Flocq: A Unified Library for Proving Floating-Point Algorithms in Coq

Author

Boldo, Sylvie ; Melquiond, Guillaume

Author_Institution

ProVal, INRIA Saclay - Ile-de-France, Orsay, France

fYear

2011

fDate

25-27 July 2011

Firstpage

243

Lastpage

252

Abstract

Several formalizations of floating-point arithmetic have been designed for the Coq system, a generic proof assistant. Their different purposes have favored some specific applications: program verification, high-level properties, automation. Based on our experience using and/or developing these libraries, we have built a new system that is meant to encompass the other ones in a unified framework. It offers a multi-radix and multi-precision formalization for various floating- and fixed-point formats. This fresh setting has been the occasion for reevaluating known properties and generalizing them. This paper presents design decisions and examples of theorems from the Flocq system: a library easy to use, suitable for automation yet high-level and generic.

Keywords

fixed point arithmetic; floating point arithmetic; program verification; Coq system; Flocq; fixed-point format; floating point algorithm; floating-point format; generic proof assistant; multiprecision formalization; multiradix formalization; program verification; unified library; Arrays; Automation; Electronic mail; Humans; Libraries; Safety; Testing; floating-point arithmetic; formal proof system; program verification;

fLanguage

English

Publisher

ieee

Conference_Titel

Computer Arithmetic (ARITH), 2011 20th IEEE Symposium on

Conference_Location

Tubingen

ISSN

1063-6889

Print_ISBN

978-1-4244-9457-6

Type

conf

DOI

10.1109/ARITH.2011.40

Filename

5992132