partial orderdomain theory, if D is a set of values including the undefined value (bottom) then we can define a partial ordering relation <= on D by
x <= y if x = bottom or x = y.The constructed set D x D contains the very undefined element, (bottom, bottom) and the not so undefined elements, (x, bottom) and (bottom, x). The partial ordering on D x D is then
(x1,y1) <= (x2,y2) if x1 <= x2 and y1 <= y2.The partial ordering on D -> D is defined by
f <= g if f(x) <= g(x) for all x in D.(No f x is more defined than g x.) A lattice is a partial ordering where all finite subsets have a least upper bound and a greatest lower bound. ("<=" is written in LaTeX as \sqsubseteq).
Last updated: 1995-02-03