# alpha conversion

1. () 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 ${\displaystyle (\lambda x.t)}$ and it is desired to have x replaced with y, then the rewritten lambda term would have the form ${\displaystyle (\lambda y.t[y/x])}$ where ${\displaystyle t[y/x]}$, "t with y instead of x", has had all free instances of x in t replaced with y.