Difference between revisions 115528824 and 115528825 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)

A concept that plays an important role in the theory is the one of a '''[[directed set|directed subset]]''' of a domain, i.e. of a non-empty subset of the order in which each two elements have some [[upper bound]]
 that is an element of this subset. In view of our intuition about domains, this means that every two pieces of information within the directed subset are ''consistently'' extended by some other element in the subset. Hence we can view directed sets as ''consistent specifications'', i.e. as sets of partial results in which no two elements are contradictory. This interpretation can be compared with the notion of a [[sequence]] in [[Mathematical analysis|analysis]], where each element is more specific t(contracted; show full)
[[Category:Domain theory|Domain theory]]
[[Category:Fixed points]]

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