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Re: XFDL and Xptr example

From: Joseph M. Reagle Jr. <reagle@w3.org>
Date: Fri, 10 Sep 1999 17:16:36 -0400
Message-Id: <>
To: "John Boyer" <jboyer@uwi.com>
Cc: "DSig Group" <w3c-ietf-xmldsig@w3.org>
At 13:20 99/09/09 -0700, John Boyer wrote:
 >Document Closure

John, could you please define "document closure"?



From The Free On-line Dictionary of Computing (15Feb98) 

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. there is no d greater
than an element which is not an element. The downward closure (or "left
closure") is similar but with d <= x and a downward closed set is one for
which there is no d less than an element which is not an element. 

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

(16 Dec 1994) 

Joseph Reagle Jr.   
Policy Analyst           mailto:reagle@w3.org
XML-Signature Co-Chair   http://w3.org/People/Reagle/
Received on Friday, 10 September 1999 18:23:01 UTC

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