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	Free variables and bound variables - Wikipedia, the free encyclopedia
		z is a free variable and x and y are bound variables; consequently the truth-value of this expression depends on the value of z, but there is nothing called x or y on which it could depend.
		In the lambda calculus, x is a bound variable in the term M = λ 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.
	en.wikipedia.org /wiki/Free_variable (773 words)

	Variable - Wikipedia, the free encyclopedia
		Variables are useful in mathematics and computer programming because they allow instructions to be specified in a general way.
		In general, a variable binds an object to a name so that the object could be accessed later, much like a person has a name and people could refer to him by that name.
		Usually, a variable is set to reside in some scope in program code, and entrance and leave of the scope coincides with the beginning and ending of a variable life, respectively.
	en.wikipedia.org /wiki/Variable (2092 words)

	bound variable Computer Encyclopedia Enterprise Resource Directory Complete Guide to Internet (Site not responding. Last check: 2007-11-06)
		A bound variable or {formal argument} in a function definition is replaced by the {actual argument} when the function is applied.
		However, x is a {free variable} of the term M when M is considered on its own.
		In logic a bound variable is a quantified variable.
	www.jaysir.com /computer-encyclopedia/b/bound-variable-computer-terms.htm (77 words)

	Logic terms and concepts : Thomas Alspaugh : UCI
		Free occurrences of the variable in the subformula of the quantification are bound by the quantifier.
		In first-order logic, variables are bound by quantifiers; any variable that is not bound by a quantifier is a free variable whose relation to the objects of the domain is unknown.
		A variable v in a formula F becomes bound if F is a subformula of a quantifier whose paramter is v; otherwise, v is free.
	www.ics.uci.edu /~alspaugh/logic/logicConcepts.html (3603 words)

	Lecture 9 - CS 330
		A variable is bound or occurs bound in an expression if it refers to the formal parameter in the expression.
		If a variable in one block is not visible because it has been redeclared in block nested within that one, we say that that variable creates a hole in the outer scope.
		A lexical address of a variable reference gives the depth of the reference from the block in which the variable was declared and the position of the variable in that declaration.
	courses.cs.byu.edu /cs330/cs330/lectures/lect-09.php (834 words)

	Primitive Expression Types
		An expression consisting of a variable is a variable reference.
		The value of the variable reference is the value to which the variable is bound.
		When the procedure is later called with some actual arguments, the environment in which the lambda expression was evaluated shall be extended by binding the variables in the formal argument list to the corresponding actual argument values, and the body of the lambda expression shall be evaluated in the extended environment.
	www.jclark.com /dsssl/IS/dsssl39.htm (822 words)

	Bound Variables in MathML
		Bound variables are central representational primitives in mathematical languages.
		In fact the handling of bound variables was the main contribution of Frege's treatment of first-order logic that is the basis for the set-theoretic foundation of mathematics.
		A variable is called a [Definition: bound variable] in an expression of the form O x.B[x], if O is a binding operator.
	www.w3.org /TR/2003/NOTE-mathml-bvar-20031110 (2620 words)

	CS242: Vocabulary
		The variable that is not defined in the current scope is looked for in the most recent activation record.
		When an expression e is subtituted for a variable x in another expression lambda y.e', without any renaming of variables, then free occurences of y within e are "captured" (ie, bound) by the binding lambda y.
		To avoid variable capture, all bound variables should be renamed so that their names are different from those of all free variables and all other bound variables.
	www.stanford.edu /class/cs242/readings/vocabulary.html (1468 words)

	[No title]
		In (lambda () ), the occurrence of is a declaration that binds all the occurrences of that variable in , unless some intervening declaration of the same variable occurs.
		A variable x occurs free in an expression E if and only if there is some use of x in E that is not bound by any declaration of x in E.
		We define the scope of a variable declaration to be the text within which references to the variable refer to the declaration.
	www.wiu.edu /mike/spring2k4/cs380/cs380_ch1_p2.html (728 words)

	Matching and Manupulating Facts
		The name of a variable, or variable identifier, is always written by a question mark followed by a symbol that is the name of the variable.
		One common use of variables is to match a value on the LHS and then assert this bound variable on the RHS.
		Variables used in patterns have an important and useful property, which can be stated as follows.
	www.massey.ac.nz /~wlxu/paper472/expsyshm/Tut3.htm (1607 words)

	Friday, February 11
		The x which appears in both of the Maple notations for this integral is equally a ``dummy variable'' (what we call a ``bound variable''); but the second one brings out an important aspect of variable binding constructions generally.
		It is possible to simplify the treatment of bound variables by regarding the construction of functions as the only variable binding operator and all other variable binding operators as operations acting on functions.
		An occurrence of a variable which is not bound is said to be free.
	math.boisestate.edu /~holmes/M387syllabus/node28.html (1055 words)

	Scheme - Expressions
		The value of the variable reference is the value stored in the location to which the variable is bound.
		Semantics: The <variable>s are bound to fresh locations holding undefined values, the <init>s are evaluated in the resulting environment (in some unspecified order), each <variable> is assigned to the result of the corresponding <init>, the <body> is evaluated in the resulting environment, and the value of the last expression in <body> is returned.
		It specifies a set of variables to be bound, how they are to be initialized at the start, and how they are to be updated on each iteration.
	www.cs.cmu.edu /afs/cs/project/ai-repository/ai/html/r4rs/r4rs_6.html (2600 words)

	Revised(5) Scheme - Expressions
		Semantics: The <variable>s are bound to fresh locations holding undefined values, the <init>s are evaluated in the resulting environment (in some unspecified order), each <variable> is assigned to the result of the corresponding <init>, the <body> is evaluated in the resulting environment, and the value(s) of the last expression in <body> is(are) returned.
		" is a variant on the syntax of
		Pattern variables match arbitrary input elements and are used to refer to elements of the input in the template.
	www.cs.iastate.edu /~leavens/ComS342-SICP/html/r5rs_6.html (4027 words)

	Untitled Document (Site not responding. Last check: 2007-11-06)
		In an abstraction lv.T, the variable v is called the formal parameter of the abstraction (or symply, the parameter) and the term T is the body.
		The idea of a bound variable tries to catch the concept of a binding between the parameter of a function and its occurrences in the body of the function.
		A variable occurrence that is not free is said to be a bound occurrence, and the variable is a bound variable in that particular scope.
	www.rivier.edu /faculty/amoreira/web/cs558a/Hands/lambda2.html (1744 words)

	4.3.3 The Matching Algorithm
		If the upper bound is a type variable bound elsewhere in the method's header, checking this upper bound constraint is deferred until the type variable is bound.
		It is illegal for a type variable to be bound more than once in a particular scope, e.g., in a method's list of explicit type parameters and in the types of its formals.
		It is also illegal to use a bound type variable as a parameter of an upper bound type before that type variable has been bound by the matching process.
	www.cs.washington.edu /research/projects/cecil/www/Vortex-Two-Zero/doc-cecil-lang/cecil-spec-90.html (440 words)

	UB CSE305 Notes 6 (Site not responding. Last check: 2007-11-06)
		The static scope of a variable is the block in which it is declared, plus all spatially (lexically) enclosed blocks, except those where it is shadowed by a declaration of another variable with the same name.
		The dynamic scope of a variable is the block in which it is declared, plus all dynamically enclosed blocks, i.e., blocks that are executed while the block in which the variable is declared is still executing.
		A stack-dynamic variable is one that is bound to an address on the stack, which is dynamically (during run-time) allocated for that purpose.
	www.cs.buffalo.edu /~shapiro/Courses/CSE305/notes6.html (3283 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		The SCOPE of a declaration of a variable X is its region, less the regions of any contained declarations of X. Each variable reference is associated with the nearest lexically enclosing declaration of the same name (not the "nearest" one in the text), as in the last example.
		E is a variable reference and E is the same as x; or 2.
		E is of the form (lambda (y) E1), wheee x occurs bound in E1 or x and y are the same variable.
	www.cs.indiana.edu /~chaynes/c311/f96/script2.txt (1413 words)

	Classical Logic
		Variables are also used to express generality, as in the mathematical assertion that for any natural number x, there is a natural number y, such that y>x and y is prime.
		All occurrences of the variable v in θ are bound in ∀v θ and ∃v θ.
		A variable that immediately follows a quantifier (as in "∀x" and "∃y") is neither free nor bound.
	plato.stanford.edu /entries/logic-classical (11934 words)

	A+ Reference: Screen Management Functions
		The object represented by the left argument is bound to that class and the name of the object is returned as the result.
		See "Assignment of Objects Bound to Display Classes" for a discussion of assigning values to objects that are bound to display classes and the refusals and error messages that can occur.
		is a one-element symbol array representing a bound object, that object is displayed on the screen in the format to which it is bound.
	www.aplusdev.org /APlusRefV2_22.html (1983 words)

	[No title]
		Variable x is "free" if it appears outside the scope of any quantifier.
		This is like local variables in programs: they "hide" values for same variable name outside current block.
		- Name of bound variables is meaningless: if A(x) is a formula with free variable x and y is a variable that does not appear anywhere (bound or free) in A(x), then forall x A(x) has exactly the same meaning as forall y A(y) (i.e., the formulas are logically equivalent to each other).
	www.cs.toronto.edu /~fpitt/CSC238/20025/lectures/N05.txt (719 words)

	The SUIF Library - Array Types
		If the bound is an integer expression, it can either be an integer known at compile time, or a SUIF variable symbol representing an integer value to be computed at run time.
		The bounds are evaluated after all sub-expressions of the array access instruction have been evaluated and before the result of the array access instruction itself.
		Symbolic bounds are typically local variables that are assigned once each at the very beginning of a procedure and used only as bounds, so their values have the same scope as the types they are used in.
	suif.stanford.edu /suif/suif1/docs/suif_63.html (727 words)

	[No title]
		Any sequence variable is in fact bound not to a list, but to the // value it represents (it can't be bound to a list of values -- this // is samep, not unifyp).
		If the variable is being bound to another variable (this will // only happen with regular variables; * variables will always be bound // to lists), add the variable to equivalent-bdgs and find the value // for the variable using subst-var.
		If the variable is a star variable and is bound to a list // consisting of another star variable then treat it the same way as // in case 1.
	www.norvig.com /ltd/test/match.dylan (4553 words)

	Variables and Declarations
		Values are bound to variables using value bindings; once a variable is bound to a value, it is bound for life.
		In this respect variables in SML are more akin to variables in mathematics than to variables in languages such as C. Similarly, types may be bound to type variables using type bindings; the type variable so defined stands for the type bound to it and can never stand for any other type.
		The binding of a variable never changes; once bound to a value, it is always bound to that value (within the scope of the binding).
	www-2.cs.cmu.edu /afs/cs/usr/rwh/public/www/introsml/core/decls.htm (1361 words)

	: Class FreeVarSet (Site not responding. Last check: 2007-11-06)
		In addition, variables may be added to the bound Variable set, which acts as an exclusion list for set membership.
		an Enumeration [Variable] of the free Variables in this.
		an Enumeration [Variable] of the bound Variables in this.
	theory.lcs.mit.edu /~mjt/IOA_Toolkit/ioa/il/util/FreeVarSet.html (218 words)

	Rules of Quantification
		Notice that the free variable (or the constant) in the conclusion may appear at more places than the original bound variable appeared in the premise; but the free variable must appear at least in all the places where the original bound variable did.
		Your choice of letter for the substitution must allow these conditions to be satisfied: the newly bound variable must occur in the conclusion everywhere the original free variable occurred in the premise; and the newly bound variable must occur in the conclusion only where the original free variable occurred in the premise.
		Equivalence E, unlike the other three quantification rules, is a replacement rule: it may be used to rewrite a schema which is a premise, or a schema which is merely part of a premise; it may be used from right to left as well as from left to right.
	www.lawrence.edu /fast/BOARDMAW/RUL_QUANT.HTML (1843 words)

	First-Order Logic: bound variables, free variables
		In essence, these are two different variables who simply happy to have the same name, but from context it's clear which one is meant.
		The choice of variable names is arbitrary, except possibly for their mnemonic value.
		So, it is always possible to consistently rename all instances of a bound variable.
	cnx.rice.edu /content/m12081/latest (496 words)

	Free variable - Computing Reference - eLook.org
		A variable referred to in a function, which is not an argument of the function.
		In lambda-calculus, x is a bound variable in the term M = \ x.
		In logic, a variable which is not quantified (see qua
	www.elook.org /computing/free-variable.htm (162 words)

	Guile Reference Manual
		A variable is said to be bound when it is associated with a name in some way, usually a symbol in a module obarray.
		When this happens, the relationship is mutual: the variable is bound to the name (in that module), and the name (in that module) is bound to the variable.
		First-class variables are especially useful for interacting with the current module system (see section 31.3 The Guile module system).
	www.delorie.com /gnu/docs/guile/guile_364.html (257 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		The bound variable f should be replaced with the argument expression Ls.(s s).
		A variable is said to be BOUND to occurrences in the body of a function for which it is the bound variable, provided no other functions within the body introduce the same bound variable, otherwise it is said to be FREE.
		Once we have declared a local variable it is accessable to subsequent blocks (begin/end pairs), and might be viewed as a global variable to these subsequent blocks.
	www.dcs.gla.ac.uk /~pat/ml/lambda/sec-4 (673 words)

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