I have been studying Haskell since the summer and have made some strides in practical use. Unfortunately for me, the fact that I still don't grasp much of the underlying theory tends to grate on me. So I am thinking of "biting the bullet" and studying some of the underlying theory, not necessarily to make me a better programmer, but simply for the peace of mind that comes with understanding the tools you use. (Although I suspect that does make one a better programmer in the end).
I should probably say something about my math background. I studied physics at the undergrad level: My math included: Diff & Integ. Calc, Linear Algebra, Diff Eq, Advanced (Vector) Calc, Complex Analysis. Although the Vector Calc class was particularly difficult for me and sort of "took the wind out of my sails" and leaving me adrift on the sea of mathematics for a long time. I always wanted to continue on with more abstract math, like algebra and group theory, to gain understanding of the beauty behind quantum physics; but for various reasons, that didn't happen. Anyway years later I still use Linear Algebra and Diff Eq quite frequently for work, and have a good practical engineer's grasp of those topics. I use advanced calculus less frequently and I use quaternions for very practical, non- theoretical way for rotation sequences in 3D. I am an expert C/C++ programmer.
So I looked around for some books. Here are two that piqued my interest: Topics In Algebra, I.N. Herstein (various publishers) - Highly recommended "classic", seems challenging but not too advanced for my background, but VERY PRICEY for 2nd Edition ($145 for new paperback); used first editions can be found for much cheaper - prompting the question, "how much has Algebra changed since 1964?"
Lambda Calculus & Combinators, Hindley & Seldin (Cambridge) - I see the name Hindley frequently while puzzling over a paragraph about Haskell and type theory. The basic idea of the lambda calculus (i.e. enough to understand how a Haskell or LISP lambda function is evaluated and the idea of currying, so you can "simulate" functions with multiple arguments) seems pretty straight forward to me - Still I'm concerned I might be jumping in the deep end here.
I have always found the responses here thoughtful and helpful. Any suggestions would be greatly appreciated.
grimey <BoulderC...@gmail.com> writes: > I studied physics at the undergrad level: My math included: Diff & > Integ. Calc, Linear Algebra, Diff Eq, Advanced (Vector) Calc, Complex > Analysis. Although the Vector Calc class was particularly difficult > for me and sort of "took the wind out of my sails" and leaving me > adrift on the sea of mathematics for a long time.
There is not much algebra there, especially if your linear algebra class was of the usual kind found in engineering curricula, where you mostly concentrate on how to solve linear systems and DE's.
> I always wanted to continue on with more abstract math, like algebra > and group theory,
You should probably add some mathematical logic to this.
> So I looked around for some books. Here are two that piqued my > interest: > Topics In Algebra, I.N. Herstein (various publishers) - Highly > recommended "classic", seems challenging but not too advanced for my > background, but VERY PRICEY for 2nd Edition ($145 for new paperback); > used first editions can be found for much cheaper - prompting the > question, "how much has Algebra changed since 1964?"
This is one of the greatest books of all time, but that price is ridiculous. Also, to be realistic, group theory isn't that relevant to Haskell; logic and category theory are much more so. Finally, there is so much good material online these days that buying dead tree books should be considered a last resort.
explains what category theory is about (not in any depth). I don't know of a good online logic book at a really introductory level. H. Schwichtenberg's lecture notes
> Lambda Calculus & Combinators, Hindley & Seldin (Cambridge) - I see > the name Hindley frequently while puzzling over a paragraph about > Haskell and type theory.
I'm not familiar with this book but it doesn't really sound ideal. I'd start with Harper's "Practical Foundatations for Programming Languages":
On Jan 11, 4:34 pm, Paul Rubin <http://phr...@NOSPAM.invalid> wrote:
> > grimey <BoulderC...@gmail.com> writes: > > I always wanted to continue on with more abstract math, like algebra > > and group theory,
> You should probably add some mathematical logic to this.
Thanks! I'll look into that. I took introductory logic from Philosophy department but that was all.
> > So I looked around for some books. Here are two that piqued my > > interest: > > Topics In Algebra, I.N. Herstein (various publishers) - Highly > > recommended "classic", seems challenging but not too advanced for my > > background, but VERY PRICEY for 2nd Edition ($145 for new paperback); > > used first editions can be found for much cheaper - prompting the > > question, "how much has Algebra changed since 1964?"
> This is one of the greatest books of all time, but that price is > ridiculous. Also, to be realistic, group theory isn't that relevant > to Haskell; logic and category theory are much more so. Finally, > there is so much good material online these days that buying dead tree > books should be considered a last resort.
Well despite your subsequent disclaimer, the phrase "one of greatest books of all time" keeps me interested. Searching around used bookstores online via Alibris uncovered an excellent-condition used hardcover 2nd Ed. for $30 - much more reasonable. I went ahead and got it anyway.
> > Lambda Calculus & Combinators, Hindley & Seldin (Cambridge) - I see > > the name Hindley frequently while puzzling over a paragraph about > > Haskell and type theory.
> I'm not familiar with this book but it doesn't really sound ideal. > I'd start with Harper's "Practical Foundatations for Programming > Languages":
OK - I'll probably pass on that dead-tree edition until I read the electronic document you recommended. Thanks again for all your suggestions and the many links, this was exactly the kind of response I was looking for. -Chip
grimey> I have been studying Haskell since the summer and have grimey> made some strides in practical use. Unfortunately for me, grimey> the fact that I still don't grasp much of the underlying grimey> theory tends to grate on me. So I am thinking of "biting grimey> the bullet" and studying some of the underlying theory, grimey> not necessarily to make me a better programmer, but simply grimey> for the peace of mind that comes with understanding the grimey> tools you use. (Although I suspect that does make one a grimey> better programmer in the end).
This book does not cover "practical" Haskell stuff like Monads and type theory, but if you are looking for a good (re)introduction to mathematics for computer science, and also a new look at Haskell this should probably be on your list.
It's not easy reading; you will have to work through the problems to really get the most value out of the text. But the problems are fun to solve and very well chosen, the paperback is cheap, and I found the text a truly pleasant way to revisit my math classes while improving my appreciation for Haskell at the same time.
There are very few books I've enjoyed reading more than this one ("Funadmental Algorithms" as a teenager who only knew 8085 assembly language many years ago, and then SICP some years later, come to mind...) even though it's made me work at the excercises harder than anything else I've probably ever read.
Me too. I started on the Haskell Road, but had to stop when school started up again. I actually got a copy of Introduction to functional programming using Haskell very recently, and it seems to cover some of the more subtleties of the language basics, but for the most part covers the kind of typical programming in haskell tutorial stuff. So I decided to struggle through two papers: one by Varmo Vene called "Categorical Programming with Inductive and Coinductive types", and also "Functional programming with overloading and higher-order polymorphism" by Mark Jones. I made the mistake of learning Haskell the way I learned java, which is fast. In Haskell, you can get things done, sure, but the fun part is playing with ideas, and seeing such elegance in the construction. So now, I am slowly going through these papers with the kind of deliberate reading that I approach classes like Real analysis with, and I think things are starting, very slowly to click. I also found a paper which I may add to my list if I can figure out the conventions used "functional programming with bananas lenses, envelopes and barbed wire" by Erik Meijer, which seems to be in the citation list of so many papers, that I feel, I had better.
I downloaded this and it looks good to me (although I am pretty close to being in the same boat as Chip as far as background goes...although I was lucky enough to delve into really neat stuff in quantum mechanics, and an excellent mathematical physics course, none of the physics math bears the remotest resemblance to anything I see in the Harper book, nor in Schwichtenberg's paper).
More out of curiosity than anything else, at what level would a bright CS student expect to confront something like Harper's text?
<jon.gallagher...@gmail.com> wrote: >Me too. I started on the Haskell Road, but had to stop when school >started up again. I actually got a copy of Introduction to functional >programming using Haskell very recently, and it seems to cover some of >the more subtleties of the language basics, but for the most part >covers the kind of typical programming in haskell tutorial stuff. So >I decided to struggle through two papers: one by Varmo Vene called >"Categorical Programming with Inductive and Coinductive types", and >also "Functional programming with overloading and higher-order >polymorphism" by Mark Jones. I made the mistake of learning Haskell >the way I learned java, which is fast. In Haskell, you can get things >done, sure, but the fun part is playing with ideas, and seeing such >elegance in the construction. So now, I am slowly going through these >papers with the kind of deliberate reading that I approach classes >like Real analysis with, and I think things are starting, very slowly >to click. I also found a paper which I may add to my list if I can >figure out the conventions used "functional programming with bananas >lenses, envelopes and barbed wire" by Erik Meijer, which seems to be >in the citation list of so many papers, that I feel, I had better.
You may wish to read this related thread from the Haskell mailing list:
(Be sure to read the related following three responses as well, since they contain the bulk of the references.)
A possible issue with _The Haskell Road to Logic, Maths and Programming_ (which I had actually suggested in that thread), by Kees Doets and Jan van Eijck, is that it isn't really related to category theory, which forms the theoretical basis for Haskell. It's more of a book that covers the prerequisite background for building sufficient mathematical sophistication for understanding the kind of mathematics that appears in category theory, even though the book isn't really related to category theory. In particular, in the above-mentioned thread, Andrzej Jaworski responded (see http://www.haskell.org/pipermail/haskell/2009-January/020934.html) as follows:
On Thu, 15 Jan 2009 05:12:19 +0100, "Andrzej Jaworski"
<hims...@poczta.nom.pl> wrote: >Doets and Eijck show good approach but their mathematics is too trivial (e.g. >combinatorics should be presented via lattice theory like Rota taught). They also miss the boat >presenting Haskell (no higher gear at all). He also wrote: >[T]here are many very good >articles addressing specific issues of Haskell's theoretical foundations (e.g. >http://www.cs.ut.ee/~varmo/papers/thesis.pdf). They however always assume more than they target to >explain making student turn around them like a dog not knowing which ball to catch first.
I agree with this specific point: Many such articles/papers are dependent on parts of other publications, which can sometimes either be dependent on other parts of the first publication, or on parts of other publications.
Regarding this point, one other reader responded in private that the problem "comes from trying to use academic papers as textbooks, a purpose for which they're not usually designed." As soon as I read this, I thought, "Aha! Exactly: That is the problem." Such academic papers usually target other researchers, but not beginner students of Haskell or even category theory, so they often assume material not covered.
One solution seems to be to focus on books specifically targeting beginner students of Haskell, or at least beginner students of category theory. The above-mentioned reader who responded in private recommended the following lecture notes:
> Lambert Meertens' "Category Theory for Program Construction":
(Note: It can be convenient to use http://www.ps2pdf.com/convert.htm to convert the PostScript file above, once gunzipped, to PDF format.)
Apparently, this paper is based on the paper "A Gentle Introduction to Category Theory - the calculational approach," by Maarten M. Fokkinga (see http://wwwhome.cs.utwente.nl/~fokkinga/mmf92b.pdf).
Apparently, Meertens has designed the exercises so that each one is designed to be doable if all the previous ones have been done, and some parts of the main text depend on the exercises, so this book may take a long time to read.
However, he has chosen not to use commutative diagrams. Every other text on category theory that I have seen so far uses them in abundance, but as Meertens explains, each one only relates to a specific category, so they may be difficult to use in meta-categorical discussion. Also, it is refreshing to see an alternative approach.
One other set of lecture notes that I have also found to be accessible is the following:
The main problem with such lecture notes is their length: Meerten's notes span 122 pages, and Barr and Wells' notes span 133 pages. It is difficult to find time to read and do all the exercises in over a hundred pages of category theory while working full-time.
(Further, in my case, it would be easier if the exercises could be done on a keyboard, instead of on pencil and paper, because I usually use my spare time after work hours during lunch or at work to study category theory, and don't have much table space. However, writing mathematical equations and proofs tends to be done much easier on pencil and paper instead of on a keyboard. I live about two and a half hours from work, and don't have enough time or desk space to do them at home, even on weekends.)
One especially elementary book on category theory that I could recommend, which unfortunately is apparently only available in a dead-tree version, is the following:
This book is reputed to be interesting even to non-mathematicians at a philosophical level. I myself have purchased a copy.
If anybody knows any other books or lecture notes on category theory that specifically target beginner students of Haskell or category theory, I would be interested. In particular, I would be especially interested in books for non-mathematicians that provide an elementary discussion of category theory without requiring the student to use pencil and paper to work through the exercises (requiring a keyboard and editor to work through the exercises is acceptable).
-- 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^
On Fri, 16 Jan 2009 17:48:35 +0900, Benjamin L. Russell
<DekuDekup...@Yahoo.com> wrote: >If anybody knows any other books or lecture notes on category theory >that specifically target beginner students of Haskell or category >theory, I would be interested. In particular, I would be especially >interested in books for non-mathematicians that provide an elementary >discussion of category theory without requiring the student to use >pencil and paper to work through the exercises (requiring a keyboard >and editor to work through the exercises is acceptable).
I forgot to mention that books with a philosophical approach, which approach category theory similarly to the way _The Little Schemer_ (http://www.amazon.com/Little-Schemer-Daniel-P-Friedman/dp/0262560992/...), by Daniel P. Friedman and Matthias Felleisen, approaches Scheme, would be especially interesting (but perhaps _Conceptual Mathematics: A First Introduction to Categories, by F. William Lawvere and Stephen Hoel Schanuel (see http://www.amazon.com/Conceptual-Mathematics-First-Introduction-Categ...), already fulfills this role, since it discusses Galileo and the flight of a bird as an example).
-- 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^
Arved Sandstrom <dces...@hotmail.com> wrote: > On Sun, 11 Jan 2009 15:34:53 -0800, Paul Rubin wrote: >> I'm not familiar with this book but it doesn't really sound ideal. I'd >> start with Harper's "Practical Foundatations for Programming Languages":
>> http://www.cs.cmu.edu/~rwh/plbook/book.pdf > More out of curiosity than anything else, at what level would a bright CS > student expect to confront something like Harper's text?
Browsing through it, I'd say that here in Germany the basic stuff in the earlier chapters are at second year level, and the bulk is at third and fourth year level, if you specialize in that subject. That would probably correspond to master's courses at English-speaking universities (students are older when they start studying in Germany, so the level is a bit different).
> On Jan 11, 4:34 pm, Paul Rubin <http://phr...@NOSPAM.invalid> wrote:
> > > Topics In Algebra, I.N. Herstein (various publishers) - Highly > > > recommended "classic", seems challenging but not too advanced for my > > > background, but VERY PRICEY for 2nd Edition ($145 for new paperback); > > > used first editions can be found for much cheaper - prompting the > > > question, "how much has Algebra changed since 1964?"
> > This is one of the greatest books of all time, but that price is > > ridiculous. Also, to be realistic, group theory isn't that relevant > > to Haskell; logic and category theory are much more so. Finally, > > there is so much good material online these days that buying dead tree > > books should be considered a last resort.
> Well despite your subsequent disclaimer, the phrase "one of greatest > books of all time" keeps me interested. > Searching around used bookstores online via Alibris uncovered an > excellent-condition used hardcover 2nd Ed. for $30 - much more > reasonable. I went ahead and got it anyway.
For the record, I actually bought _Abstract Algebra_ not _Topics In Algebra_. _Topics In Algebra_ is a pricey volume wherever I looked. _Abstract Algebra_ is probably a bit more basic, and sufficient for my purposes It's not too long, although I find you cannot read it like a dime store novel; It takes time for the concepts to sink in. Nonetheless you can get through it pretty quick if you resist the temptation to try the hard problems in the exercises. Very much helped my understanding of Algebraic Data Type and the concept of Homomorphism. I get "slightly less lost" when reading about the theory behind Haskell.
|
