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).