Categorical Logic and Type Theory

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Gulf Professional Publishing, 2001 - Mathematics - 760 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

Prospectus
1
Introduction to fibred category theory
19
Simple type theory
119
Equational Logic
169
First order predicate logic
219
Higher order predicate logic
311
The effective topos
373
Internal category theory
407
Advanced fibred category theory
509
First order dependent type theory
581
Higher order dependent type theory
645
References
735
Subject Index
743
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Page 719 - A. Carboni, S. Lack, and RFC Walters. Introduction to extensive and distributive categories.
Page 719 - JRB Cockett and D. Spencer. Strong categorical datatypes I. In RAG Seely, editor, Category Theory 1991, number 13 in CMS Conference Proceedings, pages 141-169, 1992.
Page 725 - In S. Brookes, M. Main, A. Melton, and M. Mislove, editors, Mathematical Foundations of Programming Semantics, Eleventh Annual Conference, volume 1 of Electronic Notes in Theoretical Computer Science, Tulane University, New Orleans, Louisiana, Mar.
Page 719 - About charity. Technical Report 92/480/18, Dep. Comp. Sci., Univ. Calgary, 1992. [5] JRB Cockett and D. Spencer. Strong categorical datatypes I. In RAG Seely, editor, Category Theory 1991, volume 13 of CMS Conference Proceedings, pages 141-169.

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