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Topic: Free variables and bound variables

	Free variables and bound variables: Definition and Links by Encyclopedian.com - All about Free variables and bound ...
		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.
		A free variable is a variable referred to in a function, which is not an argument of the function.
		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.
	www.encyclopedian.com /fr/Free-variable.html (417 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.
	www.wikipedia.org /wiki/Variable (2090 words)

	Free variables and bound variables : Free variable (Site not responding. Last check: 2007-10-21)
		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 isn'thing called x or y on which it could depend.
		A free variable is a variable referred to in a function, which isn't an argument of the function.
		Suppose an ideal man, free be prolonged to several centuries, in the end the natural body not just, and therefore the conclusions it points to are not tenable.
	www.termsdefined.net /fr/free-variable.html (525 words)

	PlanetMath: free and bound variables (Site not responding. Last check: 2007-10-21)
		A variable is a symbol that is supposed to range over the universe of discourse.
		There are two ways in which a variable can occur in a formula: free or bound.
		This is version 10 of free and bound variables, born on 2002-06-02, modified 2004-01-24.
	planetmath.org /encyclopedia/FreeAndBoundVariables.html (390 words)

	cs427: What are free variables? (Site not responding. Last check: 2007-10-21)
		Free variables are those variable which can be any thing i.e.
		The example in lec slide 9 has d (outside the expression) as bound variable because it has been assign the type:'Dog' while d(inside the subexpression (for all c:cathate(d,c)))is free* variable because the d can be any thing in the subexpression.
		More specifically, a variable is bound if the expression defines it with a "for all" or a "there exists".
	wiki.cs.uiuc.edu /cs427/What+are+free+variables%3F (663 words)

	Free and bound variables
		Variables that appear as subscripts to quantifiers are bound and do not exist outside their scope (the portion of the formula in which they appear).
		Bound variables are like local variables to a subroutine or variables over which you are computing definite integrals.
		Variables that are not bound are said to be free.
	vorpal.math.drexel.edu /course/founds/database/node4.html (150 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)

	bound
		\Bound (1996) is an American movie in the crime thriller genre, directed by the Wachowski brothers (of The Matrix fame).
		There are numerous twists in the plot, as he and various other characters become aware that something unusual is going on.
		Along the way, the couple form a strong lesbian relationship, and the film is often cited as one of the few movies where a lesbian couple experience a happy ending.
	www.fact-library.com /bound.html (142 words)

	Math Forum - Ask Dr. Math
		Free mentoring, October 10-23, in the Math Fundamentals Problem of the Week: Victoria in Bloom.
		Date: 01/14/99 at 11:24:14 From: Michael Kane Subject: Free variable definition I am currently reading "An Introduction to Mathematical Logic" by Church (I believe it is put out by The Princeton Press), and I am having trouble with the concept of a free variable.
		Let's call one of those numbers x," now x is a bound variable, because it has been given a meaning that's not true for all x.
	mathforum.org /library/drmath/view/52327.html (461 words)

	April Reference Manual - Functions and procedures (Site not responding. Last check: 2007-10-21)
		The variables that are declared in the equation pattern -- which are effectively the formal parameters of the procedure -- are single assignment or read-only variables.
		As noted above, a free variable is a variable that occurs in a procedure or function that is not bound by that procedure or function.
		This variable is free in the procedure, and is bound by the
	www.ugcs.caltech.edu /info/april/april_11.html (3578 words)

	Quantifiers, Variables, and Environments - slide 4 (Site not responding. Last check: 2007-10-21)
		The names it controls are called the bound variables of the quantifier, and we say "the variables are bound" by the quantifier within its scope.
		Its parameters are the bound variables, and its scope is the body of the lambda expression.
		Bound variables can be renamed by uniformly changing them in the bound variable list and throughout the scope of the controlling quantifier, provided that doing so doesn't change which
	www.swiss.ai.mit.edu /classes/6.001/ST97/JMiller/Mar13Lecture/slide4.htm (101 words)

	Free variables vs. bounded variables (Site not responding. Last check: 2007-10-21)
		Free variable: a variable is free if, given a current partial set of free variables, the variable is not non-differential dependent of any combination of the partial set of current variables.
		Bounded variable: a variable is bounded if, given a current partial set of free variable, exist an algebraic, non-differential equation that can be used to compute the variable based on the values of the current partial set of free variables.
		State variables: once we can define univocally the inner state of our entity only with the information of the current partial set of free variables, we can define that set as a set of free variables.
	www.orcero.org /irbis/md/node8.html (406 words)

	CG: 9.5 Variables
		In effect, the variable Y would first be bound to the value "Martin", then the binding would be broken, and the variable would be rebound to the value "John".
		Variables are terms just like structures and string constants, so you can use a variable anywhere you can use a term.
		A bound variable is a variable that has a value, while a free variable does not yet have a value.
	www.hum.auc.dk /cg/Module_II/1035.html (410 words)

	CG: 6.3 Variables
		For example, the variable L might have the value Romeo, which is an atom.
		A variable is is free is a variable that does not have a value.
		Variables must follow three simply syntax rules, or they are not variables.
	www.hum.auc.dk /cg/Module_II/1143.html (308 words)

	Twelf User's Guide - 2 Lexical Conventions (Site not responding. Last check: 2007-10-21)
		During parsing, identifiers are resolved as reserved identifiers, constants, bound variables, or free variables, following the usual rules of static scoping in lambda-calculi.
		Free variables in a declaration must be uppercase, bound variables and constants may be either uppercase or lowercase identifiers.
		Free uppercase identifiers in declarations represent schematic variables.
	www.cse.psu.edu /~cg522/twelf/doc/html/twelf_2.html (297 words)

	Higher-order logic - Wikipedia, the free encyclopedia
		In mathematics, higher-order logic is distinguished from first-order logic in a number of ways.
		One of these is the type of variables appearing in quantifications; in first-order logic, roughly speaking, it is forbidden to quantify over predicates.
		See second-order logic for systems in which this is permitted.
	www.wikipedia.org /wiki/Higher-order_predicate (231 words)

	FREE VARIABLE
		A variable referred to in a function, which is not an argument of the function.
		In logic, a variable which is not quantified (see quantifier).
		All intellectual property rights in and to the game are owned in the U.S.A and Canada by Hasbro Inc., and throughout the rest of the world by J.W. Spear & Sons Limited of Maidenhead, Berkshire, England, a subsidiary of Mattel Inc. Mattel and Spear are not affiliated with Hasbro.
	www.websters-online-dictionary.org /fr/free+variable.html (701 words)

	Maybe this Explains the Economic Cycle... best Free Variable (Site not responding. Last check: 2007-10-21)
		T, and a free variable of T. We say x is bound in M and free in T. ECR Europe 2003
		Free variable sequent calculi Free variable sequent calculi This is a thesis about free variable sequent calculi for first-order languages without equality.
		Free Variable -- from MathWorld Free Variable -- from MathWorld An occurrence of a variable in a logic formula which is not inside the scope of a quantifier.
	ascot.pl /th/Fourier3/Free-Variable.htm (637 words)

	Introduction to Logic: Level FourTutorials
		In the sentences "$x x is a cow" and ""x x is a cow" the variable "x" is said to be bound by the quantifier.
		In the predicate "x is a cow" it is said to be free: that is, free to be replaced by a designator.
		In the sentences the variable is not free to be replaced by a designator.
	logic.philosophy.ox.ac.uk /tutorial4/Tut4-02.htm (308 words)

	Mathematics 1 (Formal Modeling) -- 2.3.4.4 Free and Bound Variables
		(because a free variable must not be renamed).
		When stating a proposition, we usually operate with closed formulas, since their meaning is independent of any variable assignment.
		Sometimes, it is assumed that all free variables in a formula are universally quantified such that a formula
	cbl.fh-hagenberg.at /~schreine/ws2002/math1/report/index_21.html (137 words)

	Free Variables in set_of/3
		Prolog assumes that variables in a clause are implicitly universally quantified over the whole clause, and variables in a query are implicitly existentially quantified over the whole query.
		Mercury uses a different rule for implicit quantification: variables which do not occur in a clause head are existentially quantified over their closest enclosing scope.
		Notice that this is a logical, as opposed to programming, use of the term "bound variable".
	www.cs.kuleuven.ac.be /~dtai/projects/ALP/newsletter/archive_93_96/net/meta-level/free1.html (667 words)

	Deriving Static Properties of Variables through Syntactic Analysis (Site not responding. Last check: 2007-10-21)
		variable is bound in an expression if it refers to a formal parameter introduced in the expression.
		E is a variable reference and E is the same as x; or
		E is of the form (lambda (y) E'), where y is different from x and x occurs free in E'.
	www.cs.bgu.ac.il /~elhadad/advpro/course2.html (438 words)

	Abstractions
		When Nuprl unfolds some instance lhs-inst of lhs, it first matches lhs-inst against lhs, generating bindings for the free variables of lhs such that if the bindings were applied as a substitution to lhs, one would get back lhs-inst.
		A second-order binding is a binding of a second-order variable to a second-order term .
		However, note that all level-expression variables occurring in level-expression parameters in abstraction definitions are always treated as meta-parameters , so there is no need to make them explicitly meta.
	www.cs.cornell.edu /Info/Projects/NuPrl/manual.with.index/node62.html (1122 words)

	FREE-VARIABLES.html -- ACL2 Version 2.9
		(2) Look for a binding of the free variables of the hypothesis so that the corresponding instance of the hypothesis is known to be true in the current context.
		, where forcing is enabled (see force) then the hypothesis is relieved, but in the split-off goals, all free variables are bound to unusual names that call attention to this odd situation.
		When a rewrite or linear rule has free variables in the hypotheses, the user generally needs to specify whether to consider only the first instance found in steps (2) and (3) above, or instead to consider them all.
	www.cs.utexas.edu /~moore/acl2/v2-9/FREE-VARIABLES.html (1165 words)

	First-Order Logic: bound variables, free variables (Site not responding. Last check: 2007-10-21)
		In fact, the same notions of bound and free variables occur in both situations.
		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.
	cnx.rice.edu /content/m12081/latest (496 words)

	Soar Kernel: production.c Source File
		Any time we need 01028 to mark a set of identifiers and/or variables, we get a new tc_number 01029 by calling this routine, then proceed to mark various ids or vars 01030 by setting the sym->id.tc_num or sym->var.tc_num fields.
		When finished, free the cons cells in id_list and var_list (but 01312 don't call symbol_remove_ref() on the symbols in them).
		But we usually need to make sure the new variables don't 01451 overlap with those already used in a certain production--for instance, 01452 when variablizing a chunk, we don't want to introduce a new variable that 01453 conincides with the name of a variable already in an NCC in the chunk.
	www.eecs.umich.edu /~soar/sitemaker/docs/doxygen/kernel/production_8c-source.html (2843 words)

	Bound and Free Variables
		The first occurrence of x is free, whereas the second and third occurrences of x are bound, namely by the first occurrence of the quantifier
		Generally, all occurences of this variable within the quantification are bound.
		No occurrence of any variable is bound in any atomic formula.
	www.coli.uni-sb.de /cl/projects/milca/courses/coal/xhtml/SEMCON.SEC.FOL.FREEVAR.xhtml (294 words)

	Ryan's Half of the Final Review Session (Site not responding. Last check: 2007-10-21)
		We use the terms free and bound to talk about the relationship between the variables and quantifiers in an FOL sentence.
		A free variable is one that is not in the scope of any quantifier.
		A bound variable is one that IS within the scope of a quantifier.
	logic.stanford.edu /classes/cs157/prev_years/rhoulett/s4.html (109 words)

	Substitution, Free and Bound Variables
		Note that we are speaking of an occurrence of a variable as being bound - a variable can occur both bound and free in a given expression.
		Here FV1 says that the set of free variables of an expression that consists of a single variable is the set consisting of just that variable, while FV2 says that the set of free variables of a constant expression is empty.
		-abstraction is the set of free variables of its body minus the variable bound by the abstraction.
	www.cs.bham.ac.uk /research/poplog/paradigms_lectures/lambda_calculus_html.d/substitution.html (2235 words)

	CT201 Lecture 3: Quantifiers and Assertions
		In particular, a variable declaration only has the scope of the smallest structure to which it belongs, excluding any substructures with more local declarations of the same variable.
		We mark whether variable occurrences are free or bound as follows, connecting occurrences bound by the same quantifier, i.e.
		Notice that every variable symbol is marked as bound or free, including those next to quantifiers.
	www.co.umist.ac.uk /~zeng/ct201/CT201Lec3.htm (403 words)

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