Source : Free On-Line Dictionary of Computing

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)