coalesced sum definition 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
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) (i,v1) "LaTeX \sqsubseteq and "(+)" as LaTeX
\oplus - a "+" in a circle.