\kə͡ʊəlˈɛst sˈʌm], \kəʊəlˈɛst sˈʌm], \k_əʊ_ə_l_ˈɛ_s_t s_ˈʌ_m]\
Definitions of COALESCED SUM
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(Or "smash sum") In domain theory, the coalescedsum of domains A and B, A (+) B, contains all thenon-bottom elements of both domains, tagged to show whichpart 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 asingle bottom in the sum. This may be generalised to anynumber of domains.The ordering isbottom(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 " (+)" asLaTeX \oplus - a "+" in a circle.
By Denis Howe