Difference between revisions 115528829 and 115528830 on dewiki

'''Domain theory''' is a   branch of [[mathematics]] that studies special kinds of [[partially ordered set]]s (posets) commonly called '''domains'''. Consequently, domain theory can be considered as a branch of [[order theory]]. The field has major applications in [[computer science]], where it is used to specify [[denotational semantics]], especially for [[functional programming|functional programming languages]]. Domain theory formalizes the intu(contracted; show full)

One can obtain a number of other interesting special classes of ordered structures that could be suitable as "domains". We already mentioned continuous posets and algebraic posets. More special versions of both are continuous and algebraic [[complete partial order|cpos]]. Adding even further [[completeness (order theory)|completeness properties]] one obtains [[
Lattice_(order)#Continuity_and_algebraicity|continuous lattices]] and [[algebraic lattices]], which are just [[complete lattice]]s with the respective properties. For the algebraic case, one finds broader classes of posets which are still worth studying: historically, the [[Scott domain]]s were the first structures to be studied in domain theory. Still wider classes of domains are constituted by [[SFP-domain]]s, [[L-domain]]s, and [[bifinite domain]]s.

(contracted; show full)[[Category:Domain theory|Domain theory]]
[[Category:Fixed points]]

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[[fr:Théorie des domaines]]
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[[ja:領域理論]]
[[zh:域理论]]