closure

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closure

1. Politics (in a deliberative body) a procedure by which debate may be halted and an immediate vote taken
2. Geology the vertical distance between the crest of an anticline and the lowest contour that surrounds it
3. Logic the closed sentence formed from a given open sentence by prefixing universal or existential quantifiers to bind all its free variables
4. Maths the smallest closed set containing a given set
5. Psychol the tendency, first noted by Gestalt psychologists, to see an incomplete figure like a circle with a gap in it as more complete than it is

closure

[′klō·zhər]
(civil engineering)
(geology)
The vertical distance between the highest and lowest point on an anticline which is enclosed by contour lines.
(mathematics)
The union of a set and its cluster points; the smallest closed set containing the set.
Property of a mathematical set such that a specified mathematical operation that is applied to elements of the set produces only elements of the same set

closure

(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.

closure

(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).
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