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Categories for Types, by Roy L. Crole
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This textbook explains the basic principles of categorical type theory and the techniques used to derive categorical semantics for specific type theories. It introduces the reader to ordered set theory, lattices and domains, and this material provides plenty of examples for an introduction to category theory, which covers categories, functors, natural transformations, the Yoneda lemma, cartesian closed categories, limits, adjunctions and indexed categories. Four kinds of formal system are considered in detail, namely algebraic, functional, polymorphic functional, and higher order polymorphic functional type theory. For each of these the categorical semantics are derived and results about the type systems are proved categorically. Issues of soundness and completeness are also considered. Aimed at advanced undergraduates and beginning graduates, this book will be of interest to theoretical computer scientists, logicians and mathematicians specializing in category theory.
- Published on: 2012-06-05
- Platform: No Operating System
- Original language: English
- Number of items: 1
- Binding: Printed Access Code
Review
"A well-organized introduction to categorical methods of lambda calculus...The individual topics are treated in a uniform, balanced style from introduction, syntax, to categorical models and categorical-type theory correspondence." Jiri Adamek, Mathematical Reviews
Most helpful customer reviews
10 of 12 people found the following review helpful.
Excellent introduction to categories for computer scientists
By peter@opus.geg.mot.com
The book gives you all of the cateogry theory you need to study type theory. The examples are from domains that are comfortable for computer scientists. The difficult proofs are given in great detail, while other books often gloss over the details.
0 of 0 people found the following review helpful.
So maybe the best bet is to use this book as a reference
By Foo Bar
I have mixed feelings about this book. On one hand, it makes the subject look harder than it really is, because it's so detailed. On the other hand, it spells out all the details, so if you're not clear about what the details should be, well, here they are! And for the more complex languages (polymorphism, etc), it's essential to get the details right. So maybe the best bet is to use this book as a reference, when you need it, but learn the basics somewhere else. Read Lawvere's thesis from 1963 -- it's all in there.
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