From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/463 Path: news.gmane.org!not-for-mail From: categories Newsgroups: gmane.science.mathematics.categories Subject: Re: Applications for Category Theory Date: Mon, 25 Aug 1997 16:49:01 -0300 (ADT) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1241016981 25873 80.91.229.2 (29 Apr 2009 14:56:21 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 14:56:21 +0000 (UTC) To: categories Original-X-From: cat-dist Mon Aug 25 16:49:02 1997 Original-Received: by mailserv.mta.ca; id AA23520; Mon, 25 Aug 1997 16:49:01 -0300 Original-Lines: 78 Xref: news.gmane.org gmane.science.mathematics.categories:463 Archived-At: Date: Mon, 25 Aug 1997 12:13:34 -0700 From: Michael J. Healy 206-865-3123 So the question > is: are there any attempts to map category theory > (or type theory or set theory -- I am not sure where the boundaries are) > > to applications (versus theory per se), roughly analagous to Z or VDM, > that might be comprehensible to somewhat without the formal framework? > If not, is there a sequence of study you would recommend for proceeding? > > I have an undergraduate degree and have done some reading about formal > algebra and category theory, but I am not sure of the path from the > former to the latter, or if that is, in fact, the appropriate path. Any > assistance would be greatly appreciated. Thank you for your > consideration. > > - Dan (founder of Tazent Software) > I started a project here at The Boeing Company three years ago whose approach is a categorical methodology for software synthesis from specifications. We are using The Kestrel Institute's Specware system, which implements category theory, for this purpose. The Web site for Kestrel is http://www.kestrel.edu/, and click on Projects, then Modular Construction of Very large Knowledge Bases. Quite a bit is being done to translate category theory into terminology more manageable for the non-mathematician, making Specware accessible to a wider audience. Please note that the description here is mine only. I just want to share this because we have had quite a bit of success in our project, and it has put category theory on the map in our little corner of industry. Our most direct application at present is for a separate project that is developing neutral representations for knowledge- based engineering (KBE) systems, which are seeing increasing use. Our specific example at present is the representation of engineering knowledge, and the refinement of it into code, for a program that produces a kind of airplane part design given its overall size and some sizing constraints. The program was synthesized by first developing a colimit of specifications of simple theories about part geometry, materials, manufacturing processes, and a representation of real numbers. The specifications make visible the design and manufacturing rationale---the knowledge---that constitutes the constraints on the specific design. Given sizing values, the layout for a specific design can be calculated. The knowledge is re-usable because of its abstract nature, the use of diagrams and colimits in several categories to build complex specifications from simple components, and a way of implementing functorial program construction from specifications (or better yet, from diagrams). A colleague and I have an initial attempt at a paper in a poster session at the upcoming Automated Software Engineering conference (ASE`97) this November. We also have a paper to appear in the Journal of Intelligent Manufacturing and an associated technical report. A good overall background is a paper by the original developers of the approach: Jullig, R. and Srinivas, Y. V. (1993). Diagrams for Software Synthesis, in Proceedings of KBSE `93: The Eighth Knowledge-Based Software Engineering Conference, IEEE Computer Society Press, pp. 10-19. -- =========================================================================== e Michael J. Healy A FA ----------> GA (425)865-3123 | | FAX(425)865-2964 | | Ff | | Gf c/o The Boeing Company | | PO Box 3707 MS 7L-66 \|/ \|/ Seattle, WA 98124-2207 ' ' USA FB ----------> GB e "I'm a natural man." michael.j.healy@boeing.com B -or- mjhealy@u.washington.edu ============================================================================