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Geometry of Interaction and linear combinatory algebras

Published online by Cambridge University Press:  24 October 2002

SAMSON ABRAMSKY ,
ESFANDIAR HAGHVERDI  and
PHILIP SCOTT
SAMSON ABRAMSKY
Affiliation:
Oxford University Computing Laboratory, Oxford, U.K.
ESFANDIAR HAGHVERDI
Affiliation:
Department of Mathematics, University of Pennsylvania, Philadelphia, PA., U.S.A.
PHILIP SCOTT
Affiliation:
Department of Mathematics and Statistics, University of Ottawa, Ottawa, Ontario, Canada
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Abstract

We present an axiomatic framework for Girard's Geometry of Interaction based on the notion of linear combinatory algebra. We give a general construction on traced monoidal categories, with certain additional structure, that is sufficient to capture the exponentials of Linear Logic, which produces such algebras (and hence also ordinary combinatory algebras). We illustrate the construction on six standard examples, representing both the ‘particle-style’ as well as the ‘wave-style’ Geometry of Interaction.

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 12 , Issue 5 , October 2002 , pp. 625 - 665
Copyright
2002 Cambridge University Press

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