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<theory> (Or "smash sum") In domain theory, the coalesced sum of domains A and B, A (+) B, contains all the non-bottom elements of both domains, tagged to show which part of the sum they come from, and a new bottom element.
D (+) E = { bottom(D(+)E) }
U { (0,d) | d in D, d /= bottom(D) }
U { (1,e) | e in E, e /= bottom(E) }
The bottoms of the constituent domains are coalesced into a
single bottom in the sum. This may be generalised to any
number of domains.
The ordering is
bottom(D(+)E) <= v For all v in D(+)E (i,v1) <= (j,v2) iff i = j & v1 <= v2"<=" is usually written as LaTeX \sqsubseteq and "(+)" as LaTeX \oplus - a "+" in a circle.
(1994-12-22)
Nearby terms: CO2 « Coad/Yourdon « COALA « coalesced sum » Coalition for Networked Information » coarse grain » COAST
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