Difference between revisions 115528851 and 115528852 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 intuitive ideas of approximation and convergence in a very general way and has close relations to [[topology]]. An alt blah blah blah blah ernative important approach to denotational semantics in computer science is that of [[metric space]]s.

== Motivation and intuition ==

The primary motivation for the study of domains, which was initiated by [[Dana Scott]] in the late 1960s, was the search for a [[denotational semantics]] of the [[lambda calculus]]. In this blah formalism, one considers "functions" specified by certain terms in the language. In a purely [[syntax|syntactic]] way, one can go from simple functions to functions that take other functions as their input arguments. Using again just the syntactic transformations available in this formalism, one can obtain so called [[fixed point combinator]]s (the best-known of which is the [[Y combinator]]); these, by definition, have the property that ''f''('''Y''&#x(contracted; show full)[[Category:Domain theory]]
[[Category:Fixed points (mathematics)]]

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