Constructive Domain Theory as a Branch of Intuitionistic Pointfree Topology

In this paper, the notions of information base and of translation between information bases are introduced; they have a very simple intuitive interpretation and can be taken as an alternative approach to domain theory. Technically, they form a category which is equivalent to the category of Scott domains and approximable mappings. All the definitions and most of the results are inspired by the intuitionistic approach to pointfree topology as developed mainly by Martin-Löf and the first author. As in intuitionistic pointfree topology, constructivity is guaranteed by adopting the framework of Martin-Löf’s intuitionistic type theory, equipped with a few abbreviations which allow to use a standard set theoretic notation. 1991 Mathematics Subject Classification. 03B70, 06B35, 68Q55.