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All sorts of permutations (functional pearl)

Authors:

Jan Christiansen,

Nikita Danilenko,

Sandra DylusAuthors Info & Claims

ACM SIGPLAN Notices, Volume 51, Issue 9

Pages 168 - 179

https://doi.org/10.1145/3022670.2951949

Published: 04 September 2016 Publication History

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Abstract

The combination of non-determinism and sorting is mostly associated with permutation sort, a sorting algorithm that is not very useful for sorting and has an awful running time. In this paper we look at the combination of non-determinism and sorting in a different light: given a sorting function, we apply it to a non-deterministic predicate to gain a function that enumerates permutations of the input list. We get to the bottom of necessary properties of the sorting algorithms and predicates in play as well as discuss variations of the modelled non-determinism. On top of that, we formulate and prove a theorem stating that no matter which sorting function we use, the corresponding permutation function enumerates all permutations of the input list. We use free theorems, which are derived from the type of a function alone, to prove the statement.

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Cited By

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Pal ASaiki BTjoa RRichey CZhu AFlatt OWillsey MTatlock ZNandi C(2023)Equality Saturation Theory Exploration à la CarteProceedings of the ACM on Programming Languages10.1145/36228347:OOPSLA2(1034-1062)Online publication date: 16-Oct-2023
https://dl.acm.org/doi/10.1145/3622834
Braack MHenning CZiesmer J(2023)Pure strategy Nash equilibria for bargaining models of collective choiceInternational Journal of Game Theory10.1007/s00182-023-00882-z53:2(373-421)Online publication date: 27-Nov-2023
https://doi.org/10.1007/s00182-023-00882-z

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All sorts of permutations (functional pearl)

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All sorts of permutations (functional pearl)
ICFP 2016: Proceedings of the 21st ACM SIGPLAN International Conference on Functional Programming

The combination of non-determinism and sorting is mostly associated with permutation sort, a sorting algorithm that is not very useful for sorting and has an awful running time. In this paper we look at the combination of non-determinism and sorting in ...
On the combinatorics of derangements and related permutations
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Abstract
A derangement is a permutation in which no entry is at its original position. The number of derangements of [ n ] is called the “derangement number” or “de Montmort number”, and is denoted by D n. The sequence { D n } enumerates, in ...
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Permutations are sequences where each symbol in the given alphabet Σ appears exactly once. A transposition is an operation that exchanges two adjacent sublists in a permutation; if one of these sublists is restricted to be a prefix then one obtains a ...

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Information

Published In

ACM SIGPLAN Notices Volume 51, Issue 9

ICFP '16

September 2016

501 pages

ISSN:0362-1340

EISSN:1558-1160

DOI:10.1145/3022670

Editor:
Matthew Fluet

Issue’s Table of Contents

ICFP 2016: Proceedings of the 21st ACM SIGPLAN International Conference on Functional Programming
September 2016
501 pages
ISBN:9781450342193
DOI:10.1145/2951913
General Chairs:
Jacques Garrigue
Nagoya University, Japan
,
Gabriele Keller
University of New South Wales, Australia
,
Program Chair:
Eijiro Sumii
Tohoku University, Japan

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Association for Computing Machinery

New York, NY, United States

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Published: 04 September 2016

Published in SIGPLAN Volume 51, Issue 9

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Pal ASaiki BTjoa RRichey CZhu AFlatt OWillsey MTatlock ZNandi C(2023)Equality Saturation Theory Exploration à la CarteProceedings of the ACM on Programming Languages10.1145/36228347:OOPSLA2(1034-1062)Online publication date: 16-Oct-2023
https://dl.acm.org/doi/10.1145/3622834
Braack MHenning CZiesmer J(2023)Pure strategy Nash equilibria for bargaining models of collective choiceInternational Journal of Game Theory10.1007/s00182-023-00882-z53:2(373-421)Online publication date: 27-Nov-2023
https://doi.org/10.1007/s00182-023-00882-z

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