Realizability interpretation of proofs in constructive analysis

Authors:
Helmut Schwichtenberg
Affiliations:
Universität München, Mathematisches Institut, Theresienstr. 39, 80333, Munich, Germany
Venue:
Theory of Computing Systems
Year:
2008

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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.