# Derivation and Computation: Taking the Curry-Howard Correspondence Seriously

Cambridge University Press, May 18, 2000 - Mathematics - 384 pages
Mathematics is about proofs, that is the derivation of correct statements; and calculations, that is the production of results according to well-defined sets of rules. The two notions are intimately related. Proofs can involve calculations, and the algorithm underlying a calculation should be proved correct. The aim of the author is to explore this relationship. The book itself forms an introduction to 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 which codifies number-theoretic function hierarchies. Each of the book's 52 sections ends with a set of exercises, some 200 in total. These are designed to help the reader get to grips with the subject, and develop a further understanding. An appendix contains complete solutions of these exercises.

### What people are saying -Write a review

We haven't found any reviews in the usual places.

### Contents

 DERIVATION SYSTEMS 11 THE TYPED XCALCULUS 67 SUBSTITUTION ALGORITHMS 82 APPLIED XCALCULI 100 A DERIVATION SYSTEMS 215 COMPUTATION MECHANISMS 234 Exercises 245 THE TYPED COMBINATOR CALCULUS 249
 E SUBSTITUTION ALGORITHMS 279 F APPLIED XCALCULI 290 MULTIRECURSIVE ARITHMETIC 318 ORDINALS AND ORDINAL NOTATIONS 341 HIGHER ORDER RECURSION 355 POSTVIEW 371 COMMONLY USED SYMBOLS 377 Copyright

 THE TYPED XCALCULUS 264