*mbx* 3bb593bb00000000 7-Dec-1996 16:38:17 -0300,1198;000000000000-00000000 Received: by mailserv.mta.ca; id AA02294; Sat, 7 Dec 1996 16:37:00 -0400 Date: Sat, 7 Dec 1996 16:37:00 -0400 (AST) From: categories To: categories Subject: varieties Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Date: Fri, 6 Dec 1996 14:25:38 +0100 (MET) From: Jiri Rosicky A DUALITY FOR VARIETIES OF ALGEBRAS We have just proved a result we beleive is new - comments are highly appreciated. Theorem: The following two 2-categories are dually biequivalent: VAR - the category of all finitary, many-sorted varieties (O-cells) all finitary, regular right adjoints (1-cells) and all natural transformatons (2-cells) CCFP - the 2-category of all Cauchy-complete, small categories with finite products (0-cells) all finite-products preserving functors (1-cells) In particular, every variety has a "canonical" Lawvere theory formed by all retracts of all finitely generated free algebras of that variety (= of all finitely presentable projective objects). J.Adamek & J.Rosicky 7-Dec-1996 16:38:26 -0300,1116;000000000001-00000000 Received: by mailserv.mta.ca; id AA25426; Sat, 7 Dec 1996 16:38:20 -0400 Date: Sat, 7 Dec 1996 16:38:20 -0400 (AST) From: categories To: categories Subject: CT97: First Announcement Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Date: Fri, 6 Dec 96 16:31:17 -0800 From: John MacDonald Please circulate to all interested colleagues: FIRST ANNOUNCEMENT INTERNATIONAL CATEGORY THEORY MEETING (CT97) July 13-19, 1997 University of British Columbia Vancouver, Canada The conference arrival day is Sunday, July 13 and the scientific program will run from Monday, July 14 to Saturday, July 19 inclusive. Detailed information will be included in a second announcement. To preregister, and thus receive subsequent announcements, please send e-mail to johnm@math.ubc.ca with subject `preregistration'. Please provide your name and a postal address in the body of the message. 10-Dec-1996 10:23:30 -0300,4447;000000000000-00000000 Received: by mailserv.mta.ca; id AA23996; Tue, 10 Dec 1996 10:21:38 -0400 Date: Tue, 10 Dec 1996 10:21:38 -0400 (AST) From: categories To: categories Subject: my book: "Practical Foundations of Mathematics" Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Date: Mon, 9 Dec 1996 21:16:37 GMT From: Paul Taylor STOP PRESS --- see my web page for my new home telephone number Practical Foundations of Mathematics Paul Taylor to be published by Cambridge University Press http://www.dcs.qmw.ac.uk/~pt/book In the time this book has taken me to write, various friends of mine have had babies and sent them to school. I just hope someone thinks that it has been worth the effort. The emotional cost of trying to get these 500 pages finished has made me seriously reclusive, and I owe many friends and colleagues replies to letters and email, for which I would like to make a general and sincere apology. The news is that seven of the eight chapters are finished and ready to be sent to the copy editors at CUP. I would however very much like to get my colleagues' views on individual chapters, if you feel that you would like some reading matter for the yuletide vacation. Ideally I would like comments from *both* experts *and* students, as it is useful to find out what topics need better explanation. Chapter 8 is mostly there but has not been polished yet. Practical Foundations collects the methods of construction of the objects of twentieth century mathematics. Although it is mainly concerned with a framework essentially equivalent to intuitionistic ZF, the book looks forward to more subtle bases in categorical type theory and the machine representation of mathematics. Each idea is illustrated by wide-ranging examples, and followed critically along its natural path, transcending disciplinary boundaries between universal algebra, type theory, category theory, set theory and programming. The first three chapters will be essential reading for the design of courses in discrete mathematics and reasoning, especially for the ``box method'' of proof taught successfully to first year informatics students. Chapters 4, 5 and 7 are an introduction to categorical logic. Between the formal languages translations are provided which are fluent, teaching the student how to write vernacular proofs which are sound in formal logics. Chapter 6 is a new approach to term algebras, induction and recursion, which have hitherto only been treated either naively or with set theory. The final chapter proves in detail the equivalence of types and categories, in particular between generalised algebraic theories and categories with display maps. Students and teachers of computing, mathematics and philosophy will find this book both readable and of lasting value as a reference work. The titles of the chapters are as follows, though as they are not very informative, I have put a list of the section and subsection names on the web at http://www.dcs.qmw.ac.uk/~pt/book/index.html 1. First Order Reasoning 5. Limits and Colimits 2. Types and Induction 6. Algebras of Terms and Proofs 3. Posets and Lattices 7. Adjunctions 4. Cartesian Closed Categories 8. Dependent Types The whole book is 500 pages, which I suspect is rather more than any of you will be able to digest, but I would like chapters 2-8 to get some attention, as well as Section 1.1! For this reason I would like to invite you to choose a *chapter* to read, and email me with your postal address. A well annotated chapter gets a draft copy of the whole book. Please try to return your comments by email or post by mid-January; of course this deadline will slip, but it is a vain attempt at self-discipline. Finally, several people have asked me what "position" I have at QMW. The answer is -- a desk, courtesy of Edmund Robinson. No more, no less. I have an Advanced Research Fellowship until the end of September 1997, am paid by the EPSRC (research council) and am still employed by Imperial College. Paul Taylor 13-Dec-1996 00:16:03 -0300,1541;000000000000-00000000 Received: by mailserv.mta.ca; id AA19204; Fri, 13 Dec 1996 00:15:04 -0400 Date: Fri, 13 Dec 1996 00:15:04 -0400 (AST) From: categories To: categories Subject: chapters of my book Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Date: Thu, 12 Dec 1996 21:47:27 GMT From: Paul Taylor I would like to thank the almost thirty people who have offered to read chapters of my book over the vacation. I believe I have written back to everyone, but IF YOU HAVEN'T HAD AN EMAIL ACKOWLEDGEMENT PLEASE WRITE AGAIN. Unfortunately there have been some problems with out mail delivery system, and some important incoming messages have been lost recently. Things are in chaos at the moment because the Department of Computer Science at QMW is moving from one building to another (the postal address and phone numbers stay the same though). It seems that I overdid it in diverting people away from the earlier chapters to the later ones. There hasn't been much take-up on chapters 1 and 2. The second has been (re)written quite recently. If, like me, you believe that so-called "discrete math" is a mass of confused dogma and desparately in need of reform then chapter 2 will give you something to think about (I don't claim to have effected the reform). The web address for more information is http://www.dcs.qmw.ac.uk/~pt/book/index.html Paul Taylor 13-Dec-1996 16:07:13 -0300,2326;000000000001-00000000 Received: by mailserv.mta.ca; id AA12973; Fri, 13 Dec 1996 16:06:23 -0400 Date: Fri, 13 Dec 1996 16:06:23 -0400 (AST) From: categories To: categories Subject: preprint available Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Date: Fri, 13 Dec 1996 10:46:36 +0100 From: Marco Grandis The following hard-copy preprint is available M. Grandis, Variables and weak limits in categories and homotopy categories, Dip. Mat. Univ. Genova, Preprint 329 (1996). Regards, Marco Grandis Abstract. Variables in a category X are introduced, extending subobjects. Variables are well related to weak limits, as subobjects to limits; and they may be viewed as a replacement of subobjects in categories just possessing weak limits, typically homotopy categories. From a formal point of view, the Freyd embedding X --> FrX (introduced to embed the stable homotopy category of spaces into an abelian category, in Freyd, "Stable homotopy", La Jolla) allows one to reduce variables in X to distinguished subobjects in FrX (with respect to a canonical factorisation structure) and, loosely speaking, weak limits to limits. Thus, "homotopy variables" for a space X, with respect to the homotopy category HoTop, form a lattice Fib(X) of types of fibrations over X, which can be identified to the lattice of distinguished subobjects of X in Fr(HoTop). Concretely, we give here various instances of the classification of variables within finitely generated abelian groups, as a first step towards a general classification of such variables, and of homotopy variables for spaces having the homotopy type of a CW-complex. [From the Introduction: A (categorical) *variable* of an object A is an equivalence-class of morphisms with values in A, where x: X -- > A corresponds to y: Y -- > A iff there exist maps u, v such that x = yu, y = xv. Among them, the *monic* variables (having some representative which is so) can be identified to subobjects. As a motivation for the name, a morphism x: X --> A is commonly viewed within category theory as a "variable element" of A, parametrised over X.] 14-Dec-1996 16:33:44 -0300,674;000000000000-00000000 Received: by mailserv.mta.ca; id AA29449; Sat, 14 Dec 1996 16:33:03 -0400 Date: Sat, 14 Dec 1996 16:33:02 -0400 (AST) From: categories To: categories Subject: Cartesian Closed arrow categories Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Date: Fri, 13 Dec 96 16:01:11 EST From: Kathryn_Van_Stone@POP.CS.CMU.EDU Does anyone what conditions are necessary in a category C for its arrow category to be Cartesian Closed. I have come up with a solution, but it is rather mechanical. Thanks, Kathy Van Stone kvs@cs.cmu.edu 15-Dec-1996 11:02:01 -0300,1414;000000000000-00000000 Received: by mailserv.mta.ca; id AA27943; Sun, 15 Dec 1996 11:01:27 -0400 Date: Sun, 15 Dec 1996 11:01:27 -0400 (AST) From: categories To: categories Subject: Cartesian Closed arrow categories Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Date: Mon, 16 Dec 1996 11:09:14 +1100 From: Ross Street Question from Kathy Van Stone: >Does anyone what conditions are necessary in a category C for its >arrow category to be Cartesian Closed. Let's agree that a category A is cartesian closed when it has finite products and each functor a x - : A --> A has a right adjoint [a,-]. By examining the various adjunctions between A and the arrow category A' of A, or otherwise, we see that: A' is cartesian closed if and only if A is cartesian closed and, for all arrows f : a --> b, g : c --> d in A, the arrows [f,1] : [b,d] --> [a,d], [1,g] : [a,c] --> [a,d] admit a pullback P(f,g) in A. The internal hom of f, g as objects of A' is then P(f,g) --> [b,d]. Perhaps this is the mechanical answer you had already. Best regards, Ross PS: Our federal minister who has slashed funding to Australian universities is Amanda Vanstone. Would that she were interested in CCCs. 15-Dec-1996 11:02:22 -0300,1414;000000000000-00000000 Received: by mailserv.mta.ca; id AA28115; Sun, 15 Dec 1996 11:01:51 -0400 Date: Sun, 15 Dec 1996 11:01:51 -0400 (AST) From: categories To: categories Subject: Cartesian Closed arrow categories Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Date: Mon, 16 Dec 1996 11:09:14 +1100 From: Ross Street Question from Kathy Van Stone: >Does anyone what conditions are necessary in a category C for its >arrow category to be Cartesian Closed. Let's agree that a category A is cartesian closed when it has finite products and each functor a x - : A --> A has a right adjoint [a,-]. By examining the various adjunctions between A and the arrow category A' of A, or otherwise, we see that: A' is cartesian closed if and only if A is cartesian closed and, for all arrows f : a --> b, g : c --> d in A, the arrows [f,1] : [b,d] --> [a,d], [1,g] : [a,c] --> [a,d] admit a pullback P(f,g) in A. The internal hom of f, g as objects of A' is then P(f,g) --> [b,d]. Perhaps this is the mechanical answer you had already. Best regards, Ross PS: Our federal minister who has slashed funding to Australian universities is Amanda Vanstone. Would that she were interested in CCCs. 15-Dec-1996 11:02:28 -0300,801;000000000000-00000000 Received: by mailserv.mta.ca; id AA27814; Sun, 15 Dec 1996 11:02:23 -0400 Date: Sun, 15 Dec 1996 11:02:23 -0400 (AST) From: categories To: categories Subject: Re: Cartesian Closed arrow categories Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Date: Sun, 15 Dec 96 14:53 GMT From: Dr. P.T. Johnstone Assuming that by "arrow category" you mean the functor category [2,C], this is a special case of the question of when a category obtained by Artin glueing is cartesian closed. This (and related questions) was dealt with in my joint paper with Aurelio Carboni (Math. Struct. Comp. Sci. 5 (1995), 441--459). Peter Johnstone 17-Dec-1996 10:41:08 -0300,1181;000000000000-00000000 Received: by mailserv.mta.ca; id AA10259; Tue, 17 Dec 1996 10:38:33 -0400 Date: Tue, 17 Dec 1996 10:38:33 -0400 (AST) From: categories To: categories Subject: Preliminary PSSL Announcement Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Date: Tue, 17 Dec 1996 14:47:30 +0100 (MET) From: koslowj@iti.cs.tu-bs.de PRELIMINARY ANNOUNCEMENT Dear colleagues, A meeting of the Peripatetic Seminar on Sheaves and Logic will be held in Braunschweig on the weekend of May 10/11. Unless someone sneaks in a meeting during the Winter, it will be no. 63. As usual we welcome talks on category theory, sheaves, logic and related areas. A more detailed first announcement including a registration form and information about accommodation and how to get here will be sent out in February. Email: koslowj@iti.cs.tu-bs.de Postal address: Institut f"ur Theoretische Informatik TU Braunschweig Postfach 3329 D-38023 Braunschweig Germany Happy holidays, and all the best for 1997 Jiri Adamek and J"urgen Koslowski 19-Dec-1996 09:57:31 -0300,1845;000000000001-00000000 Received: by mailserv.mta.ca; id AA01122; Thu, 19 Dec 1996 09:55:35 -0400 Date: Thu, 19 Dec 1996 09:55:35 -0400 (AST) From: categories To: categories Subject: Preliminary PSSL Announcement Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Date: Thu, 19 Dec 1996 11:58:07 +0000 (GMT) From: Ronnie Brown Subject: Preliminary PSSL Announcement PRELIMINARY ANNOUNCEMENT Dear Colleagues, In view of the gap for a PSSL in the winter, we decided to offer one at Bangor: A meeting of the Peripatetic Seminar on Sheaves and Logic will be held in Bangor on the weekend of March1/2. This will be no. 63. As usual we welcome talks on category theory, sheaves, logic and related areas. A more detailed first announcement including a registration form and information about accommodation and how to get here will be sent out in January. Rail travel from airports: Manchester: about 3hr10min Birmingham International: 3hr25min London: 3hr50min from Euston, 1hr from Heathrow or Gatwick to Euston Email: r.brown@bangor.ac.uk Prof R. Brown |tel direct:+44 1248 382474 School of Mathematics |office: 382475 University of Wales, Bangor | fax: 355881 Dean St. |World Wide Web Bangor |home page: http://www.bangor.ac.uk/~mas010/ Gwynedd LL57 1UT |Symbolic Sculpture and Mathematics United Kingdom |http://www.bangor.ac.uk/~mas007/ 19-Dec-1996 15:57:48 -0300,4886;000000000000-00000000 Received: by mailserv.mta.ca; id AA19122; Thu, 19 Dec 1996 15:57:17 -0400 Date: Thu, 19 Dec 1996 15:57:16 -0400 (AST) From: categories To: categories Subject: ANNOUNCING: Xy-pic version 3.3 released! Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Date: Thu, 19 Dec 1996 20:11:04 +0100 (MET) From: Kristoffer Hogsbro Rose Dear Category Theorists, Please find enclosed a copy of the TRAILER for a new version of Xy-pic. I hope you will find it useful. Sincerely, Kristoffer H. Rose ======================================================================= ANNOUNCING the Xy-pic version 3.3 DIAGRAM TYPESETTING PACKAGE ======================================================================= This is to announce a RELEASE of the DIAGRAM TYPESETTING PACKAGE: Xy-pic 3.3 This is a maintenance release where a few more bugs of the previous major release of Xy-pic 3 (a year ago) have been eliminated and a few things have been added. It is released on December 19, 1996 because this is the fifth anniversary of Xy-pic: the first public release (version 1.40) of Xy-pic was distributed via Usenet on December 19, 1991! Xy-pic is a package for typesetting a variety of graphs and diagrams with TeX. Xy-pic works with most formats (including LaTeX, AMS-LaTeX, AMS-TeX, and plain TeX), in particular Xy-pic is provided as a LaTeX2e `supported package' (following the `CTAN LaTeX2e bundle' standard). Further details on the package are in the README file of the distribution. ----------------------------------------------------------------------- NEWS ----------------------------------------------------------------------- Xy-pic version 3 was a thorough rewrite of the prior major version, version 2 (last version 2 release was release 2.6; several beta-test releases of version 3, numbered 2.7-2.12, were made available to users). However, full backwards compatibility is maintained (except for the unavoidable but fully documented obscure cases). Release 3.3 fixes the following problems with release 3.2: * Now has `outline-only' mode for quick processing of intermediate runs! * Now has special support for in-text one-line diagrams! * Arrows now meet their end-points more precisely when these are round! * Optimised file loading! * Computer Modern and Euler-style tips use the current (LaTeX) font size! * Compiled files are more stable! * PostScript improvements! * 600 dpi fonts included in standard distribution! as well as several minor fixes in code & documentation (all described in the ChangeLog file in the source distribution). Thanks to Joerg Eich, J|rgen Koslowski, Wolfgang Gellerich, and Michel Goossens, for your bug reports! ----------------------------------------------------------------------- AVAILABILITY ----------------------------------------------------------------------- Xy-pic can be retrieved through the World Wide Web Xy-pic `home pages': URL: http://www.brics.dk/~krisrose/Xy-pic.html URL: http://www.mpce.mq.edu.au/~ross/Xy-pic.html as well as by anonymous ftp from CTAN : macros/generic/diagrams/xypic and from the private archives of the authors: ftp.brics.dk : /Staff/krisrose/TeX/ ftp.mpce.mq.edu.au : /pub/maths/TeX/ Check the README file in each location for specifics. ----------------------------------------------------------------------- CREDITS ----------------------------------------------------------------------- Xy-pic version 2 was created by Kristoffer H. Rose, then DIKU, U of Copenhagen, now BRICS, U of Aarhus. The rewrite that has become version 3 is a collaboration with Ross Moore, Macquarie U, Sydney, initiated through a visit to Macquarie (Jan-May 1994 supported by the Australian Research Council, Macquarie University, and using donated DEC equipment). Xy-pic is Copyright (c) 1991-1996 by Kristoffer H. Rose and 1994-1996 by Ross Moore under GNU COPYLEFT which means that you can use the package for any purpose but if you provide the macros or any code derived from them to a third party then you are obliged to include the entire Xy-pic package (full details in the file COPYING). ----------------------------------------------------------------------- This is the end of the announcement. Enjoy Xy-pic! ----------------------------------------------------------------------- Kristoffer Hxgsbro ROSE BRICS Department of Computer Science B3.26, +45 89423193 (fax +45 89423255) University of Aarhus, Ny Munkegade, build. 540, 8000 Erhus C, DENMARK 21-Dec-1996 14:34:55 -0300,1675;000000000001-00000000 Received: by mailserv.mta.ca; id AA06625; Sat, 21 Dec 1996 14:33:48 -0400 Date: Sat, 21 Dec 1996 14:33:48 -0400 (AST) From: categories To: categories Subject: SIC. January 25 in Paris Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Date: Sat, 21 Dec 1996 08:31:50 +0200 From: damphous@univ-tours.fr The following announcement may be of interest for those who might be be in Paris at the end of January. =========================== =========================== Chers Coll\`egues, Le prochain SIC (S\'eminaire Itin\'erant de cat\'egories) aura lieu le samedi 25 janvier de 10:30h \`a 16:30h \`a Jussieu, salle 401 couloir 45-46. Le programme est le suivant~: ---------------------------------------------------------- 10:30 : A. Burroni, Les polygraphes en informatique. 11:30 : A. Fleury, Un exemple d'automate 2-dimensionnel. ----------------------------------------------------------- 12:30 : Pause d\'ejeuner ----------------------------------------------------------- 14:15 : D. Bourn, Nature structurelle du nerf des n-groupo\"\i{}des 15:15 : J. Penon, Approche polygraphique des infini-cat\'egories non strictes. ----------------------------------------------------------- 16:15 : Organisation de la s\'eance suivante qui aura lieu le samedi 22 mars \`a Jussieu. 16:30 : FIN Bien cordialement. Ren\'e GUITART =========================== =========================== 25-Dec-1996 09:03:02 -0300,6071;000000000000-00000000 Received: by mailserv.mta.ca; id AA15049; Wed, 25 Dec 1996 09:01:59 -0400 Date: Wed, 25 Dec 1996 09:01:59 -0400 (AST) From: categories To: categories Subject: TCS Special Issue announcement. Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Date: Tue, 24 Dec 1996 22:27:26 +0000 (GMT) From: David Pym Special Issue of Theoretical Computer Science (TCS) (Editor-in-Chief: M. Nivat) on ******************************************** * Proof-search in Type-theoretic Languages * ******************************************** Guest Editors: Didier Galmiche David Pym CRIN-CNRS & UHP Nancy 1 Queen Mary & Westfield College Nancy, France University of London Algorithmic proof-search is a fundamental enabling technology throughout artificial intelligence and computer science. There is a long history of work in proof-search in a variety of systems of logic, including classical, intuitionistic, relevant, linear and modal systems, at the propositional, first- and higher-order levels. Such work has ranged from the most abstract to the most practical and has employed the full spectrum of logical techniques, from proof theory, model theory and recursion theory. Recently, there has been a great deal of work on proof-search in type-theoretic languages. Such languages are logical frameworks to represent proofs and to formalize connections between proofs and programs. Two recent workshops on "Proof-search in Type-theoretic languages" (Nancy, 1994 and Rutgers University, NJ, 1996) have provide exchanges of ideas and experiences in topics concerned with proof-search in type theory, logical frameworks and their underlying (classical, intuitionistic, linear) logics. Here again, the scope of languages studied and techniques employed has been wide, stretching to include algebraic and categorical methods. From the computational point of view, the type-theoretic component of logical languages, which may involve propositional, first-order, higher-order or polymorphic assignment regimes, introduces significant challenges for both theoreticians and implementors. *************** * TOPICS * *************** Topics of interest include, but are not restricted to: * Natural deduction, sequent calculi systems for type-theoretic languages. Based-on tableaux, matrix or resolution methods for proof-search in type-theoretic languages. * Semantic techniques in proof-search. Search vs. deduction as the basis of logic; consequences for model theory * Theorem proving and program development with type-theoretic languages: concepts, techniques, implementation and experimentation * Logic programming in type-theoretic languages as search-based computation; integration of model-theoretic semantics and imperative aspects of logic programming * Operational semantics and proof theory of search-based computation. Denotational semantics and model theory of search-based computation. * Complexity of search problems in type-theoretic languages; comparisons with non-type-theoretic systems. *************** * SUBMISSIONS * *************** Prospective contributors are warmly invited to contact both of the guest editors (see addresses below) to discuss the suitability of topics and papers. The submissions should satisfay the usual standards of scholarship, originality and high-quality of the TCS journal. * SUBMISSION DEADLINE The submission deadline is May 1, 1997. * SUBMISSION FORMAT Please submit either 4 paper copies or, preferably, a postscript file to both of the addresses given below. * SUBMISSION ADDRESSES Either: Didier Galmiche, CRIN-CNRS & UHP Nancy 1, Batiment LORIA, Campus Scientifique, B.P. 239, 54506 Vandoeuvre-les-Nancy France Didier.Galmiche@loria.fr Tel: +33 (0)3 83 59 20 15 Fax: +33 (0)3 83 41 30 79 URL: http://www.loria.fr/~galmiche or: David Pym, Department of Computer Science, Queen Mary and Westfield College, University of London, Mile End Road, London E1 4NS, England U.K. pym@dcs.qmw.ac.uk Tel: +44 (0)171 975 5237 Fax: +44 (0)181 980 6533 URL: http://www.dcs.qmw.ac.uk/~pym ---------------------------------------------------------------- Please address administrative mail regarding the lambda Prolog mailing list to lprolog-request@cis.upenn.edu. See http://www.cis.upenn.edu/~dale/lProlog.