License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ITP.2023.21
URN: urn:nbn:de:0030-drops-183963
URL: https://drops.dagstuhl.de/opus/volltexte/2023/18396/
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Larchey-Wendling, Dominique ; Monin, Jean-François

Proof Pearl: Faithful Computation and Extraction of μ-Recursive Algorithms in Coq

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LIPIcs-ITP-2023-21.pdf (0.7 MB)


Abstract

Basing on an original Coq implementation of unbounded linear search for partially decidable predicates, we study the computational contents of μ-recursive functions via their syntactic representation, and a correct by construction Coq interpreter for this abstract syntax. When this interpreter is extracted, we claim the resulting OCaml code to be the natural combination of the implementation of the μ-recursive schemes of composition, primitive recursion and unbounded minimization of partial (i.e., possibly non-terminating) functions. At the level of the fully specified Coq terms, this implies the representation of higher-order functions of which some of the arguments are themselves partial functions. We handle this issue using some techniques coming from the Braga method. Hence we get a faithful embedding of μ-recursive algorithms into Coq preserving not only their extensional meaning but also their intended computational behavior. We put a strong focus on the quality of the Coq artifact which is both self contained and with a line of code count of less than 1k in total.

BibTeX - Entry

@InProceedings{larcheywendling_et_al:LIPIcs.ITP.2023.21,
  author =	{Larchey-Wendling, Dominique and Monin, Jean-Fran\c{c}ois},
  title =	{{Proof Pearl: Faithful Computation and Extraction of \mu-Recursive Algorithms in Coq}},
  booktitle =	{14th International Conference on Interactive Theorem Proving (ITP 2023)},
  pages =	{21:1--21:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-284-6},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{268},
  editor =	{Naumowicz, Adam and Thiemann, Ren\'{e}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/18396},
  URN =		{urn:nbn:de:0030-drops-183963},
  doi =		{10.4230/LIPIcs.ITP.2023.21},
  annote =	{Keywords: Unbounded linear search, \mu-recursive functions, computational contents, Coq, extraction, OCaml}
}

Keywords: Unbounded linear search, μ-recursive functions, computational contents, Coq, extraction, OCaml
Collection: 14th International Conference on Interactive Theorem Proving (ITP 2023)
Issue Date: 2023
Date of publication: 26.07.2023
Supplementary Material: Software: https://github.com/DmxLarchey/Murec_Extraction archived at: https://archive.softwareheritage.org/swh:1:dir:4d128568b56a17277c4f69ee1805e3910665f34f


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