The algebraic semantics of recursive program schemes

  • B. Courcelle
  • M. Nivat
Invited Lectures
Part of the Lecture Notes in Computer Science book series (LNCS, volume 64)


This is a survey of general properties of recursive program schemes and classes of interpretations.


Program Scheme Algebraic Semantic Functional Interpretation Partial Computation Finite Tree 
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. [1]
    ADJ, Initial algebra semantics and continuous algebras, JACM 24 (1977) 68–95.Google Scholar
  2. [1a]
    G. Birkoff, Lattice Theory, AMS (1967).Google Scholar
  3. [2]
    S. Bloom, Varieties of ordered algebras, JCSS 13 (1976), pp 200–212.Google Scholar
  4. [3]
    R. Burstall, Proving properties of programs by Structural induction, Comp. Journal 12 (1969) 41–48.Google Scholar
  5. [4]
    R. Burstall, J. Darlington, A transformation system for developping programs, JACM 24 (1977) 44–67.CrossRefGoogle Scholar
  6. [5]
    B. Courcelle, A representation of trees by languages, to appear in TCS (1978).Google Scholar
  7. [6]
    B. Courcelle, On the definition of classes of interpretations, 4th ICALP Turku (1977) Lec, notes in Comp. Sc. Vol. 52. (Springer Verlag).Google Scholar
  8. [7]
    B. Courcelle, On recursive equations having a unique solution, Laboria report 285.Google Scholar
  9. [8]
    B. Courcelle, M. Nivat, Algebraic families of interpretations, 17th Symposium on F.O.C.S (Houston 1976) and Laboria report 189.Google Scholar
  10. [9]
    B. Courcelle, I Guessarian, On some classes of interpretations, to appear in J.C.S.S. (and Laboria report 253).Google Scholar
  11. [10]
    B. Courcelle, M. Nivat, in preparation.Google Scholar
  12. [11]
    B. Courcelle, J.C. Raoult, Completions of ordered magmas, to appear in Fundamenta Informaticae.Google Scholar
  13. [12]
    J. Darlington, R. Burstall, A system which automatically improves programs, 3rd IJCAI, SRI (1973) 537–542.Google Scholar
  14. [13]
    J. De Bakker, Recursive Procedures, Mathematical center Tract 24, Amsterdam 1971.Google Scholar
  15. [14]
    J. De Bakker, W.P. De Roewer, A calculus for recursive program schemes in Automata, Languages, Programing, (Nivat ed.) North-Holland, Amsterdam 1972.Google Scholar
  16. [15]
    G. Huet, B. Lang, Proving and applying program transformations expressed with 2nd order patterms, to appear in Acta Informatica (Laboria report 266).Google Scholar
  17. [16]
    Z. Manna, J. Vuillemin, Fixpoint approach to the Theory of Computation, CACM 15 (1972), pp 528–536.Google Scholar
  18. [17]
    G. Markowsky, B. Rosen, Bases for Chain-complete posets, IBM Jour. of Res. and Dev. vol. 20 (1976) pp 138–147.Google Scholar
  19. [18]
    J. McCarthy, A basis for a mathematical theory of computation in Computer programing and Formal systems, Braffort and Hirshberg ed., North-Holland, Amsterdam (1963).Google Scholar
  20. [19]
    J. Messeguer, On order Complete Universal Algebra and Enriched Functorial Semantics, FCT 77 (Poznan), Lecture Notes in Computer Sciences, Springer-VerlagGoogle Scholar
  21. [20]
    J. Mezei, J.B. Wright, Algebraic automata and context-free sets, Inf. and Control 11 (1967) pp 3–29.CrossRefGoogle Scholar
  22. [21]
    R. Milner, Fully abstract models of typed λ-calculi, TCS 4 (1977) 1–22.CrossRefGoogle Scholar
  23. [22]
    J.H. Morris, Another Recursion Induction Principle, CACM Vol. 14, no 5 (1971).Google Scholar
  24. [23]
    M. Nivat, On the interpretation of polyadic recursive schemes, Symposia Mathematica, vol. 15, Academic Press (1975).Google Scholar
  25. [24]
    J.W. Thatcher, E.G. Wagner, J.B. Wright, A uniform approach to inductive posets and inductive closure, to appear in T.C.S.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1978

Authors and Affiliations

  • B. Courcelle
    • 1
  • M. Nivat
    • 2
  1. 1.IRIA, RocquencourtLe ChesnayFrance
  2. 2.IRIA and University Paris 7France

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