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Journal of Automated Reasoning

, Volume 56, Issue 3, pp 367–386 | Cite as

A Heuristic Prover for Real Inequalities

  • Jeremy Avigad
  • Robert Y. Lewis
  • Cody Roux
Article

Abstract

We describe a general method for verifying inequalities between real-valued expressions, especially the kinds of straightforward inferences that arise in interactive theorem proving. In contrast to approaches that aim to be complete with respect to a particular language or class of formulas, our method establishes claims that require heterogeneous forms of reasoning, relying on a Nelson-Oppen-style architecture in which special-purpose modules collaborate and share information. The framework is thus modular and extensible. A prototype implementation shows that the method works well on a variety of examples, and complements techniques that are used by contemporary interactive provers.

Keywords

Real-valued inequalities Interactive theorem proving Automated theorem proving 

Notes

Acknowledgments

We are grateful to Leonardo de Moura and the anonymous referees for helpful corrections, information, and suggestions.

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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Carnegie Mellon UniversityPittsburghUSA
  2. 2.Draper LaboratoriesCambridgeUSA

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