Journal article 1191 views
Coinduction for Exact Real Number Computation
,
Tie Hou
Theory of Computing Systems, Volume: 43, Issue: 3-4, Pages: 394 - 408
Swansea University Author:
Ulrich Berger
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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...
| Published in: | Theory of Computing Systems |
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| ISSN: | 1432-4350 1433-0490 |
| Published: |
2008
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| Online Access: |
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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. |
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| 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 |