research-article

Histo- and dynamorphisms revisited

Authors:

Nicolas WuAuthors Info & Claims

WGP '13: Proceedings of the 9th ACM SIGPLAN workshop on Generic programming

Pages 1 - 12

https://doi.org/10.1145/2502488.2502496

Published: 28 September 2013 Publication History

Abstract

Dynamic programming algorithms embody a widely used programming technique that optimizes recursively defined equations that have repeating subproblems. The standard solution uses arrays to share common results between successive steps, and while effective, this fails to exploit the structural properties present in these problems. Histomorphisms and dynamorphisms have been introduced to expresses such algorithms in terms of structured recursion schemes that leverage this structure. In this paper, we revisit and relate these schemes and show how they can be expressed in terms of recursion schemes from comonads, as well as from recursive coalgebras. Our constructions rely on properties of bialgebras and dicoalgebras, and we are careful to consider optimizations and efficiency concerns. Throughout the paper we illustrate these techniques through several worked-out examples discussed in a tutorial style, and show how a recursive specification can be expressed both as an array-based algorithm as well as one that uses recursion schemes.

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Cited By

Yang ZWu N(2022)Fantastic Morphisms and Where to Find ThemMathematics of Program Construction10.1007/978-3-031-16912-0_9(222-267)Online publication date: 22-Sep-2022
https://doi.org/10.1007/978-3-031-16912-0_9
Willis JWu NPickering M(2020)Staged selective parser combinatorsProceedings of the ACM on Programming Languages10.1145/34090024:ICFP(1-30)Online publication date: 3-Aug-2020
https://dl.acm.org/doi/10.1145/3409002
Llorens DVilar J(2020)Easily solving dynamic programming problems in Haskell by memoization of hylomorphismsSoftware: Practice and Experience10.1002/spe.288750:12(2193-2211)Online publication date: 17-Sep-2020
https://doi.org/10.1002/spe.2887
Show More Cited By

Index Terms

Histo- and dynamorphisms revisited
1. Software and its engineering
  1. Software notations and tools
    1. General programming languages
      1. Language types
        Functional languages
2. Theory of computation
  1. Logic
  2. Semantics and reasoning
    1. Program reasoning

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cover image ACM Conferences

WGP '13: Proceedings of the 9th ACM SIGPLAN workshop on Generic programming

September 2013

92 pages

ISBN:9781450323895

DOI:10.1145/2502488

Program Chairs:
Jacques Carette
McMaster University, Canada
,
Jeremiah Willcock
Indiana University, USA

Copyright © 2013 ACM.

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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SIGPLAN: ACM Special Interest Group on Programming Languages

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 28 September 2013

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ICFP'13

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SIGPLAN

ICFP'13: ACM SIGPLAN International Conference on Functional Programming

September 28, 2013

Massachusetts, Boston, USA

Acceptance Rates

WGP '13 Paper Acceptance Rate 8 of 14 submissions, 57%;

Overall Acceptance Rate 30 of 43 submissions, 70%

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ICFP '25

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sigplan

ACM SIGPLAN International Conference on Functional Programming

October 12 - 18, 2025

Singapore , Singapore

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Cited By

Yang ZWu N(2022)Fantastic Morphisms and Where to Find ThemMathematics of Program Construction10.1007/978-3-031-16912-0_9(222-267)Online publication date: 22-Sep-2022
https://doi.org/10.1007/978-3-031-16912-0_9
Willis JWu NPickering M(2020)Staged selective parser combinatorsProceedings of the ACM on Programming Languages10.1145/34090024:ICFP(1-30)Online publication date: 3-Aug-2020
https://dl.acm.org/doi/10.1145/3409002
Llorens DVilar J(2020)Easily solving dynamic programming problems in Haskell by memoization of hylomorphismsSoftware: Practice and Experience10.1002/spe.288750:12(2193-2211)Online publication date: 17-Sep-2020
https://doi.org/10.1002/spe.2887
Sokhatskyi MMaslianko P(2018)The systems engineering of consistent pure language with effect type system for certified applications and higher languages10.1063/1.5045439(020033)Online publication date: 2018
https://doi.org/10.1063/1.5045439
Hinze RWu NGibbons J(2015)Conjugate Hylomorphisms -- OrACM SIGPLAN Notices10.1145/2775051.267698950:1(527-538)Online publication date: 14-Jan-2015
https://dl.acm.org/doi/10.1145/2775051.2676989
Hinze RWu NGibbons JRajamani SWalker D(2015)Conjugate Hylomorphisms -- OrProceedings of the 42nd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages10.1145/2676726.2676989(527-538)Online publication date: 14-Jan-2015
https://dl.acm.org/doi/10.1145/2676726.2676989

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