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DOI: 10.4230/LIPIcs.FSCD.2021.9

A Strong Call-By-Need Calculus

Authors: Thibaut Balabonski, Antoine Lanco, and Guillaume Melquiond

Published in: LIPIcs, Volume 195, 6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021)

Abstract

We present a call-by-need λ-calculus that enables strong reduction (that is, reduction inside the body of abstractions) and guarantees that arguments are only evaluated if needed and at most once. This calculus uses explicit substitutions and subsumes the existing strong-call-by-need strategy, but allows for more reduction sequences, and often shorter ones, while preserving the neededness. The calculus is shown to be normalizing in a strong sense: Whenever a λ-term t admits a normal form n in the λ-calculus, then any reduction sequence from t in the calculus eventually reaches a representative of the normal form n. We also exhibit a restriction of this calculus that has the diamond property and that only performs reduction sequences of minimal length, which makes it systematically better than the existing strategy. We have used the Abella proof assistant to formalize part of this calculus, and discuss how this experiment affected its design.

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Thibaut Balabonski, Antoine Lanco, and Guillaume Melquiond. A Strong Call-By-Need Calculus. In 6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 195, pp. 9:1-9:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{balabonski_et_al:LIPIcs.FSCD.2021.9,
  author =	{Balabonski, Thibaut and Lanco, Antoine and Melquiond, Guillaume},
  title =	{{A Strong Call-By-Need Calculus}},
  booktitle =	{6th International Conference on Formal Structures for Computation and Deduction (FSCD 2021)},
  pages =	{9:1--9:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-191-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{195},
  editor =	{Kobayashi, Naoki},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2021.9},
  URN =		{urn:nbn:de:0030-drops-142477},
  doi =		{10.4230/LIPIcs.FSCD.2021.9},
  annote =	{Keywords: strong reduction, call-by-need, evaluation strategy, normalization}
}

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DOI: 10.4230/DagSemProc.06021.4

A Proposal to add Interval Arithmetic to the C++ Standard Library

Authors: Sylvain Pion, Hervé Brönnimann, and Guillaume Melquiond

Published in: Dagstuhl Seminar Proceedings, Volume 6021, Reliable Implementation of Real Number Algorithms: Theory and Practice (2006)

Abstract

I will report on a recent effort by Guillaume Melquiond, HervÃƒÂ© Br"onnimann and myself to push forward a proposal to include interval arithmetic in the next C++ ISO standard. The goals of the standardization are to produce a unified specification which will serve as many uses of intervals as possible, together with hoping for very efficient implementations, closer to the compilers. I will describe how the standardization process works, explain some of the design choices made, and list some of the other questions arising in the process. We welcome any comment on the proposal.

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Sylvain Pion, Hervé Brönnimann, and Guillaume Melquiond. A Proposal to add Interval Arithmetic to the C++ Standard Library. In Reliable Implementation of Real Number Algorithms: Theory and Practice. Dagstuhl Seminar Proceedings, Volume 6021, pp. 1-25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)

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@InProceedings{pion_et_al:DagSemProc.06021.4,
  author =	{Pion, Sylvain and Br\"{o}nnimann, Herv\'{e} and Melquiond, Guillaume},
  title =	{{A Proposal to add Interval Arithmetic to the C++ Standard Library}},
  booktitle =	{Reliable Implementation of Real Number Algorithms: Theory and Practice},
  pages =	{1--25},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2006},
  volume =	{6021},
  editor =	{Peter Hertling and Christoph M. Hoffmann and Wolfram Luther and Nathalie Revol},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.06021.4},
  URN =		{urn:nbn:de:0030-drops-7189},
  doi =		{10.4230/DagSemProc.06021.4},
  annote =	{Keywords: Interval arithmetic, C++, ISO standard}
}

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Documents authored by Melquiond, Guillaume

A Strong Call-By-Need Calculus

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A Proposal to add Interval Arithmetic to the C++ Standard Library

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