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DOI: 10.4230/LIPIcs.ITP.2019.26

Ornaments for Proof Reuse in Coq

Authors: Talia Ringer, Nathaniel Yazdani, John Leo, and Dan Grossman

Published in: LIPIcs, Volume 141, 10th International Conference on Interactive Theorem Proving (ITP 2019)

Abstract

Ornaments express relations between inductive types with the same inductive structure. We implement fully automatic proof reuse for a particular class of ornaments in a Coq plugin, and show how such a tool can give programmers the rewards of using indexed inductive types while automating away many of the costs. The plugin works directly on Coq code; it is the first ornamentation tool for a non-embedded dependently typed language. It is also the first tool to automatically identify ornaments: To lift a function or proof, the user must provide only the source type, the destination type, and the source function or proof. In taking advantage of the mathematical properties of ornaments, our approach produces faster functions and smaller terms than a more general approach to proof reuse in Coq.

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Talia Ringer, Nathaniel Yazdani, John Leo, and Dan Grossman. Ornaments for Proof Reuse in Coq. In 10th International Conference on Interactive Theorem Proving (ITP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 141, pp. 26:1-26:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{ringer_et_al:LIPIcs.ITP.2019.26,
  author =	{Ringer, Talia and Yazdani, Nathaniel and Leo, John and Grossman, Dan},
  title =	{{Ornaments for Proof Reuse in Coq}},
  booktitle =	{10th International Conference on Interactive Theorem Proving (ITP 2019)},
  pages =	{26:1--26:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-122-1},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{141},
  editor =	{Harrison, John and O'Leary, John and Tolmach, Andrew},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2019.26},
  URN =		{urn:nbn:de:0030-drops-110816},
  doi =		{10.4230/LIPIcs.ITP.2019.26},
  annote =	{Keywords: ornaments, proof reuse, proof automation}
}

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DOI: 10.4230/LIPIcs.SNAPL.2017.2

Domain-Specific Symbolic Compilation

Authors: Rastislav Bodík, Kartik Chandra, Phitchaya Mangpo Phothilimthana, and Nathaniel Yazdani

Published in: LIPIcs, Volume 71, 2nd Summit on Advances in Programming Languages (SNAPL 2017)

Abstract

A symbolic compiler translates a program to symbolic constraints, automatically reducing model checking and synthesis to constraint solving. We show that new applications of constraint solving require domain-specific encodings that yield the required orders of magnitude improvements in solver efficiency. Unfortunately, these encodings cannot be obtained with today's symbolic compilation. We introduce symbolic languages that encapsulate domain-specific encodings under abstractions that behave as their non-symbolic counterparts: client code using the abstractions can be tested and debugged on concrete inputs. When client code is symbolically compiled, the resulting constraints use domain-specific encodings. We demonstrate the idea on the first fully symbolic checker of type systems; a program partitioner; and a parallelizer of tree computations. In each of these case studies, symbolic languages improved on classical symbolic compilers by orders of magnitude.

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Rastislav Bodík, Kartik Chandra, Phitchaya Mangpo Phothilimthana, and Nathaniel Yazdani. Domain-Specific Symbolic Compilation. In 2nd Summit on Advances in Programming Languages (SNAPL 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 71, pp. 2:1-2:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{bodik_et_al:LIPIcs.SNAPL.2017.2,
  author =	{Bod{\'\i}k, Rastislav and Chandra, Kartik and Phothilimthana, Phitchaya Mangpo and Yazdani, Nathaniel},
  title =	{{Domain-Specific Symbolic Compilation}},
  booktitle =	{2nd Summit on Advances in Programming Languages (SNAPL 2017)},
  pages =	{2:1--2:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-032-3},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{71},
  editor =	{Lerner, Benjamin S. and Bod{\'\i}k, Rastislav and Krishnamurthi, Shriram},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SNAPL.2017.2},
  URN =		{urn:nbn:de:0030-drops-71334},
  doi =		{10.4230/LIPIcs.SNAPL.2017.2},
  annote =	{Keywords: Symbolic evaluation, program synthesis, DSLs}
}

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Documents authored by Yazdani, Nathaniel

Ornaments for Proof Reuse in Coq

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Domain-Specific Symbolic Compilation

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