Revision as of 18:03, 24 November 2005 edit CarlHewitt (talk \| contribs) 5,700 edits →Fixed point semantics: Computational domains ← Previous edit		Revision as of 18:05, 24 November 2005 edit undo CarlHewitt (talk \| contribs) 5,700 edits m →Fixed point semantics Next edit →
Line 12: Computational domains have the following properties: #''Limits exist.'' 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. #''Finite elements are countable.'' anAn element <tt>x</tt> is finite (also called isolated in the ___domain literature) if and only if whenever <tt>A</tt> is directed, <tt>∨A</tt> exists and <tt>x≤∨A</tt>, there exists <tt>a∈A</tt> with <tt>x≤a</tt>. In other words, <tt>x</tt> is finite if one must go through <tt>x</tt> in order to get up to or above <tt>x</tt> via the limit process. #''Every element is the least upper bound of a countable increasing sequence of finite elements.''

Denotational semantics: Difference between revisions