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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.

This talk is part of the Microsoft Research Cambridge, public talks series.

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