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Abstract

We present a relational model of non-strict computations in an imperative, non-deterministic context. Undefinedness is represented independently of non-termination. The relations satisfy algebraic properties known from other approaches to model imperative programs; we introduce additional laws that model dependence in computations in an elegant algebraic form using partial orders. Programs can be executed according to the principle of lazy evaluation, otherwise known from functional programming languages. Local variables are treated by relational parallel composition.

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References

  1. Backhouse, R.C., de Bruin, P.J., Hoogendijk, P., Malcolm, G., Voermans, E., van der Woude, J.: Polynomial relators (extended abstract). In: Nivat, M., Rattray, C., Rus, T., Scollo, G. (eds.) Algebraic Methodology and Software Technology, pp. 303–326. Springer, Heidelberg (1992)

    Google Scholar 

  2. de Bakker, J.W.: Semantics and termination of nondeterministic recursive programs. In: Michaelson, S., Milner, R. (eds.) Automata, Languages and Programming: Third International Colloquium, pp. 435–477. Edinburgh University Press (1976)

    Google Scholar 

  3. Berghammer, R., von Karger, B.: Relational semantics of functional programs. In: Brink, C., Kahl, W., Schmidt, G. (eds.) Relational Methods in Computer Science, ch. 8, pp. 115–130. Springer, Wien (1997)

    Google Scholar 

  4. Berghammer, R., Zierer, H.: Relational algebraic semantics of deterministic and nondeterministic programs. Theoretical Computer Science 43, 123–147 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  5. Broy, M., Gnatz, R., Wirsing, M.: Semantics of nondeterministic and noncontinuous constructs. In: Bauer, F.L., Broy, M. (eds.) Program Construction. LNCS, vol. 69, pp. 553–592. Springer, Heidelberg (1979)

    Chapter  Google Scholar 

  6. Dijkstra, E.W.: A Discipline of Programming. Prentice-Hall, Englewood Cliffs (1976)

    MATH  Google Scholar 

  7. Guttmann, W.: Non-termination in Unifying Theories of Programming. In: MacCaull, W., Winter, M., Düntsch, I. (eds.) RelMiCS 2005. LNCS, vol. 3929, pp. 108–120. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  8. Guttmann, W.: Algebraic Foundations of the Unifying Theories of Programming. PhD thesis, Universität Ulm (December 2007)

    Google Scholar 

  9. Hennessy, M., Ashcroft, E.A.: The semantics of nondeterminism. In: Michaelson, S., Milner, R. (eds.) Automata, Languages and Programming: Third International Colloquium, pp. 478–493. Edinburgh University Press (1976)

    Google Scholar 

  10. Hesselink, W.H.: Programs, Recursion and Unbounded Choice. Cambridge University Press, Cambridge (1992)

    MATH  Google Scholar 

  11. Hoare, C.A.R., He, J.: Unifying theories of programming. Prentice Hall Europe (1998)

    Google Scholar 

  12. ISO/IEC. Information technology: Z formal specification notation: Syntax, type system and semantics. ISO/IEC 13568:2002(E) (July 2002)

    Google Scholar 

  13. Josephs, M.B.: Functional programming with side-effects. Science of Computer Programming 7, 279–296 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  14. Launchbury, J.: Lazy imperative programming. In: Hudak, P. (ed.) Proceedings of the ACM SIGPLAN Workshop on State in Programming Languages, Yale University Research Report YALEU/DCS/RR-968, pp. 46–56 (1993)

    Google Scholar 

  15. Launchbury, J., Peyton Jones, S.: State in Haskell. Lisp and Symbolic Computation 8(4), 293–341 (1995)

    Article  Google Scholar 

  16. Nelson, G.: A generalization of Dijkstra’s calculus. ACM Transactions on Programming Languages and Systems 11(4), 517–561 (1989)

    Article  Google Scholar 

  17. Peyton Jones, S. (ed.): Haskell 98 Language and Libraries: The Revised Report. Cambridge University Press, Cambridge (2003)

    Google Scholar 

  18. Plotkin, G.D.: A powerdomain construction. SIAM Journal on Computing 5(3), 452–487 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  19. Van Roy, P., Haridi, S.: Concepts, Techniques, and Models of Computer Programming. MIT Press, Cambridge (2004)

    Google Scholar 

  20. Schmidt, D.A.: Denotational Semantics: A Methodology for Language Development. William C. Brown Publishers (1986)

    Google Scholar 

  21. Schmidt, G.: Partiality I: Embedding relation algebras. Journal of Logic and Algebraic Programming 66(2), 212–238 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  22. Schmidt, G., Hattensperger, C., Winter, M.: Heterogeneous relation algebra. In: Brink, C., Kahl, W., Schmidt, G. (eds.) Relational Methods in Computer Science, ch. 3, pp. 39–53. Springer, Wien (1997)

    Google Scholar 

  23. Schmidt, G., Ströhlein, T.: Relationen und Graphen. Springer, Heidelberg (1989)

    MATH  Google Scholar 

  24. Schröder, B.S.W.: Ordered Sets: An Introduction. Birkhäuser, Basel (2003)

    MATH  Google Scholar 

  25. Smithson, R.E.: Fixed points of order preserving multifunctions. Proceedings of the American Mathematical Society 28(1), 304–310 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  26. Smyth, M.B.: Power domains. Journal of Computer and System Sciences 16(1), 23–36 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  27. Søndergaard, H., Sestoft, P.: Non-determinism in functional languages. The Computer Journal 35(5), 514–523 (1992)

    Article  MathSciNet  Google Scholar 

  28. Walker, J.W.: Isotone relations and the fixed point property for posets. Discrete Mathematics 48(2–3), 275–288 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  29. Woodcock, J., Davies, J.: Using Z. Prentice-Hall, Englewood Cliffs (1996)

    MATH  Google Scholar 

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Rudolf Berghammer Bernhard Möller Georg Struth

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Guttmann, W. (2008). Lazy Relations. In: Berghammer, R., Möller, B., Struth, G. (eds) Relations and Kleene Algebra in Computer Science. RelMiCS 2008. Lecture Notes in Computer Science, vol 4988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78913-0_12

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  • DOI: https://doi.org/10.1007/978-3-540-78913-0_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-78912-3

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