[Haskell-cafe] Substantial (1:10??) system dependencies of runtime performance??
Dear all, for quite a while now, I have experienced this issue with some curiosity; yesterday I had it again, when a program that took well over one hour before only needed about ten minutes, after a system reboot (recent Ubuntu) and with no browser started -- finally deciding to post this. I still can't reproduce these effects, but there is indication it is connected with browser use (mostly Google Chrome, with usually 10's of windows and ~100 folders open) and especially use of video players; closing or killing doesn't seem to set free resources, a reboot or at least suspend to disk seems to be necessary (suspend to RAM doesn't seem enough). Roughly, I would say the differences in runtime can reach a factor as much as 1:10 at many times -- and so I am curious whether this subject has already been observed or even better discussed elsewhere. I have spoken to somebody, and our only plausible conclusion was that software like web browsers is able to somewhat aggressively claim system resources higher in the privilege hierarchy (cache?? register??), so that they are not available to other programs any more. I hope this is interesting to others, too, I guess it is an issue for anybody programming computation intensive code to be run on standard systems with other applications running there, too, and having to predict the estimated runtime to the client. Maybe I have overseen some libs which are already able to scan the system state in this regard, or even tell Haskell to behave 'less nice' when other applications are known to be of lower priority?? Thanks a lot in advance, Nick ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Substantial (1:10??) system dependencies of runtime performance??
Hi Gwern, thanks for the interesting info. I quite often have processing of CSV file data of about 100M-1G done. Thanks a lot, Nick 2013/2/2 Gwern Branwen gwe...@gmail.com On Sat, Feb 2, 2013 at 3:19 PM, Nick Rudnick nick.rudn...@gmail.com wrote: Roughly, I would say the differences in runtime can reach a factor as much as 1:10 at many times -- and so I am curious whether this subject has already been observed or even better discussed elsewhere. I have spoken to somebody, and our only plausible conclusion was that software like web browsers is able to somewhat aggressively claim system resources higher in the privilege hierarchy (cache?? register??), so that they are not available to other programs any more. Maybe the Haskell program requires a lot of disk IO? That could easily lead to a big performance change since disk is so slow compared to everything else these days. You could try looking with 'lsof' to see if the browser has a ton of files open or try running the Haskell program with higher or lower disk IO priority via 'ionice'. -- gwern http://www.gwern.net ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
[Haskell-cafe] IMAGE_FILE_LARGE_ADDRESS_AWARE (4GB on Win64) ... any best practices??
Dear Haskellers, did anybody of you stumble about surprisingly having a 2GB memory limit on Win64? I admit I didn't get it at once (just about to finish a complete memcheck... ;-) -- but of course there already is a discussion of this: http://stackoverflow.com/questions/10743041/making-use-of-all-available-ram-in-a-haskell-program Unfortunately, this left me a little stupid about how to actually get a program running with IMAGE_FILE_LARGE_ADDRESS_AWARE -- did anybody try this successfully (or even not...) and has experience to share? Usually a Linuxer, I am just about to begin exploring the possibilities of Haskell on Windows, please forgive. Thanks a lot advance, Nick ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
[Haskell-cafe] Efficient temporary file storage??
Dear all, if you want to temporarily store haskell data in a file – do you have a special way to get it done efficiently? In an offline, standalone app, I am continuously reusing data volumes of about 200MB, representing Map like tables of a rather simple structure, key: (Int,Int,Int) value: [((Int,Int),LinkId)] which take quite a good deal of time to produce. Is there a recommendation about how to 'park' such data tables most efficiently in files – any format acceptable, quick loading time is the most desirable thing. Thanks a lot in advance, Nick ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] linear logic
Hi Vasili, not understanding clearly «in a categorical logic sense» -- but I can be sure you already checked out coherent spaces, which might be regarded as underlying Girard's original works in this sense?? I have a faint idea about improvements, but I don't have them present at the moment. Curiously -- is it allowed to ask about the motivation? Cheers, Nick On 02/22/2011 09:13 PM, Vasili I. Galchin wrote: Hello, What is the category that is used to interpret linear logic in a categorical logic sense? Thank you, Vasili ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
[Haskell-cafe] Possibility to implant Haskell GC into PostgreSQL interesting?
Dear all, recently, at an email conversation with pgsql hackers I had a quick shot, asking about their position to somebody replacing their palloc GC -- having roughly in mind that either here or on a Mercury mailing list (where there's a similar case with a pure declarative language and a Boehm GC), where there was a conclusion a non-pure GC would be a major hindrance to deeper interaction. Ok, I found the answer worth a discussion here; as far as I understood, they don't oppose the idea that the PostgreSQL GC might be a candidate for an update. I see three issues: (a) The most open question to me is the gain from the Haskell perspective; most critical: Would a Haskell GC inside PostgreSQL mean a significant change or rather a drop in the bucket? Once this may be answered optimistically, there comes the question about possible applications -- i.e., what can be done with such a DBMS system. Knowing about efforts like (http://groups.inf.ed.ac.uk/links/) I would like to let this open for discussion. Let me please drop here a quote that I believe their object relational efforts seem to have gotten stuck at PostgreSQL due to the conceptual clash of OO with the relational algebra underlying PostgreSQL -- which in turn seems to harmonize much better with Hindley-Milner Co. (System F??) (b) The question I personally can say least about are the expenditures to be expected for a such project. I would be very interested in some statements. I have limited knowledge about the PostgreSQL GC and would assume it is much simpler than, e.g. the GHC GC. (c) Gain from PostgreSQL perspective: This IMO should be answered easiest, hoping the Haskell GC experts to be able to answer easily how much is the overhead to be payed for pure declarativity, and the chances (e.g. parallelism, multi cores??), too. Besides it might be interesting to see inhowfar a considerable overhead problem may be alleviated by a 'plugin' architecture allowing future PostgreSQL users to switch between a set of GCs. I would be very interested about any comments, Cheers, Nick ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] H98, OOHaskell - getting started with objects in Haskell
Hi Philipp, depending on what engineering calculations you are interested in, you might like http://timber-lang.org/ , a direct descendant of O'Haskell, targeted at embedded real-time systems. If you are just stepping out of the OO programming world, it might be helpful to imagine OO as a rather narrow specialization of a concept called type, so that from the FP perspective it is just one of so many alternatives so that it gets lost a little -- which may be a useful translation to use. So the short answer to where's OO? in Haskell might just be data, while the expressive freedom of type classes / families might surprise you. There have been some people playing with cellular automata, Google helps, e.g.: http://mjsottile.wordpress.com/ http://trac.haskell.org/gloss/ Both cases might give you an impression how it's done with Haskell types. If you really are interested in using the OO class concept together with the Haskell type system by a more than practical motivation, an expert in the field who is interested in the subject for a long time is Peter Padawitz (http://fldit-www.cs.uni-dortmund.de/~peter/ http://fldit-www.cs.uni-dortmund.de/%7Epeter/); he has presented a beautiful synthesis based on category theory, swinging types (http://fldit-www.cs.uni-dortmund.de/~peter/Swinging.html http://fldit-www.cs.uni-dortmund.de/%7Epeter/Swinging.html). Of course, he did also use O'Haskell for his programming works in the past. Cheers, Nick On 01/14/2011 12:23 AM, gutti wrote: Hi, thanks for all Your answers (and again I'm amazed how active and good this forum is). I expected OOHaskell to be on the somewhat extended side, but I didn't expect it to be so uncommon. This very strong and clear feedback is indeed very valuable. I think I see the complexities of OO-programming in larger programs (unforeseen interactions), but I'm still doubtfull, that functional programming can equally adress all tasks equally efficient. I'm especially interestes in engineering calculation tasks where cellular automata could be used. In that case all u have to do is to give the class the right properties and that let it grow. Such a localised intelligence approach seems an ideal OO - task. I don't know whether something functional could achieve the same. Sounds like a nice challenge. -- I'll chew on a small example. Cheers Phil ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Small flexible projects a possible niche for Haskell - your statement, please...
Paul, this is what we are interested in... :-) Taken that Haskell has lots of combinator constructs on various levels as you said -- might I ask what are your personal favourites among them...? Your mentioning of early coding initiative taken domain experts and programmers in one person for early demand strongly reminds me of our concepts of knowledge techniques -- it is my hope that this is possible. Thanks a lot, Nick Paul Johnson wrote: On 16/07/10 05:41, Nick Rudnick wrote: In consequence, an 8-student-project with two B.Sc. theses is raised as a pilot to examine the possibilities of using Haskell in the combination small team with limited resources and experience in a startup setting - we want to find out whether Haskell can be an offer competitive whith languages like Ruby Co. in such a setting. I'm not sure exactly what you are asking, but I'm going to try to answer the question Does Haskell have a niche in small, flexible projects? I think the answer is a definite yes. I also think that Haskell can do great things in bigger projects as well, but successful technologies often start out with a niche that was previously poorly served, and then move out from there. Haskell developers generally start by writing down an axiomatic definition of the problem domain. To a developer raised in traditional top down development this looks like a jump into coding, and furthermore coding at the lowest level. In fact it is a foundation step in the architecture, because Haskell works well with a bottom up approach. The property that makes this work is composability, which says that you can take primitive elements and integrate them into bigger units without having to worry about mutual compatibility. A Haskell library will typically define a data type Foo and then have functions with types along the lines of mungFoo :: Something - Foo - Foo. This combinator style of library give you the basic building blocks for manipulating Foos, along with a guarantee that the output will always be a valid Foo. So you can build up your own applications that work at the Foo level rather than down in the coding level of flow control and updated variables like conventional programs. This lets domain experts read and comment on the code, which reduces defect rates a lot. But these combinator libraries are also highly reusable because they describe an entire domain rather than just being designed to fit a single application. So the best bet is to analyse a domain, write a combinator library that models the domain, and then produce a series of related programs for specific applications within that domain. That will let a small team be amazingly productive. Paul. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
[Haskell-cafe] Small flexible projects a possible niche for Haskell - your statement, please...
Dear all, besides good ambitions in many other areas, it is interesting to see that a great number of present Haskell projects is run by a very small number of persons and even some parts of the usual developer's toolkit, like e.g. Haddock, seem to contribute to it. Has the Haskell culture produced an environment which is especially apt for such development in small groups, possibly with low grade of division of labor? In the last three years at Duisburg-Essen university, very small but application oriented introductions to up to 100 rather non-CS centric students raised an interest whether there might be a such niche for Haskell application -- as there seems to be some evidence that certain perceptions of a steep learning curve of Haskell may be in significant correlation with an already existing imperative language culture. In consequence, an 8-student-project with two B.Sc. theses is raised as a pilot to examine the possibilities of using Haskell in the combination small team with limited resources and experience in a startup setting - we want to find out whether Haskell can be an offer competitive whith languages like Ruby Co. in such a setting. An additional focus is the question inhowfar Haskell might be an enabler in allowing a greater extent of change in the organization, like people coming and going, or choosing new roles -- here we allow to *disregard* the problem of teaching Haskell to innocents to prevent such questions from dominating the whole of the discussion: This might be another project. Our premise is the availability of a sufficient number of people at an mediocre to intermediate level in the environment. We hope this might be interesting to the Haskell community, as Haskell seems to be underrepresented in this regard, and there seem to be active prejudices by the imperative community -- which unfortunately in a positive correlation with general programming experience, to an observing third might lead to an impression that a such rejection of Haskell is a matter of computing competence. Now we -- especially the two students at their B.Sc. thesis, Markus Dönges and Lukas Fisch -- are very interested in your quote, possibly o aspects of Haskell technology you perceive as relevant or helpful, o examples in the Haskell culture / community which might be relevant, o experiences of your own and around you, and *especially*, o language properties,constructs and extensions you would see as enablers in this regard. Thank you very much in advance... :-) Nick ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Merge hsql and HDBC -- there can only be one!
Hi Chris, these are good questions -- actually, you might have mentioned Takusen, too. Clearly, HDBC is the largest of these projects, and there are lots of things well done there. Takusen has an interesting approach, and I would like to see a discussion here about the practical outcomes, as I have done no testing yet. I myself quite a time ago had an opportunity to do a Haskell job with a PostgreSQL backend for a client, where I tried out all three and got hsql running easiest. A maintainer was vacant, so I stepped in happily -- doing refactorings, fixing problems at request, giving advice to people. I can say that I am quite a little PostgreSQL centric and that I have a GIS project in sight, for which I want to try to adapt hsql. Cheers, Nick Christopher Done wrote: One thing that would be nice is a unification of the general database libraries hsql and HDBC. What is the difference between them? Why are there two, and why are there sets of drivers for both (duplication of effort?)? I've used both in the past but I can't discern a real big difference (I used the hsql-sqlite library and the HDBC-postgresql library, whichever worked...). It seems the best thing to do is either actively merge them together and encourage the community to move from one to the other -- judging from what I've read HDBC is more up to date and newer than hsql -- or have some documentation with damn good reasons to choose one or the other, because currently this is a needless source of confusion and possible duplication of effort for Haskell's database libraries. I wasn't going to post until I'd actually researched the difference myself properly but I didn't get chance to have a look over the weekend, but I thought I'd pose the question. Do people actually care about this? ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Functional programming techniques in small projects
Hi Markus, I am afraid your questions are formulated quite narrowly so that people you might like to reach might not feel addressed -- so it might be helpful to ask yourself how your subject might look in the perspective of an average Haskeller, if a such dies exist at all. At first, please explain what you understand as post mass production and how you expect this to be in a relationship with Haskell. Then, agile software development is used at projects of various sizes -- but I guess you want to use this term to emphasize *small* projects -- inhowfar do you actually require such to follow agile specifications, how about small and one-man-projects which do not follow agile at all? You are speaking about »student-driven software development«... it might be hard for some people to imagine what you mean by this and -- again -- inhowfar this relates to Haskell. Could you please be a little more explicit? All the best, Nick Markus Dönges wrote: Hello Community, I am a student from the University of Duisburg-Essen, Germany, and at the moment I am writing my bachelor thesis about Post-Mass-Prodcution Softwaresupply/ -development in case of an University administration. This approach deals with student-driven software development in which functional programming techniques (ie, Haskell) and agile development approaches matter. I am looking for opinions and statements on how small (agile) software development projects may benefit from functional programming techniques (perhaps in contrast to imperative programming techniques). Since I am at the very start, I would appreciate further literature advices. In addition, does anybody know particular people who are familiar with this topic? Any answer is appreciated :-) Regards, Markus ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] hdbc-mysql fails to compile
Hi Thomas, up to 3/3/2010 I am looking after nearly 100 Haskell newbies in their project end phase -- but Marc Weber promised to kick my ass in time so I look after the hsql-XXX repos. Anyway, I just uploaded 1.8.1, since it seems to work. Cheers, Nick Thomas Girod wrote: replying to myself. there is only one line to fix in Setup.lhs (mysqlConfigProg, _) - requireProgram verbosity mysqlConfigProgram AnyVersion (withPrograms lbi) becomes : (mysqlConfigProg, _) - requireProgram verbosity mysqlConfigProgram (withPrograms lbi) obviously the new cabal version makes a difference between requireProgram and requireProgramVersion On Thu, Feb 25, 2010 at 08:01:34PM +0100, Thomas Girod wrote: Hi there. Looks like hdbc-mysql cannot compile against GHC-6.12 -- confirmed by the hackage build logs. [1] anyone know a way to dodge the problem ? cheers, Tom [1] http://hackage.haskell.org/packages/archive/HDBC-mysql/0.6/logs/failure/ghc-6.12 ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Problems linking hsql-mysql
Hi Maciej, I will try to reproduce the error -- could you send me your both *.cabal files (for hsql hsql-mysql), if you have changed anything, and your system configuration. Is this extremely urgent? I ask this, as these days exactly the end phase of the projects of about 100 beginner Haskell students, which I am the one to look after. So I am in a little of slow motion regarding other things... ;-) But in case you are in emergency, please let me know... At first sight, I would say it looks like a configuration problem... ;-) Cheers, Nick Maciej Podgurski wrote: Hi, I have problems linking a simple test program that imports Database.HSQL.MySQL via ghc --make Test.hs. The error only occurs when importing this module of hsql-mysql-1.7.1. I pasted the building output here: http://hpaste.org/fastcgi/hpaste.fcgi/view?id=22911 (actually it was even longer but hpaste only takes 30k). When I do ghc -e main Test.hs or starting it from GHCi, everything works fine and no errors occur. So I guess all needed .lib files are there but GHC can't find them when linking (adding the flag -Lpath to mysql/lib/opt doesn't help). Anyone an idea? Best wishes, Maciej ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Category Theory woes
A place in the hall of fame and thank you for mentioning clopen... ;-) Just wanting to present open/closed as and example of improvable maths terminology, I oversaw this even more evident defect in it and even copied it into my improvement proposal, bordered/unbordered: It is questionable style to name two properties, if they can occur combined, as an antagonistic pair...! Acccordingly, it is more elegant to draw such terms from independent domains. This subject seems to drive me crazy... I actually pondered on improvement, and came to: «faceless» in replacement of «open» Rough explanation: The «limit» of a closed set can by the limit of another closed set that may even share only this limit -- a faceless set has -- under the given perspective -- no such part to «face» to beyond. Any comments? But the big question is now: What (non antagonistic) name can be found for the other property?? Any ideas...?? Cheers, Nick Ergonomic terminology comes not for free, giving a quick answer here would be «maths style» with replacing Michael Matsko wrote: Nick, Actually, clopen is a set that is both closed and open. Not one that is neither. Except in the case of half-open intervals, I can't remember talking much in topology about sets with a partial boundary. Alexander Solla wrote: Clopen means a set is both closed and open, not that it's partially bordered. Daniel Fischer wrote: And we'd be very wrong. There are sets which are simultaneously open and closed. It is bad enough with the terminology as is, throwing in the boundary (which is an even more difficult concept than open/closed) would only make things worse. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Category Theory woes
Richard O'Keefe wrote: On Feb 19, 2010, at 2:48 PM, Nick Rudnick wrote: Please tell me the aspect you feel uneasy with, and please give me your opinion, whether (in case of accepting this) you would rather choose to consider Human as referrer and Int as referee of the opposite -- for I think this is a deep question. I've read enough philosophy to be wary of treating reference as a simple concept. And linguistically, referees are people you find telling rugby players naughty naughty. Don't you mean referrer and referent? Yes, thanks. I am not a native English speaker, and in my mother tongue, a referent is somebody who refers, so I missed the guess... Such statements are exactly what I was looking for... So, as a reference is directed, it is possible to distinguish referrer ::= the one which does refer to s.th. referent ::= one which is referred to by s.th. Of course a basic point about language is that the association between sounds and meanings is (for the most part) arbitrary. I would rather like to say it is not strictly determined, as an evolutionary tendence towards, say ergonomy, cannot be overlooked, can it? Why should the terminology of mathematics be any different? ;-) Realizing an evolutionary tendence towards ergonony, is my subject... Why is a small dark floating cloud, indicating rain, called a water-dog? Water, yes, but dog? Why are the brackets at each end of a fire-place called fire-dogs? Why are unusually attractive women called foxes (the females of that species being vixens, and both sexes smelly)? :-)) The shape of the genitals, which might come into associative imagination of the hopeful observer?? (The same with cats, bears, etc.) [... desperately afraid of getting kicked out of this mailing list ;-))] Thanks for this beautiful example and, honestly, again I ask again whether we may regard this as «just noise»: In contrary, aren't such usages not paradigmatical examples of memes, which as products of memetic evolution, should be studied for their motivational value? Let me guess: Our cerebral language system is highly coupled with our intentional system, so that it helps learning to have motivating «animation» enclosed... Isn't this in use in contemporary learning environments...? The problem I see is that common maths claims an exception in claiming that, in it's domain, namings are no more than noise -- possible motivated by an extreme rejection of anything between «strictly formally determined» and «noise». This standpoint again does not realize the developments in foundations of mathematics of at least the century ago -- put roughly, this comes close to Hilbert's programme... To my mind, any of the breakthroughs of the last decades -- like incompleteness, strange attractors, algorithmic information theory, CCCs, and not the least computing science itself with metaprogramming, soft computing, its linear types/modes and monads (!) -- have to do with constructs which emancipate such claims of ex ante predetermination. Isn't category theory pretty much a part of all this? What's the logic in doggedness being a term of praise but bitchiness of opprobrium? Sexism...?? We can hope for mathematical terms to be used consistently, but asking for them to be transparent is probably too much to hope for. (We can and should use intention-revealing names in a program, but doing it across the totality of all programs is something never achieved and probably never achievable.) We have jokers: Evolutionary media, like markdown or even stylesheet may allow us to switch and translate in a moment, and many more useful gimmicks... Online collaboration platforms... And we can stay pragmatical: If we can reach a (broad, to my estimate...) public, which originally would have to say «the book has really left me dumbfounded» (so the originator of this thread) and offer them an entertaining intuitive way -- why not even in a self-configurable way? -- category theory could be introduced to contemporary culture. Personally, I can't accept statements like (in another posting) «You need a lot of training in abstraction to learn very abstract concepts. Joe Sixpack's common sense isn't prepared for that.» Instead, I think that there is good evidence to believe that there are lots of isomorphisms to be found between every day's life and terminology and concepts category theory -- *not* to be confused with its *applications to maths*... And, to close in your figurative style: Which woman gets hurt by a change of clothes? Cheers, Nick ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Restricted categories
Alexander Solla wrote: You specifically ask withConstraintsOf to accept only Suitable2's when you say withConstraintsOf :: Suitable2 m a b = m a b - (Constraints m a b - k) - k But you aren't saying that the argument of withConstraintsOf IS a Suitable2, when you say: instance (RCategory c1, RCategory c2) = RCategory (c1 :***: c2) where id = withResConstraints $ \ProdConstraints - id :***: id -- f@(f1 :***: f2) . g@(g1 :***: g2) = -- withResConstraints $ \ProdConstraints - -- withConstraintsOf f $ \ProdConstraints - -- withConstraintsOf g $ \ProdConstraints - -- (f1 . g1) :***: (f2 . g2) As I understand, Sjoerd expects this to be done at the definition of (.) in the type class RCategory, so that an instance method can relay on the constraints collected by it: class RCategory (~) where id :: Suitable2 (~) a a = a ~ a (.) :: (Suitable2 (~) b c, Suitable2 (~) a b, Suitable2 (~) a c) = b ~ c - a ~ b - a ~ c A simple example: class Show el= ExceptionNote el where comment:: Show exception= exception- el- String instance ExceptionNote Int where comment exception refId = show refId ++ : ++ show exception Here you don't need to constrain ?exception? to be of ?Show? at the instance declaration. So it does not appear wrong for Sjoerd to expect f and g to already be of Suitable2... This is exciting stuff, I am really a little astonished about the giant leap Haskell has made since my efforts to translate the examples of Rydeheart Burstall, which actually was my intro to categories, from ML to Haskell. This looks very elegant... Maybe it's time for a second edition of the unique approach of Rydeheart Burstall on basis of Haskell? Wow, really cool stuff... :-) Cheers, Nick ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Category Theory woes
IM(H??)O, a really introductive book on category theory still is to be written -- if category theory is really that fundamental (what I believe, due to its lifting of restrictions usually implicit at 'orthodox maths'), than it should find a reflection in our every day's common sense, shouldn't it? In this case, I would regard it as desirable to -- in best refactoring manner -- to identify a wording in this language instead of the abuse of terminology quite common in maths, e.g. * the definition of open/closed sets in topology with the boundary elements of a closed set to considerable extent regardable as facing to an «outside» (so that reversing these terms could even appear more intuitive, or «bordered» instead of closed and «unbordered» instead of open), or * the abuse of abandoning imaginary notions in favour person's last names in tribute to successful mathematicians... Actually, that pupils get to know a certain lemma as «Zorn's lemma» does not raise public conciousness of Mr. Zorn (even among mathematicians, I am afraid) very much, does it? * 'folkloristic' dropping of terminology -- even in Germany, where the term «ring» seems to originate from, since at least a century nowbody has the least idea it once had an alternative meaning «gang,band,group», which still seems unsatisfactory... Here computing science has explored ways to do much better than this, and it might be time category theory is claimed by computer scientists in this regard. Once such a project has succeeded, I bet, mathematicians will pick up themselves these work to get into category theory... ;-) As an example, let's play a little: Arrows: Arrows are more fundamental than objects, in fact, categories may be defined with arrows only. Although I like the term arrow (more than 'morphism'), I intuitively would find the term «reference» less contradictive with the actual intention, as this term * is very general, * reflects well dual asymmetry, * does harmoniously transcend the atomary/structured object perspective -- a an object may be in reference to another *by* substructure (in the beginning, I was quite confused lack of explicit explicatation in this regard, as «arrow/morphism» at least to me impled objekt mapping XOR collection mapping). Categories: In every day's language, a category is a completely different thing, without the least association with a reference system that has a composition which is reflective and associative. To identify a more intuitive term, we can ponder its properties, * reflexivity: This I would interpret as «the references of a category may be regarded as a certain generalization of id», saying that references inside a category represent some kind of similarity (which in the most restrictive cases is equality). * associativity: This I would interpret as «you can *fold* it», i.e. the behaviour is invariant to the order of composing references to composite references -- leading to «the behaviour is completely determined by the lower level reference structure» and therefore «derivations from lower level are possible» Here, finding an appropriate term seems more delicate; maybe a neologism would do good work. Here one proposal: * consequence/?consequentiality? : Pro: Reflects well reflexivity, associativity and duality; describing categories as «structures of (inner) consequence» seems to fit exceptionally well. The pictorial meaning of a «con-sequence» may well reflect the graphical structure. Gives a fine picture of the «intermediating forces» in observation and the «psychologism» becoming possible (- cf. CCCs, Toposes). Con: Personalized meaning has an association with somewhat unfriendly behaviour. Anybody to drop a comment on this? Cheers, Nick Sean Leather wrote: On Thu, Feb 18, 2010 at 04:27, Nick Rudnick wrote: I haven't seen anybody mentioning «Joy of Cats» by Adámek, Herrlich Strecker: It is available online, and is very well-equipped with thorough explanations, examples, exercises funny illustrations, I would say best of university lecture style: http://katmat.math.uni-bremen.de/acc/. (Actually, the name of the book is a joke on the set theorists' book «Joy of Set», which again is a joke on «Joy of Sex», which I once found in my parents' bookshelf... ;-)) This book reads quite nicely! I love the illustrations that pervade the technical description, providing comedic relief. I might have to go back a re-learn CT... again. Excellent recommendation! For those looking for resources on category theory, here are my collected references: http://www.citeulike.org/user/spl/tag/category-theory Sean ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe ___ Haskell
Re: [Haskell-cafe] Category Theory woes
Hi Daniel,
;-)) agreed, but is the word «Ring» itself in use? The same about the
English language... de.wikipedia says:
« Die Namensgebung /Ring/ bezieht sich nicht auf etwas anschaulich
Ringförmiges, sondern auf einen organisierten Zusammenschluss von
Elementen zu einem Ganzen. Diese Wortbedeutung ist in der deutschen
Sprache ansonsten weitgehend verloren gegangen. Einige
ältereVereinsbezeichnungen /wiki/Verein (wie z. B. Deutscher Ring
/wiki/Deutscher_Ring, Weißer Ring /wiki/Wei%C3%9Fer_Ring_e._V.) oder
Ausdrücke wie „Verbrecherring“ weisen noch auf diese Bedeutung hin. Das
Konzept des Ringes geht auf Richard Dedekind
/wiki/Richard_Dedekind zurück; die Bezeichnung /Ring/ wurde allerdings
von David Hilbert /wiki/David_Hilbert eingeführt.»
(http://de.wikipedia.org/wiki/Ringtheorie)
How many students are wondering confused about what is «the hollow» in a
ring every year worlwide, since Hilbert made this unreflected wording,
by just picking another term around «collection»? Although not a
mathematician, I've visited several maths lectures, for interest, having
the same problem. Then I began asking everybody I could reach -- and
even maths professors could not tell me why this thing is called a «ring».
Thanks for your examples: A «gang» {of smugglers|car thieves} shows even
the original meaning -- once knowed -- does not reflect the
characteristics of the mathematical structure.
Cheers,
Nick
Daniel Fischer wrote:
Am Donnerstag 18 Februar 2010 14:48:08 schrieb Nick Rudnick:
even in Germany, where the
term «ring» seems to originate from, since at least a century nowbody
has the least idea it once had an alternative meaning «gang,band,group»,
Wrong. The term Ring is still in use with that meaning in composites like
Schmugglerring, Autoschieberring, ...
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Re: [Haskell-cafe] Category Theory woes
Hi Hans, agreed, but, in my eyes, you directly point to the problem: * doesn't this just delegate the problem to the topic of limit operations, i.e., in how far is the term «closed» here more perspicuous? * that's (for a very simple concept) the way that maths prescribes: + historical background: «I take closed as coming from being closed under limit operations - the origin from analysis.» + definition backtracking: «A closure operation c is defined by the property c(c(x)) = c(x). If one takes c(X) = the set of limit points of X, then it is the smallest closed set under this operation. The closed sets X are those that satisfy c(X) = X. Naming the complements of the closed sets open might have been introduced as an opposite of closed.» 418 bytes in my file system... how many in my brain...? Is it efficient, inevitable? The most fundamentalist justification I heard in this regard is: «It keeps people off from thinking the could go without the definition...» Meanwhile, we backtrack definition trees filling books, no, even more... In my eyes, this comes equal to claiming: «You have nothing to understand this beyond the provided authoritative definitions -- your understanding is done by strictly following these.» Back to the case of open/closed, given we have an idea about sets -- we in most cases are able to derive the concept of two disjunct sets facing each other ourselves, don't we? The only lore missing is just a Bool: Which term fits which idea? With a reliable terminology using «bordered/unbordered», there is no ambiguity, and we can pass on reading, without any additional effort. Picking such an opportunity thus may save a lot of time and even error -- allowing you to utilize your individual knowledge and experience. I have hope that this approach would be of great help in learning category theory. All the best, Nick Hans Aberg wrote: On 18 Feb 2010, at 14:48, Nick Rudnick wrote: * the definition of open/closed sets in topology with the boundary elements of a closed set to considerable extent regardable as facing to an «outside» (so that reversing these terms could even appear more intuitive, or «bordered» instead of closed and «unbordered» instead of open), I take closed as coming from being closed under limit operations - the origin from analysis. A closure operation c is defined by the property c(c(x)) = c(x). If one takes c(X) = the set of limit points of X, then it is the smallest closed set under this operation. The closed sets X are those that satisfy c(X) = X. Naming the complements of the closed sets open might have been introduced as an opposite of closed. Hans ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Category Theory woes
Gregg Reynolds wrote: On Thu, Feb 18, 2010 at 7:48 AM, Nick Rudnick joerg.rudn...@t-online.de mailto:joerg.rudn...@t-online.de wrote: IM(H??)O, a really introductive book on category theory still is to be written -- if category theory is really that fundamental (what I believe, due to its lifting of restrictions usually implicit at 'orthodox maths'), than it should find a reflection in our every day's common sense, shouldn't it? Goldblatt works for me. Accidentially, I have Goldblatt here, although I didn't read it before -- you agree with me it's far away from every day's common sense, even for a hobby coder?? I mean, this is not «Head first categories», is it? ;-)) With «every day's common sense» I did not mean «a mathematician's every day's common sense», but that of, e.g., a housewife or a child... But I have became curious now for Goldblatt... * the definition of open/closed sets in topology with the boundary elements of a closed set to considerable extent regardable as facing to an «outside» (so that reversing these terms could even appear more intuitive, or «bordered» instead of closed and «unbordered» instead of open), Both have a border, just in different places. Which elements form the border of an open set?? As an example, let's play a little: Arrows: Arrows are more fundamental than objects, in fact, categories may be defined with arrows only. Although I like the term arrow (more than 'morphism'), I intuitively would find the term «reference» less contradictive with the actual intention, as this term Arrows don't refer. A *referrer* (object) refers to a *referee* (object) by a *reference* (arrow). Categories: In every day's language, a category is a completely different thing, without the least Not necesssarily (for Kantians, Aristoteleans?) Are you sure...?? See http://en.wikipedia.org/wiki/Categories_(Aristotle) ... If memory serves, MacLane says somewhere that he and Eilenberg picked the term category as an explicit play on the same term in philosophy. In general I find mathematical terminology well-chosen and revealing, if one takes the trouble to do a little digging. If you want to know what terminological chaos really looks like try linguistics. ;-) For linguistics, granted... In regard of «a little digging», don't you think terminology work takes a great share, especially at interdisciplinary efforts? Wouldn't it be great to be able to drop, say 20% or even more, of such efforts and be able to progress more fluidly ? -g ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: Fwd: [Haskell-cafe] Category Theory woes
Hi Mike, so an open set does not contain elements constituting a border/boundary of it, does it? But a closed set does, doesn't it? Cheers, Nick Michael Matsko wrote: - Forwarded Message - From: Michael Matsko msmat...@comcast.net To: Nick Rudnick joerg.rudn...@t-online.de Sent: Thursday, February 18, 2010 2:16:18 PM GMT -05:00 US/Canada Eastern Subject: Re: [Haskell-cafe] Category Theory woes Gregg, Topologically speaking, the border of an open set is called the boundary of the set. The boundary is defined as the closure of the set minus the set itself. As an example consider the open interval (0,1) on the real line. The closure of the set is [0,1], the closed interval on 0, 1. The boundary would be the points 0 and 1. Mike Matsko - Original Message - From: Nick Rudnick joerg.rudn...@t-online.de To: Gregg Reynolds d...@mobileink.com Cc: Haskell Café List haskell-cafe@haskell.org Sent: Thursday, February 18, 2010 1:55:31 PM GMT -05:00 US/Canada Eastern Subject: Re: [Haskell-cafe] Category Theory woes Gregg Reynolds wrote: On Thu, Feb 18, 2010 at 7:48 AM, Nick Rudnick joerg.rudn...@t-online.de mailto:joerg.rudn...@t-online.de wrote: IM(H??)O, a really introductive book on category theory still is to be written -- if category theory is really that fundamental (what I believe, due to its lifting of restrictions usually implicit at 'orthodox maths'), than it should find a reflection in our every day's common sense, shouldn't it? Goldblatt works for me. Accidentially, I have Goldblatt here, although I didn't read it before -- you agree with me it's far away from every day's common sense, even for a hobby coder?? I mean, this is not «Head first categories», is it? ;-)) With «every day's common sense» I did not mean «a mathematician's every day's common sense», but that of, e.g., a housewife or a child... But I have became curious now for Goldblatt... * the definition of open/closed sets in topology with the boundary elements of a closed set to considerable extent regardable as facing to an «outside» (so that reversing these terms could even appear more intuitive, or «bordered» instead of closed and «unbordered» instead of open), Both have a border, just in different places. Which elements form the border of an open set?? As an example, let's play a little: Arrows: Arrows are more fundamental than objects, in fact, categories may be defined with arrows only. Although I like the term arrow (more than 'morphism'), I intuitively would find the term «reference» less contradictive with the actual intention, as this term Arrows don't refer. A *referrer* (object) refers to a *referee* (object) by a *reference* (arrow). Categories: In every day's language, a category is a completely different thing, without the least Not necesssarily (for Kantians, Aristoteleans?) Are you sure...?? See http://en.wikipedia.org/wiki/Categories_(Aristotle) ... If memory serves, MacLane says somewhere that he and Eilenberg picked the term category as an explicit play on the same term in philosophy. In general I find mathematical terminology well-chosen and revealing, if one takes the trouble to do a little digging. If you want to know what terminological chaos really looks like try linguistics. ;-) For linguistics, granted... In regard of «a little digging», don't you think terminology work takes a great share, especially at interdisciplinary efforts? Wouldn't it be great to be able to drop, say 20% or even more, of such efforts and be able to progress more fluidly ? -g ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Category Theory woes
Hi Mike, of course... But in the same spirit, one could introduce a straightforward extension, «partially bordered», which would be as least as good as «clopen»... ;-) I must admit we've come a little off the topic -- how to introduce to category theory. The intent was to present some examples that mathematical terminology culture is not that exemplary as one should expect, but to motivate an open discussion about how one might «rename refactor» category theory (of 2:48 PM). I would be very interested in other people's proposals... :-) Michael Matsko wrote: Nick, That is correct. An open set contains no point on its boundary. A closed set contains its boundary, i.e. for a closed set c, Closure(c) = c. Note that for a general set, which is neither closed or open (say the half closed interval (0,1]), may contain points on its boundary. Every set contains its interior, which is the part of the set without its boundary and is contained in its closure - for a given set x, Interior(x) is a subset of x is a subset of Closure(x). Mike - Original Message - From: Nick Rudnick joerg.rudn...@t-online.de To: Michael Matsko msmat...@comcast.net Cc: haskell-cafe@haskell.org Sent: Thursday, February 18, 2010 3:15:49 PM GMT -05:00 US/Canada Eastern Subject: Re: Fwd: [Haskell-cafe] Category Theory woes Hi Mike, so an open set does not contain elements constituting a border/boundary of it, does it? But a closed set does, doesn't it? Cheers, Nick Michael Matsko wrote: - Forwarded Message - From: Michael Matsko msmat...@comcast.net To: Nick Rudnick joerg.rudn...@t-online.de Sent: Thursday, February 18, 2010 2:16:18 PM GMT -05:00 US/Canada Eastern Subject: Re: [Haskell-cafe] Category Theory woes Gregg, Topologically speaking, the border of an open set is called the boundary of the set. The boundary is defined as the closure of the set minus the set itself. As an example consider the open interval (0,1) on the real line. The closure of the set is [0,1], the closed interval on 0, 1. The boundary would be the points 0 and 1. Mike Matsko - Original Message - From: Nick Rudnick joerg.rudn...@t-online.de To: Gregg Reynolds d...@mobileink.com Cc: Haskell Café List haskell-cafe@haskell.org Sent: Thursday, February 18, 2010 1:55:31 PM GMT -05:00 US/Canada Eastern Subject: Re: [Haskell-cafe] Category Theory woes Gregg Reynolds wrote: On Thu, Feb 18, 2010 at 7:48 AM, Nick Rudnick joerg.rudn...@t-online.de mailto:joerg.rudn...@t-online.de wrote: IM(H??)O, a really introductive book on category theory still is to be written -- if category theory is really that fundamental (what I believe, due to its lifting of restrictions usually implicit at 'orthodox maths'), than it should find a reflection in our every day's common sense, shouldn't it? Goldblatt works for me. Accidentially, I have Goldblatt here, although I didn't read it before -- you agree with me it's far away from every day's common sense, even for a hobby coder?? I mean, this is not «Head first categories», is it? ;-)) With «every day's common sense» I did not mean «a mathematician's every day's common sense», but that of, e.g., a housewife or a child... But I have became curious now for Goldblatt... * the definition of open/closed sets in topology with the boundary elements of a closed set to considerable extent regardable as facing to an «outside» (so that reversing these terms could even appear more intuitive, or «bordered» instead of closed and «unbordered» instead of open), Both have a border, just in different places. Which elements form the border of an open set?? As an example, let's play a little: Arrows: Arrows are more fundamental than objects, in fact, categories may be defined with arrows only. Although I like the term arrow (more than 'morphism'), I intuitively would find the term «reference» less contradictive with the actual intention, as this term Arrows don't refer. A *referrer* (object) refers to a *referee* (object) by a *reference* (arrow). Categories: In every day's language, a category is a completely different thing, without the least Not necesssarily (for Kantians, Aristoteleans?) Are you sure...?? See http://en.wikipedia.org/wiki/Categories_(Aristotle) ... If memory serves, MacLane says somewhere that he and Eilenberg picked the term category as an explicit play on the same term in philosophy. In general I find mathematical
Re: [Haskell-cafe] Category Theory woes
Hans Aberg wrote: On 18 Feb 2010, at 19:19, Nick Rudnick wrote: agreed, but, in my eyes, you directly point to the problem: * doesn't this just delegate the problem to the topic of limit operations, i.e., in how far is the term «closed» here more perspicuous? * that's (for a very simple concept) the way that maths prescribes: + historical background: «I take closed as coming from being closed under limit operations - the origin from analysis.» + definition backtracking: «A closure operation c is defined by the property c(c(x)) = c(x). If one takes c(X) = the set of limit points of X, then it is the smallest closed set under this operation. The closed sets X are those that satisfy c(X) = X. Naming the complements of the closed sets open might have been introduced as an opposite of closed.» 418 bytes in my file system... how many in my brain...? Is it efficient, inevitable? Yes, it is efficient conceptually. The idea of closed sets let to topology, and in combination with abstractions of differential geometry led to cohomology theory which needed category theory solving problems in number theory, used in a computer language called Haskell using a feature called Currying, named after a logician and mathematician, though only one person. It is SUCCESSFUL, NO MATTER... :-) But I spoke about efficiency, in the Pareto sense (http://en.wikipedia.org/wiki/Pareto_efficiency)... Can we say that the way in which things are done now cannot be improved?? Hans, you were the most specific response to my actual intention -- could I clear up the reference thing for you? All the best, Nick Hans ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Category Theory woes
Hi Alexander, my actual posting was about rename refactoring category theory; closed/open was just presented as an example for suboptimal terminology in maths. But of course, bordered/unbordered would be extended by e.g. «partially bordered» and the same holds. Cheers, Nick Alexander Solla wrote: On Feb 18, 2010, at 10:19 AM, Nick Rudnick wrote: Back to the case of open/closed, given we have an idea about sets -- we in most cases are able to derive the concept of two disjunct sets facing each other ourselves, don't we? The only lore missing is just a Bool: Which term fits which idea? With a reliable terminology using «bordered/unbordered», there is no ambiguity, and we can pass on reading, without any additional effort. There are sets that only partially contain their boundary. They are neither open nor closed, in the usual topology. Consider (0,1] in the Real number line. It contains 1, a boundary point. It does not contain 0. It is not an open set OR a closed set in the usual topology for R. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Category Theory woes
Gregg Reynolds wrote: On Thu, Feb 18, 2010 at 1:31 PM, Daniel Fischer daniel.is.fisc...@web.de mailto:daniel.is.fisc...@web.de wrote: Am Donnerstag 18 Februar 2010 19:55:31 schrieb Nick Rudnick: Gregg Reynolds wrote: -- you agree with me it's far away from every day's common sense, even for a hobby coder?? I mean, this is not «Head first categories», is it? ;-)) With «every day's common sense» I did not mean «a mathematician's every day's common sense», but that of, e.g., a housewife or a child... Doesn't work. You need a lot of training in abstraction to learn very abstract concepts. Joe Sixpack's common sense isn't prepared for that. True enough, but I also tend to think that with a little imagination even many of the most abstract concepts can be illustrated with intuitive, concrete examples, and it's a fun (to me) challenge to try come up with them. For example, associativity can be nicely illustrated in terms of donning socks and shoes - it's not hard to imagine putting socks into shoes before putting feet into socks. A little weird, but easily understandable. My guess is that with a little effort one could find good concrete examples of at least category, functor, and natural transformation. Hmm, how is a cake-mixer like a cement-mixer? They're structurally and functionally isomorphic. Objects in the category Mixer? :-) This comes close to what I mean -- the beauty of category theory does not end at the borders of mathematical subjects... IMHO we are just beginning to discovery of the categorical world beyond mathematics, and I think many findings original to computer science, but less to maths may be of value then. And I am definitely more optimistic on «Joe Sixpack's common sense», which still surpasses a good lot of things possible with AI -- no categories at all there?? I can't believe... Both have a border, just in different places. Which elements form the border of an open set?? The boundary of an open set is the boundary of its complement. The boundary may be empty (happens if and only if the set is simultaneously open and closed, clopen, as some say). Right, that was what I meant; the point being that boundary (or border, or periphery or whatever) is not sufficient to capture the idea of closed v. open. ;-)) I did not claim «bordered» is the best choice, I just said closed/open is NOT... IMHO this also does not affect what I understand as a refactoring -- just imagine Coq had a refactoring browser; all combinations of terms are possible as before, aren't they? But it was not my aim to begin enumerating all variations of «bordered», «unbordered», «partially ordered» and STOP... Should I come QUICKLY with a pendant to «clopen» now? This would be «MATHS STYLE»...! I neither say finding an appropriate word here is a quickshot, nor I claim trying so is ridiculous, as it is impossible. I think it is WORK, which is to be done in OPEN DISCUSSION -- and that, at the long end, the result might be rewarding, similar as the effort put into a rename refactoring will reveal rewarding. ;-)) Trying a refactored category theory (with a dictionary in the appendix...) might open access to many interesting people and subjects otherwise out of reach. And deeply contemplating terminology cannot hurt, at the least... All the best, Nick ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Category Theory woes
Hans Aberg wrote: On 18 Feb 2010, at 23:02, Nick Rudnick wrote: 418 bytes in my file system... how many in my brain...? Is it efficient, inevitable? Yes, it is efficient conceptually. The idea of closed sets let to topology, and in combination with abstractions of differential geometry led to cohomology theory which needed category theory solving problems in number theory, used in a computer language called Haskell using a feature called Currying, named after a logician and mathematician, though only one person. It is SUCCESSFUL, NO MATTER... :-) But I spoke about efficiency, in the Pareto sense (http://en.wikipedia.org/wiki/Pareto_efficiency)... Can we say that the way in which things are done now cannot be improved?? Hans, you were the most specific response to my actual intention -- could I clear up the reference thing for you? That seems to be an economic theory version of utilitarianism - the problem is that when dealing with concepts there may be no optimizing function to agree upon. There is an Occam's razor one may try to apply in the case of axiomatic systems, but one then finds it may be more practical with one that is not minimal. Exactly. By this I justify my questioning of inviolability of the state of art of maths terminology -- an open discussion should be allowed at any time... As for the naming problem, it is more of a linguistic problem: the names were somehow handed by tradition, and it may be difficult to change them. For example, there is a rumor that kangaroo means I do not understand in a native language; assuming this to be true, it might be difficult to change it. Completely d'accord. This is indeed a strong problem, and I fully agree if you say that, for maths, trying this is for people with fondness for speaker's corner... :-)) But for category theory, a subject (too!) many people are complaining about, blind for its beauty, a such book -- ideally in children's language and illustrations, of course with a dictionary to original terminology in the appendix! -- could be of great positive influence on category theory itself. And the deep contemplation encompassing the *collective* creation should be most rewarding in itself -- a journey without haste into the depths of the subject. Mathematicians though stick to their own concepts and definitions individually. For example, I had conversations with one who calls monads triads, and then one has to cope with that. Yes. But isn't it also an enrichment by some way? All the best, Nick ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Category Theory woes
Alexander Solla wrote: On Feb 18, 2010, at 2:08 PM, Nick Rudnick wrote: my actual posting was about rename refactoring category theory; closed/open was just presented as an example for suboptimal terminology in maths. But of course, bordered/unbordered would be extended by e.g. «partially bordered» and the same holds. And my point was that your terminology was suboptimal for just the same reasons. The difficulty of mathematics is hardly the funny names. :-) Criticism... Criticism is good at this place... Opens up things... Perhaps you're not familiar with the development of Category theory. Hans Aberg gave a brief development. Basically, Category theory is the RESULT of the refactoring you're asking about. Category theory's beginnings are found in work on differential topology (where functors and higher order constructs took on a life of their own), and the unification of topology, lattice theory, and universal algebra (in order to ground that higher order stuff). Distinct models and notions of computation were unified, using arrows and objects. Now, you could have a legitimate gripe about current category theory terminology. But I am not so sure. We can simplify lots of things. Morphisms can become arrows or functions. Auto- can become self-. Homo- can become same-. Functors can become Category arrows. Does it help? You tell me. I think I understand what you mean and completely agree... The project in my imagination is different, I read on... But if we're ever going to do anything interesting with Category theory, we're going to have to go into the realm of dealing with SOME kind of algebra. We need examples, and the mathematically tractable ones have names like group, monoid, ring, field, sigma-algebras, lattices, logics, topologies, geometries. They are arbitrary names, grounded in history. Any other choice is just as arbitrary, if not more so. The closest thing algebras have to a unique name is their signature -- basically their axiomatization -- or a long descriptive name in terms of arbitrary names and adjectives (the Cartesian product of a Cartesian closed category and a groupoid with groupoid addition induced by). The case for Pareto efficiency is here: is changing the name of these kinds of structures wholesale a win for efficiency? The answer is no. Everybody would have to learn the new, arbitrary names, instead of just some people having to learn the old arbitrary names. Ok... Let's compare this to the monad fallacy. It is said every beginner Haskell programmer write a monad tutorial, and often falls into the monad fallacy of thinking that there is only one interpretation for monadism. Monads are relatively straightforward. Their power comes from the fact that many different kinds of things are monadic -- sequencing, state, function application. What name should we use for monads instead? Which interpretation must we favor, despite the fact that others will find it counter-intuitive? Or should we choose to not favor one, and just pick a new arbitrary name? The short answer: If the work I imagine would be done by exchanging here a word and there on the quick -- it would be again maths style, with difference only in justifying it with naivity instead of resignation. The idea I have is different: DEEP CONTEMPLATION stands in the beginning, gathering the constructive criticism of the sharpest minds possible, hard discussions and debates full of temperament -- all of this already rewarding in itself. The participants are united in the spirit to create a masterpiece, and to explore details in depths for which time was missing before. It could be great fun for everybody to improve one's deep intuition of category theory. This book might be comparable to a programming language, hypertext like a wikibook and maybe in development forever. It will have an appendix (or later a special mode) with a translation of all new termini into the original ones. I do believe deeply that this is possible. By all criticism on Bourbaki -- I was among the generation of pupils taught set theory in elementary school; looking back, I regard it as a rewarding effort. Why should category theory not be able to achieve the same, maybe with other means than plastic chips? All the best, Nick ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Category Theory woes
Daniel Fischer wrote: Am Donnerstag 18 Februar 2010 19:19:36 schrieb Nick Rudnick: Hi Hans, agreed, but, in my eyes, you directly point to the problem: * doesn't this just delegate the problem to the topic of limit operations, i.e., in how far is the term «closed» here more perspicuous? It's fairly natural in German, abgeschlossen: closed, finished, complete; offen: open, ongoing. * that's (for a very simple concept) That concept (open and closed sets, topology more generally) is *not* very simple. It has many surprising aspects. «concept» is a word of many meanings; to become more specific: Its *definition* is... the way that maths prescribes: + historical background: «I take closed as coming from being closed under limit operations - the origin from analysis.» + definition backtracking: «A closure operation c is defined by the property c(c(x)) = c(x). Actually, that's incomplete, missing are - c(x) contains x - c(x) is minimal among the sets containing x with y = c(y). Even more workload to master... This strengthens the thesis that definition recognition requires a considerable amount of one's effort... If one takes c(X) = the set of limit points of Not limit points, Berührpunkte (touching points). X, then it is the smallest closed set under this operation. The closed sets X are those that satisfy c(X) = X. Naming the complements of the closed sets open might have been introduced as an opposite of closed.» 418 bytes in my file system... how many in my brain...? Is it efficient, inevitable? The most fundamentalist justification I heard in this regard is: «It keeps people off from thinking the could go without the definition...» Meanwhile, we backtrack definition trees filling books, no, even more... In my eyes, this comes equal to claiming: «You have nothing to understand this beyond the provided authoritative definitions -- your understanding is done by strictly following these.» But you can't understand it except by familiarising yourself with the definitions and investigating their consequences. The name of a concept can only help you remembering what the definition was. Choosing obvious names tends to be misleading, because there usually are things satisfying the definition which do not behave like the obvious name implies. So if you state that the used definitions are completely unpredictable so that they have to be studied completely -- which already ignores that human brain is an analogous «machine» --, you, by information theory, imply that these definitions are somewhat arbitrary, don't you? This in my eyes would contradict the concept such definition systems have about themselves. To my best knowledge it is one of the best known characteristics of category theory that it revealed in how many cases maths is a repetition of certain patterns. Speaking categorically it is good practice to transfer knowledge from on domain to another, once the required isomorphisms could be established. This way, category theory itself has successfully torn down borders between several subdisciplines of maths and beyond. I just propose to expand the same to common sense matters... Back to the case of open/closed, given we have an idea about sets -- we in most cases are able to derive the concept of two disjunct sets facing each other ourselves, don't we? The only lore missing is just a Bool: Which term fits which idea? With a reliable terminology using «bordered/unbordered», there is no ambiguity, and we can pass on reading, without any additional effort. And we'd be very wrong. There are sets which are simultaneously open and closed. It is bad enough with the terminology as is, throwing in the boundary (which is an even more difficult concept than open/closed) would only make things worse. Really? As «open == not closed» can similarly be implied, bordered/unbordered even in this concern remains at least equal... Picking such an opportunity thus may save a lot of time and even error -- allowing you to utilize your individual knowledge and experience. I When learning a formal theory, individual knowledge and experience (except coming from similar enough disciplines) tend to be misleading more than helpful. Why does the opposite work well for computing science? All the best, Nick ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Category Theory woes
Hi Alexander, please be more specific -- what is your proposal? Seems as if you had more to say... Nick Alexander Solla wrote: On Feb 18, 2010, at 4:49 PM, Nick Rudnick wrote: Why does the opposite work well for computing science? Does it? I remember a peer trying to convince me to use the factory pattern in a language that supports functors. I told him I would do my task my way, and he could change it later if he wanted. He told me an hour later he tried a trivial implementation, and found that the source was twice as long as my REAL implementation, split across multiple files in an unattractive way, all while losing conceptual clarity. He immediately switched to using functors too. He didn't even know he wanted a functor, because the name factory clouded his interpretation. Software development is full of people inventing creative new ways to use the wrong tool for the job. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Category Theory woes
Hi, wow, a topic specific response, at last... But I wish you would be more specific... ;-) A *referrer* (object) refers to a *referee* (object) by a *reference* (arrow). Doesn't work for me. Not in Ens (sets, maps), Grp (groups, homomorphisms), Top (topological spaces, continuous mappings), Diff (differential manifolds, smooth mappings), ... . Why not begin with SET and functions... Every human has a certain age, so that there is a function, ageOf:: Human- Int, which can be regarded as a certain way of a reference relationship between Human and Int, in that by agoOf, * Int reflects a certain aspect of Human, and, on the other hand, * the structure of Human can be traced to Int. Please tell me the aspect you feel uneasy with, and please give me your opinion, whether (in case of accepting this) you would rather choose to consider Human as referrer and Int as referee of the opposite -- for I think this is a deep question. Thank you in advance, Nick ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Category Theory woes
I haven't seen anybody mentioning «Joy of Cats» by Adámek, Herrlich Strecker: It is available online, and is very well-equipped with thorough explanations, examples, exercises funny illustrations, I would say best of university lecture style: http://katmat.math.uni-bremen.de/acc/. (Actually, the name of the book is a joke on the set theorists' book «Joy of Set», which again is a joke on «Joy of Sex», which I once found in my parents' bookshelf... ;-)) Another alternative: Personally, I had difficulties with the somewhat arbitrary terminology, at times a hindrance to intuitive understanding - and found intuitive access by programming examples, and the book was «Computational Category Theory» by Rydeheart Burstall, also now available online at http://www.cs.man.ac.uk/~david/categories/book/, done with the functional language ML. Later I translated parts of it to Haskell which was great fun, and the books content is more beginner level than any other book I've seen yet. The is also a programming language project dedicated to category theory, «Charity», at the university of Calgary: http://pll.cpsc.ucalgary.ca/charity1/www/home.html. Any volunteers in doing a RENAME REFACTORING of category theory together with me?? ;-)) Cheers, Nick Mark Spezzano wrote: Hi all, I'm trying to learn Haskell and have come across Monads. I kind of understand monads now, but I would really like to understand where they come from. So I got a copy of Barr and Well's Category Theory for Computing Science Third Edition, but the book has really left me dumbfounded. It's a good book. But I'm just having trouble with the proofs in Chapter 1--let alone reading the rest of the text. Are there any references to things like Hom Sets and Hom Functions in the literature somewhere and how to use them? The only book I know that uses them is this one. Has anyone else found it frustratingly difficult to find details on easy-to-diget material on Category theory. The Chapter that I'm stuck on is actually labelled Preliminaries and so I reason that if I can't do this, then there's not much hope for me understanding the rest of the book... Maybe there are books on Discrete maths or Algebra or Set Theory that deal more with Hom Sets and Hom Functions? Thanks, Mark Spezzano. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
[Haskell-cafe] Any way to catch segmentation fault?
Hi all, doing some work with a regex library I stumbled over some segmentation faults due to illegal byte combinatations. Looking for a way to get this caught some way, I failed in finding any place at GHC (6.10.1) or Hackage libraries where this is covered -- a quick check with HUnit revealed it to be crashing by this phenomenon. So I would like to ask about the state of this issue, o Is there principally no way to (generally) catch segmentation faults?? (This would be hard to believe, as the described kind of noise is to be expected at production systems, especially with user generated content.) o Are segmentation faults «prohibited» in Haskell so the advice is just to change the used library and forget the whole stuff?? o Did I oversee the generic mechanism for catching of segmentation faults?? (If yes, do you please give me a hint??) o If no, is there a workaround which might be practicable?? Thanks a lot in advance, Dorinho ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
