Coinduction for Exact Real Number Computation

Authors:
Ulrich Berger;Tie Hou
Affiliations:
University of Wales Swansea, SA2 8PP, Swansea, Wales, UK;University of Amsterdam, Informatics Institute, Kruislaan 403, 1098 SJ, Amsterdam, The Netherlands
Venue:
Theory of Computing Systems
Year:
2008

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Abstract

This paper studies coinductive representations of real numbers by signed digit streams and fast Cauchy sequences. It is shown how the associated coinductive principle can be used to give straightforward and easily implementable proofs of the equivalence of the two representations as well as the correctness of various corecursive exact real number algorithms. The basic framework is the classical theory of coinductive sets as greatest fixed points of monotone operators and hence is different from (though related to) the type theoretic approach by Ciaffaglione and Gianantonio.