Axioms for control operators in the CPS hierarchy

Kameyama, Yutaka

doi:10.1007/s10990-007-9009-x

Cited by 14 publications

(17 citation statements)

References 31 publications

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“…One can add arbitrarily many and obtain a CPS hierarchy [41,122,150,171,233]. By default, for n layers, n continuation identifiers are enough; they denote second-class continuations: n − 1 are delimited and the last one is undelimited.…”

Section: Mae Westmentioning

confidence: 99%

“…The original typing discipline of shift and reset corresponds to the typing discipline of the CPS idioms they provide in direct style [121]. This type system still appears to be the most expressive one today [18,233,276,364]. Constructing a list of the prefixes of a given list [97] provides one of the simplest examples illustrating the need for the full power of this type system [41,Section 3.6], and in fact so does the generator of Section 1.1.6 if one uses Hughes's higher-order representation of lists, as described in Section 2.2.2, page 41 [222]: Compared to Section 1.1.6, the type 'a list has been replaced by the type 'a list -> 'a list, the empty list has been replaced by the identity function, and the reversed prefix has been replaced by a function that prepends this prefix to its argument, thereby avoiding reverse prepend altogether.…”

Section: Shift and Resetmentioning

confidence: 99%

“…Małgorzata Biernacka, Dariusz Biernacki, and the author proposed an operational foundation for delimited continuations in the CPS hierarchy [41]. Kameyama has recently axiomatized layered delimited continuations in the CPS hierarchy [232,233].…”

Section: Shift and Resetmentioning

confidence: 99%

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An Analytical Approach to Programs as Data Objects

Danvy¹

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This essay accompanies a selection of 32 articles (referred to in bold face in the text and marked with " √ " in the bibliographic references) submitted to the University of Aarhus towards a Doctor Scientiarum degree in Computer Science. The author's previous academic degree, beyond a doctoral degree in June 1986, is an Habilitationà diriger les recherches from the Université Pierre et Marie Curie (Paris VI) in France; the corresponding material was submitted in September 1992 and the degree was obtained in January 1993. The present 32 articles have all been written since 1993 and while at DAIMI. Except for one other PhD student, all co-authors are or have been the author's students here in Aarhus. * Technical summaryThis work presents an analytical approach to programs as data objects, i.e., to programs whose representation is operated upon by other programs. The approach is analytical in that a variety of program manipulations is considered and their impact on program understanding, design, and efficiency is measured.Most of the programs considered here are language processors, i.e., programs interpreting, translating, or transforming other programs. As for the program manipulations, they concern block structure and lexical scope, the representation of functions at run time, and the representation of control.ii Teknisk résuméDette arbejde praesenterer en analytisk tilgang til programmer som dataobjekter, dvs, til programmer hvis repraesentation bliver behandlet af andre programmer. Tilgangen er analytisk i og med at et udvalg af programmanipulationer bliver betragtet og deres indflydelse på program-forståelse, -design og -effektivitet bliver vurderet.De fleste programmer, der betragtes her, er sprogbehandlingsprogrammer, dvs, programmer der fortolker, oversaetter eller transformerer andre programmer. Hvad angår programmanipulationerne, vedrører de blokstruktur og leksikalsk virkefelt, repraesentation af funktioner på køretidspunktet og repraesentation af kontrol.iii

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Section: Mae Westmentioning

confidence: 99%

Section: Shift and Resetmentioning

confidence: 99%

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An Analytical Approach to Programs as Data Objects

Danvy¹

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“…This is known as the CPS hierarchy. In the following, we shall refer to it as the CPS hierarchy or λS n and adopt Kameyama's terminology [19]:…”

Section: Motivating the Stream Hierarchymentioning

confidence: 99%

“…In order to study the correspondence with CPS hierarchy, we recall Kameyama's axiomatization of λS n [19]:…”

Section: Relating the Stream Hierarchy And The Cps Hierarchymentioning

confidence: 99%

A Hierarchy for Delimited Continuations in Call-by-Name

Saurin¹

2010

Foundations of Software Science and Computational Structures

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Abstract. Λμ-calculus was introduced as a Böhm-complete extension of Parigot's λμ-calculus. Λμ-calculus, contrarily to Parigot's calculus, is a calculus of CBN delimited control as evidenced by Herbelin and Ghilezan. In their seminal paper on (CBV) delimited control, Danvy and Filinski introduced the CPS Hierarchy of control operators (shifti/reseti)i∈ω.In a similar way, we introduce in the present paper the Stream Hierarchy, a hierarchy of calculi extending and generalizing Λμ-calculus. The (Λ n )n∈ω-calculi have Church-Rosser and Böhm theorems. We then present sound and complete CPS translations for the hierarchy. Next, we investigate the operational content of the hierarchy through its abstract machines, the (Λ n )n∈ω-KAM. Finally, we establish that the Stream hierarchy is indeed a CBN analogue to the CPS hierarchy.

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Environmental Bisimulations for Delimited-Control Operators

Biernacki

Lenglet²

2013

Programming Languages and Systems

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We present a theory of environmental bisimilarity for the delimited-control operators shift and reset. We consider two different notions of contextual equivalence: one that does not require the presence of a top-level control delimiter when executing tested terms, and another one, fully compatible with the original CPS semantics of shift and reset, that does. For each of them, we develop sound and complete environmental bisimilarities, and we discuss up-to techniques.Lemma 2. For all closed terms t, either t is a normal form, or there exist a unique redex r and a unique context F such that t = F [r].Finally, we write → * v for the transitive and reflexive closure of → v , and we define the evaluation relation of λ S as follows.The result of the evaluation of a closed term, if it exists, is a normal form. If a term t admits an infinite reduction sequence, we say it diverges, written t ⇑ v . Henceforth, we use Ω = (λx.x x) (λx.x x) as an example of such a term.

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Axioms for control operators in the CPS hierarchy

Cited by 14 publications

References 31 publications

An Analytical Approach to Programs as Data Objects

An Analytical Approach to Programs as Data Objects

A Hierarchy for Delimited Continuations in Call-by-Name

Environmental Bisimulations for Delimited-Control Operators

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