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Realisability and adequacy for (co)induction

Ulrich Berger Orcid Logo, David Benton, David Benton, David Benton, Katharina Hall, Robert Rhys

Pages: 49 - 60

Swansea University Author: Ulrich Berger Orcid Logo

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DOI (Published version): 10.4230/OASIcs.CCA.2009.2258

Abstract

We prove the correctness of a formalised realisability interpretation of extensions of first-order theories by inductive and coinductive definitions in an untyped $\lambda$-calculus with fixed-points. We illustrate the use of this interpretation for program extraction by some simple examples in the...

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Published: Schloss Dagstuhl - Leibniz-Zentrum für Informatik 2009
Online Access: http://drops.dagstuhl.de/opus/volltexte/2009/2258
URI: https://cronfa.swan.ac.uk/Record/cronfa53
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first_indexed 2013-07-23T11:49:23Z
last_indexed 2018-02-09T04:27:21Z
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spelling 2013-10-17T11:56:18.4177127 v2 53 2012-02-23 Realisability and adequacy for (co)induction 61199ae25042a5e629c5398c4a40a4f5 0000-0002-7677-3582 Ulrich Berger Ulrich Berger true false 2012-02-23 SCS We prove the correctness of a formalised realisability interpretation of extensions of first-order theories by inductive and coinductive definitions in an untyped $\lambda$-calculus with fixed-points. We illustrate the use of this interpretation for program extraction by some simple examples in the area of exact real number computation and hint at further non-trivial applications in computable analysis. Book 49 60 Schloss Dagstuhl - Leibniz-Zentrum für Informatik 31 12 2009 2009-12-31 10.4230/OASIcs.CCA.2009.2258 http://drops.dagstuhl.de/opus/volltexte/2009/2258 In CCA '09, Proc. Sixth Intl. Conference on Computability and Complexity in Analysis, Ljubljana, Slovenia COLLEGE NANME Computer Science COLLEGE CODE SCS Swansea University 2013-10-17T11:56:18.4177127 2012-02-23T17:01:55.0000000 Faculty of Science and Engineering School of Mathematics and Computer Science - Computer Science Ulrich Berger 0000-0002-7677-3582 1 David Benton 2 David Benton 3 David Benton 4 Katharina Hall 5 Robert Rhys 6
title Realisability and adequacy for (co)induction
spellingShingle Realisability and adequacy for (co)induction
Ulrich Berger
title_short Realisability and adequacy for (co)induction
title_full Realisability and adequacy for (co)induction
title_fullStr Realisability and adequacy for (co)induction
title_full_unstemmed Realisability and adequacy for (co)induction
title_sort Realisability and adequacy for (co)induction
author_id_str_mv 61199ae25042a5e629c5398c4a40a4f5
author_id_fullname_str_mv 61199ae25042a5e629c5398c4a40a4f5_***_Ulrich Berger
author Ulrich Berger
author2 Ulrich Berger
David Benton
David Benton
David Benton
Katharina Hall
Robert Rhys
format Book
container_start_page 49
publishDate 2009
institution Swansea University
doi_str_mv 10.4230/OASIcs.CCA.2009.2258
publisher Schloss Dagstuhl - Leibniz-Zentrum für Informatik
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Computer Science{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Computer Science
url http://drops.dagstuhl.de/opus/volltexte/2009/2258
document_store_str 0
active_str 0
description We prove the correctness of a formalised realisability interpretation of extensions of first-order theories by inductive and coinductive definitions in an untyped $\lambda$-calculus with fixed-points. We illustrate the use of this interpretation for program extraction by some simple examples in the area of exact real number computation and hint at further non-trivial applications in computable analysis.
published_date 2009-12-31T03:03:14Z
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score 11.035634

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