Vendredi 20 Février
Heure: 
11:00  12:30 
Lieu: 
Salle B107, bâtiment B, Université de Villetaneuse 
Résumé: 
Coherence spaces for computable analysis 
Description: 
Kazushige Terui Abstract: There have been two mainstream approaches in computable analysis: the typetwo theory of effectivity (TTE) and the theory of domain representations. This paper proposes an intermediary approach based on coherence spaces, which is as concrete as TTE and as structured as domain theory.
We import various concepts from TTE such as admissibility, and provide admissible representations for the real line, Euclidean spaces and function spaces over them. This allows us to represent, for instance, a real continuous function by a stable map. A natural question is then what linear maps correspond to in terms of analysis. Our answer is that they correspond to uniformly continuous functions. This leads to an internal expression of Heine's theorem (every continuous function on a compact interval of the real line is uniformly continuous) as the existence of a certain map from a stable function space to a linear function space.
We finally illustrate an application of coherence spaces as a type system for lambda calculus, which allows us to verify local properties of real functions.
This is a joint work with Kei Matsumoto. 

