09601295_22-1.qxd:MSC 11/25/11 8:17 PM Page 1 ISSN: 0960-1295 MSCS Mathematical Structures in Computer Science Mathematical Structures MSCSFEBRUARY 2012 VOLUME 22 NUMBER 1 MSCS Mathematical Structures in Computer Science CONTENTS Interpolation for predefined types 1 A journal in the applications of categorical, algebraic ra˘zvan diaconescu and geometric methods in Computer Science Lenses, fibrations and universal translations 25 michael johnson, robert rosebrugh and r. j. wood Bisimulations for non-deterministic labelled Markov processes 43 pedro r. d’argenio, pedro sánchez terraf and nicolás wolovick FEBRUARY 2012 VOLUME 22 NUMBER 1 Relative formal topology: the binary positivity predicate comes first 69 silvio valentini FEBRUARY 2012FEBRUARY VOL Constructing a small category of setoids 103 olov wilander UME 22 NUMBER 1 22 NUMBER UME © Cambridge University Press 2012 Cambridge Journals Online For further information about this journal please go to the journal website at: journals.cambridge.org/msc Downloaded from https://www.cambridge.org/core. IP address: 170.106.33.14, on 27 Sep 2021 at 16:14:41, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0960129511000715 09601295_22-1.qxd:MSC 11/25/11 8:17 PM Page 2 Instructions for contributors Editorial policy EDITOR- IN- CHIEF Mathematical Structures in Computer Science (MSCS) is a journal of theoretical computer science which focuses on the Giuseppe Longo application of ideas from the structural side of mathematics and mathematical logic to computer science. The journal aims to bridge Laboratoire d’Informatique (CNRS) et DI, Ecole Normale Supérieure, 45, Rue D’Ulm, 75005 Paris (France), e-mail: [email protected] the gap between theoretical contributions and software design, publishing original papers or broad surveys with original perspectives in all areas of computing, provided that ideas or results from logic, algebra, geometry, category theory or other associate editors areas of logic and mathematics form a basis for the work. The journal also welcomes applications to computing based on the use of Pierre-Louis Curien Philip J. Scott specific mathematical structures (e.g. topological and order-theoretic structures) as well as on proof-theoretic notions or results. PPS – Case 7014, Université Paris 7, 2 pl. Jussieu, 75251 Paris, Cedex 05, France Department of Mathematics, University of Ottawa, 585 King Edward, Ottawa, In addition, it is interested in contributions in new interdisciplinary fields bridging computer science, quantum physics, e-mail:[email protected] Ontario K1N 9B4, Canada mathematics and information theory. In particular, papers on mathematical formalisms for quantum computation, quantum e-mail:[email protected] information processing and communication will be considered. editorial board The journal will also consider papers on computational modelling of epigenetic phenomena, protein-protein interactions, stochasticity Eugene Asarin Université de Paris VII, France Max Kanovitch Russian Humanities State University, Russia in molecular cascades. Mathematical approaches to System Biology will be welcomed, within the broad framework of post-genomic views of embryogenesis and evolution. Richard Blute University of Ottawa, Canada Stephen Lack University of Western Sydney, Australia The purpose of the journal is to increase the circulation of new very high standard results in fast growing areas which are currently influ- Cristian S. Calude The University of Auckland, New Zealand Mike Mislove Tulane University, USA encing various aspects of actual computing. Indeed, this journal is not meant to be only a ‘theory journal’ but, by choosing as a theme Robin Cockett University of Calgary, Canada Eugenio Moggi Università di Genova, Italy the use of mathematical methods of Computer Science independently of their area of application, it aims to highlight Thierry Coquand Chalmers University of Technology, Göteborg, Sweden Ugo Montanari University of Pisa, Italy connections among different topics and to encourage applications of theoretical contributions. Vincent Danos University of Edinburgh, UK Catuscia Palamidessi Ecole Polytechnique, France In order to promote the use of mathematical methods in computer science, expository and introductory papers are welcome, Rocco De Nicola Universita di Firenze, Italy Prakash Panangaden McGill University, Canada provided that there is a clear connection to computational issues or they investigate mathematical structures whose relevance to Thomas Ehrhard Université Denis Diderot, France Thierry Paul CNRS and Ecole Normale Sup., France computer science is well established. However, these contributions should be directed to the broad audience of computer scientists to which this journal is addressed. Equally, discussions of a methodological or philosophical nature concerning the foundation of Hartmut Ehrig Technische Universität Berlin, Germany Benjamin Pierce University of Pennsylvania, USA Computer Science are of interest for the journal. Martin Escardo University of Birmingham, UK Andy Pitts University of Cambridge, UK Submission of manuscripts Yuxi Fu Shanghai Jiaotong University, China Gordon D. Plotkin University of Edinburgh, UK Papers may be submitted to any member of the Editorial Board. A file .pdf should be sent accompanied by the author’s address, Nicola Gambino Università di Palermo, Italy Barry Sanders University of Calgary, Canada telephone and fax number, and e-mail address. Simon Gay University of Glasgow, UK Robert A. G. Seely McGill University, Montreal, Canada A copy of the paper together with the name of the editor chosen should also be sent to the Editor-in-Chief who will record the Alessandro Giuliani Istituto Superiore Sanità e Università Roma 1, Italy Alex Simpson University of Edinburgh, UK submission. Bob Harper Carnegie Mellon University, USA Colin Stirling University of Edinburgh, UK Submission of a paper is taken to imply that it has not been previously published and that it is not being considered for publication elsewhere. Authors of articles published in the journal assign copyright to Cambridge University Press (with certain rights Masahito Hasegawa Kyoto University, Japan Hebert Wiklicky Imperial College, UK reserved) and you will receive a copyright assignment form for signature on acceptance of your paper. Martin Hyland University of Cambridge, UK Glynn Winskel University of Cambridge, UK The publisher encourages submission of papers written in LaTeX using the MSCS LaTeX style file. The LaTeX 2.09 style file mscs.sty together with a guide to its use mscsguide.tex, or the corresponding LaTeX 2e file mscs.cls are available via anonymous ftp from the © CAMBRIDGE UNIVERSITY PRESS 2012 Cambridge University Press site at ftp.cup.cam.ac.uk in the directories /pub/texarchive/journals/latex/mscs-sty or /pub/texarchive/jour- SUBSCRIPTIONS. MSCS-Mathematical Structures in Computer Science (ISSN: 0960-1295) is published bimonthly in February, nals/latex/mscs-cls. In the directory /pub/texarchive/journals/latex/mscs-sty you will find a concatenated file called mscs.all. This file April, June, August, October and December by Cambridge University Press, The Edinburgh Building, Shaftesbury Road, contains readme.txt, mscs.sty and mscguid.tex. If you Tex mscguid.tex you will get a full set of instructions for using the style file. In Cambridge CB2 8RU, UK/Cambridge University Press, 40 West 20th Street, New York, N.Y. 10011–4211. The subscription price case of difficulties obtaining these files, there is a help-line available via e-mail; please contact [email protected]. While use (excluding VAT) of Volume 22, 2012, which includes print and electronic access, is £530 net (UK), (USA, Canada and Mexico of the MSCS LaTeX style file is preferred, ordinary LaTeX or plain TeX files can also be accepted. US $940). The electronic-only price available to institutional subscribers is £480 (USA, Canada and Mexico US $830). Single On final acceptance of their paper, authors should make accessible to the Editor-in-Chief (downloadable) the LaTeX source parts cost £95 net (USA, Canada and Mexico US $160). Prices include delivery by air. Six parts form a volume. EU subscribers code including all figures (line figures only), a file .pdf and author-defined macro and style files, together with a hard copy (outside the UK) who are not registered for VAT should add VAT at their country’s rate. VAT registered subscribers should produced using the same file. Discs should be in Apple Mac or PC format and will not be returned. The publisher reserves the provide their VAT registration number. Orders, which must be accompanied by payment, may be sent to any bookseller, subscrip- right to typeset any article by conventional means if the author’s TeX code presents problems in production. tion agent or to the publisher: Cambridge University Press, The Edinburgh Building, Shaftesbury Road, Cambridge CB2 8RU, or in Layout of manuscripts the USA, Canada and Mexico to Cambridge University Press, Journals Fulfillment Department, 100 Brook Hill Drive, West Papers should be typewritten in double spacing throughout, on one side of the paper. Please avoid footnotes if possible. Papers should Nyack, New York 10994–2133. Japanese prices for institutions are available from Kinokuniya Company Ltd, P.O. 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