Categorical Logic and Type Theory

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Elsevier, Jan 14, 1999 - Mathematics - 778 pages
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This book is an attempt to give a systematic presentation of both logic and type theory from a categorical perspective, using the unifying concept of fibred category. Its intended audience consists of logicians, type theorists, category theorists and (theoretical) computer scientists.
 

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Contents

Chapter 0 Prospectus
1
Chapter 1 Introduction to fibred category theory
19
Chapter 2 Simple type theory
119
Chapter 3 Equational Logic
169
Chapter 4 First order predicate logic
219
Chapter 5 Higher order predicate logic
311
Chapter 6 The effective topos
373
Chapter 7 Internal category theory
407
Chapter 8 Polymorphic type theory
441
Chapter 9 Advanced fibred category theory
509
Chapter 10 First order dependent type theory
581
Chapter 11 Higher order dependent type theory
645
References
717
Notation Index
735
Subject Index
743
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