Guaranteed Proofs Using Interval Arithmetic

Marc Daumas (1) , Guillaume Melquiond (1) , César Muñoz (2)

1 LIP - Laboratoire de l'Informatique du Parallélisme
2 NIA - National Institute of Aerospace [Hampton]

This paper presents a set of tools for mechanical reasoning of numerical bounds using interval arithmetic. The tools implement two techniques for reducing decorrelation: interval splitting and Taylor's series expansions. Although the tools are designed for the proof assistant system PVS, expertise on PVS is not required. The ultimate goal of the tools is to provide guaranteed proofs of numerical properties with a minimal human-theorem prover interaction.

Domaines: Arithmétique des ordinateurs

Marc Daumas, Guillaume Melquiond, César Muñoz. Guaranteed Proofs Using Interval Arithmetic. 17th IEEE Symposium on Computer Arithmetic, 2005, Cape Cod, Massachusetts, United States. pp.188-195, ⟨10.1109/ARITH.2005.25⟩. ⟨hal-00164621⟩