Advertisement

Mathematical systems theory

, Volume 8, Issue 2, pp 105–126 | Cite as

Semantic preserving translations

  • David B. Benson
Article

Abstract

Let X1, X2 be derivation systems (freex-categories) generated by context free grammars. Let X0 be a translation category withx-functorsf i :X0→X i ,i=1, 2. Let T be an Ω*-theory, a generalization of algebraic theories. LetI i :X i →T be algebraic interpretations of the derivations systems, giving the semantics of derivation systems. The translation category X0 is shown to preserve the common semantics through the translation if there is a natural transformation from the functorf2ºI2 to the functorf1ºI1. This is used to show that certain elementary conditions on well-behaved generalized2 sequential machine maps (g2sm maps) result in semantics preservation by the g2sm maps.

Keywords

Computational Mathematic Natural Transformation Elementary Condition Algebraic Theory Context Free Grammar 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    A. V. Aho andJ. D. Ullman, Syntax directed translations and the pushdown assembler,J. Comp. System Sci. 3 (1969), 37–56.Google Scholar
  2. [2]
    A. V. Aho andJ. D. Ullman, Properties of syntax directed translations,J. Comp. System Sci. 3 (1969), 319–334.Google Scholar
  3. [3]
    D. B. Benson, Syntax and semantics: a categorical view,Information and Control 17 (1970), 145–160.Google Scholar
  4. [4]
    R. M. Burstall andP. J. Landin, Programs and their proofs: an algebraic approach,Machine Intelligence 4, American Elsevier, 1969.Google Scholar
  5. [5]
    P. M. Cohn,Universal Algebra, Harper and Row, New York, 1965.Google Scholar
  6. [6]
    K. Culik, Well-translatable grammars andAlgol-like languages, inFormal Language Description Languages (T. B. Steel, Ed.), North-Holland, Amsterdam, 1966.Google Scholar
  7. [7]
    S. Eilenberg andJ. B. Wright, Automata in general algebras,Information and Control 11 (1967), 452–470.Google Scholar
  8. [8]
    T. V. Griffiths, Some remarks on derivations in general rewriting systems,Information and Control 12 (1968), 27–54.Google Scholar
  9. [9]
    G. Hotz, Eindeutigkeit und Mehrdeutigkeit formaler Sprachen,Elektron. Informationsarbeit. Kybernetik 2 (1966), 235–247.Google Scholar
  10. [10]
    E. T. Irons, A syntax directed compiler for ALGOL 60,Comm. ACM 4 (1961), 51–55.Google Scholar
  11. [11]
    D. E. Knuth, Semantics of context-free languages,Math. Systems Theory 2 (1968), 127–145.Google Scholar
  12. [12]
    F. W. Lawvere, Functorial semantics of algebraic theories,Proc. Nat. Acad. Sci. U.S.A. 50 (1963), 869–872.Google Scholar
  13. [13]
    P. M. Lewis andR. E. Stearns, Syntax directed transduction,J. Assoc. Comput. Mach. 15 (1968), 465–488.Google Scholar
  14. [14]
    S. MacLane andG. Birkhoff,Algebra, MacMillan, New York, 1967.Google Scholar
  15. [15]
    B. Pareigis,Categories and Functors, Academic Press, New York, 1970.Google Scholar
  16. [16]
    L. Petrone, Syntactic mappings of context-free languages,Proc. IFIP Congress 2 (1965), 590–591.Google Scholar
  17. [17]
    C. D. Shepard, Languages in general algebras,Conf. Record ACM Symp. Theory Comp., ACM, New York, 1969, 155–163.Google Scholar
  18. [18]
    C. P. Schnorr, Transformational classes of grammars,Information and Control 14 (1969), 252–277.Google Scholar
  19. [19]
    C. P. Schnorr andH. Walter, Pullbackkonstruktionen bei Semi-Thuesystemen,Elektron. Informationsarbeit. Kybernetik 5 (1969), 27–36.Google Scholar
  20. [20]
    J. W. Thatcher, Characterizing derivation trees of context-free grammars through a generalization of finite automata theory,J. Comp. System Sci. 1 (1967), 317–322.Google Scholar
  21. [21]
    J. W. Thatcher, Generalized2 sequential machine maps,J. Comp. System Sci. 4 (1970), 339–367.Google Scholar
  22. [22]
    F. B. Thompson, English for the computer,AFIPS Conf. Proc. 29, FJCC, Spartan Books, Washington D.C., 1966, 349–356.Google Scholar
  23. [23]
    H. Walter, Verallgemeinerte Pullbackkonstruktionen bei Semi-Thuesystemen und Grammatiken,Elektron. Informationsarbeit. Kybernetik 6 (1970), 239–254.Google Scholar
  24. [24]
    N. Wirth andH. Weber, EULER: A generalization of ALGOL and its formal definition: Part I,Comm. ACM 9 (1966), 13–23.Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1974

Authors and Affiliations

  • David B. Benson
    • 1
  1. 1.Computer Science DepartmentWashington State UniversityPullmanUSA

Personalised recommendations