Extensional Constructs in Intensional Type Theory

✍ Scribed by Martin Hofmann PhD (auth.)

• Publisher: Springer-Verlag London
• Year: 1997
• Tongue: English
• Leaves: 220
• Series: CPHC/BCS Distinguished Dissertations
• Edition: 1
• Category: Library

✦ Synopsis

Extensional Constructs in Intensional Type Theory presents a novel approach to the treatment of equality in Martin-Loef type theory (a basis for important work in mechanised mathematics and program verification). Martin Hofmann attempts to reconcile the two different ways that type theories deal with identity types. The book will be of interest particularly to researchers with mainly theoretical interests and implementors of type theory based proof assistants, and also fourth year undergraduates who will find it useful as part of an advanced course on type theory.

✦ Table of Contents

Front Matter....Pages i-xii
Introduction....Pages 1-12
Syntax and semantics of dependent types....Pages 13-54
Syntactic properties of propositional equality....Pages 55-87
Proof irrelevance and subset types....Pages 89-113
Extensionality and quotient types....Pages 115-162
Applications....Pages 163-187
Conclusions and further work....Pages 189-190
Back Matter....Pages 191-214

✦ Subjects

Mathematical Logic and Formal Languages; Logics and Meanings of Programs