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DOI: 10.4230/LIPIcs.FSCD.2016.35

Interaction Automata and the ia2d Interpreter

Authors: Stéphane Gimenez and David Obwaller

Published in: LIPIcs, Volume 52, 1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016)

Abstract

We introduce interaction automata as a topological model of computation and present the conceptual plane interpreter ia2d. Interaction automata form a refinement of both interaction nets and cellular automata models that combine data deployment, memory management and structured computation mechanisms. Their local structure is inspired from pointer machines and allows an asynchronous spatial distribution of the computation. Our tool can be considered as a proof-of-concept piece of abstract hardware on which functional programs can be run in parallel.

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Stéphane Gimenez and David Obwaller. Interaction Automata and the ia2d Interpreter. In 1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 52, pp. 35:1-35:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{gimenez_et_al:LIPIcs.FSCD.2016.35,
  author =	{Gimenez, St\'{e}phane and Obwaller, David},
  title =	{{Interaction Automata and the ia2d Interpreter}},
  booktitle =	{1st International Conference on Formal Structures for Computation and Deduction (FSCD 2016)},
  pages =	{35:1--35:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-010-1},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{52},
  editor =	{Kesner, Delia and Pientka, Brigitte},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2016.35},
  URN =		{urn:nbn:de:0030-drops-59896},
  doi =		{10.4230/LIPIcs.FSCD.2016.35},
  annote =	{Keywords: Interaction nets, computation models, parallel computation, functional programming}
}

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DOI: 10.4230/LIPIcs.CSL.2013.316

The Structure of Interaction

Authors: Stéphane Gimenez and Georg Moser

Published in: LIPIcs, Volume 23, Computer Science Logic 2013 (CSL 2013)

Abstract

Interaction nets form a local and strongly confluent model of computation that is per se parallel. We introduce a Curry–Howard correspondence between well-formed interaction nets and a deep-inference deduction system based on linear logic. In particular, linear logic itself is easily expressed in the system and its computational aspects materialise though the correspondence. The system of interaction nets obtained is a typed variant of already well-known sharing graphs. Due to a strong confluence property, strong normalisation for this system follows from weak normalisation. The latter is obtained via an adaptation of Girard's reducibility method. The approach is modular, readily gives rise to generalisations (e.g. second order, known as polymorphism to the programmer) and could therefore be extended to various systems of interaction nets.

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Stéphane Gimenez and Georg Moser. The Structure of Interaction. In Computer Science Logic 2013 (CSL 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 23, pp. 316-331, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InProceedings{gimenez_et_al:LIPIcs.CSL.2013.316,
  author =	{Gimenez, St\'{e}phane and Moser, Georg},
  title =	{{The Structure of Interaction}},
  booktitle =	{Computer Science Logic 2013 (CSL 2013)},
  pages =	{316--331},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-60-6},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{23},
  editor =	{Ronchi Della Rocca, Simona},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2013.316},
  URN =		{urn:nbn:de:0030-drops-42052},
  doi =		{10.4230/LIPIcs.CSL.2013.316},
  annote =	{Keywords: Interaction Nets, Linear Logic, Curry–Howard Correspondence, Deep Inference, Calculus of Structures, Strong Normalisation, Reducibility}
}

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Interaction Automata and the ia2d Interpreter

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The Structure of Interaction

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