Axioms for Delimited Continuations in the CPS Hierarchy

Kameyama, Yutaka

doi:10.1007/978-3-540-30124-0_34

Cited by 16 publications

(26 citation statements)

References 24 publications

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“…C 1 [x ] , as found in other studies of shift and reset [48,49,57]. In particular, the need for delimiting the captured context is a consequence of the β ctx -rule.…”

Section: A Reduction Semanticsmentioning

confidence: 78%

An Operational Foundation for Delimited Continuations in the CPS Hierarchy

Biernacka¹,

Biernacki²,

Danvy³

2004

BRICS

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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, programs can use the control operators shift i and reset i for 1 ≤ i ≤ n, the evaluator has n + 1 layers of continuations, the abstract machine has n + 1 layers of control stacks, and the reduction semantics has n + 1 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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“…C 1 [x ] , as found in other studies of shift and reset [48,49,57]. In particular, the need for delimiting the captured context is a consequence of the β ctx -rule.…”

Section: A Reduction Semanticsmentioning

confidence: 78%

An Operational Foundation for Delimited Continuations in the CPS Hierarchy

Biernacka¹,

Biernacki²,

Danvy³

2004

BRICS

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“…The clauses catering for the non-tail-recursive uses of the control continuation are expressed using the delimited-control operators shift 1 , reset 1 , shift 2 , and reset 2 [13,33,41,63,78]. The resulting evaluator is in direct style.…”

Section: Run : S * E * C * D -> Valuementioning

confidence: 99%

“…We assume a basic familiarity with Standard ML and with reasoning about pure ML programs as well as an elementary understanding of defunctionalization [32,39,86] and its left inverse, refunctionalization; of the CPS transformation [33,36,50,76,86,93] and its left inverse, the direct-style transformation; and of delimited continuations [13,33,41,48,63]. From Section 2.4, we use pure ML with delimitedcontrol operators as a meta-language.…”

Section: Prerequisites and Domain Of Discoursementioning

confidence: 99%

“…It however is not in continuation-passing style because of the non-tail calls to c, eval, and apply (in the clauses marked "*") and the occurrences of shift and reset. This pattern of control is characteristic of the CPS hierarchy [13,33,41,63]. We therefore use the delimited-control operators shift 1 , reset 1 , shift 2 , and reset 2 to write the direct-style counterpart of this evaluator (shift 2 and reset 2 are the direct-style counterparts of shift 1 and reset 1 , and shift 1 and reset 1 are synonyms for shift and reset).…”

Section: A Control-less Direct-style Counterpartmentioning

confidence: 99%

“…Murthy [78] and Kameyama [63] have investigated their jumpy counterparts in the CPS hierarchy, C 1 (i.e., C) and C 2 . Jumpy continuations therefore suggest two new simulations of the J operator.…”

Section: The C Operator and The Cps Hierarchymentioning

confidence: 99%

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A Rational Deconstruction of Landin's J Operator

Danvy¹,

Millikin²

2006

BRICS

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Landin's J operator was the first control operator for functional languages. It was specified with an extension of the SECD machine, which was the first abstract machine for functional languages. We present a family of compositional evaluation functions corresponding to this extension of the SECD machine, using a series of elementary transformations (transformation into continuation-passing style (CPS) and defunctionalization, chiefly) and their left inverses (transformation into direct style and refunctionalization). To this end, we modernize the SECD machine into a bisimilar one that operates in lock step with the original one but that (1) does not use a data stack and (2) uses the caller-save rather than the callee-save convention for environments. We then characterize the J operator in terms of CPS and in terms of delimited-control operators in the CPS hierarchy. As a byproduct, we also present a reduction semantics for applicative expressions with the J operator, based on Curien's original calculus of explicit substitutions. This reduction semantics mechanically corresponds to the modernized version of the SECD machine and to the best of our knowledge, it provides the first syntactic theory of applicative expressions with the J operator.The present work is concluded by a motivated wish to see Landin's name added to the list of co-discoverers of continuations. Methodologically, however, it mainly illustrates the value of Reynolds's defunctionalization and of refunctionalization as well as the expressive power of the CPS hierarchy (a) to account for the first control operator and the first abstract machine for functional languages and (b) to connect them to their successors.(A preliminary version appears in the proceedings of IFL 2005 [38].)

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A Rational Deconstruction of Landin’s J Operator

Danvy

Millikin

2006

Implementation and Application of Functional Languages

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Landin's J operator was the first control operator for functional languages, and was specified with an extension of the SECD machine. Through a series of meaning-preserving transformations (transformation into continuation-passing style (CPS) and defunctionalization) and their left inverses (transformation into direct style and refunctionalization), we present a compositional evaluation function corresponding to this extension of the SECD machine. We then characterize the J operator in terms of CPS and in terms of delimited-control operators in the CPS hierarchy. Finally, we present a motivated wish to see Landin's name added to the list of co-discoverers of continuations. * Extended version of an article

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Axioms for Delimited Continuations in the CPS Hierarchy

Cited by 16 publications

References 24 publications

An Operational Foundation for Delimited Continuations in the CPS Hierarchy

An Operational Foundation for Delimited Continuations in the CPS Hierarchy

A Rational Deconstruction of Landin's J Operator

A Rational Deconstruction of Landin’s J Operator

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