A certified, corecursive implementation of exact real numbers
We implement exact real numbers in the logical framework Coq using streams, i.e., infinite sequences, of digits, and characterize constructive real numbers through a minimal axiomatization. We prove that our construction inhabits the axiomatization, working formally with coinductive types and corecursive proofs. Thus we obtain reliable, corecursive algorithms for computing on real numbers. (c) 2005 Elsevier B.V. All rights reserved.
logical frameworks coq exact computation streams of digits lazy functional algorithms coinductive type theories interactive theorem proving program and system verification