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
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
Francez, N., Pnueli, A.: A proof method for cyclic programs. Acta Inf. 9 (1978) 133–157
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
Hoare, C.A.R.: An axiomatic basis for computer programming. Comm. ACM 12 (1969) 576–580, 583
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
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
Kleene, S.C.: Mathematical Logic. John Wiley & Sons, Inc., New York (1967)
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
Kröger, F.: Temporal Logic of Programs. Springer-Verlag, Berlin Heidelberg New York (1987)
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
Moszkowski B.: Reasoning about Digital Circuits. PhD thesis, Stanford University, Stanford, California (1983)
Moszkowski, B.: A temporal logic for multilevel reasoning about hardware. IEEE Computer 18 (1985) 10–19
Moszkowski, B.: Executing Temporal Logic Programs. Cambridge University Press, Cambridge, England (1986)
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.
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
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)
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)
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
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.
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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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