free variable

For the variables called "dummies" in statistics, see indicator variable. In computer programming, a free variable is a variable referred to in a function that is not a local variable or an argument of that function.In mathematics, and in other disciplines involving formal languages, including mathematical logic and computer science, a free variable is a notation that specifies which places in an expression where substitution may take place. The idea is related to a placeholder (a symbol that will later be replaced by some literal string), or a wildcard character that stands for an unspecified symbol.
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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.
2. In logic, a variable which is not quantified (see quantifier).