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.

See also closure, lambda lifting, scope.

free variable

(2)
In logic, a variable which is not quantified (see quantifier).
References in periodicals archive ?
It is clear by now that only a free variable is a real one.
Rule 2: If a free variable is under control, the status of the component set that controls it is regarded as normal.
xr)[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.
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.
1986; Kranz 1987] compiler generates very fast code by having six different closure allocation strategies for different kinds of functions; the MIT scheme compiler [Rozas 1984; Hanson 1990] implements tail-recursive procedure calls as efficiently as most explicit iteration constructs by using special closure representations and calling conventions; the Standard ML of New Jersey compiler (SML/NJ) [Appel and Macqueen 1991; Appel and Shao 1992] represents the return-continuation closure using a set of callee-save registers to achieve closure sharing and fast access to free variable bindings.
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.
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.
With this, customers will be able to fix electricity rates for a maximum 2-year period or a contract free variable tariff.
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.
Although LRLR avoids modifying the head fields of the reused cells, it reinitializes each tail field to be a free variable and then, in the recursive call, rebinds it to contain its original value.