Path: dp-news.maxwell.syr.edu!spool.maxwell.syr.edu!drn.maxwell.syr.edu!news.maxwell.syr.edu!HSNX.atgi.net!cyclone-sf.pbi.net!216.218.192.242!news.he.net!chekhov.conxion.net!news.oracle.com!not-for-mail From: "Mikito Harakiri" Newsgroups: comp.databases.theory References: <3RMQd.35$YQ1.109@news.oracle.com> <4213e7b7$0$53482$ed2619ec@ptn-nntp-reader03.plus.net> Subject: Re: grouping in tuple relational calculus Lines: 16 X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 6.00.2600.0000 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2600.0000 Message-ID: Date: Wed, 16 Feb 2005 17:21:54 -0800 NNTP-Posting-Host: 130.35.179.159 X-Trace: news.oracle.com 1108604121 130.35.179.159 (Wed, 16 Feb 2005 17:35:21 PST) NNTP-Posting-Date: Wed, 16 Feb 2005 17:35:21 PST Xref: dp-news.maxwell.syr.edu comp.databases.theory:29997 "Paul" wrote in message news:4213e7b7$0$53482$ed2619ec@ptn-nntp-reader03.plus.net... > Mikito Harakiri wrote: > > Speaking of aggregates, I always wondered why some aggregates are > > expressable by standard means (min, max can be expressed as antijoins), > > while the others aren't (sum). > > I guess that min and max only require an ordering, which is a more > fundamental concept than addition, which is required for sum. That's right, on one hand, aggregate min and max are based upon lattice join and meet binary operators, similar to sum based upon binary addition. This makes all of them to fit into aggregate framework. On the other hand, lattice implies order, and with order one can leverage antijoin.