The Calculi of Lambda-Conversion

Alonzo Church

Published by Princeton University Press 1985

The Calculi of Lambda-Conversion

Alonzo Church

Volume 6 in the series Annals of Mathematics Studies

https://doi.org/10.1515/9781400881932

Overview
Contents

About this book

The classic book that inspired Alan Turing and helped to lay the foundation for theoretical computer science

This book provides a concise introduction to the calculi of lambda-conversion first discovered by Alonzo Church and developed by him in collaboration with his students, S. C. Kleene and J. B. Rosser. The first four chapters present the calculus of lambda-conversion in detail, with subsequent chapters discussing the calculus of λ-K-conversion, the calculus of restricted λ-K-conversion, and the calculus of λ-δ-conversion, as well as the applications of the latter to symbolic logic. Gödel numbers are presented using simplified notation, and the fundamental Church-Rosser consistency theorem is discussed in full. This influential book is one that attracted the interest of Alan Turing—who later completed his PhD under Church’s supervision—and is widely credited with helping to usher in the modern age of computer science.

Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition into the twenty-first century as Princeton looks forward to publishing the major works of the new millennium.

Author / Editor information

Alonzo Church (1903–1995) was a renowned mathematician, logician, and philosopher. Together with his student Alan Turing, he is considered one of the founders of computer science. He is the author of Introduction to Mathematical Logic (Princeton).

Topics

Frontmatter Publicly Available Download PDF	i
CONTENTS Publicly Available Download PDF	v
Chapter I. INTRODUCTORY Requires Authentication Unlicensed Licensed Download PDF	1
Chapter II. LAMBDA-CONVERSION Requires Authentication Unlicensed Licensed Download PDF	8
Chapter III. LAMBDA-DEFINABILITY Requires Authentication Unlicensed Licensed Download PDF	28
Chapter IV. COMBINATIONS, GÖDEL NUMBERS Requires Authentication Unlicensed Licensed Download PDF	43
Chapter V. THE CALCULI OF λ-K-CONVERSION AND λ-δ- CONVERSION Requires Authentication Unlicensed Licensed Download PDF	58
INDEX OP THE PRINCIPAL FORMULAS INTRODUCED BY DEFINITION Requires Authentication Unlicensed Licensed Download PDF	72
BIBLIOGRAPHY Requires Authentication Unlicensed Licensed Download PDF	73
CORRECTION AND ADDITIONS Requires Authentication Unlicensed Licensed Download PDF	82