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An embedding of Ruby in Isabelle

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Automated Deduction — Cade-13 (CADE 1996)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1104))

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Abstract

This paper describes a semantical embedding of the relation based language Ruby in Zermelo-Fraenkel set theory (ZF) using the Isabelle theorem prover. A small subset of Ruby, called Pure Ruby, is embedded as a conservative extension of ZF and many useful structures used in connection with VLSI design are defined in terms of Pure Ruby. The inductive package of Isabelle is used to characterise the Pure Ruby subset to allow proofs to be performed by structural induction over the Pure Ruby elements.

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References

  1. R. Boulton, A. Gordon, M. Gordon, J. Harrison, J. Herbert, and J. Van Tassel. Experience with embedding hardware description languages in HOL. In V. Stavridou, T. F. Melham, and R. T. Boute, editors, IFIP TC10/WG 10.2 International Conference on Theorem Provers in Circuit Design: Theory, Practice and Experience, pages 129–156, Nijmegen, June 1992. North-Holland/Elsevier.

    Google Scholar 

  2. A. Dent and K. Hanna. Reasoning about array structures using a dependently typed logic. In CHDL '93. Elsevier Publishers, 1993.

    Google Scholar 

  3. M. J. C. Gordon and T. F. Melham. Introduction to HOL: A Theorem Proving Environment for Higher Order Logic. Cambridge University Press, 1993.

    Google Scholar 

  4. F. K. Hanna, M. Longley, and N. Daeche. Formal synthesis of digital systems. In Luc Claesen, editor, VLSI Design Methods. Elsevier Publishers, 1990.

    Google Scholar 

  5. G. Jones and M. Sheeran. Circuit design in Ruby. In J. Staunstrup, editor, Formal Methods for VLSI Design. Elsevier Publishers, 1990.

    Google Scholar 

  6. G. Jones and M. Sheeran. Relations and refinement in circuit design. In Morgan, editor, Proc. BCS FACS Workshop on Refinement. Springer-Verlag Workshop in Computing, 1990.

    Google Scholar 

  7. Mariam Leeser. Using Nuprl for the verification and synthesis of hardware. Philosophical Trans. of the Royal Soc. London A, 339:49–68, 1992.

    Google Scholar 

  8. R. Milner. A theory of type polymorphism in programming. Journal of Computer and System Sciences, 17:348–375, 1978.

    Article  Google Scholar 

  9. L. C. Paulson. Set theory for verification: I. from foundations to functions. Journal of Automated Reasoning, 11(3):353–389, 1993.

    Article  Google Scholar 

  10. L. C. Paulson. A fixedpoint approach to implementing (co)inductive definitions. In Alan Bundy, editor, Proceedings of the 12th International Conference on Automated Deduction, pages 148–161, Nancy, France, June 1994. Springer-Verlag LNAI 814.

    Google Scholar 

  11. L. C. Paulson. Isabelle: A Generic Theorem Prover. Springer-Verlag LNCS 828, 1994.

    Google Scholar 

  12. O. Rasmussen. A Ruby proof system. Technical Report ID-TR: 1995-161, Dept. of Computer Science, Technical University of Denmark, 1995.

    Google Scholar 

  13. Lars Rossen. Ruby algebra. In G. Jones and M. Sheeran, editors, Designing Correct Circuits, Oxford 1990, Workshops in Computing, pages 297–312. Springer-Verlag Workshop in Computing, 1991.

    Google Scholar 

  14. R. Sharp and O. Rasmussen. Transformational rewriting with Ruby. In CHDL '93, pages 231–248. Elsevier Science Publishers (North-Holland), 1993.

    Google Scholar 

  15. R. Sharp and O. Rasmussen. Using a language of functions and relations for VLSI specification. In Functional programming and Computer Architecture, FPCA '95, pages 45–54, June 1995.

    Google Scholar 

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M. A. McRobbie J. K. Slaney

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© 1996 Springer-Verlag Berlin Heidelberg

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Rasmussen, O. (1996). An embedding of Ruby in Isabelle. In: McRobbie, M.A., Slaney, J.K. (eds) Automated Deduction — Cade-13. CADE 1996. Lecture Notes in Computer Science, vol 1104. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61511-3_80

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  • DOI: https://doi.org/10.1007/3-540-61511-3_80

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61511-8

  • Online ISBN: 978-3-540-68687-3

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