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Formalization of real analysis: a survey of proof assistants and libraries†

Published online by Cambridge University Press:  02 January 2015

SYLVIE BOLDO ,
CATHERINE LELAY  and
GUILLAUME MELQUIOND
SYLVIE BOLDO
Affiliation:
Inria, LRI, bâtiment 650, Université Paris-Sud, F-91405 Orsay Cedex, France Email: Sylvie.Boldo@inria.fr
CATHERINE LELAY
Affiliation:
Inria, LRI, bâtiment 650, Université Paris-Sud, F-91405 Orsay Cedex, France Email: Sylvie.Boldo@inria.fr
GUILLAUME MELQUIOND
Affiliation:
Inria, LRI, bâtiment 650, Université Paris-Sud, F-91405 Orsay Cedex, France Email: Sylvie.Boldo@inria.fr
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Abstract

In the recent years, numerous proof systems have improved enough to be used for formally verifying non-trivial mathematical results. They, however, have different purposes and it is not always easy to choose which one is adapted to undertake a formalization effort. In this survey, we focus on properties related to real analysis: real numbers, arithmetic operators, limits, differentiability, integrability and so on. We have chosen to look into the formalizations provided in standard by the following systems: Coq, HOL4, HOL Light, Isabelle/HOL, Mizar, ProofPower-HOL, and PVS. We have also accounted for large developments that play a similar role or extend standard libraries: ACL2(r) for ACL2, C-CoRN/MathClasses for Coq, and the NASA PVS library. This survey presents how real numbers have been defined in these various provers and how the notions of real analysis described above have been formalized. We also look at the methods of automation these systems provide for real analysis.

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Paper
Information
Mathematical Structures in Computer Science , Volume 26 , Issue 7 , October 2016 , pp. 1196 - 1233
Copyright
Copyright © Cambridge University Press 2015 

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Footnotes

†

This work was supported by Project Coquelicot from RTRA Digiteo and Région Île-de-France.

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