coalesced sum

(Or "smash sum") In {domain theory}, the coalesced

sum of {domain}s 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)