Math. Struct. in Comp. Science (2015), vol. 25, pp. 1463–1465. c  Cambridge University Press 2014 doi:10.1017/S0960129513000364 First published online 13 November 2014 Preface to the special issue: Computing with infinite data: topological and logical foundations ULRICH BERGER † , VASCO BRATTKA ‡ , VICTOR SELIVANOV § , DIETER SPREEN ¶ and HIDEKI TSUIKI ‖ † Department of Computer Science, Swansea University, Singleton Park, Swansea SA2 8PP, United Kingdom Email: u.berger@swansea.ac.uk ‡ Institute for Theoretical Computer Science, Mathematics and Operations Research, Faculty of Computer Science, Universit¨ at der Bundeswehr M¨ unchen, Werner-Heisenberg-Weg 39, 85577 Neubiberg, Germany, and Department of Mathematics and Applied Mathematics, University of Cape Town, Private Bag X3, Rondebosch 7701, South Africa Email: Vasco.Brattka@cca-net.de § A.P. Ershov Institute of Informatics Systems, Russian Academy of Science, Siberian Branch, Prospekt Lavrentev 6, Novosibirsk, 630090, Russia Email: vseliv@iis.nsk.su ¶ Department of Mathematics, University of Siegen, 57068 Siegen, Germany, and Department of Decision Sciences, University of South Africa, PO Box 392, Pretoria 0003, South Africa Email: spreen@math.uni-siegen.de ‖ Graduate School of Human and Environmental Studies, Kyoto University, Yoshida-nihonmatsu-cho, Sakyo-ku, Kyoto 606-8501, Japan Email: tsuiki@i.h.kyoto-u.ac.jp Received 25 January 2013 This special issue of Mathematical Structures in Computer Science is composed mainly of papers submitted by participants of the Dagstuhl Seminar on Computing with Infinite Data: Topological and Logical Foundations. The workshop took place in the Schloss Dagstuhl - Leibniz Center for Informatics in the first half of October 2011. A major motivation for the research presented in this seminar is the still unsatisfying situation in scientific computing where the current mainstream approach uses program- ming languages that do not possess a sound mathematical semantics. As a result, there is no way to provide formal correctness proofs. The reason is that on the theoretical side, one deals with well-developed analytical theor- ies based on the non-constructive concept of a real number. Implementations, on the other hand, use floating-point realizations of real numbers, which do not have a well-studied mathematical structure. Ways to get out of these problems have been promoted under the slogan ‘Computing with Exact Real Numbers’. Well-developed practical and theoretical bases for exact real number computations and, more generally, computable analysis are provided by Scott’s Domain Theory and Weihrauch’s Type Two Theory of Effectivity. In both theories, real numbers and similar ideal objects are represented by infinite streams of finite objects. In contrast to the theory of computations on finite strings, the https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0960129513000364 Downloaded from https://www.cambridge.org/core. IP address: 192.241.80.236, on 24 Apr 2020 at 10:37:47, subject to the Cambridge Core terms of use, available at