Per Martin-L???f's work on the development of constructive type theory has had a tremendous impact on the fields of logic and the foundations of mathematics. It also has broader philosophical significance and important applications in areas such as computing science and linguistics. This volume draws together contributions from researchers whose work builds on the theory developed by Martin-L???f over the last twenty-five years. As well as celebrating the anniversary of the birth of the subject it covers many of the diverse fields which are now influenced by type theory. It is an invaluable record of current activity and includes contributions from N. G. de Bruijn and William Tait, both important figures in the early development of the subject. Also published for the first time is one of Per Martin-L???f's earliest papers.
Author(s): Giovanni Sambin, Jan M. Smith
Series: Oxford logic guides 36
Publisher: Oxford University Press
Year: 1998
Language: English
Pages: 292
Contents......Page 9
1. Yet another constructivization of classical logic......Page 10
2. Extension of Martin-Löf's type theory with record types and subtyping......Page 30
3. Type-theoretical checking and philosophy of mathematics......Page 50
4. The Hahn-Banach theorem in type theory......Page 66
5. A realizability interpretation of Martin-Löf's type theory......Page 82
6. The groupoid interpretation of type theory......Page 92
7. Analytic program derivation in type theory......Page 122
8. An intuitionistic theory of types......Page 136
9. On storage operators......Page 182
10. On universes in type theory......Page 200
11. How to believe a machine-checked proof......Page 214
12. Building up a toolbox for Martin-Löf's type theory: subset theory......Page 230
13. An introduction to well-ordering proofs in Martin-Löf's type theory......Page 254
14. Variable-free formalization of the Curry-Howard theory......Page 274
15. The forget-restore principle: a paradigmatic example......Page 284
