From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4543 Path: news.gmane.org!not-for-mail From: "Meredith Gregory" Newsgroups: gmane.science.mathematics.categories Subject: language for infinitary compositions? Date: Thu, 4 Sep 2008 16:22:34 -0700 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241020016 13781 80.91.229.2 (29 Apr 2009 15:46:56 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:46:56 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Fri Sep 5 07:41:17 2008 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 05 Sep 2008 07:41:17 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1KbYf7-0001yj-KT for categories-list@mta.ca; Fri, 05 Sep 2008 07:35:33 -0300 Content-Disposition: inline Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 10 Original-Lines: 51 Xref: news.gmane.org gmane.science.mathematics.categories:4543 Archived-At: Categorists, Is there a commonly accepted language for infinitary compositions? Here's the sort of thing i'm thinking about. There's a purely syntactic correspondence between a 'braced' notation and an infix notation for composition. Suppose we have a categorically-friendly notion of composition, say c. (Meaning the entities c composes can be viewed as morphisms in a category and c the categorical composition.) Then we can just as easily write - f c g -- c is merely making notationally explicit the interpretation of 'o' in f o g -- we're coloring the 'o', as it were or - {c| f, g |c} -- we've moved from infix to (not quite) prefix notation for the composition. The braced notation, however, is suggestive of a very powerful notational mechanism, comprehension notation. We could easily imagine a language allowing expressions of the form {c| pattern | predicate |c} which would denote pattern{subst_1} c pattern{subst_2} c ... where subst_i is a substition for 'variables' in the pattern of entities satisfying the predicate. This would allow reasoning over infinitary compositions by providing an intensional view of their interior structure. Surely, such a widget has already been invented. Can someone give me a reference? Best wishes, --greg -- L.G. Meredith Managing Partner Biosimilarity LLC 806 55th St NE Seattle, WA 98105 +1 206.650.3740 http://biosimilarity.blogspot.com