Implementing Open Call-by-Value

Accattoli, Beniamino; Guerrieri, Giulio

doi:10.1007/978-3-319-68972-2_1

Cited by 11 publications

(21 citation statements)

References 30 publications

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“…We plan to include them in a longer, journal version of this work. Open terms and evaluation under abstraction instead require more sophisticated machineries [10,9,5,11,12], whose adaptation to CbNeed and pattern matching is under development.…”

Section: Discussionmentioning

confidence: 99%

The Negligible and Yet Subtle Cost of Pattern Matching

Accattoli

Barras

2017

Programming Languages and Systems

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Abstract. The model behind functional programming languages is the closed λ-calculus, that is, the fragment of the λ-calculus where evaluation is weak (i.e. out of abstractions) and terms are closed. It is well-known that the number of β (i.e. evaluation) steps is a reasonable cost model in this setting, for all natural evaluation strategies (call-by-name / value / need). In this paper we try to close the gap between the closed λ-calculus and actual languages, by considering an extension of the λ-calculus with pattern matching. It is straightforward to prove that β plus matching steps provide a reasonable cost model. What we do then is finer: we show that β steps only, without matching steps, provide a reasonable cost model also in this extended setting-morally, pattern matching comes for free, complexity-wise. The result is proven for all evaluation strategies (name / value / need), and, while the proof itself is simple, the problem is shown to be subtle. In particular we show that qualitatively equivalent definitions of call-by-need may behave very differently.This work is part of a wider research effort, the COCA HOLA project [3].

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Section: Discussionmentioning

confidence: 99%

The Negligible and Yet Subtle Cost of Pattern Matching

Accattoli

Barras

2017

Programming Languages and Systems

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“…In this section we introduce the fireball calculus λ fire , the presentation of Open CbV we work with in this paper, and show the example of size explosion particular to the open setting. We studied alternative presentations of Open CbV in [7,9].…”

Section: The Fireball Calculus λ Fire and Open Size Explosionmentioning

confidence: 99%

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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“…There is recent work in investigating strategies to evaluate open terms, for instance open call-by-value, which is reasonable for time [4,3], but the question for space is open. On the more applied side, there is work on time and space profiling based on lazy graph reduction [21] in Haskell.…”

Section: Related and Future Workmentioning

confidence: 99%

The weak call-by-value λ-calculus is reasonable for both time and space

Forster

Kunze

Roth

2019

Proc. ACM Program. Lang.

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We study the weak call-by-value λ-calculus as a model for computational complexity theory and establish the natural measures for time and space -the number of beta-reductions and the size of the largest term in a computation -as reasonable measures with respect to the invariance thesis of Slot and van Emde Boas [STOC 84]. More precisely, we show that, using those measures, Turing machines and the weak call-by-value λ-calculus can simulate each other within a polynomial overhead in time and a constant factor overhead in space for all computations that terminate in (encodings) of "true" or "false". We consider this result as a solution to the long-standing open problem, explicitly posed by Accattoli [ENTCS 18], of whether the natural measures for time and space of the λ-calculus are reasonable, at least in case of weak call-by-value evaluation.Our proof relies on a hybrid of two simulation strategies of reductions in the weak call-by-value λ-calculus by Turing machines, both of which are insufficient if taken alone. The first strategy is the most naive one in the sense that a reduction sequence is simulated precisely as given by the reduction rules; in particular, all substitutions are executed immediately. This simulation runs within a constant overhead in space, but the overhead in time might be exponential. The second strategy is heap-based and relies on structure sharing, similar to existing compilers of eager functional languages. This strategy only has a polynomial overhead in time, but the space consumption might require an additional factor of log n, which is essentially due to the size of the pointers required for this strategy. Our main contribution is the construction and verification of a space-aware interleaving of the two strategies, which is shown to yield both a constant overhead in space and a polynomial overhead in time. ACM Subject Classification Theory of computation → Computational complexity and cryptography; Mathematics of computing → Lambda calculusKeywords and phrases invariance thesis, lambda calculus, weak call-by-value reduction, time and space complexity, abstract machines Supplement Material A Coq formalisation of the results in Section 2 and Section 3 is available at https://ps.uni-saarland.de/extras/wcbv-reasonable.

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Implementing Open Call-by-Value

Cited by 11 publications

References 30 publications

The Negligible and Yet Subtle Cost of Pattern Matching

The Negligible and Yet Subtle Cost of Pattern Matching

Abstract machines for Open Call-by-Value

The weak call-by-value λ-calculus is reasonable for both time and space

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