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Axiomatization of a functional logic language

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Book cover Algebraic and Logic Programming (ALP 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 463))

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Abstract

Functional logic languages incorporate logic programming capabilities of constraint solving within a functional language framework. We consider a prototypical functional logic language which supports definite descriptions, i.e., terms of the form “the x such that p”. Its semantics is defined in terms of flat ordered structures with ⊥ and ⊺ elements. These elements are used to represent the absence and ambiguity, respectively, of objects denoted by descriptions. We provide an equational axiomatization of the language and show that it is complete for this semantics.

Bronsard was supported by NSERC, Canada, and FCAR, Canada

The work by Reddy was supported by a grant from Motorola Corp.

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References

  1. F. L. Bauer. The Munich Project CIP. Volume 292 of LNCS, Springer-Verlag, Berlin, 1987.

    Google Scholar 

  2. F. Bronsard. Program Synthesis in a Functional Logic Language. (forthcoming Ph.D. proposal), University of Illinois, 1990.

    Google Scholar 

  3. S. L. Bloom and R. Tindell. Varieties of “if-then-else”. SIAM J. Computing, 12(4):677–707, 1983.

    Google Scholar 

  4. N. Dershowitz. Computing with rewrite systems. Technical Report ATR-83(8478)-1, Information Sciences Research Office, The Aerospace Corp., El Segundo, CA., January 1983.

    Google Scholar 

  5. J. Darlington, A. J. Field, and H. Pull. The unification of functional and logic languages. In D. DeGroot and G. Lindstrom, editors, Logic Programming: Functions, Relations and Equations, pages 37–70, Prentice-Hall, 1986.

    Google Scholar 

  6. J. Darlington and Y. K. Guo. Unification of functional and logic languages — Towards constraint functional programming. In TENCON Special Session on Functional Languages: Theory and Applications, Bombay, India, Nov 1989.

    Google Scholar 

  7. M. Fay. First-order unification in an equational theory. In Fourth Workshop on Automated Deduction, pages 161–167, Austin, Texas, 1979.

    Google Scholar 

  8. J. A. Goguen and J. Meseguer. Equality, types, modules and generics for logic programming. In Proc. 2nd Intern. Logic Prog. Conf., Uppsala, pages 115–125, 1984.

    Google Scholar 

  9. I. Guessarian and J. Meseguer. On the axiomatisation of “if-then-else”. SIAM J. Computing, 16(2):332–357, Apr 1987.

    Google Scholar 

  10. D. Hilbert and W. Ackermann. Principles of Mathematical Logic. Chelsea Pub. Co., New York, 1950. translated by L. M. Hammond, G. G. Leckie, and F. Steinhardt.

    Google Scholar 

  11. J-M. Hullot. Canonical forms and unification. In Conf. on Automated Deduction, pages 318–334, 1980.

    Google Scholar 

  12. E.C. Leisenring. Mathematical Logic and Hilbert's ε-symbol. Gordon and Breach Science Publishers, NY, 1969.

    Google Scholar 

  13. G. Lindstrom. Functional programming and the logical variable. In ACM Symp. on Princ. of Program. Languages, 1985.

    Google Scholar 

  14. R.S. Nikhil, K. Pingali, and Arvind. Id Nouveau. Technical Report CSG 265, MIT, 1986.

    Google Scholar 

  15. G. Pottinger. Ulysses: Logical Foundations of the Definition Facility. Technical Report TR 11-9, Odyssey Research Associates, Jan 1988.

    Google Scholar 

  16. U. S. Reddy. Narrowing as the operational semantics of functional languages. In Symp. on Logic Program., pages 138–151, IEEE, Boston, 1985.

    Google Scholar 

  17. U. S. Reddy. Logic Languages based on Functions: Semantics and Implementation. Technical Report UIUCDCS-R-86-1305, Univ. Illinois at Urbana-Champaign, 1986. Ph.D. thesis done at Univ. of Utah.

    Google Scholar 

  18. U. S. Reddy. On the relationship between logic and functional languages. In D. DeGroot and G. Lindstrom, editors, Logic Programming: Functions, Relations and Equations, pages 3–36, Prentice-Hall, 1986.

    Google Scholar 

  19. U. S. Reddy. Functional logic languages, Part I. In Graph Reduction, pages 401–425, Springer-Verlag, 1987. (Lecture Notes in Computer Science, Vol 279).

    Google Scholar 

  20. U. S. Reddy. Design principles for an interactive program derivation system. In Proc. AAAI-88 Workshop on Automating Software Design, pages 145–155, AAAI, 1988.

    Google Scholar 

  21. U. S. Reddy. Transformational derivation of programs using the Focus system. In Symp. Practical Software Development Environments, pages 163–172, ACM, December 1988.

    Google Scholar 

  22. U. S. Reddy. Rewriting techniques for program synthesis. In N. Dershowitz, editor, Rewriting Techniques and Appl., pages 388–403, Springer-Verlag, 1989. (LNCS Vol. 355).

    Google Scholar 

  23. J. R. Slagle. Automated theorem-proving for theories with simplifiers, commutativity and associativity. Journal of the ACM, 21(4):622–642, 1974.

    Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, The University of Illinois at Urbana-Champaign, 61801, Urbana, IL

    Francois Bronsard & Uday S. Reddy

Authors
  1. Francois Bronsard
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  2. Uday S. Reddy
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Hélène Kirchner Wolfgang Wechler

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© 1990 Springer-Verlag Berlin Heidelberg

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Bronsard, F., Reddy, U.S. (1990). Axiomatization of a functional logic language. In: Kirchner, H., Wechler, W. (eds) Algebraic and Logic Programming. ALP 1990. Lecture Notes in Computer Science, vol 463. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-53162-9_33

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  • DOI: https://doi.org/10.1007/3-540-53162-9_33

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53162-3

  • Online ISBN: 978-3-540-46738-0

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