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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: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/18396/
Larchey-Wendling, Dominique ;
Monin, Jean-François
Proof Pearl: Faithful Computation and Extraction of μ-Recursive Algorithms in Coq
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}
}
