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Intuitionistic fixed point logic

Ulrich Berger, Hideki Tsuiki

Annals of Pure and Applied Logic, Volume: 172, Issue: 3, Start page: 102903

Swansea University Author: Ulrich Berger

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DOI (Published version): 10.1016/j.apal.2020.102903

Abstract

The logical system IFP introduced in this paper supports program extraction from proofs, unifying theoretical and practical advantages: Based on first-order logic and powerful strictly positive inductive and coinductive definitions, IFP support abstract axiomatic mathematics with a large amount of c...

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Published in: Annals of Pure and Applied Logic
ISSN: 0168-0072
Published: Elsevier BV 2021
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa55847
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last_indexed 2021-01-29T04:20:35Z
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spelling 2021-01-28T16:08:23.1833346 v2 55847 2020-12-07 Intuitionistic fixed point logic 61199ae25042a5e629c5398c4a40a4f5 Ulrich Berger Ulrich Berger true false 2020-12-07 The logical system IFP introduced in this paper supports program extraction from proofs, unifying theoretical and practical advantages: Based on first-order logic and powerful strictly positive inductive and coinductive definitions, IFP support abstract axiomatic mathematics with a large amount of classical logic. The Haskell-like target programming language has a denotational and an operational semantics which are linked through a computational adequacy theorem that extends to infinite data. Program extraction is fully verified and highly optimised, thus extracted programs are guaranteed to be correct and free of junk. A case study in exact real number computation underpins IFP's effectiveness. Journal Article Annals of Pure and Applied Logic 172 3 102903 Elsevier BV 0168-0072 Proof theory, realizability, program extraction , induction , coinduction , exact real number computation 1 3 2021 2021-03-01 10.1016/j.apal.2020.102903 COLLEGE NANME COLLEGE CODE Swansea University 2021-01-28T16:08:23.1833346 2020-12-07T13:55:25.7737826 Faculty of Science and Engineering School of Mathematics and Computer Science - Computer Science Ulrich Berger 1 Hideki Tsuiki 2 55847__18963__173ee186f9b34a89a7170fed3e1516c8.pdf main.pdf 2021-01-05T10:58:28.3121082 Output 585632 application/pdf Accepted Manuscript true 2021-10-09T00:00:00.0000000 Distributed under the terms of a Creative Commons Attribution, Non-Commercial, NoDerivatives (CC-BY-NC-ND) Licence. true eng https://creativecommons.org/licenses/by-nc-nd/4.0/
title Intuitionistic fixed point logic
spellingShingle Intuitionistic fixed point logic
Ulrich Berger
title_short Intuitionistic fixed point logic
title_full Intuitionistic fixed point logic
title_fullStr Intuitionistic fixed point logic
title_full_unstemmed Intuitionistic fixed point logic
title_sort Intuitionistic fixed point logic
author_id_str_mv 61199ae25042a5e629c5398c4a40a4f5
author_id_fullname_str_mv 61199ae25042a5e629c5398c4a40a4f5_***_Ulrich Berger
author Ulrich Berger
author2 Ulrich Berger
Hideki Tsuiki
format Journal article
container_title Annals of Pure and Applied Logic
container_volume 172
container_issue 3
container_start_page 102903
publishDate 2021
institution Swansea University
issn 0168-0072
doi_str_mv 10.1016/j.apal.2020.102903
publisher Elsevier BV
college_str Faculty of Science and Engineering
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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
document_store_str 1
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description The logical system IFP introduced in this paper supports program extraction from proofs, unifying theoretical and practical advantages: Based on first-order logic and powerful strictly positive inductive and coinductive definitions, IFP support abstract axiomatic mathematics with a large amount of classical logic. The Haskell-like target programming language has a denotational and an operational semantics which are linked through a computational adequacy theorem that extends to infinite data. Program extraction is fully verified and highly optimised, thus extracted programs are guaranteed to be correct and free of junk. A case study in exact real number computation underpins IFP's effectiveness.
published_date 2021-03-01T11:59:54Z
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score 10.959048

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