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powerdomain
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powerdomain : FOLDOC
powerdomain
The powerdomain of a domain D is a domain containing some of the {subsets} of D. Due to the asymmetry condition in the definition of a {partial order} (and therefore of a domain) the powerdomain cannot contain all the subsets of D. This is because there may be different sets X and Y such that X <= Y and Y <= X which, by the asymmetry condition would have to be considered equal.
There are at least three possible orderings of the subsets of a powerdomain:
Egli-Milner:
X <= Y iff for all x in X, exists y in Y: x <= y
and for all y in Y, exists x in X: x <= y

("The other domain always contains a related element").
Hoare or Partial Correctness or Safety:
X <= Y iff for all x in X, exists y in Y: x <= y

("The bigger domain always contains a bigger element").
Smyth or Total Correctness or Liveness:
X <= Y iff for all y in Y, exists x in X: x <= y

("The smaller domain always contains a smaller element").
If a powerdomain represents the re


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