closures meaning

• [Computer]
  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).

• The railway is under threat of closure.
• The ring c is called the integral closure of a in b.
• The workers are sitting in against the factory closures.
• These laws have not proved sufficient for closure of the problem.
• We have got all the nurses with us in our fight to stop closures.
• I could not bring myself to accept the absolute closure of the inland sea.
• Receptiveness was regarded as the time between flower opening and closure.
• The closure of the car factory had a knock-on effect on the tyre manufacturers.
• It is a bleak look-out for the coal industry as the number of pit closures increases.
• Any difference between values for successive occupations must be considered as a closure error.

• "closures" meaning in Chinese: [经] 停业
• "closures" meaning in Russian: Замыкания