Consistent Hoare powerdomains.
Powerdomains are well known structures in domain theory. The Hoare powerdomain is the free inflationary semilattice over a continuous domain with the continuous Scott join operation. In applications the join operation is often partial, giving so called consistent joins rather than all joins. In that context the authors define the consistent Hoare powerdomain, a free algebra over a continuous domain with Scott continuous consistent joins. Briefly introducing the very few concepts needed for the construction the authors present the consistent Hoare powerdomain as the set \(R\Gamma_C(L)\); the set of nonempty relatively consistent Scott closed sets of a continuous domain \(L\), and show that if \(L\) is algebraic, then so is \(R\Gamma_C(L)\).
scientific article; zbMATH DE number 6369779