  We present an abstract machine and a reduction semantics for the
lambda-calculus extended with control operators that give access to delimited
continuations in the CPS hierarchy. The abstract machine is derived from an
evaluator in continuation-passing style (CPS); the reduction semantics (i.e., a
small-step operational semantics with an explicit representation of evaluation
contexts) is constructed from the abstract machine; and the control operators
are the shift and reset family. We also present new applications of delimited
continuations in the CPS hierarchy: finding list prefixes and normalization by
evaluation for a hierarchical language of units and products.
