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1 definition found
 for domain theory
From The Free On-line Dictionary of Computing (18 March 2015) :

  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)
  

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