A class of program schemes based on tree rewriting systems

  • B. Courcelle
  • F. Lavandier
Contributed Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 159)


This work studies certain "by-case" recursive definitions in terms of an appropriate class of proram schemes. These definitions do not use explicitly the if ... then ... else ... construct and their semantics is better defined "operationally" i.e. by means of an associated rewriting system than "denotationally" i.e. as the least fix-point of some operator. They appear in many different situations: denotational semantics, attribute grammars, algorithms in formal languages theory, functions on some quotient-algebra, and correspond closely to certain PROLOG programs.


Recursive Call Program Scheme Denotational Semantic Algebraic Semantic Recursive Scheme 


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  1. [1]
    B. COURCELLE, Infinite trees in normal form and recursive equations having a unique solution. Math. Systems Theory 13 (1979), p.131–180.CrossRefGoogle Scholar
  2. [2]
    B. COURCELLE, Fundamental properties of infinite trees, Report AAI, no8202 (1982), Université de Bordeaux I, to appear in Theor. Comput. Sci.1983.Google Scholar
  3. [3]
    B. COURCELLE, An axiomatic approach to the Korenjak-Hopcroft algorithms; to appear Math. Systems Theory.Google Scholar
  4. [4]
    B. COURCELLE, P. FRANCHI-ZANNETTACCI, Attribute grammars and recursive program schemes; Theor. Comput. Sci. 17 (1982), p.163–191 and p.235–257.CrossRefGoogle Scholar
  5. [5]
    B. COURCELLE, F. LAVANDIER, Définitions récursives par cas; Report AAI no8103 (1981), Université de Bordeaux I, submitted for publication.Google Scholar
  6. [6]
    B. COURCELLE, M. NIVAT, The algebraic semantics of recursive program schemes; MFCS'78, Lec. Notes Comput. Sci. 64, p.16–30.Google Scholar
  7. [7]
    E. FRIEDMAN, Equivalence problems for deterministic context-free languages and monadic recursion schemes, J. Comput. System Sci. 14 (1977), p.334–359.Google Scholar
  8. [8]
    S. GARLAND, D. LUCKHAM, Program schemes, recursion schemes and formal languages, J. Comput. System Sci. 7 (1973), p.119–160.Google Scholar
  9. [9]
    J. GOGUEN, J. THATCHER, E. WAGNER, J. WRIGHT, Initial algebra semantics and continuous algebras, J. Assoc. Comput. Mach. 24 (1977), p.68–95.Google Scholar
  10. [10]
    I. GUESSARIAN, Algebraic semantics, Lec. Notes Comput. Sci.99, Springer-Verlag, 1981.Google Scholar
  11. [11]
    G. HUET, Confluent reductions, abstract properties and applications to term rewriting systems, J. Assoc. Comput. Mach.27 (1980), p.797–821.Google Scholar
  12. [12]
    G. HUET, J.M. HULLOT, Proofs by induction in equational theories with constructors; J. Comput.System Sci. 25 (1982), p.239–266.CrossRefGoogle Scholar
  13. [13]
    G. HUET, J.J. LEVY, Call by need computations in nonambiguous linear term rewriting systems; Laboria report 359, (1979).Google Scholar
  14. [14]
    G. HUET, D. OPPEN, Equations and rewrite rules, a survey. Proceedings of the International Symposium on Formal Languages Theory, Santa Barbara, California (December 10–14 1979), Academic Press, 1980.Google Scholar
  15. [15]
    F. LAVANDIER, Sur les systèmes de définitions récursives par cas. Application à la sémantique dénotationnelle; Thèse de 3ème cycle, Université de Bordeaux I (1982).Google Scholar
  16. [16]
    Z. MANNA, A. SHAMIR, The theoretical aspects of the optimal fixedpoint; SIAM J. on Comput. 5 (1976), p.414–426.CrossRefGoogle Scholar
  17. [17]
    B. MAYOH, Attribute grammars and mathematical semantics; SIAM J. on Comput. 10 (1981), p.503–518.CrossRefGoogle Scholar
  18. [18]
    M. NIVAT, On the interpretation of polyadic recursive program schemes; Symposia Mathematica 15, Academic Press (1975), p.255–281.Google Scholar
  19. [19]
    J.C. RAOULT, J. VUILLEMIN, Operational and semantic equivalence between recursive programs, J. Assoc. Comput. Mach. 27 (1980), p. 772–796.Google Scholar
  20. [20]
    B. ROSEN, Tree manipulation systems and Church-Rosser theorems; J. Assoc. Comput. Mach. 20 (1973), p.160–187.Google Scholar
  21. [21]
    J. STOY, Semantic models, in Theoretical Foundations of Programming Methodology; M. Broy and G. Schmidt eds., D. Reidel Pub. Co., Dordrecht, Holland 1982, p.293–325.Google Scholar
  22. [22]
    R. TENNENT, The denotational semantics of programming languages, Comm. of ACM 19-8 (1976), p.437–453.Google Scholar
  23. [23]
    S. WALKER, H. STRONG, Characterizations of flow-chartable recursions; J. Comput. System Sci. 7 (1973), p.404–447.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1983

Authors and Affiliations

  • B. Courcelle
    • 1
  • F. Lavandier
    • 2
  1. 1.Université de Bordeaux I U.E.R. Mathématiques et InformatiqueTalence CedexFrance
  2. 2.Départment InformatiqueUniversité de Bordeaux I I.U.T. "A"Talence CedexFrance

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