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)
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)
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)
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.
Disjunctive well-foundedness, size-change termination, and well-quasi-orders are examples of techniques that have been successfully applied to program termination. Although these works originate in different communities, they rely on closely related principles and both employ similar arguments from Ramsey theory. At the same time there is a notable absence… (More)