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CarlHewitt (talk | contribs) →Fixed point semantics: information on Denotations |
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==Fixed point semantics==
The denotational theory of computational system semantics is concerned with finding mathematical objects that represent what systems do. The theory makes use of a computational mathematical [[Domain theory|___domain]] <'''Denotations''', ≤>. Examples of such objects are partial functions, sets of states, and [[Actor model|Actor]] event scenarios. The relationship <tt>x≤y</tt> means that <tt>x</tt> can computationally evolve to <tt>y</tt>. If the denotations are partial functions, for example, <tt>f≤g</tt> may mean that <tt>f</tt> agrees with <tt>g</tt> on all values for which <tt>f</tt> is defined. If the denotations are [[Actor model|Actor]] event diagram scenarios, <tt>x≤y</tt> means that
As computation continues, the denotations should become better and have a limit so if we have <tt>∀i∈ω x<sub>i<sub>≤x<sub>i+1<sub> then the [[least upper bound]] <tt>∨<sub>i∈ω</sub> x<sub>i</sub></tt> should exist. The property just stated is called ω-completeness.
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