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

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.

Contributors

Pascal Hitzler

Anthony Karel Seda

Conference

Publication date: July 2001

Publication date (Print): July 2001

Pages: 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

DOI: 10.14236/ewic/IWFM2001.6

Copyright statement: © Pascal Hitzler et al. Published by BCS Learning and Development Ltd. 5th Irish Workshop on Formal Methods, Dublin, Ireland

License:

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/

Conference name: 5th Irish Workshop on Formal Methods

Conference acronym: IWFM

Conference number: 5

Conference location: Dublin, Ireland

Conference date: 16-17 July 2001

Conference sponsor: Electronic Workshops in Computing (eWiC)

Conference theme: Irish Workshop on Formal Methods

Product

Product Information: 1477-9358BCS Learning & Development

Self URI (article page): https://www.scienceopen.com/hosted-document?doi=10.14236/ewic/IWFM2001.6

Self URI (journal page): https://ewic.bcs.org/

Categories

Series title: Electronic Workshops in Computing