Path: dp-news.maxwell.syr.edu!spool.maxwell.syr.edu!news-spur1.maxwell.syr.edu!news.maxwell.syr.edu!wns14feed!worldnet.att.net!199.45.49.37!cyclone1.gnilink.net!spamkiller2.gnilink.net!gnilink.net!trndny01.POSTED!9244eeff!not-for-mail From: "David Cressey" Newsgroups: comp.databases.theory References: <1149302073.665332.55470@i40g2000cwc.googlegroups.com> <1149473583.137221.224950@g10g2000cwb.googlegroups.com> <1149532272.555992.105140@i39g2000cwa.googlegroups.com> Subject: Re: Aggregation (with GBY) is Relational Division Lines: 91 X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 6.00.2800.1409 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1409 Message-ID: Date: Tue, 06 Jun 2006 00:26:58 GMT NNTP-Posting-Host: 71.127.7.224 X-Complaints-To: abuse@verizon.net X-Trace: trndny01 1149553618 71.127.7.224 (Mon, 05 Jun 2006 20:26:58 EDT) NNTP-Posting-Date: Mon, 05 Jun 2006 20:26:58 EDT Xref: dp-news.maxwell.syr.edu comp.databases.theory:41046 "Marshall" wrote in message news:1149532272.555992.105140@i39g2000cwa.googlegroups.com... > David Cressey wrote: > > "Marshall" wrote in message > > > > > Actually, I had kind of a jolt reading something Bob Badour > > > wrote recently about defining aggregates as either a fold > > > or an expression written in terms of folds. (He did not use > > > the term "fold".) Thus, avg(x) can be defined as simply > > > sum(x) / count(). > > > > I disagree. avg(x) can be defined as simply sum(x) / count(x). > > > > This may seem like nitpicking. I think it's reasonably important. > > > > If you do select avg(x), sum(x)/count(*), sum(x)/count(x) from some_view > > > > you are going to get a difference when there are rows in the view that > > contain NULL in the x column. Try it and see. > > .... yeah, I see what you mean. If I define it as sum(x) / count(), > then I'm not counting and summing the same things. > > Compared with sum(x) / count(x), in which the sum and > the count *are* of the same thing. So this *isn't* just an > issue with SQL's mixing of empty-set semantics and > unknown semantics. > > > > This relates to a comment about managing missing data in SQL that I didn't > > take very much to heart. > > > > PS: can you point me to a web site that will explain "fold" to me? > > I did a bit of searching and came up with a short intro: > > http://www.cse.unsw.edu.au/~en1000/haskell/hof.html > > The functional languages don't have the RA, but they do have > map, filter, and fold. Not as good, but closer than anything > else. > > Fold is simply inserting a binary operator "in between" the elements > in a collection. Usually an ordered, collection, alas. Since it's an > ordered collection, they have to do the extra work to take order > into account, so you have both foldl and foldr, depending on > whether you start at the "left" end of the list or the "right". > (Beginning > vs. end.) > > Interestingly, the obvious conclusion about the type of the function > being folded is that it should be > > 'a, 'a -> 'a > > a simple binary function on a single domain. > > But in fact, the most general version of the function is > > 'a, 'b -> 'b > > For example, we can reverse a list using fold. > > Given a function append(element, list) that > returns a list like the one it is passed, but with element tacked > on the end, we can fold append over a list and reverse it. > > foldl(append, [], [1, 2, 3]) > > returns [3, 2, 1] > > Fold depends on being able to separate the first element of a list > from the rest, and on the ability to recognize an empty list, but > I don't think it needs anything else. > > > Marshall > Marshall, Thanks for the info on fold. I think I'm going to try to learn this one. It looks useful. So fold needs car, cdr, and nil, but nothing else. Hmmmmmmm.......