(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.