Functional semantics of parsing actions, and left recursion elimination as continuation passing
Pages 91 - 102
Abstract
Parsers, whether constructed by hand or automatically via a parser generator tool, typically need to compute some useful semantic information in addition to the purely syntactic analysis of their input. Semantic actions may be added to parsing code by hand, or the parser generator may have its own syntax for annotating grammar rules with semantic actions. In this paper, we take a functional programming view of such actions. We use concepts from the semantics of mostly functional programming languages and adapt them to give meaning to the actions of the parser. Specifically, the semantics is inspired by the categorical semantics of lambda calculi and the use of premonoidal categories for the semantics of effects in programming languages. This framework is then applied to our leading example, the transformation of grammars to eliminate left recursion. The syntactic transformation of left-recursion elimination leads to a corresponding semantic transformation of the actions for the grammar. We prove the semantic transformation correct and relate it to continuation passing style, a widely studied transformation in lambda calculi and functional programming.
References
[1]
A. V. Aho, R. Sethi, and J. D. Ullman. Compilers - Principles, Techniques and Tools. Addison Wesley, 1985.
[2]
A. W. Appel and J. Palsberg. Modern Compiler Implementation in Java. Cambridge University Press, 1997.
[3]
A. Baars, S. Doaitse Swierstra, and M. Viera. Typed transformations of typed grammars: The left corner transform. Electron. Notes Theor. Comput. Sci., 253:51--64, September 2010. ISSN 1571-0661. URL http://dx.doi.org/10.1016/j.entcs.2010.08.031.
[4]
C. Barker. Continuations in natural language. In Proceedings of the Fourth ACM SIGPLAN Continuations Workshop (CW'04). University of Birmingham Computer Science technical report CSR-04-1, 2004.
[5]
J. Berdine, P. W. O'Hearn, U. Reddy, and H. Thielecke. Linear continuation passing. Higher-order and Symbolic Computation, 15 (2/3):181--208, 2002.
[6]
O. Danvy and A. Filinski. Representing control, a study of the CPS transformation. Mathematical Structures in Computer Science, 2(4): 361--391, Dec. 1992.
[7]
M. Felleisen and D. P. Friedman. Control operators, the SECDmachine, and the λ-calculus. In M. Wirsing, editor, Formal Description of Programming Concepts, pages 193--217. North-Holland, 1986.
[8]
J. A. Goguen, J. W. Thatcher, E. G. Wagner, and J. B. Wright. Initial algebra semantics and continuous algebras. Journal of the ACM, 24 :68--95, 1977.
[9]
C. A. Gunther. Semantics of Programming Languages. MIT Press, 1992.
[10]
J. Hughes. Generalising monads to arrows. Science of Computer. Programming, 37(1--3):67--111, 2000.
[11]
G. Hutton and E. Meijer. Monadic parsing in Haskell. Journal of Functional Programming, 8(4):437--444, 1998.
[12]
D. E. Knuth. Semantics of context-free languages. Mathematical Systems Theory, 2(2):127--145, 1968.
[13]
J. Lambek. The mathematics of sentence structure. American Mathematical Monthly, 65(3):154--170, 1958.
[14]
P. J. Landin. The mechanical evaluation of expressions. The Computer Journal, 6(4):308--320, Jan. 1964.
[15]
W. Lohmann, G. Riedewald, and M. Stoy. Semantics-preserving migration of semantic rules during left recursion removal in attribute grammars. Electronic Notes in Theoretical Compututer Science, 110: 133--148, 2004.
[16]
S. Mac Lane. Categories for the Working Mathematician. Springer Verlag, 1971.
[17]
E. Moggi. Computational lambda calculus and monads. In Proceedings, Fourth Annual Symposium on Logic in Computer Science (LICS), pages 14--23, 1989. ISBN 0-8186-1954-6.
[18]
K. B. Oege de Moor and S. D. Swierstra. First class attribute grammars. Informatica: An International Journal of Computing and Informatics, 24(2):329--341, June 2000. ISSN ISSN 0350-5596. Special Issue: Attribute grammars and their Applications.
[19]
T. Parr and K. Fisher. LL(*): the foundation of the ANTLR parser generator. In PLDI. ACM, 2011. ISBN 978-1-4503-0663-8.
[20]
R. Paterson. A new notation for arrows. In ICFP. ACM, 2001. ISBN 1-58113-415-0.
[21]
G. D. Plotkin. Call-by-name, call-by-value, and the λ-calculus. Theoretical Computer Science, 1(2):125--159, 1975.
[22]
J. Power and E. Robinson. Premonoidal categories and notions of computation. Mathematical Structures in Computer Science, 7(5): 453--468, 1997.
[23]
J. Power and H. Thielecke. Environments, continuation semantics and indexed categories. In M. Abadi and T. Ito, editors, Proceedings TACS'97, number 1281 in LNCS, pages 391--414. Springer Verlag, 1997.
[24]
J. Power and H. Thielecke. Closed Freyd- and kappa-categories. In J. Wiedermann, P. van Emde Boas, and M. Nielsen, editors, Proceedings 26th International Colloquium on Automata, Languages and Programming (ICALP), number 1644 in LNCS, pages 625--634. Springer Verlag, 1999.
[25]
J. C. Reynolds. Definitional interpreters for higher-order programming languages. In Proceedings of the 25th ACM National Conference, pages 717--740. ACM, Aug. 1972.
[26]
J. C. Reynolds. Definitional interpreters for higher-order programming languages. Higher-Order and Symbolic Computation, 11(4):363--397, 1998. Reprint of a conference paper {25}.
[27]
D. Sitaram and M. Felleisen. Control delilmiters and their hierarchies. Lisp and Symbolic Computation, 3(1):67--99, 1990.
[28]
G. Steele. Rabbit: A compiler for Scheme. Technical Report AI TR 474, Artificial Intelligence Laboratory, Massachusetts Institute of Technology, May 1978.
[29]
C. Strachey and C. P. Wadsworth. Continuations: A mathematical semantics for handling full jumps. Technical Monograph PRG-11, Oxford University Computing Laboratory, Jan. 1974.
[30]
S. D. Swierstra. Combinator parsers: a short tutorial. In A. Bove, L. Barbosa, A. Pardo, and J. Sousa Pinto, editors, Language Engineering and Rigorous Software Development, volume 5520 of LNCS, pages 252--300. Spinger, 2009.
[31]
H. Thielecke. From control effects to typed continuation passing. In Principles of Programming Languages (POPL'03), pages 139--149. ACM, 2003.
[32]
P. Wadler. Theorems for free! In Proceedings of the 4th International Conference on Functional Programming and Computer Architecture (FPCA'89), London, 11--13 September 1989, pages 347--359. ACM Press, New York, 1989.
Index Terms
- Functional semantics of parsing actions, and left recursion elimination as continuation passing
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September 2012
226 pages
ISBN:9781450315227
DOI:10.1145/2370776
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Published: 19 September 2012
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