# bound variable

## 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.

## 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.

\ 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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