Keywords:Control Operator, Operational Semantics, Continuation-Passing-Style Hierarchy, Native Implementation.
We explore the hierarchy of control induced by successive transformations into continuation-passing style (CPS) in the presence of ``control delimiters'' and ``composable continuations''. Specifically, we investigate the structural operational semantics associated with the CPS hierarchy.
To this end, we characterize an operational notion of continuation semantics. We relate it to the traditional CPS transformation and we use it to account for the control operator ``shift'' and the control delimiter ``reset'' operationally. We then transcribe the resulting continuation semantics in ML, thus obtaining a native and modular implementation of the entire hierarchy. We illustrate it with several examples, the most significant of which is layered monads.