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HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt età la diffusion… (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)

Dedicated to Roger Hindley for his 60th Birthday We use a syntactical notion of Kripke models to obtain interpretations of subsystems of arithmetic in their intuitionistic counterparts. This yields in particular a new proof of Buss' result that the Skolem functions of Bounded Arithmetic are polynomial time computable.

We present a simple type-checker for a language with dependent types and let expressions, with a simple proof of correctness.