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Algebraic semantics of recursive flowchart schemes

  • Hartmut Schmeck
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 140)

Abstract

In this paper we have shown how algebraic semantics can be defined for recursive γ-flowchart schemes using the freeness results for reducible γ-flowcharts. This considerably extends the algebraic characterization of flowcharts as begun by Elgot and Shepherdson [ES1][ES2].

Our results contrast with those of Gallier [G1][G3] in that they are derived independent of the special choice of γ.

In [S2] an example is given where γ-flowcharts represent nondeterministic programs on a stack machine thus providing an extension of the target language used by Thatcher, Wagner, and Wright in [ADJ6]. The results of this paper might lead to an extension of their compiler correctness results to programming languages incorporating recursive structures.

Keywords

Partial Order Algebraic Theory Interior Vertex Algebraic Semantic Algebraic Characterization 
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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References

  1. [AC]
    Allen, F.E., Cocke, J.: Graph Theoretic Constructs for Control Flow Analysis. IBM Research Report RC3922, 1972Google Scholar
  2. [ADJ1]
    Goguen, J.A., Thatcher, J.W., Wright, J.B.: Rational Algebraic Theories and Fixed Point Solutions. Proc. 17th Symp. Found. of Comput. Sci., Houston, Texas, 147–158 (1976)Google Scholar
  3. [ADJ2]
    Goguen, J.A., Thatcher, J.W., Wagner, E.G., Wright, J.B.: Initial Algebra Semantics and Continuous Algebras. J. Assoc. Comput. Mach. 24, 68–95(1977)MathSciNetCrossRefGoogle Scholar
  4. [ADJ3]
    Wagner, E.G., Thatcher, J.W., Wright, J.B.: Free Continuous Theories. IBM Research Report RC6906, 1977Google Scholar
  5. [ADJ4]
    Thatcher, J.W., Wagner, E.G., Wright, J.B.: Notes on Algebraic Fundamentals for Theoretical Computer Science. Lect. Notes, 3 rd Advanced Course Found. of Comput. Sci., Amsterdam, 1978Google Scholar
  6. [ADJ5]
    Wagner, E.G., Wright, J.B., Thatcher, J.W.: Many-Sorted and Ordered Algebraic Theories. IBM Research Report RC7595, 1979Google Scholar
  7. [ADJ6]
    Thatcher, J.W., Wagner, E.G., Wright, J.B.: More on Advice on Structuring Compilers and Proving Them Correct. Theor. Comput. Sci. 15, 223–249 (1981)CrossRefGoogle Scholar
  8. [BT]
    Bloom, S.L., Tindell, R.: Algebraic and Graph-Theoretic Characterizations of Structured Flowchart Schemes. Theor. Comput. Sci. 9, 265–286 (1979)MathSciNetCrossRefGoogle Scholar
  9. [E1]
    Elgot, C.C.: Monadic Computation and Iterative Algebraic Theories. Proc. Logic Colloquium 1973, North-Holland, 175–230(1975)Google Scholar
  10. [E2]
    Elgot, C.C.: Structured Programming With and Without GOTO Statements. IEEE Trans. Soft. Eng., Vol. SE-2, 41–53(1976)MathSciNetCrossRefGoogle Scholar
  11. [ES1]
    Elgot, C.C., Shepherdson, J.C.: A Semantically Meaningful Characterization of Reducible Flowchart Schemes. Theor. Comput. Sci. 8, 325–357 (1979)MathSciNetCrossRefGoogle Scholar
  12. [ES2]
    Elgot, C.C., Shepherdson, J.C.: An Equational Axiomatization of the Algebra of Reducible Flowchart Schemes. IBM Research Report RC8221, 1980Google Scholar
  13. [G1]
    Gallier, J.H.: Semantics and Correctness of Classes of Deterministic and Nondeterministic Recursive Programs. Ph. D. Dissertation, UCLA, 1977Google Scholar
  14. [G2]
    Gallier, J.H.: Recursion Schemes and Generalized Interpretations. Proc. 6th ICALP, Graz, 1979, Lect. Notes Comput. Sci. 71, 256–270(1979)CrossRefGoogle Scholar
  15. [G3]
    Gallier, J.H.: Nondeterministic Flowchart Programs With Recursive Procedures: Semantics and Correctness I, II. Theor. Comput. Sci. 13, 193–224, 239–270(1981)MathSciNetCrossRefGoogle Scholar
  16. [G4]
    Gallier, J.H.: Recursion-Closed Algebraic Theories. J. Comput. Syst. Sci. 23, 69–105(1981)MathSciNetCrossRefGoogle Scholar
  17. [HU1]
    Hecht, M.S., Ullman, J.D.: Flow Graph Reducibility. SIAM J. Comput. 1, 188–202(1972)MathSciNetCrossRefGoogle Scholar
  18. [HU2]
    Hecht, M.S., Ullman, J.D.: Characterization of Reducible Flow Graphs. J. Assoc. Comput. Mach. 21, 367–375(1974)MathSciNetCrossRefGoogle Scholar
  19. [ML]
    MacLane, S.: Kategorien. Springer Verlag, 1972Google Scholar
  20. [N]
    Nivat, M.: On the Interpretation of Recursive Polyadic Program Schemes, Symposia Mathematica, Vol. 15, Academic Press, 225–281 (1975)Google Scholar
  21. [S1]
    Schmeck, H.: Zur algebraischen Charakterisierung reduzierbarer Flu\diagramme. Bericht 3/81, Inst. f. Inform. u. Prakt. Math., Universität Kiel, 1981Google Scholar
  22. [S2]
    Schmeck, H.: Algebraic Characterization of Reducible Flowcharts. Submitted for Publication, 1981Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1982

Authors and Affiliations

  • Hartmut Schmeck
    • 1
  1. 1.Institut für Informatik und Praktische MathematikChristian-Albrechts-Universität KielDeutschland

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