Certified Exact Transcendental Real Number Computation in Coq

  • Russell O’Connor
Conference paper

DOI: 10.1007/978-3-540-71067-7_21

Volume 5170 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
O’Connor R. (2008) Certified Exact Transcendental Real Number Computation in Coq. In: Mohamed O.A., Muñoz C., Tahar S. (eds) Theorem Proving in Higher Order Logics. TPHOLs 2008. Lecture Notes in Computer Science, vol 5170. Springer, Berlin, Heidelberg

Abstract

Reasoning about real number expressions in a proof assistant is challenging. Several problems in theorem proving can be solved by using exact real number computation. I have implemented a library for reasoning and computing with complete metric spaces in the Coq proof assistant and used this library to build a constructive real number implementation including elementary real number functions and proofs of correctness. Using this library, I have created a tactic that automatically proves strict inequalities over closed elementary real number expressions by computation.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Russell O’Connor
    • 1
  1. 1.Institute for Computing and Information Science Faculty of ScienceRadboud University NijmegenNetherlands