Abstract machines for Open Call-by-Value

Accattoli, Beniamino; Guerrieri, Giulio

doi:10.1016/j.scico.2019.03.002

Cited by 12 publications

(11 citation statements)

References 27 publications

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“…As shown by Accattoli and Guerrieri [15], in an open (but not strong) setting, substituting abstractions on-demand is not mandatory for reasonability. They also show, however, that it makes nonetheless sense to study it because it is mandatory for obtaining efficient implementations, as it reduces the complexity of the overhead from quadratic to linear with respect to the size of the initial term.…”

Section: The Need For Useful Sharingmentioning

confidence: 99%

“…In a line of work by Accattoli and co-authors [8,14,15,11] aimed at developing a theory of CbV beyond the usual closed case, it became clear that there is an alternative and better route to the strong setting. The idea is to consider the intermediate open setting (rather than the head one) obtained by enabling evaluation in arguments and open terms (as in the strong case), while still forbidding evaluation in abstraction bodies (as in the closed case).…”

Section: Introductionmentioning

confidence: 99%

“…Useful sharing for the strong case then amounts to understanding how open useful sharing and the iteration interact, which is very subtle and yet is an orthogonal problem. Studying the open case first is the progression followed recently by Accattoli and co-authors to obtain a reasonable cost model for Strong CbV [8,15,10].…”

Section: Introductionmentioning

confidence: 99%

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Useful Open Call-by-Need

Accattoli¹,

Leberle²

2021

Preprint

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This paper studies useful sharing, which is a sophisticated optimization for λ-calculi, in the context of call-by-need evaluation in presence of open terms. Useful sharing turns out to be harder to manipulate in call-byneed than in call-by-name or call-by-value, because call-by-need evaluates inside environments, making it harder to specify when a substitution step is useful. We isolate the key involved concepts and prove the correctness of useful sharing in this setting.

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Section: The Need For Useful Sharingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Useful Open Call-by-Need

Accattoli¹,

Leberle²

2021

Preprint

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“…Crumbling: The SCAM builds on the theory of CbV abstract machines developed by Accattoli and co-authors [45], [24], [23], [25]. In particular, it relies on the crumbling technique of [25], which essentially is a specific presentation of the transformation into administrative normal forms by Flanagan et al [46], [47].…”

Section: Introducing the Scammentioning

confidence: 99%

Strong Call-by-Value is Reasonable, Implosively

Accattoli¹,

Condoluci²,

Coen³

2021

Preprint

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Whether the number of β-steps in the λ-calculus can be taken as a reasonable cost model (that is, polynomially related to the one of Turing machines) is a delicate problem, which depends on the notion of evaluation strategy. Since the nineties, it is known that weak (that is, out of abstractions) call-by-value evaluation is a reasonable strategy while Lévy's optimal parallel strategy, which is strong (that is, it reduces everywhere), is not. The strong case turned out to be subtler than the weak one. In 2014 Accattoli and Dal Lago have shown that strong call-by-name is reasonable, by introducing a new form of useful sharing and, later, an abstract machine with an overhead quadratic in the number of β-steps.Here we show that strong call-by-value evaluation is also reasonable, via a new abstract machine realizing useful sharing and having a linear overhead. Moreover, our machine uses a new mix of sharing techniques, adding on top of useful sharing a form of implosive sharing, which on some terms brings an exponential speed-up. We give an example of family that the machine executes in time logarithmic in the number of β-steps.

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“…An abstract machine is typically deterministic and it makes specific choices when searching for redices, i.e., it implements a specific reduction strategy of the calculus. Accattoli et al in his work on the complexity of abstract machines [3,2,8] advocate the following notion of reasonability: a machine is called reasonable if it simulates the strategy with the time overhead bounded by a polynomial in the number of β-steps and in the size of the initial term.…”

Section: Introductionmentioning

confidence: 99%

Strong Call by Value is Reasonable for Time

Biernacka¹,

Charatonik²,

Drab³

2021

Preprint

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The invariance thesis of Slot and van Emde Boas states that all reasonable models of computation simulate each other with polynomially bounded overhead in time and constant-factor overhead in space. In this paper we show that a family of strong call-by-value strategies in the λ-calculus are reasonable for time. The proof is based on a construction of an appropriate abstract machine, systematically derived using Danvy et al.'s functional correspondence that connects higher-order interpreters with abstract-machine models by a well-established transformation technique. This is the first machine that implements a strong CbV strategy and simulates β-reduction with the overhead polynomial in the number of β-steps and in the size of the initial term. We prove this property using a form of amortized cost analysis à la Okasaki.

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Abstract machines for Open Call-by-Value

Cited by 12 publications

References 27 publications

Useful Open Call-by-Need

Useful Open Call-by-Need

Strong Call-by-Value is Reasonable, Implosively

Strong Call by Value is Reasonable for Time

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