Free Variable

A Free Variable is a variable in a mathematical function that is free to take on one or more values.

• AKA: Unbound Parameter.
  • …
• Counter-Example(s):
  • a Bound Variable.
• See: Free Model Variable, Free Model Parameter, Mathematical Model.

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References

2011

• (Wikipedia, 2011) ⇒ http://en.wikipedia.org/wiki/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 that specifies places in an expression where substitution may take place. 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.

    The variable x becomes a bound variable, for example, when we write :[math]\displaystyle{ \forall x, (x + 1)^2 = x^2 + 2x + 1. }[/math] or :[math]\displaystyle{ \exists x \text{ such that } x^2 = 2. }[/math] 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.

    In computer programming, a free variable is a variable referred to in a function that is not a local variable or an argument of that function. An upvalue is a free variable that has been bound (closed over) with a closure. Note that variable "freeness" only applies in lexical scoping: there is no distinction, and hence no closures, when using dynamic scope.

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

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