Difference between revisions 115528823 and 115528824 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) descriptions of what a domain of computation should be, we can turn to the computations themselves. Clearly, these have to be functions, taking inputs from some computational domain and returning outputs in  some (possibly different) domain. However, one would also expect that the output of a function will contain more information when the information content of the input is increased. Formally, this means that we want a function to be '''[[monotonic]]'''.

When dealing with 
dcpos'''[[complete partial order|dcpos]]''', one might also want computations to be compatible with the formation of limits of a directed set. Formally, this means that, for some function ''f'', the image ''f''(''D'') of a directed set ''D'' (i.e. the set of the images of each element of ''D'') is again directed and has as a least upper bound the image of the least upper bound of ''D''. One could also say that ''f'&#(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]]