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Basic Category Theory for Computer Scientists (Foundations of Computing) - Benjamin C. Pierce
Paperback Published: 1991-08-07 114 pages Amazon Sales Rank: 360229 List Price: $26.00 Lowest New Price: $18.96 (8 available) Lowest Used price: $16.99 (7 available)
Category theory is a branch of pure mathematics that is becoming an increasingly important tool in theoretical computer science, especially in programming language semantics, domain theory, and concurrency, where it is already a standard language of discourse. Assuming a minimum of mathematical preparation, Basic Category Theory for Computer Scientists provides a straightforward presentation of the basic constructions and terminology of category theory, including limits, functors, natural transformations, adjoints, and cartesian closed categories. Four case studies illustrate applications of category theory to programming language design, semantics, and the solution of recursive domain equations. A brief literature survey offers suggestions for further study in more advanced texts. Benjamin C. Pierce received his doctoral degree from Carnegie Mellon University. Contents: Tutorial. Applications. Further Reading. Similar Books
A Good Read (4) - This book is not exactly what I would call easy going. I've managed to get through half of it in 7 months. However, I can say, with absolute confidence, that if you do the problems you will learn. Most everything I've seen on category theory is a confusing mixture of different notations with seemingly identical meanings (but in fact the meanings are totally different). This book is no exception. Often, I have resorted to IRC to sort things out when some notation is simply impenetrable to me. My mathematical training stopped at complex calculus, so this may not apply to you if you've had abstract algebra or something a little more 'meta'. There seems to be one typographical error, but I am not sure. In the example on the adjunction between products and exponentiation, the right adjoint is listed as "(_)^A x A" but in the diagrams it ends up as "(_)^A". This may be a sensible ellision, but it is not explained anywhere in the text and of it's not easy to find these things on the internet. Good Introduction (4) - I have been reading several different category theory texts recently, and this one was very succinct and accessible. Particularly useful for understanding functional programming. Basic crib sheet for category theory (2) - Anyone coming to this book from Pierce's "Types and Programming Languages" will be disappointed. While his "Types ..." book is a model of clear exposition, this book reads like a set of notes jotted down on the back on an envelope. The extensive bibliographic sections are more than fifteen years out of date. Much of the material referenced is no longer in print, and recent developments are, of course, not mentioned. Those seeking a very gentle introduction to category theory would do better with the book by Lawvere and Schanuel, who cover more of category theory than Pierce. Mathematically mature computer science readers will find everything they need to know about the subject in Mac Lane's book. Really expensive for a set of notes... (3) - You can find better introductions to category theory available on the net for free. And I'm not talking about P2P! Try searching for Lambert Meertens, Marten Fokkinga, and Jaap Van Oosten, for example. If you have some money to spend, get Barr and Wells, Category Theory for Computing Science. It's a great book, *way* better than this! Too terse (3) - This is a very short book: 70 pages of text + a bibliography. The first 50 pages are about general category theory, and the last 20 pages are specifically for computer scientists. My interest is in general category theory, and I bought this because I have a BS in CS and thought I'd find plenty of familiar examples. Unfortunately this book doesn't have nearly enough examples. I found it easier to skim some undergrad abstract algebra books in the library (groups, rings, vector spaces) and then continuing with category theory intros written for math students. |