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Published in:
2005 | OriginalPaper | Chapter
Real Number Calculations and Theorem Proving
Authors : César Muñoz, David Lester
Published in: Theorem Proving in Higher Order Logics
Publisher: Springer Berlin Heidelberg
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Wouldn’t it be nice to be able to
conveniently
use ordinary real number expressions within proof assistants? In this paper we outline how this can be done within a theorem proving framework. First, we formally establish upper and lower bounds for trigonometric and transcendental functions. Then, based on these bounds, we develop a rational interval arithmetic where real number calculations can be performed in an algebraic setting. This pragmatic approach has been implemented as a strategy in PVS. The strategy provides a safe way to perform explicit calculations over real numbers in formal proofs.