Generic transformation of data structures

We consider the notion of a (data) format where each format defines a family of data structures. These formats arose from the theory of databases. Previous works have investigated the notion of generic transformations of data structures between formats. We give a novel grouptheoretic view of genericity which unifies the original approaches of Hull-Yap and Aho-Ullman. Among the results are: A necessary and sufficient condition for the existence of generic embeddings; the fact that digraphs cannot be generically embedded in hypergraphs; the striking fact that there is no hypergraph on more than two vertices with the alternating group as its automorphism group, and combinatorial techniques for counting structures with a prescribed automorphism group.