Preface

Preface

IAS Special Year on Univalent Foundations

A Special Year on

Univalent Foundations

of Mathematics was held in 2012-13 at the Institute for Advanced Study, School of Mathematics, organized by Steve Awodey, Thierry Coquand, and Vladimir Voevodsky. The following people were the official participants.

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3

Peter Aczel

Benedikt Ahrens

Thorsten Altenkirch

Steve Awodey

Bruno Barras

Andrej Bauer

Yves Bertot

Marc Bezem

Thierry Coquand

Eric Finster

Daniel Grayson

Hugo Herbelin

André Joyal

Dan Licata

Peter Lumsdaine

Assia Mahboubi

Per Martin-Löf

Sergey Melikhov

Alvaro Pelayo

Andrew Polonsky

Michael Shulman

Matthieu Sozeau

Bas Spitters

Benno van den Berg

Vladimir Voevodsky

Michael Warren

Noam Zeilberger

There were also the following students, whose participation was no less valuable.

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3

Carlo Angiuli

Anthony Bordg

Guillaume Brunerie

Chris Kapulkin

Egbert Rijke

Kristina Sojakova

In

addition

, there were the following short- and long-term visitors, including student visitors, whose contributions to the Special Year were also essential.

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3

Jeremy Avigad

Cyril Cohen

Robert Constable

Pierre-Louis Curien

Peter Dybjer

Martín Escardó

Kuen-Bang Hou

Nicola Gambino

Richard Garner

Georges Gonthier

Thomas Hales

Robert Harper

Martin Hofmann

Pieter Hofstra

Joachim Kock

Nicolai Kraus

Nuo Li

Zhaohui Luo

Michael Nahas

Erik Palmgren

Emily Riehl

Dana Scott

Philip Scott

Sergei Soloviev

About this book

We did not set out to write a book. The present work has its origins in our collective attempts to develop a new style of “

informal type theory

” that can be read and understood by a human being, as a

complement

to a formal proof that can be checked by a

machine

.
Univalent foundations is closely tied to the idea of a

foundation of mathematics

that can be implemented in a computer proof assistant. Although such a formalization is not part of this book, much of the material presented here was actually done first in the fully formalized setting inside a proof assistant, and only later “unformalized” to arrive at the

presentation

you find before you — a remarkable

inversion

of the usual state of affairs in formalized mathematics.

Each of the above-named

individuals

contributed something to the Special Year — and so to this book — in the form of ideas, words, or deeds. The spirit of collaboration that prevailed throughout the year was truly extraordinary.

Special thanks are due to the Institute for Advanced Study, without which this book would obviously never have come to be. It proved to be an ideal setting for the creation of this new branch of mathematics: stimulating, congenial, and supportive. May some trace of this unique atmosphere linger in the pages of this book, and in the future

development

of this new field of study.

The Univalent Foundations Program

Institute for Advanced Study

Princeton, April 2013

Title

Preface

Canonical name

Preface

Date of creation

2013-11-09 2:13:51

Last modified on

2013-11-09 2:13:51

Owner

PMBookProject (1000683)

Last modified by

PMBookProject (1000683)

Numerical id

1

Author

PMBookProject (1000683)

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Application

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msc 03B15

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