Towards a Typed Geometry of Interaction | Zendy

Esfandiar Haghverdi | Zendy; Philip Scott | Zendy

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Towards a Typed Geometry of Interaction

Author(s) -

Esfandiar Haghverdi,

Philip Scott

Publication year - 2005

Publication title -

lecture notes in computer science

Language(s) - English

Resource type - Book series

SCImago Journal Rank - 0.249

H-Index - 400

eISSN - 1611-3349

pISSN - 0302-9743

DOI - 10.1007/11538363_16

Subject(s) - soundness , orthogonality , completeness (order theory) , linear logic , trace (psycholinguistics) , interpretation (philosophy) , invariant (physics) , multiplicative function , mathematics , computer science , algebra over a field , calculus (dental) , algorithm , discrete mathematics , pure mathematics , geometry , programming language , medicine , mathematical analysis , linguistics , philosophy , dentistry , mathematical physics

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.

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