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DOI: 10.4230/LIPIcs.TYPES.2013.84

Extracting Imperative Programs from Proofs: In-place Quicksort

Authors: Ulrich Berger, Monika Seisenberger, and Gregory J. M. Woods

Published in: LIPIcs, Volume 26, 19th International Conference on Types for Proofs and Programs (TYPES 2013)

Abstract

The process of program extraction is primarily associated with functional programs with less focus on imperative program extraction. In this paper we consider a standard problem for imperative programming: In-place Quicksort. We formalize a proof that every array of natural numbers can be sorted and apply a realizability interpretation to extract a program from the proof. Using monads we are able to exhibit the inherent imperative nature of the extracted program. We see this as a first step towards an automated extraction of imperative programs. The case study is carried out in the interactive proof assistant Minlog.

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Ulrich Berger, Monika Seisenberger, and Gregory J. M. Woods. Extracting Imperative Programs from Proofs: In-place Quicksort. In 19th International Conference on Types for Proofs and Programs (TYPES 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 26, pp. 84-106, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{berger_et_al:LIPIcs.TYPES.2013.84,
  author =	{Berger, Ulrich and Seisenberger, Monika and Woods, Gregory J. M.},
  title =	{{Extracting Imperative Programs from Proofs: In-place Quicksort}},
  booktitle =	{19th International Conference on Types for Proofs and Programs (TYPES 2013)},
  pages =	{84--106},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-72-9},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{26},
  editor =	{Matthes, Ralph and Schubert, Aleksy},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2013.84},
  URN =		{urn:nbn:de:0030-drops-46274},
  doi =		{10.4230/LIPIcs.TYPES.2013.84},
  annote =	{Keywords: Program Extraction, Verification, Realizability, Imperative Programs, In-Place Quicksort,Computational Monads, Minlog}
}

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Extracting Imperative Programs from Proofs: In-place Quicksort

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