free variable

1 definition found

free variable - Free On-line Dictionary of Computing (26 May 2007) :

  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).