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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.

2. In logic a bound variable is a quantified variable.

See quantifier.

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