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. © Springer-Verlag Berlin Heidelberg 2006.
CITATION STYLE
Schwichtenberg, H. (2006). Inverting monotone continuous functions in constructive analysis. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 3988 LNCS, pp. 490–504). Springer Verlag. https://doi.org/10.1007/11780342_50
Mendeley helps you to discover research relevant for your work.