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Towards a Typed Geometry of Interaction

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Computer Science Logic (CSL 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3634))

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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.

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Author information

Authors and Affiliations

  1. School of Informatics, Indiana University, Bloomington, IN 47406, USA

    Esfandiar Haghverdi

  2. Dept. of Mathematics & Statistics, University of Ottawa, Ottawa, Ontario, Canada, K1N 6N5

    Philip J. Scott

Authors
  1. Esfandiar Haghverdi
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  2. Philip J. Scott
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Editor information

Editors and Affiliations

  1. Oxford University Computing Laboratory, Wolfson Building, Parks Road, OX1 3QD, Oxford, United Kingdom

    Luke Ong

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© 2005 Springer-Verlag Berlin Heidelberg

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Haghverdi, E., Scott, P.J. (2005). Towards a Typed Geometry of Interaction. In: Ong, L. (eds) Computer Science Logic. CSL 2005. Lecture Notes in Computer Science, vol 3634. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11538363_16

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  • DOI: https://doi.org/10.1007/11538363_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28231-0

  • Online ISBN: 978-3-540-31897-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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