Twenty-Five Years of Constructive Type Theory: Proceedings of a Congress held in Venice, October 1995 (Oxford Logic Guides, 36)

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. 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 Per Martin-Löf's work on the development of constructive type theory has been of huge significance in the fields of logic and the foundations of mathematics. It is also of broader philosophical significance, and has 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-Löf 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 areas of current activity, but also contains 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-Löf's earliest papers. Annotation Per Martin-Lf'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-Lf 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-Lf's earliest papers The aim of this paper is to provide a way of extracting the constructive content of a certain family of classical proofs directly from the proofs themselves.