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Meaning of COALESCED SUM

 
Computing Dictionary
 
 Definition: 

(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
           U 
           U 

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.

 

 

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