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Compositional Reasoning using Interval Temporal Logic and Tempura

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1536))

Abstract

We present a compositional methodology for specification and proof using Interval Temporal Logic (ITL). After given an introduction to ITL, we show how fixpoints of various ITL operators provide a flexible way to modularly reason about safety and liveness. In addition, some new techniques are described for compositionally transforming and refining ITL specifications. We also consider the use of ITL’s programming language subset Tempura as a tool for testing the kinds of specifications dealt with here.

The research described here has been kindly supported by EPSRC research grant GR/K25922.

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References

  1. Dutertre, B.: On first order interval temporal logic. In: 10th Annual IEEE Symposium on Logic in Computer Science. IEEE Computer Society Press, Los Alamitos, California (1995) 36–43

    Google Scholar 

  2. Francez, N., Pnueli, A.: A proof method for cyclic programs. Acta Inf. 9 (1978) 133–157

    Article  MATH  MathSciNet  Google Scholar 

  3. Halpern J., Manna Z., Moszkowski B.: A hardware semantics based on temporal intervals. In: Diaz, J. Ed. Proceedings of the 10th International Colloquium on Automata, Languages and Programming (ICALP’83). Lecture Notes in Computer Science Vol. 154. Springer-Verlag, Berlin Heidelberg New York (1983) 278–291

    Chapter  Google Scholar 

  4. Hoare, C.A.R.: An axiomatic basis for computer programming. Comm. ACM 12 (1969) 576–580, 583

    Article  MATH  Google Scholar 

  5. Jones, C.B.: Specification and design of (parallel) programs. In: Mason, R.E.A. Ed. Proceedings of Information Processing’ 83. North Holland Publishing Co., Amsterdam (1983) 321–332

    Google Scholar 

  6. Kesten, Y., Pnueli, A.: A complete proof system for QPTL. In: Proc. 10th IEEE Symp. on Logic in Computer Science. IEEE Computer Society Press, Los Alamitos, California (1995) 2–12

    Google Scholar 

  7. Kleene, S.C.: Mathematical Logic. John Wiley & Sons, Inc., New York (1967)

    MATH  Google Scholar 

  8. Kono, S.: A combination of clausal and non clausal temporal logic programs. In: Fisher, M., Owens, R. Eds. Executable Modal and Temporal Logics. Lecture Notes in Computer Science, Vol. 897. Springer-Verlag, Berlin Heidelberg New York (1995) 40–57

    Google Scholar 

  9. Kröger, F.: Temporal Logic of Programs. Springer-Verlag, Berlin Heidelberg New York (1987)

    MATH  Google Scholar 

  10. Manna, Z.: Verification of sequential programs: temporal axiomatization. In: Broy, M., Schmidt, G. Eds., Theoretical Foundations of Programming Methodology. D. Reidel Publishing Co. (1982) 53–102

    Google Scholar 

  11. Moszkowski B.: Reasoning about Digital Circuits. PhD thesis, Stanford University, Stanford, California (1983)

    Google Scholar 

  12. Moszkowski, B.: A temporal logic for multilevel reasoning about hardware. IEEE Computer 18 (1985) 10–19

    Google Scholar 

  13. Moszkowski, B.: Executing Temporal Logic Programs. Cambridge University Press, Cambridge, England (1986)

    Google Scholar 

  14. Moszkowski, B.: Some very compositional temporal properties. In: Olderog, E.-R. Ed. Programming Concepts, Methods and Calculi. IFIP Transactions, Vol. A-56, North-Holland (1994) 307–326.

    Google Scholar 

  15. Moszkowski, B.: Compositional reasoning about projected and infinite time. In: Proceedings of the First IEEE International Conference on Engineering of Complex Computer Systems (ICECCS’95). IEEE Computer Society Press, Los Alamitos, California (1995) 238–245

    Chapter  Google Scholar 

  16. Moszkowski, B.: Embedding imperative constructs in interval temporal logic. Internal memorandum EE/0895/M1. Dept. of Elec. and Elec. Eng., Univ. of Newcastle, Newcastle upon Type, UK (1995)

    Google Scholar 

  17. Moszkowski, B.: Using temporal fixpoints to compositionally reason about liveness. In: BCS-FACS 7th Refinement Workshop, “Electronic Workshops in Computing” series. Springer-Verlag, London (1996)

    Google Scholar 

  18. Paech, B.: Gentzen-systems for propositional temporal logics. In: Börger, E. et al. Eds. Proceedings of the 2nd Workshop on Computer Science Logic. Lecture Notes in Computer Science. Vol. 385. Springer-Verlag, Berlin Heidelberg New York (1988) 240–253

    Google Scholar 

  19. Rosner, R., Pnueli, A.: A choppy logic. In: Proceedings of the 1st Annual IEEE Symposium on Logic in Computer Science. IEEE Computer Society Press, Los Alamitos, California (1986) 306–314.

    Google Scholar 

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© 1998 Springer-Verlag Berlin Heidelberg

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Moszkowski, B.C. (1998). Compositional Reasoning using Interval Temporal Logic and Tempura. In: de Roever, WP., Langmaack, H., Pnueli, A. (eds) Compositionality: The Significant Difference. COMPOS 1997. Lecture Notes in Computer Science, vol 1536. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49213-5_17

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  • DOI: https://doi.org/10.1007/3-540-49213-5_17

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65493-3

  • Online ISBN: 978-3-540-49213-9

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