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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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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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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 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.
Keywords: Exact real number computation, coinduction, corecursion, signed digit streams.
College: Faculty of Science and Engineering
Issue: 3-4
Start Page: 394
End Page: 408