Derivation and Computation: Taking the Curry-Howard Correspondence Seriously / Edition 1

by H. Simmons

Overview

The two notions of proofs and calculations are intimately related. Proofs can involve calculations, and the algorithm underlying a calculation should be proved correct. This volume explores this key relationship and introduces simple type theory. Starting from the familiar propositional calculus, the author develops the central idea of an applied lambda-calculus. This is illustrated by an account of Gödel's T, a system that codifies number-theoretic function hierarchies. Each of the book's 52 sections ends with a set of exercises, some 200 in total. An appendix contains complete solutions of these exercises.

Product Details

ISBN-13:	9780521771733
Publisher:	Cambridge University Press
Publication date:	05/18/2000
Series:	Cambridge Tracts in Theoretical Computer Science , #51
Edition description:	New Edition
Pages:	412
Product dimensions:	6.22(w) x 9.29(h) x 1.02(d)

Table of Contents

Introduction; Preview; Part I. Development and Exercises: 1. Derivation systems; 2. Computation mechanisms; 3. The typed combinator calculus; 4. The typed l-calculus; 5. Substitution algorithms; 6. Applied l-calculi; 7. Multi-recursive arithmetic; 8. Ordinals and ordinal notation; 9. Higher order recursion; Part II. Solutions: A. Derivation systems; B. Computation mechanisms; C. The typed combinator calculus; D. The typed l-calculus; E. Substitution algorithms; F. Applied l-calculi; G. Multi-recursive arithmetic; H. Ordinals and ordinal notation; I. Higher order recursion; Postview; Bibliography; Commonly used symbols; Index.

Editorial Reviews

"The book is rather snappily written. It's informal, breezy - sometimes positively jaunty - and always directed to the reader. It can't be emphasized enough that the great thing about this book is its many well-chosen, completely solved exercises. This alone makes it a valuable text, especially for self-study."
Robert J. Irwin, Hamilton College for SIGACT News

From the Publisher