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A Co-inductive Approach to Real Numbers

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Types for Proofs and Programs (TYPES 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1956))

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Abstract

We define constructive real numbers in the logical framework Coq using streams, i.e. infinite sequences of digits. Co-inductive types and co-inductive proofs permit to work naturally on this representation. We prove our representation satisfies a set of basic properties which we propose as a set of axioms for constructive real numbers.

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Author information

Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Universitá di Udine, via delle Scienze, 206 - 33100, Udine, Italy

    Alberto Ciaffaglione & Pietro Di Gianantonio

Authors
  1. Alberto Ciaffaglione
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  2. Pietro Di Gianantonio
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Editor information

Editors and Affiliations

  1. Department of Computing Science, Chalmers University of Technology and University of Göteborg, 41296, Göteborg, Sweden

    Thierry Coquand , Peter Dybjer , Bengt Nordström  & Jan Smith , ,  & 

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© 2000 Springer-Verlag Berlin Heidelberg

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Ciaffaglione, A., Di Gianantonio, P. (2000). A Co-inductive Approach to Real Numbers. In: Coquand, T., Dybjer, P., Nordström, B., Smith, J. (eds) Types for Proofs and Programs. TYPES 1999. Lecture Notes in Computer Science, vol 1956. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44557-9_7

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  • DOI: https://doi.org/10.1007/3-540-44557-9_7

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41517-6

  • Online ISBN: 978-3-540-44557-9

  • eBook Packages: Springer Book Archive

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