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Computing with continuous objects: a uniform co-inductive approach

Published online by Cambridge University Press:  19 August 2021

Dieter Spreen Open the ORCID record for Dieter Spreen [Opens in a new window]
Dieter Spreen*
Affiliation:
Department of Mathematics, University of Siegen, Siegen 57068, Germany Email: spreen@math.uni-siegen.de
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Abstract

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A uniform approach to computing with infinite objects like real numbers, tuples of these, compacts sets and uniformly continuous maps is presented. In the work of Berger, it was shown how to extract certified algorithms working with the signed digit representation from constructive proofs. Berger and the present author generalised this approach to complete metric spaces and showed how to deal with compact sets. Here, we unify this work and lay the foundations for doing a similar thing for the much more comprehensive class of compact Hausdorff spaces occurring in applications. The approach is of the same computational power as Weihrauch’s Type-Two Theory of Effectivity.

Keywords

Computingiterative function systemtopologycompact setinductive/co-inductive definitionprogram extraction
Type
Paper
Information
Mathematical Structures in Computer Science , Volume 31 , Issue 2 , February 2021 , pp. 144 - 192
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2021. Published by Cambridge University Press

Footnotes

*

This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 731143.

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