Typed self-interpretation by pattern matching
Authors: 
Barry Jay, Jens PalsbergAuthors Info & Claims
Barry Jay, Jens PalsbergAuthors Info & ClaimsAbstract
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.
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References
[1]
Harold Abelson, Gerald Jay Sussman, and Julie Sussman. Structure and Interpretation of Computer Programs. MIT Press, 1985.
[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.
[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.
[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.
[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.
[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.
[14]
Masami Hagiya. Meta-circular interpreter for a strongly typed language. Journal of Symbolic Computation, 8(6):651--680, 1989.
[15]
R. Hindley and J. P. Seldin. Introduction to Combinators and Lambda-calculus. Cambridge University Press, 1986.
[16]
Barry Jay. Pattern Calculus: Computing with Functions and Structures. Springer, 2009.
[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.
[19]
C. B. Jay. The pattern calculus. ACM Transactions on Programming Languages and Systems (TOPLAS), 26(6):911--937, November 2004.
[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.
[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.
[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.
[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.
[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.
[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.
[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).
[33]
Armin Rigo and Samuele Pedroni. Pypy's approach to virtual machine construction. In OOPSLA Companion, pages 044--953, 2006.
[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.
[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.
[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.
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September 2011470 pagesISBN:9781450308656DOI:10.1145/2034773- General Chairs:
- Manuel Chakravarty,
- Zhenjiang Hu,
- Program Chair:
- Olivier Danvy
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Published: 19 September 2011
Published in SIGPLAN Volume 46, Issue 9
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