StackOverflow2013

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plurals

PO
primarykey
Id
430451
data
AcceptedAnswerId
0
AnswerCount
0
ClosedDate
CommentCount
0
CommunityOwnedDate
CreationDate
2009-01-10T02:49:32.193
FavoriteCount
0
LastActivityDate
2009-01-10T02:49:32.193
LastEditDate
LastEditorUserId
0
OwnerUserId
3525
ParentId
430324
PostTypeId
2
Score
7
ViewCount
0
LastEditorDisplayName
text
Body
The term "closure" is used an a variety of ways, mostly tracking back to a Mathematical concept of completion, in some sense. <ul> <li>An operator is "closed over" a set of values if applying that operator to values from the set always produces a value from the given set. For example, addition is closed over the integers, but division isn't (4 / 2 is integral, but 5 / 2 isn't). So addition of integers is somehow "complete" in a sense that division isn't.</li> <li>The "transitive" closure of a relation "completes" the relation by following (all possible) multiple applications. In everyday terms, the concept of "is a descendent of" is the transitive closure of the relation "is a child of".</li> <li>A functional "closure" is "completed" by e.g. specifying how the free variables are to be resolved. In the pseudo-code expression: <pre><code>bump = function(x) (x + y) </code></pre> <code>x</code> is the argument to <code>bump</code>, but the definition seems to leave "open" the question of resolving <code>y</code>. On the other hand, if we define: <pre><code>bumper = function(y) (function(x) (x + y)) </code></pre> then invoking <code>bumper</code> returns a function which adds the original argument of <code>bumper</code> to the created function's argument, so that: <pre><code>add3 = bumper(3) </code></pre> is equivalent to defining: <pre><code>add3 = function(x) (x + 3) </code></pre> The nested definition is "closed over" (or completed by) the variables available at the point of its definition.</li> </ul> So, in effect, the uses of "closure" above all have different specific meanings, and at first glance seem unrelated, but there's a subtle underlying relationship.
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PostParentId
1. POClosures and Context Free Grammars
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 PTQuestion
PostTypePostTypeId
1. PTAnswer
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UserOwnerUserId
1. USjoel.neely
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PostsAcceptedAnswerId
1. POClosures and Context Free Grammars
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1. VO
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2. VO
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3. VO
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