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.

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.