Effectuses, land of probabilities

Titouan Carette
ENS Lyon

Date(s) : 20/10/2016   iCal
11 h 00 min - 12 h 00 min

Curry-Howard isomorphism is a well known game which consists in translating concepts of computer science into logical ones and vice versa. Thus, when physicists came with quantum computation, it was just a question of time before logians tried to play with this new toy. But quantum world is wild and brings many challenges. Effectuses are a proposition to adress those. They are categories designed to deal with quantum and probabilistic programs. This approach reveals striking connections between physics, mathematics and computer science. Among them is the Isbell duality, a mathematical phenomenon making a link between Djisktra’s predicates transformers view on programs and Heisenberg’s interpretation of quantum mechanic. The presentation will slowly and friendly present effectuses before focusing on the Isbell category-theoretical machinery and its consequences.



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