An Abstract Machine for Strong Call by Value

Biernacka, Małgorzata; Biernacki, Dariusz; Charatonik, Witold; Drab, Tomasz

doi:10.1007/978-3-030-64437-6_8

Cited by 11 publications

(21 citation statements)

References 19 publications

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“…Another virtual machine for strong CbV was derived by Ager et al [10] from Aehlig and Joachimski's normalization function [9]. Recently, a strong call-by-need strategy has been proposed by Kesner et al [12], and the corresponding abstract machine has been derived by Biernacka et al [14]. Finally, in a recent work [13], Biernacka et al introduced the first abstract machine for strong CbV, and more specifically for the right-to-left strong CbV strategy.…”

Section: Related Workmentioning

confidence: 99%

“…Recently, a strong call-by-need strategy has been proposed by Kesner et al [12], and the corresponding abstract machine has been derived by Biernacka et al [14]. Finally, in a recent work [13], Biernacka et al introduced the first abstract machine for strong CbV, and more specifically for the right-to-left strong CbV strategy. That machine has been derived by a series of systematic transformation steps from a standard normalizationby-evaluation function for the CbV lambda calculus.…”

Section: Related Workmentioning

confidence: 99%

“…The main technical goal of our work is to construct a reasonable (in the formal sense defined above) abstract machine for strong CbV. This has been a nontrivial [1,4] open problem (partial results include [7,8,13]) and an important step in the research program aimed at developing the complexity analysis of the Coq main abstract machine formulated by Accattoli [2]. Since there are known simulations of Turing machines in the lambda calculus and of abstract machines by Turing machines, the existence of such a machine implies reasonability (for time) of strong CbV in the sense of Slot and van Emde Boas.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Strong Call by Value is Reasonable for Time

Biernacka¹,

Charatonik²,

Drab³

2021

Preprint

Self Cite

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“…The phase searching for values is instead left-to-right, because it also performs garbage collection, which cannot be done right-to-left. Our mixed order is hinted at in Biernacka et al [16] as a possible optimization of their right-to-left strong machine.…”

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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“…The first known abstract machine computing the normal form of a term is due to Crégut [Cré90] and implements normal order reduction. More recently, several lines of work have transposed the known evaluation strategies to strong reduction strategies or abstract machines: call-by-value [GL02, BBCD20, ACSC21], call-by-name [ABM15], and call-by-need [BBBK17,BC19]. Some non-advertised strong extensions of call-by-name or call-by-need can also be found in the internals of proof assistants, notably Coq.…”

Section: Introductionmentioning

confidence: 99%

A strong call-by-need calculus

Balabonski¹,

Lanco²,

Melquiond³

2021

Preprint

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We present a call-by-need λ-calculus that enables strong reduction (that is, reduction inside the body of abstractions) and guarantees that arguments are only evaluated if needed and at most once. This calculus uses explicit substitutions and subsumes the existing strong-call-by-need strategy, but allows for more reduction sequences, and often shorter ones, while preserving the neededness.The calculus is shown to be normalizing in a strong sense: Whenever a λ-term t admits a normal form n in the λ-calculus, then any reduction sequence from t in the calculus eventually reaches a representative of the normal form n. We also exhibit a restriction of this calculus that has the diamond property and that only performs reduction sequences of minimal length, which makes it systematically better than the existing strategy. We have used the Abella proof assistant to formalize part of this calculus, and discuss how this experiment affected its design. In particular, it led us to derive a new description of call-by-need reduction based on inductive rules.

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An Abstract Machine for Strong Call by Value

Cited by 11 publications

References 19 publications

Strong Call by Value is Reasonable for Time

Strong Call by Value is Reasonable for Time

Strong Call-by-Value is Reasonable, Implosively

A strong call-by-need calculus

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