On Wed, 14 Jan 2009 04:37:33 +0100, "Andrzej Jaworski" <[email protected]> wrote:
>[...] > >Programmers learning Haskell should forget that they are programmers and try >to think mathematically. Along that line, then, for example, where would you place, say, _The Haskell Road to Logic, Maths and Programming_ (see http://homepages.cwi.nl/~jve/HR/)? That book does not seem to focus on category theory, though; would you recommend an alternative book on that subject? If so, then which of the following would you recommend (these are just a few that I know of): Category Theory Books: Conceptual Mathematics: A First Introduction to Categories (Paperback) An elementary introduction http://www.amazon.com/Conceptual-Mathematics-First-Introduction-Categories/dp/0521478170 An introduction to category theory in four easy movements A somewhat informal, reportedly in-depth introduction to category theory, which some students have described as being intricately layered http://www.cs.man.ac.uk/~hsimmons/BOOKS/CatTheory.pdf Category Theory by Magic A somewhat more advanced text than _An introduction to category theory in four easy movements_ http://www.cs.man.ac.uk/~hsimmons/MAGIC-CATS/CourseNotes.pdf Toposes, Triples and Theories An often-referenced introduction to category theory, reportedly discussing monads as "triples" http://www.cwru.edu/artsci/math/wells/pub/ttt.html Categories and Computer Science Reportedly a straightforward introduction to category theory, with many examples from computer science http://www.cambridge.org/us/catalogue/catalogue.asp?isbn=0521419972 Arrow, Structures and Functors - The Categorical Imperative According to the HaskellWiki page on category theory (see http://haskell.org/haskellwiki/Category_theory), an out-of-print book covering monads and the Yoneda lemma, with very little prerequisite knowledge Category Theory Lecture Notes: Category Theory Lecture Notes for ESSLLI Distilled version of _Toposes, Triples and Theories,_ discussing category theory from a computer science perspective http://www.math.upatras.gr/~cdrossos/Docs/B-W-LectureNotes.pdf A Gentle Introduction to Category Theory - the calculational approach Another set of lecture notes referenced on the HaskellWiki page on category theory http://wwwhome.cs.utwente.nl/~fokkinga/mmf92b.html One difficulty with the above titles is that they do not provide Haskell-specific programming examples to help to illustrate the concepts. To address this problem, would you recommend books on categorical programming with examples in Haskell? Categorical Programming with Examples in Haskell: Categorical Programming with Inductive and Coinductive Types A thesis on categorical programming, exploring inductive and coinductive types, and several programming constructs related to them in Haskell http://www.cs.ut.ee/~varmo/papers/thesis.pdf (Actually, I just discovered the last title on the above HaskellWiki page on category theory.) If you have any other specific titles to recommend in category theory, for students of various levels of mathematical proficiency and computer science background, I would be very interested. I would believe that having specific Haskell code to help interact with the categorical examples would help to motivate study of the abstract theory for many programmers. One problem that many people have with studying abstract theory in isolation is that they often tend to lose motivation unless they can see how the theory directly relates to and influences the semantics and data structures in the code. Having specific examples of Haskell code to tie together immediately with the abstract theory would most likely help to motivate and maintain interest. -- Benjamin L. Russell -- Benjamin L. Russell / DekuDekuplex at Yahoo dot com http://dekudekuplex.wordpress.com/ Translator/Interpreter / Mobile: +011 81 80-3603-6725 "Furuike ya, kawazu tobikomu mizu no oto." -- Matsuo Basho^ _______________________________________________ Haskell mailing list [email protected] http://www.haskell.org/mailman/listinfo/haskell
