# 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.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

## 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).