research-article

Functional programming with structured graphs

Authors:

Bruno C.d.S. Oliveira,

William R. CookAuthors Info & Claims

ICFP '12: Proceedings of the 17th ACM SIGPLAN international conference on Functional programming

Pages 77 - 88

https://doi.org/10.1145/2364527.2364541

Published: 09 September 2012 Publication History

Abstract

This paper presents a new functional programming model for graph structures called structured graphs. Structured graphs extend conventional algebraic datatypes with explicit definition and manipulation of cycles and/or sharing, and offer a practical and convenient way to program graphs in functional programming languages like Haskell. The representation of sharing and cycles (edges) employs recursive binders and uses an encoding inspired by parametric higher-order abstract syntax. Unlike traditional approaches based on mutable references or node/edge lists, well-formedness of the graph structure is ensured statically and reasoning can be done with standard functional programming techniques. Since the binding structure is generic, we can define many useful generic combinators for manipulating structured graphs. We give applications and show how to reason about structured graphs.

References

[1]

M. Abbott, T. Altenkirch, C. McBride, and N. Ghani. δ for data: Differentiating data structures. Fundam. Inf., 65:1--28, 2004.

Digital Library

[2]

A. V. Aho, R. Sethi, and J. D. Ullman. Compilers: Principles, Techniques and Tools. Addison-Wesley, 1988.

Digital Library

[3]

R. Atkey. Syntax for free: Representing syntax with binding using parametricity. In TLCA'09, 2009.

Digital Library

[4]

A. Baars, S. Doaitse Swierstra, and M. Viera. Typed transformations of typed grammars: The left corner transform. Electron. Notes Theor. Comput. Sci., 253(7), 2010.

Digital Library

[5]

R. Bird and R. Paterson. Generalised folds for nested datatypes. Formal Aspects of Computing, 11:11--2, 1999.

Digital Library

[6]

R. S. Bird and L. G. L. T. Meertens. Nested datatypes. In MPC '98, 1998.

Digital Library

[7]

J. A. Brzozowski. Derivatives of regular expressions. J. ACM, 11, 1964.

Digital Library

[8]

P. P. Chen. The entity-relationship model - toward a unified view of data. ACM Trans. Database Syst., 1(1):9--36, 1976.

Digital Library

[9]

A. Chlipala. Parametric higher-order abstract syntax for mechanized semantics. In ICFP'08, 2008.

Digital Library

[10]

N. A. Danielsson. Total parser combinators. In ICFP'10, 2010.

Digital Library

[11]

J. Despeyroux, A. Felty, and A. Hirschowitz. Higher-order abstract syntax in Coq. In TLCA'95, 1995.

Digital Library

[12]

D. Devriese and F. Piessens. Explicitly recursive grammar combinators - a better model for shallow parser DSLs. In PADL 2011, 2011.

Digital Library

[13]

M. Erwig. Inductive graphs and functional graph algorithms. J. Funct. Program., 11, 2001.

Digital Library

[14]

L. Fegaras and T. Sheard. Revisiting catamorphisms over datatypes with embedded functions (or, programs from outer space). In POPL'96, 1996.

Digital Library

[15]

N. Ghani, M. Hamana, T. Uustalu, and V Vene. Representing cyclic structures as nested datatypes. In TFP'06, 2006.

[16]

J. Gibbons. An initial-algebra approach to directed acyclic graphs. In MPC '95, 1995.

Digital Library

[17]

J. Gibbons. Datatype-generic programming. In Spring School on Datatype-Generic Programming, volume 4719 of Lecture Notes in Computer Science. Springer-Verlag, 2007.

Digital Library

[18]

J. Gibbons and B. C. d. S. Oliveira. The essence of the iterator pattern. J. Funct. Program., 19(3-4), 2009.

Digital Library

[19]

A. Gill. Type-safe observable sharing in Haskell. In Haskell'09, 2009.

Digital Library

[20]

M. Hamana. Initial algebra semantics for cyclic sharing tree structures. Logical Methods in Computer Science, 6(3), 2010.

[21]

F. Honsell, M. Miculan, and I. Scagnetto. An axiomatic approach to metareasoning on nominal algebras in hoas. In ICALP '01, 2001.

Digital Library

[22]

J. Hughes. Lazy memo-functions. In FPCA'85, 1985.

Digital Library

[23]

P. Jansson and J. Jeuring. Polyp - a polytypic programming language extension. In POPL'97, 1997.

Digital Library

[24]

X. Leroy, D. Doligez, A. Frisch, J. Garrigue, D. Rémy, and J. Vouillon. The OCaml system (release 3.12): Documentation and user's manual. Institut National de Recherche en Informatique et en Automatique, 2011.

[25]

C.Martin, J. Gibbons, and I. Bayley. Disciplined, efficient, generalised folds for nested datatypes. Form. Asp. Comput., 16, 2004.

Digital Library

[26]

C. Mcbride and R. Paterson. Applicative programming with effects. J. Funct. Program., 18(1), 2008.

Digital Library

[27]

E. Meijer and G. Hutton. Bananas in space: extending fold and unfold to exponential types. In FPCA'95, 1995.

Digital Library

[28]

M. Might, D. Darais, and D. Spiewak. Parsing with derivatives: a functional pearl. In ICFP '11, 2011.

Digital Library

[29]

R. Milner, M. Tofte, R. Harper, and D. Macqueen. The Definition of Standard ML - Revised. The MIT Press, 1997.

[30]

B. C. d. S. Oliveira and Andres Löh. Abstract syntax graphs for domain specific languages. Unpublished. Manuscript available at http://ropas.snu.ac.kr/~bruno/papers/ASGDSL.pdf, 2012.

[31]

S. Peyton Jones et al. The Haskell 98 language and libraries: The revised report. Journal of Functional Programming, 13(1):0--255, 2003.

[32]

S. Peyton Jones, D. Vytiniotis, S. Weirich, and M. Shields. Practical type inference for arbitrary-rank types. J. Funct. Program., 17:1--82, 2007.

Digital Library

[33]

S. Peyton Jones, D. Vytiniotis, S. Weirich, and G. Washburn. Simple unification-based type inference for GADTs. In ICFP'06, 2006.

Digital Library

[34]

F. Pfenning and C. Elliot. Higher-order abstract syntax. In PLDI '88, 1988.

Digital Library

[35]

F. Pottier. Lazy least fixed points in ML. Unpublished. Manuscript available at http://gallium.inria.fr/~fpottier/publis/fpottier-fix.pdf, 2009.

[36]

J. C. Reynolds. Types, abstraction and parametric polymorphism. In IFIP Congress, pages 513--523, 1983.

[37]

P. Wadler. Theorems for free! In FPCA '89, 1989.

Digital Library

[38]

P. Wadler. The essence of functional programming. In POPL'92, 1992.

Digital Library

[39]

G. Washburn and S. Weirich. Boxes go bananas: Encoding higher-order abstract syntax with parametric polymorphism. Journal of Functional Programming, 18:87--140, 2008.

Digital Library

Cited By

Bahr PHutton G(2024)Beyond Trees: Calculating Graph-Based Compilers (Functional Pearl)Proceedings of the ACM on Programming Languages10.1145/36746388:ICFP(370-394)Online publication date: 15-Aug-2024
https://dl.acm.org/doi/10.1145/3674638
Mell SBastani OZdancewic S(2023)Ideograph: A Language for Expressing and Manipulating Structured DataElectronic Proceedings in Theoretical Computer Science10.4204/EPTCS.377.4377(65-84)Online publication date: 1-Apr-2023
https://doi.org/10.4204/EPTCS.377.4
IWASAKI HEMOTO KMORIHATA AMATSUZAKI KHU Z(2022)Fregel: a functional domain-specific language for vertex-centric large-scale graph processingJournal of Functional Programming10.1017/S095679682100027732Online publication date: 20-Jan-2022
https://doi.org/10.1017/S0956796821000277
Show More Cited By

Index Terms

Functional programming with structured graphs
1. Software and its engineering
  1. Software notations and tools
    1. General programming languages
      1. Language features
      2. Language types
        Functional languages
2. Theory of computation
  1. Semantics and reasoning
    1. Program constructs

Recommendations

Functional programming with structured graphs
ICFP '12

This paper presents a new functional programming model for graph structures called structured graphs. Structured graphs extend conventional algebraic datatypes with explicit definition and manipulation of cycles and/or sharing, and offer a practical and ...
Abstract syntax graphs for domain specific languages
PEPM '13: Proceedings of the ACM SIGPLAN 2013 workshop on Partial evaluation and program manipulation

This paper presents a representation for embedded domain specific languages (EDSLs) using abstract syntax graphs (ASGs). The purpose of this representation is to deal with the important problem of defining operations that require observing or preserving ...
A Characterization of $K_{2,4}$-Minor-Free Graphs

We provide a complete structural characterization of $K_{2,4}$-minor-free graphs. The 3-connected $K_{2,4}$-minor-free graphs consist of nine small graphs on at most eight vertices, together with a family of planar graphs that contains $2n-8$ ...

Comments

Information & Contributors

Information

Published In

cover image ACM Conferences

ICFP '12: Proceedings of the 17th ACM SIGPLAN international conference on Functional programming

September 2012

392 pages

ISBN:9781450310543

DOI:10.1145/2364527

General Chair:
Peter Thiemann
University of Freiburg, Germany
,
Program Chair:
Robby Findler
Northwestern University, USA

ACM SIGPLAN Notices Volume 47, Issue 9
ICFP '12
September 2012
368 pages
ISSN:0362-1340
EISSN:1558-1160
DOI:10.1145/2398856
Issue’s Table of Contents

Copyright © 2012 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 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]

Sponsors

SIGPLAN: ACM Special Interest Group on Programming Languages

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 09 September 2012

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Research-article

Conference

ICFP'12

Sponsor:

SIGPLAN

ICFP'12: ACM SIGPLAN International Conference on Functional Programming

September 9 - 15, 2012

Copenhagen, Denmark

Acceptance Rates

ICFP '12 Paper Acceptance Rate 32 of 88 submissions, 36%;

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

28
Total Citations
View Citations
562
Total Downloads

Downloads (Last 12 months)13
Downloads (Last 6 weeks)4

Reflects downloads up to 15 Oct 2024

Other Metrics

View Author Metrics

Citations

Cited By

Bahr PHutton G(2024)Beyond Trees: Calculating Graph-Based Compilers (Functional Pearl)Proceedings of the ACM on Programming Languages10.1145/36746388:ICFP(370-394)Online publication date: 15-Aug-2024
https://dl.acm.org/doi/10.1145/3674638
Mell SBastani OZdancewic S(2023)Ideograph: A Language for Expressing and Manipulating Structured DataElectronic Proceedings in Theoretical Computer Science10.4204/EPTCS.377.4377(65-84)Online publication date: 1-Apr-2023
https://doi.org/10.4204/EPTCS.377.4
IWASAKI HEMOTO KMORIHATA AMATSUZAKI KHU Z(2022)Fregel: a functional domain-specific language for vertex-centric large-scale graph processingJournal of Functional Programming10.1017/S095679682100027732Online publication date: 20-Jan-2022
https://doi.org/10.1017/S0956796821000277
Nguyen MWu N(2022)Folding over Neural NetworksMathematics of Program Construction10.1007/978-3-031-16912-0_5(129-150)Online publication date: 22-Sep-2022
https://doi.org/10.1007/978-3-031-16912-0_5
Matsuda KAsada KSchultz UYallop J(2017)A functional reformulation of UnCAL graph-transformations: or, graph transformation as graph reductionProceedings of the 2017 ACM SIGPLAN Workshop on Partial Evaluation and Program Manipulation10.1145/3018882.3018883(71-82)Online publication date: 2-Jan-2017
https://dl.acm.org/doi/10.1145/3018882.3018883
Dexter PLiu YChiu K(2016)Lazy graph processing in HaskellACM SIGPLAN Notices10.1145/3241625.297601451:12(182-192)Online publication date: 8-Sep-2016
https://dl.acm.org/doi/10.1145/3241625.2976014
Ploeg AClaessen KBuiras P(2016)The Key monad: type-safe unconstrained dynamic typingACM SIGPLAN Notices10.1145/3241625.297600851:12(146-157)Online publication date: 8-Sep-2016
https://dl.acm.org/doi/10.1145/3241625.2976008
Emoto KMatsuzaki KHu ZMorihata AIwasaki H(2016)Think like a vertex, behave like a function! a functional DSL for vertex-centric big graph processingACM SIGPLAN Notices10.1145/3022670.295193851:9(200-213)Online publication date: 4-Sep-2016
https://dl.acm.org/doi/10.1145/3022670.2951938
Dexter PLiu YChiu KMainland G(2016)Lazy graph processing in HaskellProceedings of the 9th International Symposium on Haskell10.1145/2976002.2976014(182-192)Online publication date: 8-Sep-2016
https://dl.acm.org/doi/10.1145/2976002.2976014
Ploeg AClaessen KBuiras PMainland G(2016)The Key monad: type-safe unconstrained dynamic typingProceedings of the 9th International Symposium on Haskell10.1145/2976002.2976008(146-157)Online publication date: 8-Sep-2016
https://dl.acm.org/doi/10.1145/2976002.2976008
Show More Cited By

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.

Full Access

Get this Publication

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Media

Figures

Other

Tables

View Table of Contents