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}.
2. In {logic}, a variable which is not quantified (see
{quantifier}).