Relation Algebraic Domain Constructions

Abstract Aiming at a constructive approach to domain theory, the definition of domains with deflations is presented. This class of domains is closed with respect to the common domain constructions. Another concern of this paper is to provide a formal calculus for a uniform algebraic treatment of order theoretic and functional aspects of domain theory. The abstract relation algebra turns out to be an appropriate technical means for the characterization and construction of domains. As partial functions present no problems in relation algebra, domains need not contain an additional ⊥-element and functions between domains are generally not total. Using symmetric quotients the relation algebraic approach is extended to cope with higher order functions.

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