alpha conversion

One of the three rewrite rules of lambda calculus, in which a bound variable of a lambda term is replaced by another variable across its entire scope. So if there is a lambda term of the form (λx.t) and it is desired to have x replaced with y, then the rewritten lambda term would have the form (λy.t[y/x]) where t[y/x], "t with y instead of x", has had all free instances of x in t replaced with y.