Theorem Proving in Higher Order Logics

Volume 5170 of the series Lecture Notes in Computer Science pp 246-261

Certified Exact Transcendental Real Number Computation in Coq

  • Russell O’ConnorAffiliated withInstitute for Computing and Information Science Faculty of Science, Radboud University Nijmegen

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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.