The (In)Efficiency of interaction

Accattoli, Beniamino; Lago, Ugo Dal; Vanoni, Gabriele

doi:10.1145/3434332

Cited by 12 publications

(6 citation statements)

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“…In particular, for head reduction, which in CbN is the reduction characterizing solvability. De Carvalho's seminal work has been extended to many notions of reduction and formalisms.A first wave was inspired directly from his original work [21,34,35,47,61], and a second wave [6,7,10,11,16,23,31,[55][56][57] started after the revisitation of de Carvalho's technique by Accattoli et al [8].…”

Section: From Multi Types To Call-by-value Solvabilitymentioning

confidence: 99%

The Theory of Call-by-Value Solvability (long version)

Accattoli¹,

Guerrieri²

2022

Preprint

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The denotational semantics of the untyped -calculus is a well developed field built around the concept of solvable terms, which are elegantly characterized in many different ways. In particular, unsolvable terms provide a consistent notion of meaningless term. The semantics of the untyped call-by-value -calculus (CbV) is instead still in its infancy, because of some inherent difficulties but also because CbV solvable terms are less studied and understood than in call-by-name. On the one hand, we show that a carefully crafted presentation of CbV allows us to recover many of the properties that solvability has in call-by-name, in particular qualitative and quantitative characterizations via multi types. On the other hand, we stress that, in CbV, solvability plays a different role: identifying unsolvable terms as meaningless induces an inconsistent theory.

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Section: From Multi Types To Call-by-value Solvabilitymentioning

confidence: 99%

The Theory of Call-by-Value Solvability (long version)

Accattoli¹,

Guerrieri²

2022

Preprint

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“…For example, in this case, we do not discuss about the size of the input pointers, because it can be absorbed in the polynomial overhead. 7 Intuitively, reasonability holds because in the simulation of Turing machines (the reasonable reference model), i.e. in the execution of the encoding of Turing machines into the -calculus, the exponential gap does not show up.…”

Section: Pmentioning

confidence: 99%

Multi Types and Reasonable Space (Long Version)

Accattoli¹,

Lago²,

Vanoni³

2022

Preprint

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and Vanoni have recently proved that the space used by the Space KAM, a variant of the Krivine abstract machine, is a reasonable space cost model for the -calculus accounting for logarithmic space, solving a longstanding open problem. In this paper, we provide a new system of multi types (a variant of intersection types) and extract from multi type derivations the space used by the Space KAM, capturing into a type system the space complexity of the abstract machine. Additionally, we show how to capture also the time of the Space KAM, which is a reasonable time cost model, via minor changes to the type system.

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“…After this was clarified (in the positive) by Accattoli and Dal Lago [5], de Carvalho's work has been revisited by Accattoli, Graham-Lengrand, and Kesner in 2018 [7]. The revisitation started a new wave of works adapting de Carvalho's study to many evaluation strategies and extensions of the λ-calculus, including call-byvalue [9], call-by-need [10], a linear logic presentation of call-by-push-value [16], the λµ-calculus [35], the λ-calculus with pattern matching [13], the probabilistic λ-calculus [19], and the abstract machine underlying the geometry of interaction [6]. All these works provide bounds of kind 1, and some of them also of kind 2, but none of them deals with those of kind 3 (bounds from composable types).…”

Section: A De Carvalho's Semantical Boundsmentioning

confidence: 99%

Semantic Bounds and Strong Call-by-Value Normalization

Accattoli¹,

Guerrieri²,

Leberle³

2021

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This paper explores two topics at once: the use of denotational semantics to bound the evaluation length of functional programs, and the semantics of strong (that is, possibly under abstractions) call-by-value evaluation.About the first, we analyze de Carvalho's seminal use of relational semantics for bounding the evaluation length of λ-terms, starting from the presentation of the semantics as an intersection types system. We focus on the part of his work which is usually neglected in its many recent adaptations, despite being probably the conceptually deeper one: how to transfer the bounding power from the type system to the relational semantics itself. We dissect this result and re-understand it via the isolation of a simpler size representation property.About the second, we use relational semantics to develop a semantical study of strong call-by-value evaluation, which is both a delicate and neglected topic. We give a semantic characterization of terms normalizable with respect to strong evaluation, providing in particular the first result of adequacy with respect to strong call-by-value. Moreover, we extract bounds about strong evaluation from both the type systems and the relational semantics.Essentially, we use strong call-by-value to revisit de Carvalho's semantic bounds, and de Carvalho's technique to provide semantical foundations for strong call-by-value. B. The Semantics of Strong Call-by-ValuePlotkin's call-by-value λ-calculus [44] is at the heart of programming languages such as OCaml and proof assistants such as Coq. In the study of programming languages, call-by-value (CbV) evaluation is usually weak, that is, it does not reduce under abstractions, and terms are assumed to be closed, i.e., without free variables. These constraints give rise to an elegant framework-we call it Closed CbV, following [8].It often happens, however, that one needs to go beyond Closed CbV by considering Strong CbV, which is the extended setting where reduction under abstractions is allowed and terms may be open, or the intermediate framework of Open CbV, where evaluation is weak but terms are not necessarily closed. The need arises, most notably, when describing the implementation model of Coq, as done by Grégoire and Leroy [28], to realize the essential conversion test for dependent types. Other motivations lie in the study of bisimulations by Lassen [37], partial evaluation [34], or various topics of a semantical or logical nature, recalled below.Naïve Extension of CbV. In call-by-name (CbN) turning to open terms or strong evaluation is harmless because CbN does not impose any special form to the arguments of β-redexes. On the contrary, turning to Open or Strong CbV is delicate. While some fundamental properties such as confluence and standardization hold also in such cases, as showed by Plotkin's himself [44], others-typically of a semantical nature-break as soon as one considers open terms.The problems of Strong CbV can be traced back to Plotkin's seminal paper, where he points out the incompleteness of CbV with respe...

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The (In)Efficiency of interaction

Cited by 12 publications

References 75 publications

The Theory of Call-by-Value Solvability (long version)

The Theory of Call-by-Value Solvability (long version)

Multi Types and Reasonable Space (Long Version)

Semantic Bounds and Strong Call-by-Value Normalization

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