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Fusion on Languages

  • Roland Backhouse
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2028)

Abstract

Many functions on context-free languages can be expressed in the form of the least fixed point of a function whose definition mimics the grammar of the given language. This paper presents the basic theory that explains when a function on a context-free language can be defined in this way. The contributions are: a novel definition of a regular algebra capturing division properties, several theorems showing how complex regular algebras are built from simpler ones, and the application of fixed point theory and Galois connections to practical programming problems.

Keywords

Edit Distance Recursive Equation Input String Edit Operation Empty Word 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. [AP72]
    A. V. Aho and T.G. Peterson. A minimum-distance error-correcting parser for context-free languages. SIAM J. Computing, 1:305–312, 1972.zbMATHCrossRefMathSciNetGoogle Scholar
  2. [AU72]
    Alfred V. Aho and Jeffrey D. Ullman. The theory of parsing, translation and compiling, volume 1 of Series in Automatic Computation. Prentice-Hall, 1972.Google Scholar
  3. [BC75]
    R.C. Backhouse and B.A. Carré. Regular algebra applied to path-finding problems. Journal of the Institute of Mathematics and its Applications, 15:161–186, 1975.zbMATHMathSciNetCrossRefGoogle Scholar
  4. [CC77]
    Patrick Cousot and Radhia Cousot. Abstract interpretation: A unifed lattice model for static analysis of programs by construction or approximation of fixpoints. In Conference Record of the Fourth Annual ACM Symposium on Principles of Programming Languages, pages 238–252, Los Angeles, California, January 1977.Google Scholar
  5. [CC79]
    Patrick Cousot and Radhia Cousot. Systematic design of program analysis frameworks. In Conference Record of the Sixth Annual ACM Symposium on Principles of Programming Languages, pages 269–282, San Antonio, Texas, January 1979.Google Scholar
  6. [Con71]
    J.H. Conway. Regular Algebra and Finite Machines. Chapman and Hall, London, 1971.zbMATHGoogle Scholar
  7. [Dij59]
    E.W. Dijkstra. A note on two problems in connexion with graphs. Numerische Mathematik, 1:269–271, 1959.Google Scholar
  8. [Dil39]
    R.P. Dilworth. Non-commutative residuated lattices. Transactions of the American Mathematical Society, 46:426–444, 1939.zbMATHCrossRefMathSciNetGoogle Scholar
  9. [DS90]
    Edsger W. Dijkstra and Carel S. Scholten. Predicate Calculus and Program Semantics. Texts and monographs in Computer Science. Springer-Verlag, 1990.Google Scholar
  10. [HH86]
    C.A.R. Hoare and Jifeng He. The weakest prespecification. Fundamenta Informaticae, 9:51–84, 217-252, 1986.zbMATHMathSciNetGoogle Scholar
  11. [HS64]
    J. Hartmanis and R.E. Stearns. Pair algebras and their application to automata theory. Information and Control, 7(4):485–507, 1964.CrossRefMathSciNetGoogle Scholar
  12. [JS94]
    J. Jeuring and S.D. Swierstra. Bottom-up grammar analysis ― a functional formulation ―. In Donald Sannella, editor, Proceedings Programming Languages and Systems, ESOP’ 94, volume 788 of LNCS, pages 317–332, 1994.Google Scholar
  13. [JS95]
    J. Jeuring and S.D. Swierstra. Constructing functional programs for grammar analysis problems. In S. Peyton Jones, editor, Proceedings Functional Programming Languages and Computer Architecture, FPCA’ 95, June 1995.Google Scholar
  14. [Knu77]
    D.E. Knuth. A generalization of Dijkstra’s shortest path algorithm. Information Processing Letters, 6 (1):1–5, 1977.Google Scholar
  15. [Koz91]
    Dexter Kozen. A completeness theorem for Kleene algebras and the algebra of regular events. In Proc. 6th Annual IEEE Symp. on Logic in Computer Science, pages 214–225. IEEE Society Press, 1991.Google Scholar
  16. [LS86]
    J. Lambek and P.J. Scott. Introduction to Higher Order Categorical Logic, volume 7 of Studies in Advanced Mathematics. Cambridge University Press, 1986.Google Scholar
  17. [Ore44]
    Oystein Ore. Galois connexions. Transactions of the American Mathematical Society, 55:493–513, 1944.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Roland Backhouse
    • 1
  1. 1.University of NottinghamGermany

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