Difference between revisions 115528826 and 115528827 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)

If ''f'' is a continuous function on a poset ''D'' then it has a least fixed point, given as the least upper bound of all finite iterations of ''f'' on the least element ''0'': V<sub>n in '''N'''</sub> ''f'' <sup>n</sup>(''0'').


==Generalizations==

*[http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.55.903&rep=rep1&type=pdf Synthetic domain theory]
*[http://homepages.inf.ed.ac.uk/als/Research/topological-domain-theory.html Topological domain theory]⏎
⏎
==See also==
*[[Scott domain]]
*[[Scott information system]]
*[[Type theory]]
*[[Category theory]]

== Literature ==

(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]]