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 orderedset, 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)