closure

n 1: approaching a particular destination; a coming closer; a

narrowing of a gap; "the ship's rapid rate of closing

gave them little time to avoid a collision" [syn: {closing}]

2: a rule for ending debate in a deliberative body [syn: {cloture},

{gag rule}]

3: an obstruction in a pipe or tube; "we had to call a plumber

to clear out the blockage in the drainpipe" [syn: {blockage},

{block}, {occlusion}, {stop}, {stoppage}]

4: the act of blocking [syn: {blockage}, {occlusion}]

5: termination of operations [syn: {closedown}, {closing}, {shutdown}]

v : terminate and take a vote; "Closure a debate" [syn: {cloture}]

closure

1. 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. 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).

(1994-12-16)