# free variable

## free variable

[¦frē ′ver·ē·ə·bəl]
(mathematics)
In logic, a variable that has an occurrence which is not within the scope of a quantifier and thus can be replaced by a constant.

## free variable

(1)
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 . T, and a free variable of T. We say x is bound in M and free in T. If T contains a subterm \ 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.

## free variable

(2)
In logic, a variable which is not quantified (see quantifier).
References in periodicals archive ?
02 contract notice (below ojeu threshold or call offs of any value): The School of Chemistry is seeking to enhance its research and teaching activity through the acquisition of a Cryogen Free Variable Temperature Cryostat.
It is clear by now that only a free variable is a real one.
Consequently, we have that for any formula [phi] [member of] L and a particular operator [exists.sub.n] uniquely determined by the position of the existentially quantified variable in the tuple of free variables in [phi] (otherwise n=0 if this quantified variable is not a free variable in 0), I(([there exists]x)([phi]) = [exists.sub.n] (I(([phi])).
* Rule 2: If a free variable is under control, the status of the component set that controls it is regarded as normal.
With respect to the query evaluation, we denote B [??] [phi]([x.sub.1],...,[x.sub.r])[[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]], the fact that the formula [phi] evaluates to true, when interpreted by the structure B, with the element [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] assigned to the free variable [x.sub.j], for 1 [less than or equal to][s.sub.j][less than or equal to]n, 1[less than or equal to]j[less than or equal to]r.
The predication of the manner phrase kuai with such a propositional sentential subject will violate the SRMP, as the sentential subject ta bu pao does not contain any free variable, let alone a free event or situation variable required by the predicate kuai.
This is not always desirable because (1) there are only a limited number of registers on the target machine, and (2) allocating all free variables in registers can add pressures to functions that have f as a free variable.
Turning to the invariance proposition, the coefficient on the FREE variable is positive but insignificant.
Though the necessity of identity does not carry over to descriptions, it does carry over to collections: Marcus distinguishes sharply, as should we all, between 'assortments', which are given by their members, and 'classes', which are given by abstraction from formulas with a free variable. An assortment has its members necessarily, and assortments are, if equal, necessarily so, but the same does not hold of classes.
As is well-known, every decidable set (of formulae) is representable in arithmetic, i.e., if X is a decidable set (of formulae), there is a formula, [phi], of one free variable such that: if [alpha] [element of] X then [phi](<[alpha]>) [element of] N if [alpha] [not an element of] X then [logical not][phi](<[alpha]>) [element of] N (where <[alpha]> is the numeral of the code of [alpha]).
A free variable is treated neither as a focus variable nor as a doubtful variable but nevertheless must be included in an estimating equation as dictated by economic theory, e.g., price in a demand equation.
Leeds Building Society is offering a penalty free variable rate that lasts for the full term of the mortgage and has very low set-up costs.

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