  Given a programming language, can we give a monadic denotational semantics
that is stable under language extension? Models containing only a single monad
are not stable. Models based on type-and-effect systems, in which there is a
monad for every set of operations in the language, are. Cartwright and
Felleisen, and Wadler, conjectured such monadic semantics can be generated. We
describe a new general method of constructing stable models from standard
monadic models, based on factorizations of monad morphisms. We show that under
certain conditions factorizations induce a monad for every set of operations,
and explain why the conditions usually hold. We also describe preliminary work
using fibrations for logical relations generated from these factorization
systems for proving the correctness of the resulting model.
