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## Re: [ontolog-forum] HOL decidability [Was: using SKOS forcontrolled valu

 To: , "'[ontolog-forum] '" "Rich Cooper" Wed, 13 Oct 2010 15:43:56 -0700 <20101013224401.04A83138D02@xxxxxxxxxxxxxxxxx>
 Thanks Ed,   Comments below:   Sincerely, Rich Cooper EnglishLogicKernel.com Rich AT EnglishLogicKernel DOT com 9 4 9 \ 5 2 5 - 5 7 1 2   -----Original Message----- From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Ed Barkmeyer Sent: Wednesday, October 13, 2010 3:23 PM To: [ontolog-forum] Subject: Re: [ontolog-forum] HOL decidability [Was: using SKOS forcontrolled values for controlledvocabulary]   I shouldn't get into this, but...   Rich Cooper wrote: > Thanks for the routine, but that is not an iterator of primes; it is > an iterator of integers.  By iterating through all the integers, your > routine finds primes, but it does not iterate the primes.  The fact > that you close the scope around tests for primes doesn’t make it an > iterator.  >  >  >  > The idea behind the iterator is to produce one new one, given the old > one as a starting point. >    That is one version of the inductive model of iteration.  The more robust version is to produce the next one, given all predecessors.  And of course, Bill's code does just that.  The "all predecessors" approach is equally valid mathematically, and it works for spaces with partial orderings, while the "from n, produce n+1" approach does not (in general).   Since the claim I made was that there is no function that iterates the primes, why is all that extra profundity necessary?  I didn't introduce "the inductive model of iteration", or distinguish among models, so why do you bring that up anyway?  It doesn't matter what you use if it can't do the job of iterating primes, and I don't mean generating and testing primes, which you mistake as iterating them.       Rich's model doesn't work for Fibonacci numbers, either, even though you only need two predecessors.     Since I never claimed it would work for Fibonacci numbers, why does that matter, and what has that got to do with iterating primes?     I suppose it would work for Cauchy enumeration of n-tuples, which is the common countability proof technique.   But has nothing to do with iterating primes.  Where are you exploring with this crazy quilt of off the wall associations?   >  > The method you are using is often called Eratosthenes’ Sieve, which is > a well known method to calculate primes, but NOT to iterate them.  >   The difference is in what is being enumerated inside the code. >    Well, more carefully, the Sieve of Eratosthenes is an iterative algorithm for producing all prime numbers.   It is an algorithm which iterates over the integers, not the primes; it generates and tests the integers to identify primes.  That's the Sieve part.   I am familiar with the term "iterator" only as a software object, and OBTW, java.util.Iterator is class of somewhat diverse "objects" (algorithms), none of which takes an instance and produces the next.  Instead, each has a retained state, and each invocation of next() produces the successor state and returns the corresponding instance of the "collection".    Any iterator which uses the method you endorsed will fail the first usage; it takes too long to generate the next one.  And I didn't claim that Java iterators are well written, or obey good engineering principles, so why are you introducing yet another off the wall association?   Thinking of prime numbers as an infinite collection, such an "iterator" will be seen to produce the primes in order starting from an initial state, while the actual implementation mechanism is "encapsulated" (and might well be the Sieve).  IMO, that is actually pretty close to the mathematical notion, in which the creature is categorized by a certain set of properties that it exhibits, regardless of what other bizarre properties it may have.  Which only means that a Java "iterator" is not a Rich Cooper "iterator".   A Java iterator SHOULD be a Rich Cooper iterator, but if it is written to use your generate and test method, it certainly isn't a good iterator, and doesn't serve the purpose.  Sorry.     So, as far as I can tell, Rich asserts that Bill's algorithm is not an instance of the definition Rich assigns to "iterator" above.  I agree.  Now, how that relates to decidability, which is about the existence of an algorithm that terminates in finite time, I am at a loss to understand.   The ontolog forum exploder does seem to be a study in "free association."   You're the one who free associated all through this email - so look at where the trail shows you have been.     -Ed   >  >  > -Rich >  >  >  > Sincerely, >  > Rich Cooper >  > EnglishLogicKernel.com >  > Rich AT EnglishLogicKernel DOT com >  > 9 4 9 \ 5 2 5 - 5 7 1 2 >  > ------------------------------------------------------------------------ >  > *From:* ontolog-forum-bounces@xxxxxxxxxxxxxxxx > [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] *On Behalf Of *Bill > Andersen > *Sent:* Wednesday, October 13, 2010 12:52 PM > *To:* [ontolog-forum] ; Rich Cooper > *Subject:* Re: [ontolog-forum] HOL decidability [Was: using SKOS > forcontrolled values for controlledvocabulary] >  >  >  > On Oct 13, 2010, at 01:56 , Rich Cooper wrote: >  >  >  > Hi Duane, yes, iterators in software were what I tried to convey > there.  There is no function that will iterate the primes.  By pairing > each prime in ascending order with any other iterated set, you create > unique prime keys for each element of that set, keys that cannot be > factored.  >  >  >  > Thanks for your inputs, >  > -Rich >  >  >  > Hi Rich >  >  >  > Here's a fixed precision implementation of a prime iterator, along the > lines Chris Menzel described. >  >  >  > Enjoy >  > ------------ >  >  >  > package foo; >  >  >  > import java.util.Iterator; >  >  >  > public class PrimeIterator implements Iterator { >  >  >  >        private Integer n = 2; >  >       >  >        @Override >  >        public boolean hasNext() { >  >               // Thanks to _Euclid_ :-D >  >               return true; >  >        } >  >       >  >        private boolean isPrime(Integer n) { >  >               Integer i = 2; >  >               while (i < n) { >  >                      if ((n % i) == 0) { >  >                            // _divisible_ by i < n >  >                            return false; >  >                      } >  >                      i++; >  >               } >  >               return true; >  >        } >  >  >  >        @Override >  >        public Integer next() { >  >               while (!isPrime(n)) { >  >                      n++; >  >               } >  >               Integer tmp = n; >  >               n++; >  >               return tmp; >  >        } >  >  >  >        @Override >  >        public void remove() { >  >               throw new UnsupportedOperationException(); >  >        } >  >       >  >        public static void main(String[] argz) { >  >               PrimeIterator iter = new PrimeIterator(); >  >               while (iter.hasNext()) { >  >                      System.out.println(iter.next()); >  >               } >  >        } >  >  >  > } >  >  >  > Bill Andersen >  > Highfleet, Inc. (www.highfleet.com ) >  > 3600 O'Donnell Street, Suite 600 >  > Baltimore, MD 21224 >  > Office: +1.410.675.1201 >  > Cell: +1.443.858.6444 >  > Fax: +1.410.675.1204 >  >  >  >  >  >  >  >  >    -- Edward J. Barkmeyer                        Email: edbark@xxxxxxxx National Institute of Standards & Technology Manufacturing Systems Integration Division 100 Bureau Drive, Stop 8263                Tel: +1 301-975-3528 Gaithersburg, MD 20899-8263                FAX: +1 301-975-4694   "The opinions expressed above do not reflect consensus of NIST,  and have not been reviewed by any Government authority."     _________________________________________________________________ Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/  Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/  Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx Shared Files: http://ontolog.cim3.net/file/ Community Wiki: http://ontolog.cim3.net/wiki/ To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx
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