We present \emph{relative monads} in a polymorphic call-by-push-value (CBPV) calculus as a common abstraction for stack-based implementations of effects. This brings the powerful abstraction of monadic programming to lower-level stack-based languages. We demonstrate the applicability of the relative monad abstraction by modeling stack-based implementations of common monads used in functional programming as relative monads such as exceptions, state, continuations and free monads.

Next, we demonstrate that relative monads in CBPV are more compositional than monads in pure languages. First, while the use of monads allows for the use of embedded call-by-value programming in a pure language using do-notation, in contrast a relative monad allows for embedded CBPV programming within a CBPV programming language. This means that all code in CBPV can be reinterpreted to work with an arbitrary relative monad. Inspired by this, we extend our CBPV calculus with a new feature called ``monadic blocks'' that allow for reinterpretation of code with respect to any user-defined monad. We then show that monadic blocks allow us to take any monad implementation in CBPV and automatically derive the corresponding monad transformer, a process which is not automatic for monads in pure languages.

All examples are executable in Zydeco, a stack-based functional language we have designed and implemented based on polymorphic CBPV and extended with monadic blocks.