36 citations · 143 across the 40 of their papers we have counts for
4 papers · 1 filter
Constructive sheaf models of type theory
Thierry Coquand, Fabian Ruch, Christian Sattler
We generalise sheaf models of intuitionistic logic to univalent type theory over a small category with a Grothendieck topology. We use in a crucial way that we have constructive mo…
Regular entailment relations
Thierry Coquand, Henri Lombardi, Stefan Neuwirth
Inspired by the work of Lorenzen on the theory of preordered groups in the forties and fifties, we define regular entailment relations and show a crucial theorem for this structure…
Failure of Normalization in Impredicative Type Theory with Proof-Irrelevant Propositional Equality
Andreas Abel, Thierry Coquand
Normalization fails in type theory with an impredicative universe of propositions and a proof-irrelevant propositional equality. The counterexample to normalization is adapted from…
Canonicity and homotopy canonicity for cubical type theory
Thierry Coquand, Simon Huber, Christian Sattler
Cubical type theory provides a constructive justification of homotopy type theory. A crucial ingredient of cubical type theory is a path lifting operation which is explained comput…