Abstract
We introduce a new construction—FS+-domain—and prove that the category withFS+-domains as objects and Scott continuous functions as morphisms is a Cartesian closed category. We obtain that the Plotkin powerdomainPP(L)over anFS-domainLis anFS+-domain.
Highlights
Prove that We obtain tthheatctahteegPolroytkwinithpoFwSe+r-ddoommaaiinnsPaPs(Lo)bojevcetrs and Scott continuous an FS-domain L is an Powerdomains are very important structures in Domain theory, which play an important role in modeling the semantics of nondeterministic programming languages
We have a problem whether the Plotkin powerdomain can be characterized by some special FSdomain
We will show that the Plotkin powerdomain PP(L) over an FS-domain L is an FS+-domain, where the Plotkin powerdomain is the free dcpo-semilattice over a continuous dcpo
Summary
Powerdomains are very important structures in Domain theory, which play an important role in modeling the semantics of nondeterministic programming languages. Recall the definition of FS-domain: a dcpo L is called an FS-domain if idL is approximated directly by a family of finitely separated Scott continuous functions. A dcpo L is called an FS+-domain if it is a +semilattice and there exists a directed family of finitely separated Scott continuous and +-semilattice homomorphisms which can approximate idL. An FS∧-domain is a continuous dcpo ∧semilattice where id is approximated by a directed family of finitely separated Scott continuous functions preserving finite infs. Note that the category with FS+-domains as objects and Scott continuous and +-semilattice homomorphisms as morphisms is not a Cartesian closed category generally, because the evaluation maps do not preserve the finite +operation
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