bound variable

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bound variable

[¦bau̇nd ′ver·ē·ə·bəl]
(mathematics)
In logic, a variable that occurs within the scope of a quantifier, and cannot be replaced by a constant.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

bound variable

(1)
A bound variable or formal argument in a function definition is replaced by the actual argument when the function is applied. In the lambda abstraction

\ x . M

x is the bound variable. However, x is a free variable of the term M when M is considered on its own. M is the scope of the binding of x.

bound variable

(2)
In logic a bound variable is a quantified variable. See quantifier.
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