Logic for exact real arithmetic

摘要

Continuing earlier work of the first author with U. Berger, K. Miyamoto andH. Tsuiki, it is shown how a division algorithm for real numbers given as astream of signed digits can be extracted from an appropriate formal proof. Theproperty of being a real number represented as a stream is formulated by meansof coinductively defined predicates, and formal proofs involve coinduction. Theproof assistant Minlog is used to generate the formal proofs and extract theircomputational content as terms of the underlying theory, a form of type theoryfor finite or infinite data. Some experiments with running the extracted termare described, after its translation to Haskell.