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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 ( X → Y ) 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.

            Content

            Author and article information

            Contributors
            Conference
            July 2001
            July 2001
            : 1-18
            Affiliations
            [0001]Artificial Intelligence Institute

            Dresden University of Technology

            Dresden

            Germany

            www.wv.inf.tu-dresden.de/~pascal/
            [0002]Department of Mathematics

            University College Cork

            Cork

            Ireland

            maths.ucc.ie/staff/seda/
            Article
            10.14236/ewic/IWFM2001.6
            5d9aeac7-96b8-4e5e-be71-c517d5c0fbcc
            © 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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