View source for Free variables and bound variables

In [[mathematics]], and in other disciplines involving [[Formal language|formal languages]], including [[mathematical logic]] and [[computer science]], a '''free variable''' is a [[Mathematical notation|notation]] that specifies places in an [[Expression (mathematics)|expression]] where [[Substitution (logic)|substitution]] may take place.

== Description ==

Some older books use the terms ''real variable'' '''free variable'''  and ''apparent variable'' for ''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.[1] 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. For example, the variable x becomes a bound variable when we write:

    'For all x, (x + 1)2 = x2 + 2x + 1.'

or

    'There exists x such that x2 = 2.'

In either of these propositions, it does not matter logically whether we use x or some other letter. However, it could be confusing to use the same letter again elsewhere in some compound proposition. That is, free variables become bound, and then in a sense retire from being available as stand-in values for other values in the creation of formulae.

== Dummy variable ==

The term "dummy variable" is also sometimes used for a bound variable (more often in general mathematics than in computer science), but that use can create an ambiguity with the definition of dummy variables in [[regression analysis]].

== See also ==

* [[Computer programming]]
* [[Computer science]]
* [[Expression (mathematics)]]
* [[Formal language]]
* [[Mathematical logic]]
* [[Mathematical notation]]
* [[Mathematics]]
* [[Substitution (logic)]]

== External links ==

* [https://en.wikipedia.org/wiki/Free_variables_and_bound_variables Free variables and bound variables] @ Wikipedia