A Generic Framework for Genericity

Recently, generic programming becomes of a major interest in several programming paradigms. A recurrent idea to achieve genericity is to specify algorithms on their convenient data structure, and to allow these speciications to be instantiated onto a large number of neighboring data structures. Polytypic programming, shapely types and generic attribute grammars are generic programming methods related to this approach. A framework for generic programming is proposed to embed these methods. It consists in tools for automatic generation of morphisms between data structures, and for program composition. Thanks to this compositional approach, the complete specialization of generic programs could be advantageously delegated to a general and powerful mechanism of \symbolic composition", which performs deforestation and partial evaluation .