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A Normalizing Computation Rule for Propositional Extensionality in Higher-Order Minimal Logic

. 2 4 5 6 7 8 9 10 11 Cyril Cohen, Thierry Coquand, Simon Huber, and Anders M?rtberg. Cubical type theory: a constructive interpretation of the univalence axiom. CoRR, abs/1611.02108, 2016. URL: http

Realizability at Work: Separating Two Constructive Notions of Finiteness

We elaborate in detail a realizability model for Martin-L�f dependent type theory with the purpose to analyze a subtle distinction between two constructive notions of finiteness of a set A. The two notions are: (1) A is Noetherian: the empty list can be constructed from lists over A containing duplicates by a certain inductive shortening process; (2) A is streamless: every...

An Adequacy Theorem for Dependent Type Theory

We present a domain model of dependent type theory and use it to prove basic metatheoretic properties. In particular, we prove that two convertible terms have the same Böhm tree. The method used is reminiscent of the use of “inclusive predicates” in domain theory.

The Univalence Axiom in Cubical Sets

In this note we show that Voevodsky’s univalence axiom holds in the model of type theory based on cubical sets as described in Bezem et al. (in: Matthes and Schubert (eds.) 19th international conference on types for proofs and programs (TYPES 2013), Leibniz international proceedings in informatics (LIPIcs), Schloss Dagstuhl-Leibniz-Zentrum für Informatik, Dagstuhl, Germany, vol...

Cubical Type Theory: A Constructive Interpretation of the Univalence Axiom

, Thierry Coquand, and Guilhem Moulin . A presheaf model of parametric type theory . Electr. Notes Theor. Comput. Sci. , 319 : 67 - 82 , 2015 . doi:10. 1016/j.entcs. 2015 . 12 .006. Jean-Philippe Bernardy and

The Ackermann Award 2016

, the jury also included a representative of SigLog (the ACM Special Interest Group on Logic and Computation). The members of the jury were: Thierry Coquand (Chalmers University of Gothenburg), Anuj

The Independence of Markov�s Principle in Type Theory

( 6 ): 1143 - 1148 , 12 1963 . In Proceedings of Second IEEE Symposium on Logic in Computer Science , pages 183 - 193 , 1987 . Thierry Coquand and Guilhem Jaber . A note on forcing and type theory

Non-Constructivity in Kan Simplicial Sets

Philosophical Society, 146:45–55, 2009. 9 10 11 12 13 14 Marc Bezem and Thierry Coquand . A Kripke model for simplicial sets . TCS , 2015 . doi:10 .1016/j.tcs. 2015 . 01 .035. Greg Friedman . An elementary

A Model of Type Theory in Cubical Sets

. Homotopy theoretic models of identity types . Mathematical Proceedings of the Cambridge Philosophical Society , 146 : 45 - 55 , 2009 . Bruno Barras , Thierry Coquand, and Simon Huber . A generalization of ... Takeuti-Gandy interpretation . To appear in Mathematical Structures in Computer Science , 2013 . Marc Bezem and Thierry Coquand . A Kripke model for simplicial sets . Preprint , 2013 . Erret Bishop

The Ackermann Award 2012

vice-president of EACSL, and one member of the LICS organizing committee. The members of the jury were Thierry Coquand (University of Gothenburg), Anuj Dawar (University of Cambridge), the vice