Theory of Computing Systems

, Volume 43, Issue 3–4, pp 583–602 | Cite as

Realizability interpretation of proofs in constructive analysis

Article

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. It turns out that even in the logical term language—a version of Gödel’s T—evaluation is reasonably efficient.

Keywords

Realizability Continuous inverse function Intermediate value theorem Program extraction Non-computational quantifier 

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Mathematisches InstitutUniversität MünchenMunichGermany

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