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Cambridge Tracts in Theoretical Computer Science #51: Derivation and Computation: Taking the Curry-Howard Correspondence Seriously

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Cambridge Tracts in Theoretical Computer Science #51: Derivation and Computation: Taking the Curry-Howard Correspondence Seriously Cover

 

Synopses & Reviews

Publisher Comments:

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.

Synopsis:

The is an introduction to simple type theory, exploring the relationship between proof and calculation. Each of its 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. An appendix contains complete solutions to them.

Synopsis:

Two of the fundamental notions of mathematics, proof and calculation, 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. Each of its 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.

Synopsis:

Introduction to simple type theory; 200 exercises with complete solutions.

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.

Product Details

ISBN:
9780521771733
Editor:
Van Rijsbergen, C. J.
Author:
Simmons, H.
Editor:
Van Rijsbergen, C. J.
Author:
C. J. van Rijsbergen
Author:
Simmons, Harold
Author:
Van Rijsbergen, C. J.
Publisher:
Cambridge University Press
Location:
Cambridge
Subject:
General
Subject:
Logic
Subject:
Combinatorics
Subject:
Proof theory
Subject:
Lambda calculus.
Subject:
Type theory.
Subject:
General Mathematics
Subject:
Curry-Howard isomorphism
Subject:
Mathematics-Logic and Philosophy
Edition Description:
Hardcover
Series:
Cambridge Tracts in Theoretical Computer Science
Series Volume:
51
Publication Date:
20000631
Binding:
Hardcover
Grade Level:
Professional and scholarly
Language:
English
Illustrations:
23 tables 193 exercises
Pages:
410
Dimensions:
9.25x6.24x1.06 in. 1.40 lbs.

Related Subjects

Computers and Internet » Computers Reference » General
Science and Mathematics » History of Science » General
Science and Mathematics » Mathematics » Combinatorics
Science and Mathematics » Mathematics » Foundations and Logic
Science and Mathematics » Mathematics » Logic and Philosophy

Cambridge Tracts in Theoretical Computer Science #51: Derivation and Computation: Taking the Curry-Howard Correspondence Seriously New Hardcover
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Product details 410 pages Cambridge University Press - English 9780521771733 Reviews:
"Synopsis" by , The is an introduction to simple type theory, exploring the relationship between proof and calculation. Each of its 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. An appendix contains complete solutions to them.
"Synopsis" by , Two of the fundamental notions of mathematics, proof and calculation, 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. Each of its 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.
"Synopsis" by , Introduction to simple type theory; 200 exercises with complete solutions.
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