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From The Free On-line Dictionary of Computing (05 January 2017) [foldoc]:
coalesced sum
smash sum
(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)