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domain theory
(foldoc) | 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, Y which is the set of
functions from domain X to domain Y with the ordering f 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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