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Coinduction for Exact Real Number Computation

Ulrich Berger Orcid Logo, Tie Hou

Theory of Computing Systems, Volume: 43, Issue: 3-4, Pages: 394 - 408

Swansea University Author: Ulrich Berger Orcid Logo

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DOI (Published version): 10.1007/s00224-007-9017-6

Abstract

This paper studies coinductive representations of real numbers bysigned digit streams and fast Cauchy sequences. It is shown how theassociated coinductive principle can be used to give straightforwardand easily implementable proofs of the equivalence of the tworepresentations as well as the correctn...

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Published in: Theory of Computing Systems
ISSN: 1432-4350 1433-0490
Published: 2008
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URI: https://cronfa.swan.ac.uk/Record/cronfa133
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spelling 2013-06-14T12:56:23.5297019 v2 133 2012-02-23 Coinduction for Exact Real Number Computation 61199ae25042a5e629c5398c4a40a4f5 0000-0002-7677-3582 Ulrich Berger Ulrich Berger true false 2012-02-23 SCS This paper studies coinductive representations of real numbers bysigned digit streams and fast Cauchy sequences. It is shown how theassociated coinductive principle can be used to give straightforwardand easily implementable proofs of the equivalence of the tworepresentations as well as the correctness of various corecursiveexact real number algorithms. The basic framework is the classicaltheory of coinductive sets as greatest fixed points of monotoneoperators and hence is different from (though related to) the typetheoretic approach by Ciaffaglione and Gianantonio. Journal Article Theory of Computing Systems 43 3-4 394 408 1432-4350 1433-0490 Exact real number computation, coinduction, corecursion, signed digit streams. 31 12 2008 2008-12-31 10.1007/s00224-007-9017-6 COLLEGE NANME Computer Science COLLEGE CODE SCS Swansea University 2013-06-14T12:56:23.5297019 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 Tie Hou 2
title Coinduction for Exact Real Number Computation
spellingShingle Coinduction for Exact Real Number Computation
Ulrich Berger
title_short Coinduction for Exact Real Number Computation
title_full Coinduction for Exact Real Number Computation
title_fullStr Coinduction for Exact Real Number Computation
title_full_unstemmed Coinduction for Exact Real Number Computation
title_sort Coinduction for Exact Real Number Computation
author_id_str_mv 61199ae25042a5e629c5398c4a40a4f5
author_id_fullname_str_mv 61199ae25042a5e629c5398c4a40a4f5_***_Ulrich Berger
author Ulrich Berger
author2 Ulrich Berger
Tie Hou
format Journal article
container_title Theory of Computing Systems
container_volume 43
container_issue 3-4
container_start_page 394
publishDate 2008
institution Swansea University
issn 1432-4350
1433-0490
doi_str_mv 10.1007/s00224-007-9017-6
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
document_store_str 0
active_str 0
description This paper studies coinductive representations of real numbers bysigned digit streams and fast Cauchy sequences. It is shown how theassociated coinductive principle can be used to give straightforwardand easily implementable proofs of the equivalence of the tworepresentations as well as the correctness of various corecursiveexact real number algorithms. The basic framework is the classicaltheory of coinductive sets as greatest fixed points of monotoneoperators and hence is different from (though related to) the typetheoretic approach by Ciaffaglione and Gianantonio.
published_date 2008-12-31T03:02:54Z
_version_ 1763749474602057728
score 11.013371

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