2004
DOI: 10.7146/brics.v11i29.21854
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An Operational Foundation for Delimited Continuations in the CPS Hierarchy

Abstract: We present an abstract machine and a reduction semantics for the λ-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 n of the CPS hierarchy,… Show more

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Cited by 15 publications
(25 citation statements)
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“…For example, in order to collect the solutions found by a backtracking algorithm implemented with shift 1 and reset 1 , one has to employ shift 2 and reset 2 , so that there is no interference between searching and emitting the results of the search. The CPS hierarchy was also envisaged to account for nested computations in hierarchical structures [7]. In the hierarchy, a shift operator of level i captures the context up to the first enclosing reset i or reset j with j > i.…”
Section: Cbn Pure Contextsmentioning
confidence: 99%
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“…For example, in order to collect the solutions found by a backtracking algorithm implemented with shift 1 and reset 1 , one has to employ shift 2 and reset 2 , so that there is no interference between searching and emitting the results of the search. The CPS hierarchy was also envisaged to account for nested computations in hierarchical structures [7]. In the hierarchy, a shift operator of level i captures the context up to the first enclosing reset i or reset j with j > i.…”
Section: Cbn Pure Contextsmentioning
confidence: 99%
“…6 In the original semantics, the evaluation context of level i + 1 is a list (a stack, really) of evaluation contexts of level i separated by control delimiters of level i (contexts of level 1 are just the standard CBV evaluation contexts.) and the number of context layers is fixed [7]. However, when dynamic name generation is included in the calculus, comparing two terms becomes more difficult, as prompts with the same purpose can be generated with different names.…”
Section: Cbn Pure Contextsmentioning
confidence: 99%
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“…A term t either uniquely reduces to another term, or is an eager normal form: it is either a value v, an open stuck term F [xv], or a control-stuck term E[Sv]. The latter cannot reduce further since it lacks a reset enclosing S. In the original reduction semantics [6], derived from the higher-order evaluator implementing the denotational semantics of shift and reset [12], it was assumed that programs are evaluated in an enclosing top-level reset. Here, however, we consider a relaxed semantics [9] that lifts this requirement.…”
Section: Delimited-control Operatorsmentioning
confidence: 99%