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.