Parameter-reduction of higher level grammars

  • Helmut Seidl
Part of the Lecture Notes in Computer Science book series (LNCS, volume 299)


A higher level (OI-)grammar is called terminating, if for every accessible term t there is at least one terminal term which can be derived from t. A grammar is called parameter-reduced, if it is terminating and has no superfluous parameters.

For every grammar G of level n>0 which generates at least one term we construct grammars R(G) and P(G) such that R(G) and P(G) generate the same language as G but are terminating and paramter-reduced, respectively.

We introduce a hierarchy of restrictions to the deletion capability of the grammars which allow a gradual decrease in the complexity of the algorithms from n-iterated exponential time to polynomial time.


Formal Parameter Tree Language Derivation Rule Terminal Symbol Tree Transducer 
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.


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  1. Ab85.
    S. Abramsky: Strictness analysis and polymorphic invariance. Programs as Data Objects, Proc. of a Workshop Copenhagen, Denmark, 1985, Lecture Notes in Comp. Sci. 217 pp. 1–23Google Scholar
  2. Ah74.
    A.V. Aho, J.E. Hopcroft, J.D. Ullman: The Design and Analysis of Computer Algorithms. Addison Wesley, Reading, MA, 1974Google Scholar
  3. ArDau76.
    A. Arnold, M Dauchet: Un theoreme de duplication pour les forets algebriques. JCSS 13, 1976, pp. 223–244Google Scholar
  4. ArDau78.
    A. Arnold, M. Dauchet: Forets algebriques et homomorphismes inverses. Inf. and Control 37, 1978, pp. 182–196Google Scholar
  5. ArLe80.
    A. Arnold, B. Leguy: Une propriete des forets algebriques "de Greibach". Inf. and Control 46, 1980, pp. 108–134Google Scholar
  6. Ba81.
    H.P. Barendregt: The Lambda-Calculus. North Holland, Amsterdam, 1981Google Scholar
  7. BuHa85.
    G.L. Burn, C.L. Hankin, S. Abramsky: The theory of strictness analysis for higher order functions. Programs as Data Objects, Proc. of a Workshop, Copenhagen, Denmark 1985, Lecture Notes in Comp. Sci. 217, pp. 46–66Google Scholar
  8. ClaJo85.
    C. Clack, S.L.P. Jones: Strictness analysis — a practical approach. Functional Programming Languages and Computer Architecture, Lecture Notes in Comp. Sci. 201, 1985, pp. 35–49Google Scholar
  9. Cou78.
    B. Courcelle: A representation of trees by languages. TCS 6, 1978, pp. 255–279 and TCS 7, 1978, pp. 25–55Google Scholar
  10. Cou86.
    B. Courcelle: Equivalences and transformations of regular systems — applications to recursive program schemes and grammars. TCS 42, 1986, pp. 1–122Google Scholar
  11. Da77a.
    W. Damm: Higer type program schemes and their tree languages. Proc. 3. GI-Conf. on Th. Comp. Sci. Lecture Notes in Comp. Sci. 48, 1977, S. 51–72Google Scholar
  12. Da77b.
    W. Damm: Languages defined by higher type program schemes. Proc. 4th Int. Coll. on Automata, Languages and Programming Lecture Notes in Comp. Sci. 52, 1977, pp. 164–179Google Scholar
  13. Da79.
    W. Damm: An algebraic extension of the Chomsky-hierarchy. Proc. Conf. on Math. Foundations of Comp. Sci. Lecture Notes in Comp. Sci. 74, 1979, pp. 266–276Google Scholar
  14. Da82.
    W. Damm: The IO-and OI-hierarchies. TCS 20, 1982, pp. 95–205Google Scholar
  15. DaFe80.
    W. Damm, E. Fehr: A schematological approach to the analysis of the procedure concept in ALGOL-languages. Proc. 5ieme Colloque sur les Arbres en Algebre et en Programmation, 1980, pp. 130–134Google Scholar
  16. DaFeIn78.
    W. Damm, E. Fehr, K. Indermark: Higher type recursion and self-application as control structures. In: E. Neuhold (ed.): Formal Description of Programming Concepts, North Holland, Amsterdam, 1978, pp. 461–487Google Scholar
  17. DaGoe82.
    W. Damm, A. Goerdt: An automata-theoretical characterization of the OI-hierarchy. Inf. and Comp. 71, 1986, pp. 1–32Google Scholar
  18. DaGue81.
    W. Damm, I. Guessarian: Combining T and level N. Tech. Report Laboratoire Informatique Theorique et Programmation 81–11, 1981Google Scholar
  19. DaGue83.
    W. Damm, I. Guessarian: Implementation techniques for recursive tree transducers on higher order data types. Tech. Report Laboratoire Informatique Theorique et Programmation 83–16, 1983Google Scholar
  20. EnSch77/78.
    J. Engelfriet, E.M. Schmidt; IO and OI. JCSS 15, 1977, pp. 328–353, and JCSS 16, 1978, pp. 67–99Google Scholar
  21. En83.
    J. Engelfriet: Iterated pushdown automata and complexity classes. Proc. 15th STOC, 1983, pp. 365–373Google Scholar
  22. Fi68.
    M.J. Fischer: Grammars with macro-like productions. Proc. 9th IEEE Conf. on Switching and Automata Theory, 1968, pp. 131–141Google Scholar
  23. FoLei83.
    S. Fortune, D. Leivant, M. o'Donnell: The expressiveness of simple and second order type structures. JACM 30, 1983, pp. 151–185Google Scholar
  24. Ga84.
    J.H. Gallier: n-Rational algebras. SIAM J. of Computing 13, 1984, pp. 750–794Google Scholar
  25. Gue79.
    I. Guessarian: Program transformations and algebraic semantics. TCS 9, 1979, pp. 39–65Google Scholar
  26. HuYou86.
    P. Hudak, J. Young: Higher-order strictness analysis in untyped lambda calculus. Proc. of the 13th Ann. Symp. on Principles of Programming Languages, 1986, pp. 97–109Google Scholar
  27. Le80.
    B. Leguy: Reductions, transformations et classification des grammairs algebriques d'arbres. These de 3ieme cycle Lille, 1980Google Scholar
  28. Le81.
    B. Leguy: Grammars without erasing rules, the OI-case. Proc. 6ieme Colloque sur les Arbres en Algebre et on Progammation, 1981, Lecture Notes in Comp. Sci. 112, pp. 268–273Google Scholar
  29. Mai74.
    T.S.E. Maibaum: A generalized approach to formal languages. JCSS 8, 1974, pp. 409–439Google Scholar
  30. Ma74.
    A.N. Maslov: The hierarchy of indexed languages of an arbitrary level. Soviet. Math. Dokt. 15(14), 1974, pp. 1170–1174Google Scholar
  31. Mi77.
    R. Milner: Fully abstract models of typed lambda-calculus. TCS 4, 1977, pp. 1–22Google Scholar
  32. My80.
    A. Mycroft: The theory and practice of transforming call-by-need into call-by-value. Proc.4th Colloque International sur la Programmation Paris, 1980, pp. 269–281Google Scholar
  33. Pa78.
    W.J. Paul: Kompexitätstheorie. Teubner Stuttgart, 1978Google Scholar
  34. Sch78.
    E.M. Schmidt: Succinctness of description of contextfree, regular and finite languages. Datalogisk Afdelning Report DAIMI PB-84, Aarhus Univ., 1978Google Scholar
  35. Sei86.
    H. Seidl: Regularität bei Grammatiken höherer Stufe. Diss. Thesis, Frankfurt/Main, 1986Google Scholar
  36. Sei87.
    H. Seidl: Parameter-reduction of Higher Level Grammars. To appear in TCSGoogle Scholar
  37. Wa75.
    M. Wand: An algebraic formulation of the Chomsky-hierarchy. Category Theory Applications to Computation and Control, Lecture Notes in Comp. Sci. 25, 1975, pp. 209–219.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Helmut Seidl
    • 1
  1. 1.Fachbereich InformatikJohann Wolfgang Goethe-UniversitätFrankfurt/Main

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