Twenty-Five Years of Constructive Type Theory: Proceedings of a Congress held in Venice, October 1995

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Overview


Per Martin-Löf'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-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 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-Löf's earliest papers.
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Product Details

  • ISBN-13: 9780198501275
  • Publisher: OUP Oxford
  • Publication date: 10/28/1998
  • Series: Oxford Logic Guides Series , #36
  • Pages: 296
  • Product dimensions: 6.30 (w) x 9.30 (h) x 0.80 (d)

Meet the Author

University of Padua

Chalmers University of Technology

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Table of Contents

1 Yet another constructivization of classical logic 1
2 Extension of Martin-Lof's type theory with record types and subtyping 21
3 Type-theoretical checking and philosophy of mathematics 41
4 The Hahn-Banach theorem in type theory 57
5 A realizability interpretation of Martin-Lof's type theory 73
6 The groupoid interpretation of type theory 83
7 Analytic program derivation in type theory 113
8 An intuitionistic theory of types 127
9 On storage operators 173
10 On universes in type theory 191
11 How to believe a machine-checked proof 205
12 Building up a toolbox for Martin-Lof's type theory: subset theory 221
13 An introduction to well-ordering proofs in Martin-Lof's type theory 245
14 Variable-free formalization of the Curry-Howard theory 265
15 The forget-restore principle: a paradigmatic example 275
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