Modular Grammars and Splitting of Catamorphisms

Eric Badouel (1) , Rodrigue D. Djeumen (1)

1 S4 - System synthesis and supervision, scenarios

An abstract context-free grammar can be viewed as a system of polynomial functors. The initial algebra of this functor coincides with its least fixed-point; and this fixed-point can be computed by a method of substitution using Bek\`{\i}c theorem. By doing so the system of polynomial functors is transformed into a related system of regular functors. We introduce a splitting operation on algebras producing an algebra for the resulting system of regular functors from an algebra of the original system of polynomial functors. This transformation preserves the interpretation function (catamorphism). The end result is a class of (extended) abstract context-free grammars, associated with regular functors. This class seems to be well-adapted to the modular design of domain-specific embedded languages.

Mots clés: Context-Free Grammars; Catamorphisms; Bekic Theorem; Modularity

Domaines: Mathématique discrète [cs.DM]

Eric Badouel, Rodrigue D. Djeumen. Modular Grammars and Splitting of Catamorphisms. [Research Report] RR-6313, INRIA. 2007, pp.17. ⟨inria-00175793v2⟩