On second-order iterative monads

Jiří Adámek, Stefan Milius, Jiří Velebil
2011 Theoretical Computer Science  
B. Courcelle studied algebraic trees as precisely the solutions of all recursive program schemes for a given signature in Set. He proved that the corresponding monad is iterative. We generalize this to recursive program schemes over a given finitary endofunctor H of a "suitable" category. A monad is called second-order iterative if every guarded recursive program scheme has a unique solution in it. We construct two second-order iterative monads: one, called the second-order rational monad, S H
more » ... is proved to be the initial secondorder iterative monad. The other one, called the context-free monad, C H , is a quotient of S H and in the original case of a polynomial endofunctor H of Set we prove that C H is the monad studied by B. Courcelle. The question whether these two monads are equal is left open.
doi:10.1016/j.tcs.2011.04.027 fatcat:6kfrfynsdvdonffunsash6b6cu