# 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

Collins Discovery Encyclopedia, 1st edition © HarperCollins Publishers 2005

## 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

McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

## 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.

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).

("<=" is written in LaTeX as \subseteq and the upward closure of X in D is written \uparrow_\D X).

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