Is alpha-conversion easy?

Abstract

We present a new lambda-calculus with explicit substitutions and named variables. Renaming of bound variables in this calculus is explicit (there is a special rewrite rule) and can be delayed. Contexts (environments) are not sets or lists without multiplicity, but have a more complicated structure. There is a natural order on the set of contexts. A "set" of free variables is not a set, but a context in the new sense. New definitions simplify working with alpha-conversion.