Description
Book SynopsisThe 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.
Trade Review'A well-written introduction to proof theory and its connections with computability.' Leon Harkleroad, Zentralblatt für Mathematik
'… 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
Table of ContentsIntroduction; 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.
