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Real Number Calculations and Theorem Proving

  • César Muñoz
  • David Lester
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3603)

Abstract

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.

Keywords

Theorem Prove Interval Arithmetic Transcendental Function Proof Assistant High Order Logic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • César Muñoz
    • 1
  • David Lester
    • 2
  1. 1.National Institute of AerospaceHamptonUSA
  2. 2.University of ManchesterManchesterUK

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