Free variables and bound variables

In mathematics, and in other disciplines involving formal languages, including mathematical logic and computer science, a free variable is a notation (symbol) that specifies places in an expression where substitution may take place and is not a parameter of this or any container expression. Some older books use the terms real variable and apparent variable for free variable and bound variable. 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. In mathematics, and in other disciplines involving formal languages, including mathematical logic and computer science, a free variable is a notation (symbol) that specifies places in an expression where substitution may take place and is not a parameter of this or any container expression. Some older books use the terms real variable and apparent variable for free variable and bound variable. 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. In computer programming, the term free variable refers to variables used in a function that are neither local variables nor parameters of that function. The term non-local variable is often a synonym in this context. A bound variable is a variable that was previously free, but has been bound to a specific value or set of values called domain of discourse or universe. For example, the variable x becomes a bound variable when we write: