Explicit Descriptions of Power Domains
Let D be a domain. The lower power domain can be defined by
- P = {closure | Ø∈A⊆D} where
-
-
-
- closure = {d∈D | ∃X⊆D, X directed, d = X, and ∀x∈X ∃a∈A x≤a}.
-
-
In other words, P is the collection of downward-closed subsets of D that are also closed under existing least upper bounds of directed sets in D. Note that while the ordering on P is given by the subset relation, least upper bounds do not in general coincide with unions.
It is important to check which properties of domains are preserved by the power domain constructions. For example, the Hoare powerdomain of an ω-complete domain is again ω-complete.
Read more about this topic: Power Domains
Famous quotes containing the words explicit, descriptions, power and/or domains:
“... the Ovarian Theory of Literature, or, rather, its complement, the Testicular Theory. A recent camp follower ... of this explicit theory is ... Norman Mailer, who has attributed his own gift, and the literary gift in general, solely and directly to the possession of a specific pair of organs. One writes with these organs, Mailer has said ... and I have always wondered with what shade of ink he manages to do it.”
—Cynthia Ozick (b. 1928)
“Our Lamaze instructor . . . assured our class . . . that our cervix muscles would become “naturally numb” as they swelled and stretched, and deep breathing would turn the final explosions of pain into “manageable discomfort.” This descriptions turned out to be as accurate as, say a steward advising passengers aboard the Titanic to prepare for a brisk but bracing swim.”
—Mary Kay Blakely (20th century)
“In night when colours all to black are cast,
Distinction lost, or gone down with the light;
The eye—a watch to inward senses placed,
Not seeing, yet still having power of sight—
Gives vain alarums to the inward sense”
—Fulke Greville (1554–1628)
“I shall be a benefactor if I conquer some realms from the night, if I report to the gazettes anything transpiring about us at that season worthy of their attention,—if I can show men that there is some beauty awake while they are asleep,—if I add to the domains of poetry.”
—Henry David Thoreau (1817–1862)