LOWER BAG DOMAINS

Article type: Research Article

Authors: Heckmann, Reinhold

Affiliations: FB 14 – Informatik, Universität des Saarlandes, Postfach 151150, D-66041 Saarbrücken, Germany, e-mail: heckmann@cs.uni-sb.de

Abstract: Two lower bag domain constructions are introduced: the initial construction which gives free lower monoids, and the final construction which is defined explicitly in terms of second order functions. The latter is analyzed closely. For sober dcpo's, the elements of the final lower bag domains can be described concretely as bags. For continuous domains, initial and final lower bag domains coincide. They are continuous again and can be described via a basis which is constructed from a basis of the argument domain. The lower bag domain construction preserves algebraicity and the properties I and M, but does not preserve bounded completeness, property L, or bifiniteness.

DOI: 10.3233/FI-1995-2433

Journal: Fundamenta Informaticae, vol. 24, no. 3, pp. 259-281, 1995