Computation by interaction for space-bounded functional programming

Lago, Ugo Dal; Schöpp, Ulrich

doi:10.1016/j.ic.2015.04.006

Cited by 13 publications

(10 citation statements)

References 37 publications

(61 reference statements)

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“…The key point is that the token does not store information about every single β-redex, thus disentangling space-consumption from time-consumption. In other words, GoI machines are good candidates for space-efficient implementation schemes, as first shown by Schöpp and coauthors [23,51]. The price to pay is that the machine wastes a lot of time to retrieve β-redexes, so that time is sacrificed for space.…”

Section: Introductionmentioning

confidence: 99%

“…The GoI has been studied in relationship with implementations of functional languages, by Gonthier, Abadi and Levy, who studied Lévy's optimal evaluation [34], and by Mackie with his GoI machine for PCF [41], Gödel System T [42], and-with Fernandez-for call-by-value [30]. The space-efficiency studied by Dal Lago and Schöpp [23] is exploited by Mazza in [44] and, together with Terui, in [45]. Dal Lago and coauthors have also introduced variants of the IAM acting on proof nets for a number of extensions of the λcalculus [19][20][21]24].…”

Section: Introductionmentioning

confidence: 99%

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The Machinery of Interaction

Accattoli

Lago

Vanoni

2020

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

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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.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The Machinery of Interaction

Accattoli

Lago

Vanoni

2020

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

Self Cite

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“…The key point is that the token does not store information about every single β-redex, thus disentangling space-consumption from timeconsumption. In other words, GoI machines are good candidates for space-efficient implementation schemes, as first shown by Dal Lago and Schöpp [DLS16]. The price to pay is that the machine wastes a lot of time to retrieve β-redexes, so that time is sacrificed for space.…”

Section: Introductionmentioning

confidence: 99%

“…The GoI has also been studied in relationship with implementation of functional languages, by Gonthier, Abadi and Levy as a proof methodology in the study of optimal implementations [GAL92], and by Mackie with his GoI machine for PCF [Mac95] and Gödel System T [Mac17]. Recently, the space-efficiency studied by Dal Lago and Schöpp [DLS16] has been exploited by Mazza in [Maz15] and, together with Terui, in [MT15]. Dal Lago and coauthors have also introduced variants of the IAM acting on proof nets for a number of extensions of the λ-calculus…”

Section: Introductionmentioning

confidence: 99%

The Abstract Machinery of Interaction (Long Version)

Accattoli¹,

Lago²,

Vanoni³

2020

Preprint

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We provide an original reformulation of the IAM, an abstract machine introduced by Danos and Regnier based on Girard's Geometry of Interaction. We present our machine as acting directly on λ-terms, rather than on linear logic proof nets. The inductive nature of the λ-calculus allows direct and self-contained proofs of soundness and adequacy. Moreover, we improve on the literature showing that the denotational semantics induced by our machine is invariant for open terms and erasing steps, solving a notorious issue of the Geometry of Interaction.

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“…The interactionbased approach is also convenient for the complexity analysis of programs, e.g. Dal Lago and Schöpp's IntML type system of logarithmic-space evaluation [7], and Dal Lago et al's linear dependent type system of polynomialtime evaluation [5,6].…”

Section: Introduction 1token-passing Abstract Machines For λ-Calculusmentioning

confidence: 99%

The Dynamic Geometry of Interaction Machine: A Call-by-need Graph Rewriter

Muroya,

Ghica

2017

Preprint

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Girard's Geometry of Interaction (GoI), a semantics designed for linear logic proofs, has been also successfully applied to programming language semantics. One way is to use abstract machines that pass a token on a fixed graph along a path indicated by the GoI. These token-passing abstract machines are space efficient, because they handle duplicated computation by repeating the same moves of a token on the fixed graph. Although they can be adapted to obtain sound models with regard to the equational theories of various evaluation strategies for the lambda calculus, it can be at the expense of significant time costs. In this paper we show a token-passing abstract machine that can implement evaluation strategies for the lambda calculus, with certified time efficiency. Our abstract machine, called the Dynamic GoI Machine (DGoIM), rewrites the graph to avoid replicating computation, using the token to find the redexes. The flexibility of interleaving token transitions and graph rewriting allows the DGoIM to balance the trade-off of space and time costs. This paper shows that the DGoIM can implement call-by-need evaluation for the lambda calculus by using a strategy of interleaving token passing with as much graph rewriting as possible. Our quantitative analysis confirms that the DGoIM with this strategy of interleaving the two kinds of possible operations on graphs can be classified as "efficient" following Accattoli's taxonomy of abstract machines.But if GoI-style techniques are to be used in a practical setting they need to extend beyond call-by-name, not just correctly but also efficiently. Interleaving Token Passing with Graph RewritingA token jumping, rather than following a path, can be seen as a simple form of short-circuiting that path, which is a simple form of graph-rewriting. This idea first occurs in Mackie's work as a compiler optimisation technique [20] and is analysed in more depth theoretically by Danos and Regnier in the so-called Interaction Abstract Machine [9]. More general graph-rewriting-based semantics have been used in a system called virtual reduction [8], where rewriting occurs along paths indicated by GoI, but without any token-actions. The most operational presentation of the combination of token-passing and jumping was given by Fernández and Mackie [11]. The interleaving of token actions and rewriting is also found in Sinot's interaction nets [26,27]. We can reasonably think of the DGoIM as their abstract-machine realisation.We build on these prior insights by adding more general, yet still efficient, graph-rewriting facilities to the setting of a GoI token-passing abstract machine. We call an abstract machine that interleaves token passing with graph rewriting the Dynamic GoI Machine (DGoIM), and we define it as a state transition system with transitions for token passing as well as transitions for graph rewriting. What connects these two kinds of transitions is the token trajectory through the graph, its path. By examining it, the DGoIM can detect redexes and trigger rewriting actions.T...

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Computation by interaction for space-bounded functional programming

Cited by 13 publications

References 37 publications

The Machinery of Interaction

The Machinery of Interaction

The Abstract Machinery of Interaction (Long Version)

The Dynamic Geometry of Interaction Machine: A Call-by-need Graph Rewriter

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