Derivation and Computation: Taking the Curry-Howard Correspondence Seriously

ISBN-13: 9780521771733 / Angielski / Twarda / 2000 / 412 str.

Harold Simmons; H. Simmons; C. J. Van Rijsbergen

Opis

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 Godel'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.

Recenzje

'… recommended for the student or researcher who's been exposed to bits and pieces of the Curry-Howard correspondence, but wants a sharper idea of the big picture and is willing to work through the exercises to see how the details fit together. Simmons has succeeded in pulling together the main fruits of the correspondence for simple types in a single text. … 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.' ACM SIGACT News

Spis treści

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.