10 th International Workshop on Coalgebraic Methods in Computer Science

Solutions of recursive program schemes over a given signature Σ were characterized by Bruno Courcelle as precisely the context-free (or algebraic) Σ-trees. These are the finite and infinite Σ-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 “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 Σ-trees of Courcelle. Our result builds on a result by N. Ghani et al on solutions of algebraic systems.