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# Type theory and formal proof : an introduction

Author: R P Nederpelt; Herman Geuvers Cambridge ; New York : Cambridge University Press, 2014. Print book : EnglishView all editions and formats "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 culminating in 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 formalize mathematics. The only prerequisites are a good knowledge of undergraduate algebra and analysis. 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 familiarize themselves with the material"--  Read more... (not yet rated) 0 with reviews - Be the first.

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Document Type: Book R P Nederpelt; Herman Geuvers Find more information about: R P Nederpelt Herman Geuvers 9781107036505 110703650X 874733138 xxv, 436 pages ; 26 cm 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 Î»C; 8. Definitions; 9. Extension of Î»C with definitions; 10. Rules and properties of Î»D; 11. Flag-style natural deduction in Î»D; 12. Mathematics in Î»D: a first attempt; 13. Sets and subsets; 14. Numbers and arithmetic in Î»D; 15. An elaborated example; 16. Further perspectives; Appendix A. Logic in Î»D; Appendix B. Arithmetical axioms, definitions and lemmas; Appendix C. Two complete example proofs in Î»D; Appendix D. Derivation rules for Î»D; References; Index of names; Index of technical notions; Index of defined constants; Index of subjects. Rob Nederpelt, Eindhoven University of Technology, the Netherlands, Herman Geuvers, Radbound University Nijmegen, and Eindhoven University of Technology, the Netherlands.

### Abstract:

A gentle introduction for graduate students and researchers in the art of formalizing mathematics on the basis of type theory.  Read more...

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