Consistent Hoare powerdomains

Yuan, Yayan; Kou, Hui

doi:10.1016/j.topol.2014.09.002

Cited by 5 publications

(4 citation statements)

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“…This section is an introduction to the concepts and results about the consistent Hoare powerdomains over domains and dcpos. For more details, refer to [1,2,10]. In this paper, the order relation on each family of sets is the set-theoretic inclusion relation.…”

Section: Preliminariesmentioning

confidence: 99%

“…Definition 2.1. [10] A consistent inflationary semilattice is a dcpo P with a Scott continuous binary partial operator ↑ defined only for consistent pairs of points that satisfies three equations for commutativity x ↑ y = y ↑ x, associativity x ↑ (y ↑ z) = (x ↑ y) ↑ z and idempotency x ↑ x = x together with the inequality x ≤ x ↑ y for x, y, z ∈ P . The free consistent inflationary semilattice over a dcpo P is called the consistent Hoare powerdomain over P and denoted by H c (P ).…”

Section: Preliminariesmentioning

confidence: 99%

“…Theorem 2.2. [10] Let L be a domain. The consistent Hoare powerdomain H c (P ) over L can be realized as RΓ C (L) where ↑ = .…”

Section: Preliminariesmentioning

confidence: 99%

“…The standard construction of a Hoare powerdomain consists all nonempty Scott closed subsets Γ(P ) of the dcpo P , order given by the inclusion relation. In [10], Yuan and Kou introduced a new type of powerdomain, called the consistent Hoare powerdomain. The new powerdomain over a dcpo is a free algebra where the inflationary operator delivers joins only for consistent pairs.…”

Section: Introductionmentioning

confidence: 99%

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A characterization of the consistent Hoare powerdomains over dcpos

Zhang¹,

Li²,

Zhang³

2018

Preprint

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It has been shown that for a dcpo P , the Scott closure of Γ c (P ) in Γ(P ) is a consistent Hoare powerdomain of P , where Γ c (P ) is the family of nonempty, consistent and Scott closed subsets of P , and Γ(P ) is the collection of all nonempty Scott closed subsets of P . In this paper, by introducing the notion of a −existing set, we present a direct characterization of the consistent Hoare powerdomain: the set of all −existing Scott closed subsets of a dcpo P is exactly the consistent Hoare powerdomain of P . We also introduce the concept of an F -Scott closed set over each dcpo-∨ ↑ -semilattice. We prove that the Scott closed set lattice of a dcpo P is isomorphic to the family of all F -Scott closed sets of P 's consistent Hoare powerdomain.

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Section: Preliminariesmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

“…Theorem 2.2. [10] Let L be a domain. The consistent Hoare powerdomain H c (P ) over L can be realized as RΓ C (L) where ↑ = .…”

Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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