Skip to main content Accessibility help
×
Home
Hostname: page-component-55597f9d44-t4qhp Total loading time: 0.239 Render date: 2022-08-08T07:38:25.550Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "useNewApi": true } hasContentIssue true

Extending partial combinatory algebras

Published online by Cambridge University Press:  01 August 1999

INGE BETHKE
Affiliation:
University of Nijmegen, Department of Computer Science, Email: inge@cs.vu.nl
JAN WILLEM KLOP
Affiliation:
University of Nijmegen, Department of Computer Science, and CWI, Amsterdam and Vrije Universiteit Amsterdam, Department of Computer Science, Email: jwk@cwi.nl
ROEL de VRIJER
Affiliation:
Vrije Universiteit Amsterdam, Department of Computer Science, Email: rdv@cs.vu.nl

Abstract

We give a negative answer to the question of whether every partial combinatory algebra can be completed. The explicit counterexample will be an intricately constructed term model. The construction and the proof that it works depend heavily on syntactic techniques. In particular, it provides a nice example of reasoning with elementary diagrams and descendants. We also include a domain-theoretic proof of the existence of an incompletable partial combinatory algebra.

Type
Research Article
Copyright
© 1999 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.)
3
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.

Extending partial 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.

Extending partial 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.

Extending partial 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? *