Inverting monotone continuous functions in constructive analysis

Authors:
Helmut Schwichtenberg
Affiliations:
Mathematisches Institut der Ludwig–Maximilians–Universität, München, Germany
Venue:
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
Year:
2006

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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. 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.