If all functions (N → N) → N are continuous then 0 = 1. This is a theorem of intensional (and hence of extensional) intuitionistic dependent-type theories, with existence in the formulation of continuity expressed as a Σ type via the Curry-Howard interpretation. With an intuitionistic notion of anonymous existence, defined as the propositional truncation of Σ, it is consistent that all such fun...

In this paper we provide a brief overview of the two mathematical constructions presented by Yves André during the first two session of Ircam’s “Mathematical School for Musicians and other Non-Mathematicians”. After discussing a musical application of Operator Theory we try to suggest the possible connection between Jean-Yves Girard’s Geometry of Interaction (based on a special case of von Neum...