984.

E. Palmgren, On universes in type theory In Twenty-five years of constructive type theory, pp.191-204, 1998.

R. Saillard, Dedukti: a universal proof checker, Foundation of Mathematics for Computer-Aided Formalization Workshop, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00833992

V. Siles and H. Herbelin, Pure Type System conversion is always typable, Journal of Functional Programming, vol.1, issue.02, pp.153-180, 2012.
DOI : 10.1017/S0956796805005770
URL : https://hal.archives-ouvertes.fr/inria-00497177

C. Development and T. , The Coq Reference Manual, version 8, 2012.

S. Van-benthem-jutting, J. Mckinna, and R. Pollack, Checking algorithms for Pure Type Systems, Types for Proofs and Programs, number 806 in Lecture Notes in Computer Science, pp.19-61, 1994.
DOI : 10.1007/3-540-58085-9_71

H. Floris-van-doorn, F. Geuvers, and . Wiedijk, Explicit convertibility proofs in pure type systems, Proceedings of the Eighth ACM SIGPLAN International Workshop on Logical Frameworks & Meta-languages: Theory & Practice, LFMTP'13, pp.25-36, 2013.

V. Vincent and . Oostrom, Confluence for Abstract and Higher-Order Rewriting, 1994.