Journal article 1123 views
From coinductive proofs to exact real arithmetic: theory and applications
Ulrich Berger 
,
Reinhard Kahle
,
Reinhard Kahle
Logical Methods in Computer Science, Volume: 7, Issue: 1
Swansea University Author:
Ulrich Berger
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DOI (Published version): 10.2168/LMCS-7(1:8)2011
Abstract
<p>Based on a new coinductive characterization of continuous functions we extract certified programs for exact real number computation from constructive proofs. The extracted programs construct and combine exact real number algorithms with respect to the binary signed digit representation of r...
| Published in: | Logical Methods in Computer Science |
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| ISSN: | 1860-5974 |
| Published: |
2011
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa5271 |
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| Abstract: |
<p>Based on a new coinductive characterization of continuous functions we extract certified programs for exact real number computation from constructive proofs. The extracted programs construct and combine exact real number algorithms with respect to the binary signed digit representation of real numbers. The data type corresponding to the coinductive definition of continuous functions consists of finitely branching non-wellfounded trees describing when the algorithm writes and reads digits. We discuss several examples including the extraction of programs for polynomials up to degree two and the definite integral of continuous maps.</p> |
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| College: |
Faculty of Science and Engineering |
| Issue: |
1 |