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  • Textbook
  • © 2004

Interactive Theorem Proving and Program Development

Coq’Art: The Calculus of Inductive Constructions

  • First book providing the theoretical foundations
  • A broad spectrum of applications of the theorem proving system Coq
  • Includes supplementary material: sn.pub/extras

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Table of contents (16 chapters)

  1. Front Matter

    Pages I-XXV
  2. A Brief Overview

    • Yves Bertot, Pierre Castéran
    Pages 1-11
  3. Types and Expressions

    • Yves Bertot, Pierre Castéran
    Pages 13-42
  4. Propositions and Proofs

    • Yves Bertot, Pierre Castéran
    Pages 43-72
  5. Dependent Products or Pandora’s Box

    • Yves Bertot, Pierre Castéran
    Pages 73-103
  6. Everyday Logic

    • Yves Bertot, Pierre Castéran
    Pages 105-135
  7. Inductive Data Types

    • Yves Bertot, Pierre Castéran
    Pages 137-186
  8. Tactics and Automation

    • Yves Bertot, Pierre Castéran
    Pages 187-210
  9. Inductive Predicates

    • Yves Bertot, Pierre Castéran
    Pages 211-250
  10. * Functions and Their Specifications

    • Yves Bertot, Pierre Castéran
    Pages 251-284
  11. * Extraction and Imperative Programming

    • Yves Bertot, Pierre Castéran
    Pages 285-307
  12. * A Case Study

    • Yves Bertot, Pierre Castéran
    Pages 309-324
  13. * The Module System

    • Yves Bertot, Pierre Castéran
    Pages 325-346
  14. ** Infinite Objects and Proofs

    • Yves Bertot, Pierre Castéran
    Pages 347-376
  15. ** Foundations of Inductive Types

    • Yves Bertot, Pierre Castéran
    Pages 377-406
  16. * General Recursion

    • Yves Bertot, Pierre Castéran
    Pages 407-432
  17. * Proof by Reflection

    • Yves Bertot, Pierre Castéran
    Pages 433-448
  18. Back Matter

    Pages 449-472

About this book

Coq is an interactive proof assistant for the development of mathematical theories and formally certified software. It is based on a theory called the calculus of inductive constructions, a variant of type theory.

This book provides a pragmatic introduction to the development of proofs and certified programs using Coq. With its large collection of examples and exercises it is an invaluable tool for researchers, students, and engineers interested in formal methods and the development of zero-fault software.

Reviews

From the reviews of the first edition:

"This book serves as a Coq user manual, supporting both beginners and experts in the use of Coq and its underlying theory. … Numerous exercises further enhance the utility as a learning aid. A supporting website provides downloadable source for all the examples and solutions to the exercises. As an introduction to Coq the book is self-contained … . The book is also comprehensive … . In summary, the book is an essential companion for every Coq user … ." (Valentin F. Goranko, Zentralblatt MATH, Vol. 1069, 2005)

Authors and Affiliations

  • Inria Sophia Antipolis, Sophia Antipolis Cedex, France

    Yves Bertot

  • LaBRI and Inria Futurs LabRI, Université Bordeaux I, Talence Cedex, France

    Pierre Castéran

Bibliographic Information

Buy it now

Buying options

eBook USD 69.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 89.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 119.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access