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Power domains supporting recursion and failure

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CAAP '92 (CAAP 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 581))

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Abstract

Following the program of Moggi, the semantics of a simple non-deterministic functional language with recursion and failure is described by a monad. We show that this monad cannot be any of the known power domain constructions, because they do not handle non-termination properly. Instead, a novel construction is proposed and investigated. It embodies both nondeterminism (choice and failure) and possible non-termination caused by recursion.

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References

  1. S. Abramsky. A domain equation for bisimulation. Information and Computation, 92:161–218, 1991.

    Google Scholar 

  2. A. Asperti and G. Longo. Categories, Types, and Structures. Foundations of Computing Series. The MIT Press, 1991.

    Google Scholar 

  3. W.F. Clocksin and C.S. Mellish. Programming in Prolog. Springer-Verlag, 1984.

    Google Scholar 

  4. C.A. Gunter. Relating total and partial correctness interpretations of non-deterministic programs. In P. Hudak, editor, Principles of Programming Languages (POPL '90), pages 306–319. ACM, 1990.

    Google Scholar 

  5. R. Heckmann. A functional language for the specification of complex tree transformations. In H. Ganzinger, editor, ESOP '88, pages 175–190. Lecture Notes in Computer Science 300, Springer-Verlag, 1988.

    Google Scholar 

  6. R. Heckmann. Power Domain Constructions. PhD thesis, Universität des Saarlandes, 1990.

    Google Scholar 

  7. R. Heckmann. Power domain constructions. Science of Computer Programming, 1991. to appear.

    Google Scholar 

  8. R. Hoofman. Powerdomains. Technical Report RUU-CS-87-23, Rijksuniversiteit Utrecht, November 1987.

    Google Scholar 

  9. M.C.B Hennessy and G.D. Plotkin. Full abstraction for a simple parallel programming language. In J. Becvar, editor, Foundations of Computer Science, pages 108–120. Lecture Notes in Computer Science 74, Springer-Verlag, 1979.

    Google Scholar 

  10. J.D. Lawson. The versatile continuous order. In Michael G. Main, A. Melton, Michael Mislove, and D. Schmidt, editors, Mathematical Foundations of Programming Language Semantics (MFPLS '87), pages 565–622. Lecture Notes in Computer Science 298, Springer-Verlag, 1988.

    Google Scholar 

  11. J. Lambek and P.J. Scott. Introduction to Higher Order Categorical Logic, volume 7 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, 1986.

    Google Scholar 

  12. S. MacLane. Categories for the Working Mathematician. Springer-Verlag, 1971.

    Google Scholar 

  13. E. Moggi. Computational lambda-calculus and monads. In 4th LICS Conference. IEEE, 1989.

    Google Scholar 

  14. E. Moggi. A modular approach to denotational semantics. In D.H. Pitt, P.-L. Curien, S. Abramsky, A.M. Pitts, A. Poigné, and D.E. Rydeheard, editors, Category Theory and Computer Science, pages 138–139. Lecture Notes in Computer Science 530, Springer-Verlag, 1991.

    Google Scholar 

  15. E. Moggi. Notions of computation and monads. Information and Computation, 93:55–92, 1991.

    Google Scholar 

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

    Article  Google Scholar 

  17. M.B. Smyth. Power domains. Journal of Computer and System Sciences, 16:23–36, 1978.

    Google Scholar 

  18. M.B. Smyth and G.D. Plotkin. The category-theoretic solution of recursive domain equations. SIAM Journal on Computing, 11:761–783, 1982.

    Google Scholar 

  19. P. Wadler. Comprehending monads. In Symposium on Lisp and Functional Programming, pages 61–78. ACM, 1990.

    Google Scholar 

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J. -C. Raoult

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© 1992 Springer-Verlag Berlin Heidelberg

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Heckmann, R. (1992). Power domains supporting recursion and failure. In: Raoult, J.C. (eds) CAAP '92. CAAP 1992. Lecture Notes in Computer Science, vol 581. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55251-0_9

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  • DOI: https://doi.org/10.1007/3-540-55251-0_9

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55251-2

  • Online ISBN: 978-3-540-46799-1

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