The indexed state monad is not the only indexed monad out there; it's not even the only useful one. In this tutorial, we will explore another indexed monad, this time one that encapsulates the full power of delimited continuations: the indexed continuation monad.
The relationship between the indexed and regular state monads holds true as well for the indexed and regular continuation monads, but while the indexed state monad allows us to keep a state while changing its type in a type-safe way, the indexed continuation monad allows us to manipulate delimited continuations while the return type of the continuation block changes arbitrarily. This, unlike the regular continuation monad, allows us the full power of delimited continuations in a dynamic language like Scheme while still remaining completely statically typed.