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Realisability for Induction and Coinduction with Applications to Constructive Analysis

Ulrich Berger Orcid Logo

Journal of Universal Computer Science, Volume: 16, Issue: 18, Pages: 2535 - 2555

Swansea University Author: Ulrich Berger Orcid Logo

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DOI (Published version): 10.3217/jucs-016-18-2535

Abstract

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

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Published in: Journal of Universal Computer Science
ISSN: 0948-6968
Published: 2010
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URI: https://cronfa.swan.ac.uk/Record/cronfa7893
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first_indexed 2013-07-23T11:59:43Z
last_indexed 2018-02-09T04:36:35Z
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spelling 2015-10-14T16:13:02.4677452 v2 7893 2012-02-23 Realisability for Induction and Coinduction with Applications to Constructive Analysis 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 λ-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. Journal Article Journal of Universal Computer Science 16 18 2535 2555 0948-6968 coinduction, constructive analysis, program extraction, realisability 28 9 2010 2010-09-28 10.3217/jucs-016-18-2535 http://www.jucs.org/jucs_16_18/realisability_for_induction_and COLLEGE NANME Computer Science COLLEGE CODE SCS Swansea University 2015-10-14T16:13:02.4677452 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
title Realisability for Induction and Coinduction with Applications to Constructive Analysis
spellingShingle Realisability for Induction and Coinduction with Applications to Constructive Analysis
Ulrich Berger
title_short Realisability for Induction and Coinduction with Applications to Constructive Analysis
title_full Realisability for Induction and Coinduction with Applications to Constructive Analysis
title_fullStr Realisability for Induction and Coinduction with Applications to Constructive Analysis
title_full_unstemmed Realisability for Induction and Coinduction with Applications to Constructive Analysis
title_sort Realisability for Induction and Coinduction with Applications to Constructive Analysis
author_id_str_mv 61199ae25042a5e629c5398c4a40a4f5
author_id_fullname_str_mv 61199ae25042a5e629c5398c4a40a4f5_***_Ulrich Berger
author Ulrich Berger
author2 Ulrich Berger
format Journal article
container_title Journal of Universal Computer Science
container_volume 16
container_issue 18
container_start_page 2535
publishDate 2010
institution Swansea University
issn 0948-6968
doi_str_mv 10.3217/jucs-016-18-2535
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://www.jucs.org/jucs_16_18/realisability_for_induction_and
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 λ-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 2010-09-28T03:09:53Z
_version_ 1763749914223837184
score 11.035634

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