The ##-calculus is a re#nement of the #-calculus where substitutionsare manipulated explicitly. The ##-calculus provides a settingfor studying the theory of substitutions, with pleasant mathematicalproperties. It is also a useful bridge between the classical #-calculusand concrete implementations.#Digital Equipment Corporation, Systems Research Center.yEcole Normale Sup#erieure; part of this work was completed while at Digital EquipmentCorporation, Systems Research Center.z...