Towards a Typed Geometry of Interaction

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Towards a Typed Geometry of Interaction
Abstract. Girard’s Geometry of Interaction (GoI) develops a mathematical framework for modelling the dynamics of cut-elimination. We introduce a typed version of GoI, called Multiobject GoI (MGoI) for multiplicative linear logic without units in categories which include previous (untyped) GoI models, as well as models not possible in the original untyped version. The development of MGoI depends on a new theory of partial traces and trace classes, as well as an abstract notion of orthogonality (related to work of Hyland and Schalk) We develop Girard’s original theory of types, data and algorithms in our setting, and show his execution formula to be an invariant of Cut Elimination. We prove Soundness and Completeness Theorems for the MGoI interpretation in partially traced categories with an orthogonality.
Esfandiar Haghverdi, Philip J. Scott
Added 26 Jun 2010
Updated 26 Jun 2010
Type Conference
Year 2005
Where CSL
Authors Esfandiar Haghverdi, Philip J. Scott
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