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Towards a Non-Commutative Logic of Effects,

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I will present work-in-progress (with Jonas Frey and Paul-André Melliès) aimed at establishing closer links between the theory of computational effects and linear logic in the broad sense. Starting from an analogy between polarity and “Isbell duality”, I will describe a new categorical interpretation of (polarized, non-commutative) linear logic, and suggest its potential applications for describing and reasoning about programs with side effects. In particular, I will consider as a case study Reynolds’ equation “intvar = intexp & intacc”, defining an integer variable (in the Forsythe language) as the intersection of an integer expression and an integer acceptor.

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