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      VDM♣ meets LCF: Domain-Theoretic and Topological Aspects of VDM♣

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      5th Irish Workshop on Formal Methods (IWFM)

      Irish Workshop on Formal Methods

      16-17 July 2001

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          Abstract

          We discuss the domain-theoretic and topological content of the operator calculus used in the Irish School of the Vienna Development Method (VDM♣) of formal systems development. Thus, we examine the Scott continuity, or otherwise, of the basic operators used in this calculus when viewed as operators on the domain ( XY) of partial functions mapping X into Y. It turns out that the override, one of the more important of the basic operators, is not Scott continuous, and in order to overcome this problem we introduce another topology, which we call here the strong Cantor topology, by means of the topological tool of convergence classes. Indeed, the strong Cantor topology is the smallest topology which refines the Scott and Lawson topologies and is such that, with respect to it, all the basic operators we consider are continuous. Furthermore, we examine the role of the strong Cantor topology in relation to indexed monoids, both with and without units, and display them as topological monoids in the strong Cantor topology. The totality of our results gives considerable support to the view that the strong Cantor topology is the topology of formal methods.

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          Author and article information

          Contributors
          Conference
          July 2001
          July 2001
          : 1-18
          Affiliations
          Artificial Intelligence Institute

          Dresden University of Technology

          Dresden

          Germany

          www.wv.inf.tu-dresden.de/~pascal/
          Department of Mathematics

          University College Cork

          Cork

          Ireland

          maths.ucc.ie/staff/seda/
          Article
          10.14236/ewic/IWFM2001.6
          © Pascal Hitzler et al. Published by BCS Learning and Development Ltd. 5th Irish Workshop on Formal Methods, Dublin, Ireland

          This work is licensed under a Creative Commons Attribution 4.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

          5th Irish Workshop on Formal Methods
          IWFM
          5
          Dublin, Ireland
          16-17 July 2001
          Electronic Workshops in Computing (eWiC)
          Irish Workshop on Formal Methods
          Product
          Product Information: 1477-9358BCS Learning & Development
          Self URI (journal page): https://ewic.bcs.org/
          Categories
          Electronic Workshops in Computing

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