Abstract continuations: a mathematical semantics for handling full jumps

Felleisen, Matthias; Wand, Mitchell; Friedman, Daniel P.; Duba, Bruce F.

doi:10.1145/62678.62684

Cited by 81 publications

(94 citation statements)

References 11 publications

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“…By analogy, the data-structure continuation of the breadthfirst program is a queue. We conjecture that the queue-based program could be mechanically obtained from the direct-style one by some kind of 'abstract CPS transformation' [23,51], but fleshing out this conjecture falls out of the scope of this article.…”

Section: Programming With Delimited Continuationsmentioning

confidence: 99%

“…Unlike shift and reset, whose definition is based on CPS, control and prompt are specified by representing delimited continuations as a list of stack frames and their composition as the concatenation of these representations [23]. Such a concatenation function is defined as follows:…”

Section: An Abstract Machine For Control and Promptmentioning

confidence: 99%

“…While this format has been an active topic of study [5,19,26,28,31,37,39,45,47,50,54,57,62], it also has been felt as a straightjacket both from a semantics point of view [19,20,22,23,34,35,58] and from a programming point of view [11,12,14,15], where one would like to relax the tail-call constraint and compose continuations.…”

Section: Introductionmentioning

confidence: 99%

“…In direct style, composable continuations are also accessed with control operators such as Felleisen et al's control (alias F ) [22,23,58] and Danvy and Filinski's shift (alias S) [15,16]. These control operators also give access to the current continuation as a first-class value; activating such a first-class continuation also has the effect of resuming the computation at the point where this continuation was captured; the then-current continuation, however, is then resumed.…”

Section: Introductionmentioning

confidence: 99%

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On the dynamic extent of delimited continuations

Biernacki

Danvy

Shan

2005

Information Processing Letters

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We show that breadth-first traversal exploits the difference between the static delimited-control operator shift (alias S) and the dynamic delimited-control operator control (alias F). For the last 15 years, this difference has been repeatedly mentioned in the literature but it has only been illustrated with one-line toy examples. Breadth-first traversal fills this vacuum.We also point out where static delimited continuations naturally give rise to the notion of control stack whereas dynamic delimited continuations can be made to account for a notion of 'control queue.'

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Section: Programming With Delimited Continuationsmentioning

confidence: 99%

Section: An Abstract Machine For Control and Promptmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On the dynamic extent of delimited continuations

Biernacki

Danvy

Shan

2005

Information Processing Letters

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“…In many articles about reduction semantics, though, compound contexts are constructed by composing an elementary context on the left rather than on the right [11,13]. For the λ-calculus under call by value, the grammar of reduction contexts then reads as follows.…”

Section: Reduction Contextsmentioning

confidence: 99%

Refocusing in Reduction Semantics

Danvy¹,

Nielsen²

2004

BRICS

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The evaluation function of a reduction semantics (i.e., a small-step operational semantics with an explicit representation of the reduction context) is canonically defined as the transitive closure of (1) decomposing a term into a reduction context and a redex, (2) contracting this redex, and (3) plugging the contractum in the context. Directly implementing this evaluation function therefore yields an interpreter with a worst-case overhead, for each step, that is linear in the size of the input term.We present sufficient conditions over the constituents of a reduction semantics to circumvent this overhead, by replacing the composition of (3) plugging and (1) decomposing by a single "refocus" function mapping a contractum and a context into a new context and a new redex, if any. We also show how to construct such a refocus function, we prove the correctness of this construction, and we analyze the complexity of the resulting refocus function.The refocused evaluation function of a reduction semantics implements the transitive closure of the refocus function, i.e., a "pre-abstract machine." Fusing the refocus function with the trampoline function computing the transitive closure gives a state-transition function, i.e., an abstract machine. This abstract machine clearly separates between the transitions implementing the congruence rules of the reduction semantics and the transitions implementing its reduction rules. The construction of a refocus function therefore shows how to mechanically obtain an abstract machine out of a reduction semantics, which was done previously on a case-by-case basis.We illustrate refocusing by mechanically constructing Felleisen et al.'s CK machine from a call-by-value reduction semantics of the lambda-calculus, and by constructing a substitution-based version of Krivine's machine from a call-by-name reduction semantics of the lambda-calculus. We also mechanically construct three one-pass CPS transformers from three quadratic context-based CPS transformers for the lambda-calculus.

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MobileML: A Programming Language for Mobile Computation

Hashimoto

Yonezawa

2000

Coordination Languages and Models

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Abstract continuations: a mathematical semantics for handling full jumps

Cited by 81 publications

References 11 publications

On the dynamic extent of delimited continuations

On the dynamic extent of delimited continuations

Refocusing in Reduction Semantics

MobileML: A Programming Language for Mobile Computation

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