Berger, Ulrich - From coinductive proofs to exact real arithmetic: theory and applications

lmcs:1109 - Logical Methods in Computer Science, March 24, 2011, Volume 7, Issue 1
From coinductive proofs to exact real arithmetic: theory and applications

Authors: Berger, Ulrich

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.


Source : oai:arXiv.org:1101.2162
DOI : 10.2168/LMCS-7(1:8)2011
Volume: Volume 7, Issue 1
Published on: March 24, 2011
Submitted on: June 25, 2015
Keywords: Computer Science - Logic in Computer Science,03F60


Share

Browsing statistics

This page has been seen 26 times.
This article's PDF has been downloaded 25 times.