Theory of Computing Systems

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

Realizability interpretation of proofs in constructive analysis

  • Helmut Schwichtenberg


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.


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


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© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Mathematisches InstitutUniversität MünchenMunichGermany

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