Coinductive Proofs for Basic Real Computation

Part of the Lecture Notes in Computer Science book series (LNCS, volume 3988)

Abstract

We describe two representations for real numbers, signed digit streams and Cauchy sequences. We give coinductive proofs for the correctness of functions converting between these two representations to show the adequacy of signed digit stream representation. We also show a coinductive proof for the correctness of a corecursive program for the average function with regard to the signed digit stream representation. We implemented this proof in the interactive proof system Minlog. Thus, reliable, corecursive functions for real computation can be guaranteed, which is very helpful in formal software development for real numbers.

Keywords

Real computation Coinductive proof Signed digit streams Computability Minlog 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Tie Hou
    • 1
  1. 1.University of Wales SwanseaSwanseaUK

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