Skip to main content Accessibility help
×
Home
Hostname: page-component-684899dbb8-662rr Total loading time: 0.332 Render date: 2022-05-17T09:25:05.304Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "useNewApi": true }

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.)
77
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Geometry of Interaction and linear combinatory algebras
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

Geometry of Interaction and linear combinatory algebras
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

Geometry of Interaction and linear combinatory algebras
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *