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Free variables and bound variables - Wikipedia, the free ...

That is, free variables become bound, and then in a sense retire from being available as stand-in values for other values in the creation of formulae. ...
http://en.wikipedia.org/wiki/Free_variables_and_bound_variables

Free Variable

Welcome to free-variable.org! This site has been set up by Paul ... Plus, free variable' seems quite apt now that I'm away from the binder of organised ...
http://free-variable.org/

The Free Variable

The breakthroughs in technology come from the smaller companies, David Bamford says. ... The Free Variable © 2010 All Rights Reserved. Free WordPress Themes | Fresh WordPress ...
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Variable (programming) - Wikipedia, the free encyclopedia

The variable can be referenced by identifiers. In contemporary ... See also: Free variables and bound variables. The scope of a variable describes where in a ...
http://en.wikipedia.org/wiki/Variable_(programming)

free variable

free variable is a weblog about interesting trivia related to technology, design, music, media, philosophy, and theology. You should subscribe ...
http://blog.willbenton.com/

free variable from FOLDOC

T, and a free variable of T. We say x is bound in M and free in T. If ... Variables bound at the top level of a program are technically free variables within the ...
http://foldoc.org/free+variable

free variable - Wiktionary

free variable. Definition from Wiktionary, a free dictionary. Jump to: navigation, search ... variable that is not bound to a storage location. Czech: volná ...
http://en.wiktionary.org/wiki/free_variable

Free Variables Calculation in the Term_ds Module

Free variables set of an ordinary term is a union of the free variables of its term_terms ... Free variables set of a (FOVar v) is a singleton set consisting of v. ...
http://metaprl.org/developer-guide/term_ds_free_vars.html

Jeremy Hylton: Inconceivable: locals() and free variables

It works if the variable happens to be free in the text of the function containing the eval, but only then. ... It returns free variables as well as local variables. The name ...
http://jeremyhylton.blogspot.com/2007/02/locals-and-free-variables.html

PlanetMath: free and bound variables

free and bound variables. In the entry first-order language, I have mentioned the use of variables without mentioning what variables really are. ...
http://planetmath.org/encyclopedia/BoundVariable.html

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Q.	How do you use a C++ program to execute another program with a parameter/variable?	Related Search: Programming & Design
	I need a program to execute a simulation program a specific number of times. Each time the simulation should be slightly different, so I created a variable that makes the appropriate changes. How can I make a program both run the simulation AND specify the parameter? I can also change the simulation if I have to. Actually, the whole reason I have to do this is because the simulation can't free all of its memory unless it closes. Instead, is there a way to free ALL memory except for the variable and start over? That would have the same effect. Thanks! Well actually, I didn't write the code to start with, I'm just working with it. And the person who wrote it has disappeared off the face of the earth. but how DO you call a program with arguments? That's what I can't figure out. What's the actual procedure? By the way, I'm using visual c++ on windows (as foolish as it is)
A.	- How can I make a program both run the simulation AND specify the parameter? - Take advantage of the command line arguments. That is, when calling a program, you can also give it arguments. These arguments are accessible from main's definition (int main (int argc, char argv[]) ). - Actually, the whole reason I have to do this is because the simulation can't free* all of its memory unless it closes. - Which suggests really bad code and program design. So to deal with bad code and inefficiencies, your idea is to repeatedly open and close the program, another layer of inefficiency. Does this sound OK to you? - Instead, is there a way to free ALL memory except for the variable and start over? - The big question is, how is this memory being allocated in the first place. And why are you unable to control when it is deallocated? EDIT: Well, as I said, the big, ugly hack here is to use command line arguments that you can pass into a program. So if you have a third party program to control, create a controlling program that repeatedly calls it, modifying the arguments as needed. Calling the commands is OS specific, and you haven't mentioned which one you are on. In any case, Linux has a set of commands to spawn other processes, as does the Windows API (Look at CreateProcess in MSDN). You'll have to Google to find out what works on your OS. My points about this being inefficient still remain. But it's an option. The other one is to refactor the code and clean it up so memory isn't leaking everywhere. Generally speaking, if you see a lot of new and delete left and right, without any sense of good memory management, it's a lot of terrible code. I don't know what you're working with, so you'll have to make a few judgement calls and see whether a hack cuts it or something more involved is worth it.

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In mathematics, and in other disciplines involving formal languages, including mathematical logic and computer science, a free variable is a notation that specifies places in an expression where substitution may take place. The idea is related to a placeholder (a symbol that will later be replaced by some literal string), or a wildcard character that stands for an unspecified symbol.

The variable x becomes a bound variable, for example, when we write

'For all x, (x + 1)² = x² + 2x + 1.'

'There exists x such that x² = 2.'

In either of these propositions, it does not matter logically whether we use x or some other letter. However, it could be confusing to use the same letter again elsewhere in some compound proposition. That is, free variables become bound, and then in a sense retire from being available as stand-in values for other values in the creation of formulae.

In computer programming, a free variable is a variable referred to in a function that is not a local variable or an argument of that function.^[1] An upvalue is a free variable that has been bound (closed over) with a closure. Note that variable "freeness" only applies in lexical scoping, There's no distinction when using dynamic scope. That's also why there are no closures in dynamic scope.

The term "dummy variable" is also sometimes used for a bound variable (more often in general mathematics than in computer science), but that use creates an ambiguity with the definition of dummy variables in regression analysis.

1 Examples
- 1.1 Variable-binding operators
2 Formal explanation
- 2.1 Function expressions
3 Natural language
4 See also
5 References

[edit] Examples

Before stating a precise definition of free variable and bound variable, the following are some examples that perhaps make these two concepts clearer than the definition would:

In the expression

$\sum_{k=1}^{10} f(k,n),$

n is a free variable and k is a bound variable; consequently the value of this expression depends on the value of n, but there is nothing called k on which it could depend.

In the expression

$\int_0^\infty x^{y-1} e^{-x}\,dx,$

y is a free variable and x is a bound variable; consequently the value of this expression depends on the value of y, but there is nothing called x on which it could depend.

In the expression

$\lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h},$

x is a free variable and h is a bound variable; consequently the value of this expression depends on the value of x, but there is nothing called h on which it could depend.

In the expression

$\forall x\ \exists y\ \varphi(x,y,z),$

z is a free variable and x and y are bound variables; consequently the logical value of this expression depends on the value of z, but there is nothing called x or y on which it could depend.

[edit] Variable-binding operators

The following

$\sum_{x\in S} \quad\quad \prod_{x\in S} \quad\quad \int_0^\infty\cdots\,dx \quad\quad \lim_{x\to 0} \quad\quad \forall x \quad\quad \exists x \quad\quad \psi x$

are variable-binding operators. Each of them binds the variable x.

Note that many of these are operators which act on functions of the bound variable. In more complicated contexts, such notations can become awkward and confusing. It can be useful to switch to notations which make the binding explicit, such as

$\sum_{1 \, \ldots \, 10} \left( k \mapsto f(k,n) \right)$

for sums or

$D \left( x \mapsto x^2 + 2x + 1 \right) \,$

for differentiation.

[edit] Formal explanation

Tree summarizing the syntax of the expression $\forall x\, (\exists y\, A(x) \vee B(z))$

Variable-binding mechanisms occur in different contexts in mathematics, logic and computer science but in all cases they are purely syntactic properties of expressions and variables in them. For this section we can summarize syntax by identifying an expression with a tree whose leaf nodes are variables, constants, function constants or predicate constants and whose non-leaf nodes are logical operators. This expression can then be determined by doing an inorder traversal of the tree. Variable-binding operators are logical operators that occur in almost every formal language. Indeed languages which do not have them are either extremely inexpressive or extremely difficult to use. A binding operator Q takes two arguments: a variable v and an expression P, and when applied to its arguments produces a new expression Q(v, P). The meaning of binding operators is supplied by the semantics of the language and does not concern us here.

Variable binding relates three things: a variable v, a location a for that variable in an expression and a non-leaf node n of the form Q(v, P). Note: we define a location in an expression as a leaf node in the syntax tree. Variable binding occurs when that location is below the node n.

In the lambda calculus, x is a bound variable in the term M = λ x . T, and a free variable of T. We say x is bound in M and free in T. If T contains a subterm λ x . U then x is rebound in this term. This nested, inner binding of x is said to "shadow" the outer binding. Occurrences of x in U are free occurrences of the new x.

Variables bound at the top level of a program are technically free variables within the terms to which they are bound but are often treated specially because they can be compiled as fixed addresses. Similarly, an identifier bound to a recursive function is also technically a free variable within its own body but is treated specially.

A closed term is one containing no free variables.

[edit] Function expressions

To give an example from mathematics, consider an expression which defines a function

$f = \left[ (x_1, \ldots , x_n) \mapsto \operatorname{t} \right]$

where t is an expression. t may contain some, all or none of the x₁, ..., x_n and it may contain other variables. In this case we say that function definition binds the variables x₁, ..., x_n.

In this manner, function definition expressions of the kind shown above can be thought of as the variable binding operator, analogous to the lambda expressions of lambda calculus. Other binding operators, like the summation sign, can be thought of as higher-order functions applying to a function. So, for example, the expression

$\sum_{x \in \mathbb{A}}{x^2}$

could be treated as a notation for

$\sum_{\mathbb{A}}{(x \mapsto x^2)}$

where $\sum_{\mathbb{S}}{f}$ is an operator with two parameters—a one-parameter function, and a set to evaluate that function over. The other operators listed above can be expressed in similar ways; for example, the universal quantifier $\forall x \in \mathbb{S}\ P(x)$ can be thought of as an operator that evaluates to the logical conjunction of the boolean-valued function P applied over the (possibly infinite) set S.

[edit] Natural language

This section requires expansion.

When analyzed in formal semantics, natural languages can be seen to have free and bound variables. In English, personal pronouns like he, she, they, etc. can act as free variables.

Lisa found her book.

In the sentence above, the pronoun her is a free variable. It may refer to the previously mentioned Lisa or to any other female. In other words, her book could be referring to Lisa's book (an instance of coreference) or to a book that belongs to a different female (e.g. Jane's book). Whoever the referent of her is can be established according the situational (i.e. pragmatic) context. The identity of the referent can be shown using coindexing subscripts where i indicates one referent and j indicates a second referent (different from i). Thus, the sentence Lisa found her book has the following interpretations:

Lisa_i found her_i book. (interpretation #1: her = Lisa)

Lisa_i found her_j book. (interpretation #2: her = female that is not Lisa)

However, reflexive pronouns, such as himself, herself, themselves, etc., and reciprocal pronouns, such as each other, act as bound variables. In a sentence like the following:

Jane hurt herself.

the reflexive herself can only refer to the previously mentioned antecedent Jane. It can never refer to a different female person. In other words, the person being hurt yesterday and the person doing the hurting are both the same person, i.e. Jane. The semantics of this sentence is abstractly: JANE hurt JANE. And it cannot be the case that this sentence could mean JANE hurt LISA. The reflexive herself must refer and can only refer to the previously mentioned Jane. In this sense, the variable herself is bound to the noun Jane that occurs in subject position. Indicating the coindexation, the first interpretation with Jane and herself coindexed is permissible, but the other interpretation where they are not coindexed is ungrammatical (the ungrammatical interpretation is indicated with an asterisk):

Jane_i hurt herself_i. (interpretation #1: herself = Jane)

*Jane_i hurt herself_j. (interpretation #2: herself = a female that is not Jane)

Note that the coreference binding can be represented using a lambda expression as mentioned in the previous Formal explanation section. The sentence with the reflexive could be represented as

((λx(x hurt x))(Jane))

Pronouns can also behave in a different way. In the sentence below

Ashley met her.

the pronoun her can only refer to a female that is not Ashley. This means that it can never have a reflexive meaning equivalent to Ashley met herself. The grammatical and ungrammatical interpretations are:

*Ashley_i met her_i. (interpretation #1: her = Ashley)

Ashley_i met her_j. (interpretation #2: her = a female that is not Ashley)

The first interpretation is impossible, but the second interpretation is grammatical (and in this case, is the only interpretation).

Thus, it can be seen that reflexives and reciprocals are bound variables (known technically as anaphors) while true pronouns can be free variables in some grammatical structures or variables that cannot be bound in other grammatical structures.

The binding phenomena found in natural languages was particularly important to the syntactic theory Government and binding theory (see also: Binding (linguistics)).

[edit] See also

[edit] References

A small part of this article was originally based on material from the Free On-line Dictionary of Computing and is used with permission under the GFDL. Most of what now appears here is the result of later editing.

^ Free variables in Lisp

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