Type Theory and Formal Proof
eBook - PDF

Type Theory and Formal Proof

An Introduction

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

Type Theory and Formal Proof

An Introduction

About this book

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.

Frequently asked questions

Yes, you can cancel anytime from the Subscription tab in your account settings on the Perlego website. Your subscription will stay active until the end of your current billing period. Learn how to cancel your subscription.
No, books cannot be downloaded as external files, such as PDFs, for use outside of Perlego. However, you can download books within the Perlego app for offline reading on mobile or tablet. Learn more here.
Perlego offers two plans: Essential and Complete
  • Essential is ideal for learners and professionals who enjoy exploring a wide range of subjects. Access the Essential Library with 800,000+ trusted titles and best-sellers across business, personal growth, and the humanities. Includes unlimited reading time and Standard Read Aloud voice.
  • Complete: Perfect for advanced learners and researchers needing full, unrestricted access. Unlock 1.4M+ books across hundreds of subjects, including academic and specialized titles. The Complete Plan also includes advanced features like Premium Read Aloud and Research Assistant.
Both plans are available with monthly, semester, or annual billing cycles.
We are an online textbook subscription service, where you can get access to an entire online library for less than the price of a single book per month. With over 1 million books across 1000+ topics, we’ve got you covered! Learn more here.
Look out for the read-aloud symbol on your next book to see if you can listen to it. The read-aloud tool reads text aloud for you, highlighting the text as it is being read. You can pause it, speed it up and slow it down. Learn more here.
Yes! You can use the Perlego app on both iOS or Android devices to read anytime, anywhere — even offline. Perfect for commutes or when you’re on the go.
Please note we cannot support devices running on iOS 13 and Android 7 or earlier. Learn more about using the app.
Yes, you can access Type Theory and Formal Proof by Rob Nederpelt,Herman Geuvers in PDF and/or ePUB format, as well as other popular books in Computer Science & Programming Languages. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Cover
  2. Half-title
  3. Title page
  4. Copyright information
  5. Dedication
  6. Table of contents
  7. Foreword
  8. Preface
  9. Acknowledgements
  10. Greek alphabet
  11. 1 Untyped lambda calculus
  12. 2 Simply typed lambda calculus
  13. 3 Second order typed lambda calculus
  14. 4 Types dependent on types
  15. 5 Types dependent on terms
  16. 6 The Calculus of Constructions
  17. 7 The encoding of logical notions in λC
  18. 8 Definitions
  19. 9 Extension of λC with definitions
  20. 10 Rules and properties of λD
  21. 11 Flag-style natural deduction in λD
  22. 12 Mathematics in λD: a first attempt
  23. 13 Sets and subsets
  24. 14 Numbers and arithmetic in λD
  25. 15 An elaborated example
  26. 16 Further perspectives
  27. Appendix A Logic in λD
  28. Appendix B Arithmetical axioms, definitions and lemmas
  29. Appendix C Two complete example proofs in λD
  30. Appendix D Derivation rules for λD
  31. References
  32. Index of names
  33. Index of definitions
  34. Index of symbols
  35. Index of subjects