Improving the lazy Krivine machine

Friedman, Daniel P.; Ghuloum, Abdulaziz; Siek, Jeremy G.; Winebarger, Onnie Lynn

doi:10.1007/s10990-007-9014-0

Cited by 20 publications

(7 citation statements)

References 15 publications

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“…Our unchaining optimisation is a lazy variant of an optimisation that repeatedly appeared in the literature on abstract machines, often with reference to space consumption and space leaks, for instance in [3] as well as in Wand's [33] (section 2), Friedman et al's [34] (section 4), and Sestoft's [35] (section 4).…”

Section: Related Workmentioning

confidence: 99%

On the Relative Usefulness of Fireballs

Accattoli

Coen

2015

2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science

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Abstract-In CSL-LICS 2014, Accattoli and Dal Lago [1]showed that there is an implementation of the ordinary (i.e. strong, pure, call-by-name) λ-calculus into models like RAM machines which is polynomial in the number of β-steps, answering a long-standing question. The key ingredient was the use of a calculus with useful sharing, a new notion whose complexity was shown to be polynomial, but whose implementation was not explored. This paper, meant to be complementary, studies useful sharing in a call-by-value scenario and from a practical point of view. We introduce the Fireball Calculus, a natural extension of call-by-value to open terms, that is an intermediary step towards the strong case, and we present three results. First, we adapt and refine useful sharing, refining the metatheory. Then, we introduce the GLAMoUr a simple abstract machine implementing the Fireball Calculus extended with useful sharing. Its key feature is that usefulness of a step is testedsurprisingly-in constant time. Third, we provide a further optimisation that leads to an implementation having only a linear overhead with respect to the number of β-steps.

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Section: Related Workmentioning

confidence: 99%

On the Relative Usefulness of Fireballs

Accattoli

Coen

2015

2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science

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“…More generally, the issue of renaming chains, and the optimization used in [29] for lowering the overhead of CBN, repeatedly appear in the literature on abstract machines, often with reference to space consumption and space leaks, for instance in Wand's [32] (section 2), Friedman et al's [17] (section 4), and Sestoft's [30] (section 4). None of these works, however, provides a complexity analysis of the problem nor of the solution.…”

Section: Introductionmentioning

confidence: 99%

On the value of variables

Accattoli¹,

Coen²

2017

Information and Computation

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Call-by-value and call-by-need λ-calculi are defined using the distinguished syntactic category of values. In theoretical studies, values are variables and abstractions. In more practical works, values are usually defined simply as abstractions. This paper shows that practical values lead to a more efficient process of substitution-for both call-by-value and call-by-need-once the usual hypothesis for implementations hold (terms are closed, reduction does not go under abstraction, and substitution is done in micro steps, replacing one variable occurrence at a time). Namely, the number of substitution steps becomes linear in the number of β-redexes, while theoretical values only provide a quadratic bound. We complete the picture by showing that the same quadratic / linear bounds also hold for theoretical / practical versions of call-by-name.

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“…Theoretical studies rather dealt with the strong λ-calculus, and it is only since the seminal work of Abramsky and Ong [1] that theoreticians started to take the closed case seriously. Dually, practical studies mostly ignored strong evaluation, with the notable exception of Crégut [19] and some recent work [25,13,2]. Strong evaluation is however essential in the implementation of proof assistants or higher-order logic programming, typically for type-checking with dependent types as in the Edinburgh Logical Framework Summing up, our work does not improve the known bound on the asymptotic overhead of abstract machines for Open CbV, as the one obtained in [10] is already optimal.…”

Section: Introductionmentioning

confidence: 83%

Abstract machines for Open Call-by-Value

Accattoli

Guerrieri

2019

Science of Computer Programming

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The theory of the call-by-value λ-calculus relies on weak evaluation and closed terms, that are natural hypotheses in the study of programming languages. To model proof assistants, however, strong evaluation and open terms are required. Open call-by-value is the intermediate setting of weak evaluation with (possibly) open terms, on top of which Grégoire and Leroy designed one of the abstract machines of Coq. This paper provides a theory of abstract machines for the fireball calculus, the simplest presentation of open callby-value. The literature contains machines that are either simple but inefficient, as they have an exponential overhead, or efficient but heavy, as they rely on a labeling of environments and a technical optimization. We introduce a machine that is simple and efficient: it does not use labels and it implements the fireball calculus within a bilinear overhead. Moreover, we provide a new fine understanding of how different optimizations impact on the complexity of the overhead, and evidence that the time cost model we work with is minimal.

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Improving the lazy Krivine machine

Cited by 20 publications

References 15 publications

On the Relative Usefulness of Fireballs

On the Relative Usefulness of Fireballs

On the value of variables

Abstract machines for Open Call-by-Value

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