Extensional Constructs in Intensional Type Theory

1. Front Matter

   Pages i-xii

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2. Introduction

   • Martin Hofmann

   Pages 1-12

3. Syntax and semantics of dependent types

   • Martin Hofmann

   Pages 13-54

4. Syntactic properties of propositional equality

   • Martin Hofmann

   Pages 55-87

5. Proof irrelevance and subset types

   • Martin Hofmann

   Pages 89-113

6. Extensionality and quotient types

   • Martin Hofmann

   Pages 115-162

7. Applications

   • Martin Hofmann

   Pages 163-187

8. Conclusions and further work

   • Martin Hofmann

   Pages 189-190

9. Back Matter

   Pages 191-214

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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.

• calculus
• decidability
• equality
• identity
• mathematics
• program verification
• proof
• semantics
• theorem proving
• type theory
• types
• verification

• Fachbereich Mathematik, Technische Hochschule Darmstadt, Darmstadt, Germany

  Martin Hofmann

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