The Calculi Of Lambda Conversion
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The Calculi of Lambda-Conversion
Author: Alonzo Church
language: en
Publisher: Princeton University Press
Release Date: 2016-03-02
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.
Lambda Calculus with Types
Author: Henk Barendregt
language: en
Publisher: Cambridge University Press
Release Date: 2013-06-20
This handbook with exercises reveals in formalisms, hitherto mainly used for hardware and software design and verification, unexpected mathematical beauty. The lambda calculus forms a prototype universal programming language, which in its untyped version is related to Lisp, and was treated in the first author's classic The Lambda Calculus (1984). The formalism has since been extended with types and used in functional programming (Haskell, Clean) and proof assistants (Coq, Isabelle, HOL), used in designing and verifying IT products and mathematical proofs. In this book, the authors focus on three classes of typing for lambda terms: simple types, recursive types and intersection types. It is in these three formalisms of terms and types that the unexpected mathematical beauty is revealed. The treatment is authoritative and comprehensive, complemented by an exhaustive bibliography, and numerous exercises are provided to deepen the readers' understanding and increase their confidence using types.
An Introduction to Functional Programming Through Lambda Calculus
Author: Greg Michaelson
language: en
Publisher: Courier Corporation
Release Date: 2013-04-10
Well-respected text for computer science students provides an accessible introduction to functional programming. Cogent examples illuminate the central ideas, and numerous exercises offer reinforcement. Includes solutions. 1989 edition.