downward closed ==>
closure
1. <programming> In a reduction system, a closure is a data structure
that holds an expression and an environment of variable bindings in which that
expression is to be evaluated. The variables may be local or global. Closures
are used to represent unevaluated expressions when implementing functional
programming languages with lazy evaluation. In a real implementation, both
expression and environment are represented by pointers.
A suspension is a closure which includes a flag to say whether or not it has
been evaluated. The term "thunk" has come to be synonymous with "closure" but
originated outside functional programming.
2. <theory> In domain theory, given a partially ordered set, D and a
subset, X of D, the upward closure of X in D is the union over all x in X of the
sets of all d in D such that x <= d. Thus the upward closure of X in D contains
the elements of X and any greater element of D. A set is "upward closed" if it
is the same as its upward closure, i.e. any d greater than an element is also an
element. The downward closure (or "left closure") is similar but with d <= x. A
downward closed set is one for which any d less than an element is also an
element.
("<=" is written in LaTeX as \subseteq and the upward closure of X in D is
written \uparrow_{D} X).
(19941216)
Nearby terms:
closed set « closed term « Clos network « closure
» closure conversion » Clover » clover key
