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The Convex Powerdomain in a Category of Posets Realized By Cpos
 In Proc. Category Theory and Computer Science
, 1995
"... . We construct a powerdomain in a category whose objects are posets of data equipped with a cpo of "intensional" representations of the data, and whose morphisms are those monotonic functions between posets that are "realized" by continuous functions between the associated cpos. ..."
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. We construct a powerdomain in a category whose objects are posets of data equipped with a cpo of "intensional" representations of the data, and whose morphisms are those monotonic functions between posets that are "realized" by continuous functions between the associated cpos. The category of cpos is contained as a full subcategory that is preserved by lifting, sums, products and function spaces. The construction of the powerdomain uses a cpo of binary trees, these being intensional representations of nondeterministic computation. The powerdomain is characterized as the free semilattice in the category. In contrast to the other type constructors, the powerdomain does not preserve the subcategory of cpos. Indeed we show that the powerdomain has interesting computational properties that differ from those of the usual convex powerdomain on cpos. We end by considering the solution of recursive domain equations. The surprise here is that the limitcolimit coincidence fails. Nevertheless, ...
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"... A FullyAbstract Model for the πcalculus This paper provides both a fully abstract (domaintheoretic) model for the πcalculus and a universal (settheoretic) model for the finite πcalculus with respect to strong late bisimulation and congruence. This is done by: considering categorical models, def ..."
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A FullyAbstract Model for the πcalculus This paper provides both a fully abstract (domaintheoretic) model for the πcalculus and a universal (settheoretic) model for the finite πcalculus with respect to strong late bisimulation and congruence. This is done by: considering categorical models, defining a metalanguage for these models, and translating the πcalculus into the metalanguage. A technical novelty of our approach is an abstract proof of full abstraction: The result on full abstraction for the finite πcalculus in the settheoretic model is axiomatically extended to the whole πcalculus with respect to the domaintheoretic interpretation. In this proof, a central role is played by the description of nondeterminism as a free construction and by the equational theory of the metalanguage.