Power Domains As Free Models of Theories of Non-determinism
Domain theorists have come to understand power domains abstractly as free models for theories of non-determinism. Just as the finite-powerset construction is the free semilattice, the powerdomain constructions should be understood abstractly as free models of theories of non-determinism. By changing the theories of non-determinism, different power domains arise.
The abstract characterisation of powerdomains is often the easiest way to work with them, because explicit descriptions are so intricate. (One exception is the Hoare powerdomain, which has a rather straightforward description.)
Read more about this topic: History Of Power Domains
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