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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. 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.〔(Free variables in Lisp )〕 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 = ''x''2 + 2''x'' + 1.' or :'There exists ''x'' such that ''x''2 = 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. 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. ==Examples== Before stating a precise definition of free variable and bound variable, the following are some examples that perhaps make these two concepts clearer than the definition would: In the expression : ''n'' is a free variable and ''k'' is a bound variable; consequently the value of this expression depends on the value of ''n'', but there is nothing called ''k'' on which it could depend. In the expression : ''y'' is a free variable and ''x'' is a bound variable; consequently the value of this expression depends on the value of ''y'', but there is nothing called ''x'' on which it could depend. In the expression : ''x'' is a free variable and ''h'' is a bound variable; consequently the value of this expression depends on the value of ''x'', but there is nothing called ''h'' on which it could depend. In the expression : ''z'' is a free variable and ''x'' and ''y'' are bound variables; consequently the logical value of this expression depends on the value of ''z'', but there is nothing called ''x'' or ''y'' on which it could depend. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「free variables and bound variables」の詳細全文を読む スポンサード リンク
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