  We present an elaboration of inductive definitions down to a universe of
datatypes. The universe of datatypes is an internal presentation of strictly
positive families within type theory. By elaborating an inductive definition --
a syntactic artifact -- to its code -- its semantics -- we obtain an
internalized account of inductives inside the type theory itself: we claim that
reasoning about inductive definitions could be carried in the type theory, not
in the meta-theory as it is usually the case. Besides, we give a formal
specification of that elaboration process. It is therefore amenable to formal
reasoning too. We prove the soundness of our translation and hint at its
correctness with respect to Coq's Inductive definitions.
  The practical benefits of this approach are numerous. For the type theorist,
this is a small step toward bootstrapping, ie. implementing the inductive
fragment in the type theory itself. For the programmer, this means better
support for generic programming: we shall present a lightweight deriving
mechanism, entirely definable by the programmer and therefore not requiring any
extension to the type theory.
