research-article

Typed self-interpretation by pattern matching

Authors:

Jens PalsbergAuthors Info & Claims

ICFP '11: Proceedings of the 16th ACM SIGPLAN international conference on Functional programming

Pages 247 - 258

https://doi.org/10.1145/2034773.2034808

Published: 19 September 2011 Publication History

Abstract

Self-interpreters can be roughly divided into two sorts: self-recognisers that recover the input program from a canonical representation, and self-enactors that execute the input program. Major progress for statically-typed languages was achieved in 2009 by Rendel, Ostermann, and Hofer who presented the first typed self-recogniser that allows representations of different terms to have different types. A key feature of their type system is a type:type rule that renders the kind system of their language inconsistent.

In this paper we present the first statically-typed language that not only allows representations of different terms to have different types, and supports a self-recogniser, but also supports a self-enactor. Our language is a factorisation calculus in the style of Jay and Given-Wilson, a combinatory calculus with a factorisation operator that is powerful enough to support the pattern-matching functions necessary for a self-interpreter. This allows us to avoid a type:type rule. Indeed, the types of System F are sufficient. We have implemented our approach and our experiments support the theory.

Supplementary Material

MP4 File (_talk10.mp4)

Download
53.67 MB

References

[1]

Harold Abelson, Gerald Jay Sussman, and Julie Sussman. Structure and Interpretation of Computer Programs. MIT Press, 1985.

Digital Library

[2]

Henk Barendregt. Self-interpretations in lambda calculus. J. Funct. Program, 1(2):229--233, 1991.

[3]

HP Barendregt. Handbook of Logic in Computer Science (vol. 2): Background: Computational Structures: Abramski,S (ed), chapter Lambda Calculi with Types. Oxford University Press, Inc., New York, NY, 1993.

Digital Library

[4]

Michel Bel. A recursion theoretic self interpreter for the lambda-calculus. http://www.belxs.com/michel/#selfint.

[5]

Alessandro Berarducci and Corrado Böhm. A self-interpreter of lambda calculus having a normal form. In CSL, pages 85--99, 1992.

Digital Library

[6]

Mathieu Boespflug. From self-interpreters to normalization by evaluation. In Olivier Danvy, editor, Proceedings of Workshop on Normalization by Evaluation, 2009.

[7]

bondi programming language. www-staff.it.uts.edu.au/~cbj/bondi.

[8]

Reg Braithwaite. The significance of the meta-circular interpreter. http://weblog.raganwald.com/2006/11/significance-of-meta-circular_22.html, November 2006.

[9]

Jacques Carette, Oleg Kiselyov, and Chung chieh Shan. Finally tagless, partially evaluated: Tagless staged interpreters for simpler typed languages. Journal of Functional Programming, 19(5):509--543, 2009.

Digital Library

[10]

Olivier Danvy and Pablo E. Martínez López. Tagging, encoding, and Jones optimality. In Proceedings of ESOP'03, European Symposium on Programming, pages 335--347. Springer-Verlag (LNCS), 2003.

Digital Library

[11]

Sir Arthur Conan Doyle. The Sign of the Four. Lippincott's Monthly Magazine, February 1890.

[12]

Brendan Eich. Narcissus. http://mxr.mozilla.org/mozilla/source/js/narcissus/jsexec.js, 2010.

[13]

J-Y. Girard, Y. Lafont, and P. Taylor. Proofs and Types. Tracts in Theoretical Computer Science. Cambridge University Press, 1989.

Digital Library

[14]

Masami Hagiya. Meta-circular interpreter for a strongly typed language. Journal of Symbolic Computation, 8(6):651--680, 1989.

Digital Library

[15]

R. Hindley and J. P. Seldin. Introduction to Combinators and Lambda-calculus. Cambridge University Press, 1986.

Digital Library

[16]

Barry Jay. Pattern Calculus: Computing with Functions and Structures. Springer, 2009.

Digital Library

[17]

Barry Jay and Thomas Given-Wilson. A combinatory account of internal structure. Journal of Symbolic Logic, 2011. To appear. http://www-staff.it.uts.edu.au/~cbj/Publications/factorisation.pdf.

[18]

Barry Jay and Delia Kesner. First-class patterns. Journal of Functional Programming, 19(2):191--225, 2009.

Digital Library

[19]

C. B. Jay. The pattern calculus. ACM Transactions on Programming Languages and Systems (TOPLAS), 26(6):911--937, November 2004.

Digital Library

[20]

S.C. Kleene. Introduction to Methamathematics. van Nostrand, 1952.

[21]

Stephen C. Kleene. λ-definability and recursiveness. Duke Math. J., pages 340--353, 1936.

[22]

Konstantin Läufer and Martin Odersky. Self-interpretation and reflection in a statically typed language. In Proceedings of OOPSLA Workshop on Reflection and Metalevel Architectures. ACM, October 1993.

[23]

Oleg Mazonka and Daniel B. Cristofani. A very short self-interpreter. http://arxiv.org/html/cs/0311032v1, November 2003.

[24]

J. C. Mitchell. Polymorphic type inference and containment. Information and Computation, 1985.

Digital Library

[25]

Torben Æ. Mogensen. Efficient self-interpretations in lambda calculus. Journal of Functional Programming, 2(3):345--363, 1992. See also DIKU Report D-128, Sep 2, 1994.

[26]

Torben Æ. Mogensen. Linear-time self-interpretation of the pure lambda calculus. Higher-Order and Symbolic Computation, 13(3):217--237, 2000.

Digital Library

[27]

Greg Morrisett, David Walker, Karl Crary, and Neal Glew. From System F to typed assembly language. In Proceedings of POPL'98, 25th Annual SIGPLAN-SIGACT Symposium on Principles of Programming Languages, pages 85--97, 1998.

Digital Library

[28]

Matthew Naylor. Evaluating Haskell in Haskell. The Monad.Reader, 10:25--33, 2008.

[29]

Frank Pfenning and Peter Lee. Metacircularity in the polymorphic λ-calculus. Theoretical Computer Science, 89(1):137--159, 1991.

Digital Library

[30]

Didier Rémy. Simple, partial type-inference for System F based on type-containment. In Proceedings of the tenth ACM SIGPLAN international conference on Functional programming, ICFP '05, pages 130--143, New York, NY, USA, 2005. ACM.

Digital Library

[31]

Tillmann Rendel, Klaus Ostermann, and Christian Hofer. Typed self-representation. In Proceedings of PLDI'09, ACM SIGPLAN Conference on Programming Language Design and Implementation, pages 293--303, June 2009.

Digital Library

[32]

John C. Reynolds. Definitional interpreters for higher-order programming languages. In Proceedings of 25th ACM National Conference, pages 717--740. ACM Press, 1972. The paper later appeared in Higher-Order and Symbolic Computation, 11, 363--397 (1998).

Digital Library

[33]

Armin Rigo and Samuele Pedroni. Pypy's approach to virtual machine construction. In OOPSLA Companion, pages 044--953, 2006.

Digital Library

[34]

Andreas Rossberg. HaMLet. http://www.mpi-sws.org/rossberg/hamlet, 2010.

[35]

Fangmin Song, Yongsen Xu, and Yuechen Qian. The self-reduction in lambda calculus. Theoretical Computer Science, 235(1):171--181, March 2000.

Digital Library

[36]

Walid Taha, Henning Makholm, and John Hughes. Tag elimination and Jones-optimality. In Proceedings of PADO'01, Programs as Data Objects, Second Symposium, pages 257--275, 2001.

Digital Library

[37]

Terese. Term Rewriting Systems, volume 53 of Tracts in Theoretical Computer Science. Cambridge University Press, 2003.

[38]

John Tromp. Binary lambda calculus and combinatory logic. In Kolmogorov Complexity and Applications, 2006. A Revised Version is available at http://homepages.cwi.nl/tromp/cl/LC.pdf.

[39]

J. B. Wells. Typability and type checking in the second-order λ-calculus are equivalent and undecidable. In Proceedings of LICS'94, Ninth Annual IEEE Symposium on Logic in Computer Science, 1994.

[40]

Wikipedia. Pypy. http://en.wikipedia.org/wiki/PyPy, 2010.

[41]

Wikipedia. Rubinius. http://en.wikipedia.org/wiki/Rubinius, 2010.

[42]

Tetsuo Yokoyama and Robert Glück. A reversible programming language and its invertible self-interpreter. In Proceedings of PEPM'07, ACM Symposium on Partial Evaluation and Semantics-Based Program Manipulation, 2007.

Digital Library

Cited By

Jay BHermenegildo MIgarashi A(2019)A simpler lambda calculusProceedings of the 2019 ACM SIGPLAN Workshop on Partial Evaluation and Program Manipulation10.1145/3294032.3294085(1-9)Online publication date: 14-Jan-2019
https://dl.acm.org/doi/10.1145/3294032.3294085
Brown MPalsberg J(2017)Jones-optimal partial evaluation by specialization-safe normalizationProceedings of the ACM on Programming Languages10.1145/31581022:POPL(1-28)Online publication date: 27-Dec-2017
https://dl.acm.org/doi/10.1145/3158102
Brown MPalsberg J(2017)Typed self-evaluation via intensional type functionsACM SIGPLAN Notices10.1145/3093333.300985352:1(415-428)Online publication date: 1-Jan-2017
https://dl.acm.org/doi/10.1145/3093333.3009853
Show More Cited By

Index Terms

Typed self-interpretation by pattern matching
1. Software and its engineering
2. Theory of computation
  1. Logic
    1. Proof theory
  2. Semantics and reasoning
    1. Program semantics
      1. Operational semantics

Recommendations

Typed self-interpretation by pattern matching
ICFP '11

Self-interpreters can be roughly divided into two sorts: self-recognisers that recover the input program from a canonical representation, and self-enactors that execute the input program. Major progress for statically-typed languages was achieved in ...
Typed path polymorphism
Abstract
Path polymorphism enables the definition of functions uniformly applicable to arbitrary recursively specified data structures. Path polymorphic function declarations rely on patterns of the form x y (i.e. the application ...
Meta-programming with well-typed code analysis
SAC '15: Proceedings of the 30th Annual ACM Symposium on Applied Computing

Structure-analyzing metaprograms remain largely type-unsafe. In programming languages that support meta-programming, the type system is not strong enough to guarantee that well-typed metaprograms produce only well-typed programs. Banning facilities for ...

Comments

Information & Contributors

Information

Published In

cover image ACM Conferences

ICFP '11: Proceedings of the 16th ACM SIGPLAN international conference on Functional programming

September 2011

470 pages

ISBN:9781450308656

DOI:10.1145/2034773

General Chairs:
Manuel Chakravarty
University of New South Wales, Australia
,
Zhenjiang Hu
National Institute of Informatics, Japan
,
Program Chair:
Olivier Danvy
Aarhus University, Denmark

ACM SIGPLAN Notices Volume 46, Issue 9
ICFP '11
September 2011
456 pages
ISSN:0362-1340
EISSN:1558-1160
DOI:10.1145/2034574
Issue’s Table of Contents

Copyright © 2011 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: 19 September 2011

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Research-article

Conference

ICFP '11

Sponsor:

SIGPLAN

ICFP '11: ACM SIGPLAN International Conference on Functional Programming

September 19 - 21, 2011

Tokyo, Japan

Acceptance Rates

ICFP '11 Paper Acceptance Rate 33 of 92 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

12
Total Citations
View Citations
420
Total Downloads

Downloads (Last 12 months)5
Downloads (Last 6 weeks)0

Reflects downloads up to 03 Feb 2025

Other Metrics

View Author Metrics

Citations

Cited By

Jay BHermenegildo MIgarashi A(2019)A simpler lambda calculusProceedings of the 2019 ACM SIGPLAN Workshop on Partial Evaluation and Program Manipulation10.1145/3294032.3294085(1-9)Online publication date: 14-Jan-2019
https://dl.acm.org/doi/10.1145/3294032.3294085
Brown MPalsberg J(2017)Jones-optimal partial evaluation by specialization-safe normalizationProceedings of the ACM on Programming Languages10.1145/31581022:POPL(1-28)Online publication date: 27-Dec-2017
https://dl.acm.org/doi/10.1145/3158102
Brown MPalsberg J(2017)Typed self-evaluation via intensional type functionsACM SIGPLAN Notices10.1145/3093333.300985352:1(415-428)Online publication date: 1-Jan-2017
https://dl.acm.org/doi/10.1145/3093333.3009853
Brown MPalsberg JCastagna GGordon A(2017)Typed self-evaluation via intensional type functionsProceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages10.1145/3009837.3009853(415-428)Online publication date: 1-Jan-2017
https://dl.acm.org/doi/10.1145/3009837.3009853
Brown MPalsberg J(2016)Breaking through the normalization barrier: a self-interpreter for f-omegaACM SIGPLAN Notices10.1145/2914770.283762351:1(5-17)Online publication date: 11-Jan-2016
https://dl.acm.org/doi/10.1145/2914770.2837623
Brown MPalsberg JBodik RMajumdar R(2016)Breaking through the normalization barrier: a self-interpreter for f-omegaProceedings of the 43rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages10.1145/2837614.2837623(5-17)Online publication date: 11-Jan-2016
https://dl.acm.org/doi/10.1145/2837614.2837623
Lester M(2015)Control Flow Analysis for SF Combinator CalculusElectronic Proceedings in Theoretical Computer Science10.4204/EPTCS.199.4199(51-67)Online publication date: 7-Dec-2015
https://doi.org/10.4204/EPTCS.199.4
Brown MPalsberg J(2015)Self-Representation in Girard's System UACM SIGPLAN Notices10.1145/2775051.267698850:1(471-484)Online publication date: 14-Jan-2015
https://dl.acm.org/doi/10.1145/2775051.2676988
Brown MPalsberg JRajamani SWalker D(2015)Self-Representation in Girard's System UProceedings of the 42nd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages10.1145/2676726.2676988(471-484)Online publication date: 14-Jan-2015
https://dl.acm.org/doi/10.1145/2676726.2676988
Given-Wilson THuang FJay BCarette JWillcock J(2013)Multi-polymorphic programming in bondiProceedings of the 9th ACM SIGPLAN workshop on Generic programming10.1145/2502488.2502493(53-60)Online publication date: 28-Sep-2013
https://dl.acm.org/doi/10.1145/2502488.2502493
Show More Cited By

View Options

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.

Figures

Tables

Media

View Table of Conten