Lambda calculus with types
Author(s)
Bibliographic Information
Lambda calculus with types
（Perspectives in logic）
Association for Symbolic Logic , Cambridge University Press, 2013
Available at / 18 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
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Note
Includes bibliographical references (p. 791-813) and index
"Association for Symbolic Logic."
Description and Table of Contents
Description
This handbook with exercises reveals in formalisms, hitherto mainly used for hardware and software design and verification, unexpected mathematical beauty. The lambda calculus forms a prototype universal programming language, which in its untyped version is related to Lisp, and was treated in the first author's classic The Lambda Calculus (1984). The formalism has since been extended with types and used in functional programming (Haskell, Clean) and proof assistants (Coq, Isabelle, HOL), used in designing and verifying IT products and mathematical proofs. In this book, the authors focus on three classes of typing for lambda terms: simple types, recursive types and intersection types. It is in these three formalisms of terms and types that the unexpected mathematical beauty is revealed. The treatment is authoritative and comprehensive, complemented by an exhaustive bibliography, and numerous exercises are provided to deepen the readers' understanding and increase their confidence using types.
Table of Contents
- List of contributors
- Preface
- Introduction
- Part I. Simple Types: 1. The simply typed lambda calculus
- 2. Properties
- 3. Tools
- 4. Definability, unification and matching
- 5. Extensions
- 6. Applications
- Part II. Recursive Types: 7. The systems
- 8. Properties of recursive types
- 9. Properties of terms with types
- 10. Models
- 11. Applications
- Part III. Intersection Types: 12. An exemplary system
- 13. Type assignment systems
- 14. Basic properties
- 15. Type and lambda structures
- 16. Filter models
- 17. Advanced properties and applications
- Bibliography
- Symbol index
- Names index
- Definitions index.
by "Nielsen BookData"
