Proof nets and the call-by-value λ-calculus

Accattoli, Beniamino

doi:10.1016/j.tcs.2015.08.006

“…outside exponential boxes). The exact correspondence has many technical intricacies, which are outside the scope of this paper, anyway it can be recovered by composing the translation of the value substitution calculus (another extension of Plotkin's λ v ) into LL proof-nets (see [1]), and the encoding (studied in [4]) of λ sh into the value substitution calculus. The relational semantics studied here is nothing but the relational semantics for LL (see [17]) restricted to fragment of LL that is the image of Girard's call-by-value translation.…”

Section: Discussionmentioning

confidence: 99%

Towards a Semantic Measure of the Execution Time in Call-by-Value lambda-Calculus

Guerrieri

¹

2019

Electron. Proc. Theor. Comput. Sci.

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We investigate the possibility of a semantic account of the execution time (i.e. the number of β v -steps leading to the normal form, if any) for the shuffling calculus, an extension of Plotkin's call-by-value λ -calculus. For this purpose, we use a linear logic based denotational model that can be seen as a nonidempotent intersection type system: relational semantics. Our investigation is inspired by similar ones for linear logic proof-nets and untyped call-by-name λ -calculus. We first prove a qualitative result: a (possibly open) term is normalizable for weak reduction (which does not reduce under abstractions) if and only if its interpretation is not empty. We then show that the size of type derivations can be used to measure the execution time. Finally, we show that, differently from the case of linear logic and call-by-name λ -calculus, the quantitative information enclosed in type derivations does not lift to types (i.e. to the interpretation of terms). To get a truly semantic measure of execution time in a call-by-value setting, we conjecture that a refinement of its syntax and operational semantics is needed.

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“…In [2] it has been shown that λ vsub and λ sh can be embedded in each other preserving termination and divergence. Interestingly, both calculi are inspired by an analysis of Girard's "boring" call-by-value translation of λ -terms into linear logic proof-nets [20,1] according to the linear recursive type o = !o !o, or equivalently o = ! (o o).…”

Section: The Shuffling Calculusmentioning

confidence: 99%

Towards a Semantic Measure of the Execution Time in Call-by-Value lambda-Calculus

Guerrieri¹

2018

EasyChair Preprints

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We investigate the possibility of a semantic account of the execution time (i.e. the number of β v -steps leading to the normal form, if any) for the shuffling calculus, an extension of Plotkin's call-by-value λ -calculus. For this purpose, we use a linear logic based denotational model that can be seen as a nonidempotent intersection type system: relational semantics. Our investigation is inspired by similar ones for linear logic proof-nets and untyped call-by-name λ -calculus. We first prove a qualitative result: a (possibly open) term is normalizable for weak reduction (which does not reduce under abstractions) if and only if its interpretation is not empty. We then show that the size of type derivations can be used to measure the execution time. Finally, we show that, differently from the case of linear logic and call-by-name λ -calculus, the quantitative information enclosed in type derivations does not lift to types (i.e. to the interpretation of terms). To get a truly semantic measure of execution time in a call-by-value setting, we conjecture that a refinement of its syntax and operational semantics is needed.

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“…Boxes are represented by extra nodes requiring additional rules for book-keeping. To palliate this problem, several extensions of interaction nets have been proposed (see e.g., [1,2,22]). In [2], a representation of intuitionistic logic proofs (or λ -terms) is given by means of higher-order port-graphs (HOPG).…”

Section: Figure 1: Sample Starting Graphmentioning

confidence: 99%

Attributed Hierarchical Port Graphs and Applications

Ene

¹

,

Fernández

²

,

Pinaud

³

2018

Electron. Proc. Theor. Comput. Sci.

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We present attributed hierarchical port graphs (AHP) as an extension of port graphs that aims at facilitating the design of modular port graph models for complex systems. AHP consist of a number of interconnected layers, where each layer defines a port graph whose nodes may link to layers further down the hierarchy; attributes are used to store user-defined data as well as visualisation and run-time system parameters. We also generalise the notion of strategic port graph rewriting (a particular kind of graph transformation system, where port graph rewriting rules are controlled by user-defined strategies) to deal with AHP following the Single Push-out approach. We outline examples of application in two areas: functional programming and financial modelling.

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Proof nets and the call-by-value λ-calculus

Cited by 29 publications

References 31 publications

Towards a Semantic Measure of the Execution Time in Call-by-Value lambda-Calculus

Towards a Semantic Measure of the Execution Time in Call-by-Value lambda-Calculus

Towards a Semantic Measure of the Execution Time in Call-by-Value lambda-Calculus

Attributed Hierarchical Port Graphs and Applications

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