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We introduce a universe of regular datatypes with variable binding information, for which we define generic formation and elimination (i.e. induction /recursion) operators. We then define a generic αequivalence relation over the types of the universe based on name-swapping, and derive iteration and induction principles which work modulo α-conversion capturing Barendregt's Variable Convention. We instantiate the resulting framework so as to obtain the λ -Calculus and System F, for which we derive substitution operations and substitution lemmas for α-conversion and substitution composition. The whole work is carried out in Constructive Type Theory and machine-checked by the system Agda.