bound variable definition

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.

(01 Apr 2006)