Recursive Program Schemes and Context-Free Monads

Authors:
Jiří Adámek;Stefan Milius;Jiří Velebil
Affiliations:
Institut für Theoretische Informatik, Technische Universität Braunschweig, Germany;Institut für Theoretische Informatik, Technische Universität Braunschweig, Germany;Faculty of Electrical Engineering, Czech Technical University of Prague, Czech Republic
Venue:
Electronic Notes in Theoretical Computer Science (ENTCS)
Year:
2010

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Abstract

Solutions of recursive program schemes over a given signature @S were characterized by Bruno Courcelle as precisely the context-free (or algebraic) @S-trees. These are the finite and infinite @S-trees yielding, via labelling of paths, context-free languages. Our aim is to generalize this to finitary endofunctors H of general categories: we construct a monad C^H ''generated'' by solutions of recursive program schemes of type H, and prove that this monad is ideal. In case of polynomial endofunctors of Set our construction precisely yields the monad of context-free @S-trees of Courcelle. Our result builds on a result by N. Ghani et al on solutions of algebraic systems.