Difference between revisions 115528840 and 115528841 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)alculus, in which a genuine (total) function is associated with each lambda term. Such a model would formalize a link between the lambda calculus as a purely syntactic system and the lambda calculus as a notational system for manipulating concrete mathematical functions. The [[Combinator calculus]] is such a model. However, the elements of the Combinator calculus are functions from functions to functions; in order for the elements of a model of the lambda calculus to be of arbitrary domain and range, they 
wcould be limited to beingnot be true functions, only [[partial functions]] only.

Scott got around this difficulty by formalizing a notion of "partial" or "incomplete" information to represent computations that have not yet returned a result. This was modeled by considering, for each domain of computation (e.g. the natural numbers), an additional element that represents an ''undefined'' output, i.e. the "result" of a computation that never ends. In addition, the domain of computation is equipped with an ''ordering relation&#x(contracted; show full)[[Category:Domain theory]]
[[Category:Fixed points]]

[[fa:نظریه دامنه]]
[[fr:Théorie des domaines]]
[[ko:도메인 이론]]
[[ja:領域理論]]
[[zh:域理论]]