Abstract:
We present an abstract machine and a reduction semantics for
the 
-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. At level
of the CPS hierarchy, programs can use the control operators shift
and reset for
, the evaluator has 
layers of
continuations, the abstract machine has layers of control stacks, and
the reduction semantics has layers of evaluation contexts.
-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. At level
of the CPS hierarchy, programs can use the control operators shift
and reset for
, the evaluator has layers of
continuations, the abstract machine has layers of control stacks, and
the reduction semantics has layers of evaluation contexts.
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.
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