meaning of coalesced sum

1. coalesced sum 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 = bottomD+E U 0,d | d in D, d /= bottomD U 1,e | e in E, e /= bottomE 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 bottomD+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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coalesced sum |

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