research-article

Functional pearl: la tour d'Hanoï

Author:

Ralf HinzeAuthors Info & Claims

ICFP '09: Proceedings of the 14th ACM SIGPLAN international conference on Functional programming

Pages 3 - 10

https://doi.org/10.1145/1596550.1596555

Published: 31 August 2009 Publication History

Get Access

Abstract

This pearl aims to demonstrate the ideas of wholemeal and projective programming using the Towers of Hanoi puzzle as a running example. The puzzle has its own beauty, which we hope to expose along the way.

Supplementary Material

JPG File (functionalpearllatourdhanoionvimeo.jpg)

Download
7.85 KB

MP4 File (functionalpearllatourdhanoionvimeo.mp4)

Download
68.27 MB

References

[1]

Backhouse, Roland, and Maarten Fokkinga. 2001. The associativity of equivalence and the Towers of Hanoi problem. Information Processing Letters 77:71--76.

Digital Library

Google Scholar

[2]

Bird, Richard, and Oege de Moor. 1997. Algebra of Programming. London: Prentice Hall Europe.

Digital Library

Google Scholar

[3]

Buneman, Peter, and Leon Levy. 1980. The Towers of Hanoi problem. Information Processing Letters 10(4-5):243--244.

Crossref

Google Scholar

[4]

Er, M.C. 1983. An analysis of the generalized Towers of Hanoi problem. BIT 23:429--435.

Crossref

Google Scholar

[5]

Gardner, Martin. 1972. Mathematical games: The curious properties of the Gray code and how it can be used to solve puzzles. Scientific American 227(2):106--109. Reprinted, with Answer, Addendum, and Bibliography, as Chapter 2 of Knotted Doughnuts and Other Mathematical Entertainments, W. H. Freeman and Co., New York, 1986.

Crossref

Google Scholar

[6]

Hinze, Ralf. 2008. Functional Pearl: Streams and Unique Fixed Points. In Proceedings of the 2008 International Conference on Functional Programming, ed. Peter Thiemann, 189--200. ACM Press.

Digital Library

Google Scholar

[7]

Knuth, Donald E. 2005. The Art of Computer Programming, Volume 4, Fascicle 2: Generating All Tuples and Permutations. Addison-Wesley Publishing Company.

Digital Library

Google Scholar

[8]

Korittky, Joachim. 1998. Functional METAPOST. Diplomarbeit, Universitat Bonn.

Google Scholar

[9]

Stockmeyer, Paul K. 2005. The Tower of Hanoi: A bibliography. Available from http://www.cs.wm.edu/~pkstoc/biblio2.pdf.

Google Scholar

Cited By

View all

HINZE RMARTIN C(2018)Batcher's odd-even merging network revealedJournal of Functional Programming10.1017/S095679681800016328Online publication date: 4-Jun-2018
https://doi.org/10.1017/S0956796818000163
Cosman BJhala R(2017)Local refinement typingProceedings of the ACM on Programming Languages10.1145/31102701:ICFP(1-27)Online publication date: 29-Aug-2017
https://dl.acm.org/doi/10.1145/3110270
Cosman BJhala R(2017)Local refinement typingProceedings of the ACM on Programming Languages10.1145/31102701:ICFP(1-27)Online publication date: 29-Aug-2017
https://doi.org/10.1145/3110270

Index Terms

Functional pearl: la tour d'Hanoï
1. Software and its engineering
  1. Software notations and tools
    1. General programming languages
      1. Language features
        Frameworks
        Patterns
        Recursion
      2. Language types
        Functional languages

Recommendations

Functional pearl: la tour d'Hanoï
ICFP '09

This pearl aims to demonstrate the ideas of wholemeal and projective programming using the Towers of Hanoi puzzle as a running example. The puzzle has its own beauty, which we hope to expose along the way.
On the treewidth of Hanoi graphs
Highlights
- Analysis of Hanoi graphs, which arise from the classic Tower of Hanoi puzzle.
- ...
Abstract
The objective of the well-known Tower of Hanoi puzzle is to move a set of discs one at a time from one of a set of pegs to another, while keeping the discs sorted on each peg. We propose an adversarial variation in which the first ...
The worst Hanoi graphs

The ''Towers of Hanoi'' is a problem that has been extensively studied and frequently generalized. We are interested in its generalization to arbitrary directed graphs and ask how many moves are required in a given graph to move n disks from the ...

Comments

Information & Contributors

Information

Published In

ICFP '09: Proceedings of the 14th ACM SIGPLAN international conference on Functional programming

August 2009

364 pages

ISBN:9781605583327

DOI:10.1145/1596550

General Chair:
Graham Hutton
University of Nottingham
,
Program Chair:
Andrew Tolmach
Portland State University

ACM SIGPLAN Notices Volume 44, Issue 9
ICFP '09
September 2009
343 pages
ISSN:0362-1340
EISSN:1558-1160
DOI:10.1145/1631687
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 ACM 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]

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 31 August 2009

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Research-article

Conference

ICFP '09

Sponsor:

ICFP '09: ACM SIGPLAN International Conference on Functional Programming

August 31 - September 2, 2009

Edinburgh, Scotland

Acceptance Rates

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

Upcoming Conference

ICFP '25

Sponsor:
sigplan

ACM SIGPLAN International Conference on Functional Programming

October 12 - 18, 2025

Singapore , Singapore

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

3
Total Citations
View Citations
759
Total Downloads

Downloads (Last 12 months)6
Downloads (Last 6 weeks)0

Reflects downloads up to 09 Nov 2024

Other Metrics

View Author Metrics

Citations

Cited By

View all

HINZE RMARTIN C(2018)Batcher's odd-even merging network revealedJournal of Functional Programming10.1017/S095679681800016328Online publication date: 4-Jun-2018
https://doi.org/10.1017/S0956796818000163
Cosman BJhala R(2017)Local refinement typingProceedings of the ACM on Programming Languages10.1145/31102701:ICFP(1-27)Online publication date: 29-Aug-2017
https://dl.acm.org/doi/10.1145/3110270
Cosman BJhala R(2017)Local refinement typingProceedings of the ACM on Programming Languages10.1145/31102701:ICFP(1-27)Online publication date: 29-Aug-2017
https://doi.org/10.1145/3110270

View Options

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Cited By

Index Terms

Recommendations

Functional pearl: la tour d'Hanoï

On the treewidth of Hanoi graphs

The worst Hanoi graphs