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A coinductive approach to computing with compact sets / Ulrich, Berger

Journal of Logic and Analysis

Swansea University Author: Ulrich, Berger

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DOI (Published version): 10.4115/jla.2016.8.3

Abstract

Exact representations of real numbers such as the signed digit representation or more generally linear fractional representations or the infinite Gray code represent real numbers as infinite streams of digits. In earlier work by the first author it was shown how to extract certified algorithms worki...

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Published in: Journal of Logic and Analysis
ISSN: 17599008
Published: 2016
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa28975
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Abstract: Exact representations of real numbers such as the signed digit representation or more generally linear fractional representations or the infinite Gray code represent real numbers as infinite streams of digits. In earlier work by the first author it was shown how to extract certified algorithms working with the signed digit representations from constructiveproofs. In this paper we lay the foundation for doing a similar thing with nonempty compact sets. It turns out that a representation by streams of finitely many digits is impossible and instead trees are needed.
Keywords: Proof theory, realizability, program extraction, coinduction, computable analysis, compact sets