Thierry Coquand

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We present a possible computational content of the negative translation of classical analysis with the Axiom of Choice Our interpretation seems computationally more direct than the one based on G odel s Dialectica interpretation Interestingly this interpretation uses a re nement of the realizibility semantics of the absurdity proposition which is not(More)
We present a model of type theory with dependent product, sum, and identity, in cubical sets. We describe a universe and explain how to transform an equivalence between two types into an equality. We also explain how to model propositional truncation and the circle. While not expressed internally in type theory, the model is expressed in a constructive(More)
We present a method for providing semantic interpretations for languages with a type system featuring inheritance polymorphism. Our approach is illustrated on an extension of the language Fun of Cardelli and Wegner, which we interpret via a translation into an extended polymorphic lambda calculus. Our goal is to interpret inheritances in Fun via coercion(More)