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All sorts of permutations (functional pearl)

Authors:

Jan Christiansen,

Nikita Danilenko,

Sandra DylusAuthors Info & Claims

ICFP 2016: Proceedings of the 21st ACM SIGPLAN International Conference on Functional Programming

Pages 168 - 179

https://doi.org/10.1145/2951913.2951949

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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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
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

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All sorts of permutations (functional pearl)

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All sorts of permutations (functional pearl)
ICFP '16

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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Published In

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

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

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

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Association for Computing Machinery

New York, NY, United States

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Published: 04 September 2016

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ICFP'16

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SIGPLAN

ICFP'16: ACM SIGPLAN International Conference on Functional Programming

September 18 - 24, 2016

Nara, Japan

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Overall Acceptance Rate 333 of 1,064 submissions, 31%

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ICFP '25

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October 12 - 18, 2025

Singapore , Singapore

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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
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

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