Coherence and Consistency in Domains (Extended Outline)

Almost all of the categories normally used as a mathematical foundation for denotational semantics satisfy a condition known as consistent completeness. The goal of this paper is to explore the possibility of using a different condition that of coherence which has its origins in topology and logic. In particular, we concentrate on those posets whose principal ideals are algebraic lattices and whose topologies are coherent. These form a cartesian closed category which has fixed points for domain equations. It is shown that a "universal domain" exists. Since the construction of this domain seems to be of general significance, a categorical treatment is provided and its relationship to other applications discussed. Comments University of Pennsylvania Department of Computer and Information Science Technical Report No. MSCIS-88-20. This technical report is available at ScholarlyCommons: http://repository.upenn.edu/cis_reports/616 COHERENCE AND CONSISTENCY IN DOMAINS (EXTENDED OUTLINE) Carl A. Gunter Achim Jung MS-CIS-88-20 LlNC LAB 106 Department of Computer and Information Science School of Engineering and Applied Science University of Pennsylvania Philadelphia, PA 191 04