### Abstract

Language | English |
---|---|

Place of Publication | Cambridge |

Publisher | Cambridge University Press |

Number of pages | 436 |

ISBN (Print) | 978-1-107-03650-5 |

DOIs | |

State | Published - 2014 |

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### Cite this

*Type theory and formal proof : an introduction*. Cambridge: Cambridge University Press. DOI: 10.1017/CBO9781139567725

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*Type theory and formal proof : an introduction*. Cambridge University Press, Cambridge. DOI: 10.1017/CBO9781139567725

**Type theory and formal proof : an introduction.** / Nederpelt, R.P.; Geuvers, J.H.

Research output: Book/Report › Book › Academic

TY - BOOK

T1 - Type theory and formal proof : an introduction

AU - Nederpelt,R.P.

AU - Geuvers,J.H.

PY - 2014

Y1 - 2014

N2 - A gentle introduction for graduate students and researchers in the art of formalizing mathematics on the basis of type theory. 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.

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

U2 - 10.1017/CBO9781139567725

DO - 10.1017/CBO9781139567725

M3 - Book

SN - 978-1-107-03650-5

BT - Type theory and formal proof : an introduction

PB - Cambridge University Press

CY - Cambridge

ER -