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  • Ulf Norell, Andreas Abel, Catarina Coquand, Thierry Coquand, Nils Anders Danielsson, Peter Dybjer
  • 2007
Towards a practical programming language based on dependent type theory Ulf Norell Abstract Dependent type theories [ML72] have a long history of being used for theorem proving. One aspect of type theory which makes it very powerful as a proof language is that it mixes deduction with computation. This also makes type theory a good candidate for(More)
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 GG odel's Dialectica interpretation 10, 18]. Interestingly, this interpretation uses a reenement of the realizibility semantics of the absurdity proposition, which(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)
Formal topology is today an established topic in the development of constructive, that is intuitionistic and predicative, mathematics. Many classical results of general topology have been already brought into the realm of constructive mathematics by using formal topology and also new light on basic topological notions was gained with this approach which(More)
This thesis contains an investigation of Coquand's Calculus of Constructions, a basic impredicative Type Theory. We review syntactic properties of the calculus, in particular decidability of equality and type-checking, based on the equality-as-judgement presentation. We present a set-theoretic notion of model, CC-structures, and use this to give a new(More)