Inverting Monotone Continuous Functions in Constructive Analysis

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

Abstract

We prove constructively (in the style of Bishop) that every monotone continuous function with a uniform modulus of increase has a continuous inverse. The proof is formalized, and a realizing term extracted. This term can be applied to concrete continuous functions and arguments, and then normalized to a rational approximation of say a zero of a given function. It turns out that even in the logical term language “normalization by evaluation” is reasonably efficient.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Helmut Schwichtenberg
    • 1
  1. 1.Mathematisches Institut der Ludwig–Maximilians–UniversitätMünchenGermany

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