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}.