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Other titles in the Cambridge Tracts in Theoretical Computer Science series:
Cambridge Tracts in Theoretical Computer Science #51: Derivation and Computation: Taking the CurryHoward Correspondence Seriouslyby Harold Simmons
Synopses & ReviewsPublisher 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 lambdacalculus. This is illustrated by an account of Gödel's T, a system that codifies numbertheoretic 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 ContentsIntroduction; Preview; Part I. Development and Exercises: 1. Derivation systems; 2. Computation mechanisms; 3. The typed combinator calculus; 4. The typed lcalculus; 5. Substitution algorithms; 6. Applied lcalculi; 7. Multirecursive 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 lcalculus; E. Substitution algorithms; F. Applied lcalculi; G. Multirecursive arithmetic; H. Ordinals and ordinal notation; I. Higher order recursion; Postview; Bibliography; Commonly used symbols; Index.
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