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Type Theory and Formal Proof
An Introduction

$82.00 (P)

  • Date Published: December 2014
  • availability: Available
  • format: Hardback
  • isbn: 9781107036505

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About the Authors
  • Type theory is a fast-evolving field at the crossroads of logic, computer science and mathematics. This gentle step-by-step introduction is ideal for graduate students and researchers who need to understand the ins and outs of the mathematical machinery, the role of logical rules therein, the essential contribution of definitions and the decisive nature of well-structured proofs. The authors begin with untyped lambda calculus and proceed to several fundamental type systems, including the well-known and powerful Calculus of Constructions. The book also covers the essence of proof checking and proof development, and the use of dependent type theory to formalise mathematics. The only prerequisite is a basic knowledge of undergraduate mathematics. Carefully chosen examples illustrate the theory throughout. Each chapter ends with a summary of the content, some historical context, suggestions for further reading and a selection of exercises to help readers familiarise themselves with the material.

    • Gives insight into a variety of type systems and their relative power
    • Provides background for the use of proof assistants such as Coq
    • Students can test their understanding through 125 end-of-chapter exercises
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    Product details

    • Date Published: December 2014
    • format: Hardback
    • isbn: 9781107036505
    • length: 466 pages
    • dimensions: 254 x 173 x 28 mm
    • weight: 0.98kg
    • contains: 35 b/w illus. 125 exercises
    • availability: Available
  • Table of Contents

    Foreword
    Preface
    Acknowledgements
    Greek alphabet
    1. Untyped lambda calculus
    2. Simply typed lambda calculus
    3. Second order typed lambda calculus
    4. Types dependent on types
    5. Types dependent on terms
    6. The Calculus of Constructions
    7. The encoding of logical notions in λC
    8. Definitions
    9. Extension of λC with definitions
    10. Rules and properties of λD
    11. Flag-style natural deduction in λD
    12. Mathematics in λD: a first attempt
    13. Sets and subsets
    14. Numbers and arithmetic in λD
    15. An elaborated example
    16. Further perspectives
    Appendix A. Logic in λD
    Appendix B. Arithmetical axioms, definitions and lemmas
    Appendix C. Two complete example proofs in λD
    Appendix D. Derivation rules for λD
    References
    Index of names
    Index of technical notions
    Index of defined constants
    Index of subjects.

  • Resources for

    Type Theory and Formal Proof

    Rob Nederpelt, Herman Geuvers

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  • Authors

    Rob Nederpelt, Technische Universiteit Eindhoven, The Netherlands
    Rob Nederpelt was Lecturer in Logic for Computer Science until his retirement. Currently he is a guest researcher in the Faculty of Mathematics and Computer Science at Eindhoven University of Technology, The Netherlands.

    Herman Geuvers, Radboud Universiteit Nijmegen
    Herman Geuvers is Professor in Theoretical Informatics at the Radboud University Nijmegen, and Professor in Proving with Computer Assistance at Eindhoven University of Technology, both in The Netherlands.

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