Hostname: page-component-848d4c4894-p2v8j Total loading time: 0.001 Render date: 2024-05-24T21:03:19.092Z Has data issue: false hasContentIssue false

Geometry of Interaction and linear combinatory algebras

Published online by Cambridge University Press:  24 October 2002

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

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
Copyright
2002 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)