Computer Arithmetic and Formal Proofs: Verifying Floating-point Algorithms With the Coq System

Boldo, Sylvie/ Melquiond, Guillaume

ISBN 10: 1785481126 / ISBN 13: 9781785481123

Edité par Elsevier Science Ltd, 2017

A propos de cet article

306 pages. 9.00x6.00x1.00 inches. In Stock. N° de réf. du vendeur __1785481126

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Titre : Computer Arithmetic and Formal Proofs: ...

Éditeur : Elsevier Science Ltd

Date d'édition : 2017

Reliure : Hardcover

Etat : Brand New

A propos de ce titre

Synopsis :

Computer Arithmetic and Formal Proofs: Floating-point Algorithms with the Coq System explores floating-point arithmetic, a tool that is ubiquitous in modern computing as the tool of choice to approximate real numbers. Due to its limited range and precision, its use can become quite involved and cause numerous failures. This book explains how to avoid this and increase confidence in floating-point software by using the computer-assisted verification of correctness proof (the Coq proof assistant), the tool that is comprehensively discussed throughout this book.

• Describes the notions of specification and weakest precondition computation and their practical use
• Shows how to tackle algorithms that extend beyond the realm of simple floating-point arithmetic
• Includes real analysis and a case study about numerical analysis

Présentation de l'éditeur:

Floating-point arithmetic is ubiquitous in modern computing, as it is the tool of choice to approximate real numbers. Due to its limited range and precision, its use can become quite involved and potentially lead to numerous failures. One way to greatly increase confidence in floating-point software is by computer-assisted verification of its correctness proofs.

This book provides a comprehensive view of how to formally specify and verify tricky floating-point algorithms with the Coq proof assistant. It describes the Flocq formalization of floating-point arithmetic and some methods to automate theorem proofs. It then presents the specification and verification of various algorithms, from error-free transformations to a numerical scheme for a partial differential equation. The examples cover not only mathematical algorithms but also C programs as well as issues related to compilation.  

• Describes the notions of specification and weakest precondition computation and their practical use
• Shows how to tackle algorithms that extend beyond the realm of simple floating-point arithmetic
• Includes real analysis and a case study about numerical analysis