Twenty Five Years of Constructive Type Theory
Series: Oxford Logic Guides; 36;
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Product details:
- Publisher Clarendon Press
- Date of Publication 15 October 1998
- ISBN 9780198501275
- Binding Hardback
- No. of pages292 pages
- Size 242x161x20 mm
- Weight 588 g
- Language English 0
Categories
Short description:
Martin-Löf Type Theory is both an important and practical formalization and a focus for a charismatic view of the foundations of mathematics. Per Martin-Löf's work has been of huge significance in the fields of logic and the foundations of mathematics, and has important applications in areas such as computing science and linguistics. This volume celebrates the twenty-fifth anniversary of the birth of the subject, and is an invaluable record both of areas of current activity and of the early development of the subject. Also published for the first time is one of Per Martin-Löf's earliest papers.
MoreLong description:
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.
The book presents a good survey of the current state of the subject.
Table of Contents:
Yet another constructivization of classical logic
Extension of Martin-Löf's type theory with record types
Type-theoretical checking and philosophy of mathematics
The Hahn-Banach theorem in type theory
A realizability interpretation of Martin-Löf's type theory
The groupoid interpretation of type theory
An intuitionistic theory of types
Analytic program derivation in type theory
About storage operators
On universes in type theory
How to believe a machine-checked proof
Building up a toolbox for Martin-Löf's type theory: subset theory
An introduction to well-ordering proofs in Martin-Löf's type theory
Variable-free formalization of the Curry-Howard theory
The forget-restore principle: a paradigmatic example
