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  domain theory
       
           A branch of mathematics introduced by Dana Scott in
          1970 as a mathematical theory of programming languages, and
          for nearly a quarter of a century developed almost exclusively
          in connection with denotational semantics in computer
          science.
       
          In denotational semantics of programming languages, the
          meaning of a program is taken to be an element of a domain.  A
          domain is a mathematical structure consisting of a set of
          values (or "points") and an ordering relation, <= on those
          values.  Domain theory is the study of such structures.
       
          ("<=" is written in LaTeX as \subseteq)
       
          Different domains correspond to the different types of object
          with which a program deals.  In a language containing
          functions, we might have a domain X -> Y which is the set of
          functions from domain X to domain Y with the ordering f <= g
          iff for all x in X, f x <= g x.  In the pure lambda-calculus
          all objects are functions or applications of functions to
          other functions.  To represent the meaning of such programs,
          we must solve the recursive equation over domains,
       
          	D = D -> D
       
          which states that domain D is ({isomorphic to) some function
          space from D to itself.  I.e. it is a fixed point D = F(D)
          for some operator F that takes a domain D to D -> D.  The
          equivalent equation has no non-trivial solution in set
          theory.
       
          There are many definitions of domains, with different
          properties and suitable for different purposes.  One commonly
          used definition is that of Scott domains, often simply called
          domains, which are omega-algebraic, consistently complete
          CPOs.
       
          There are domain-theoretic computational models in other
          branches of mathematics including dynamical systems,
          fractals, measure theory, integration theory,
          probability theory, and stochastic processes.
       
          See also abstract interpretation, bottom, pointed
          domain.
       
          (1999-12-09)
       
       

  domain theory
     n.
     (lb en mathematics) A branch of mathematics that studies special
  kinds of partially ordered sets (posets) commonly called domains.

  domain theory
     n.
     (lb en mathematics) A branch of mathematics that studies special
  kinds of partially ordered sets (posets) commonly called domains.

  domain theory
     n.
     (lb en mathematics) A branch of mathematics that studies special
  kinds of partially ordered sets (posets) commonly called domains.

  domain theory
     n.
     (lb en mathematics) A branch of mathematics that studies special
  kinds of partially ordered sets (posets) commonly called domains.