Crumbling Abstract Machines

Proceedings of the 22nd International Symposium on Principles and Practice of Declarative Programming

Lago

Vanoni

2020

Self Cite

This paper revisits the Interaction Abstract Machine (IAM), a machine based on Girard's Geometry of Interaction, introduced by Mackie and Danos & Regnier. It is an unusual machine, not relying on environments, presented on linear logic proof nets, and whose soundness proof is convoluted and passes through various other formalisms. Here we provide a new direct proof of its correctness, based on a variant of Sands's improvements, a natural notion of bisimulation. Moreover, our proof is carried out on a new presentation of the IAM, defined as a machine acting directly on λ-terms, rather than on linear logic proof nets. CCS CONCEPTS • Theory of computation → Lambda calculus; Abstract machines.

Section: Leveled Contextsmentioning

confidence: 99%

The Machinery of Interaction

Proceedings of the 22nd International Symposium on Principles and Practice of Declarative Programming

Lago

Vanoni

2020

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“…(Linear) logical reading. Our partitioning of transitions into β, substitution and commutative ones admits a proof-theoretical view, as machine transitions can be seen as cut-elimination steps [15,12]. Substitution and β transitions correspond to principal cases in cut-elimination.…”

Section: Lemma 4 (One-step Simulationmentioning

confidence: 99%

Abstract machines for Open Call-by-Value

Science of Computer Programming

Guerrieri

2019

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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.

“…Before 2014, the topic had been mostly neglectedÐthe only two counterexamples being Blelloch and Greiner [1995]; Sands et al [2002]. Since 2014Ðmotivated by advances on time cost models for the λ-calculus by Accattoli and Dal Lago [2016]Ðthe topic has actively been studied [Accattoli et al 2014;Accattoli and Barras 2017;Accattoli et al 2019a;.…”

Section: Introductionmentioning

confidence: 99%

The (In)Efficiency of interaction

Proc. ACM Program. Lang.

Lago

Vanoni

2021

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Evaluating higher-order functional programs through abstract machines inspired by the geometry of the interaction is known to induce space efficiencies, the price being time performances often poorer than those obtainable with traditional, environment-based, abstract machines. Although families of lambda-terms for which the former is exponentially less efficient than the latter do exist, it is currently unknown how general this phenomenon is, and how far the inefficiencies can go, in the worst case. We answer these questions formulating four different well-known abstract machines inside a common definitional framework, this way being able to give sharp results about the relative time efficiencies. We also prove that non-idempotent intersection type theories are able to precisely reflect the time performances of the interactive abstract machine, this way showing that its time-inefficiency ultimately descends from the presence of higher-order types.